d ft study of small molecul es/cl uster -...
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DFT Study of Small molecules/Cluster
A Thesis submitted to the University of Lucknow For the Degree of
Doctor of Philosophy
in Physics
By
Vijay Narayan
Under the Supervision
of
Dr. Leena Sinha
Department of Physics
University of Lucknow
Lucknow – 226007, (U.P.)
INDIA
(2012)
Dedicated
to
bade Bhaiya
&
Bhabhi Ji
C E R T I F I C A T E
This is to certify that all the regulations necessary for the submission of
Ph.D. thesis “DFT Study Of Small Molecules/Cluster” by Vijay
Narayan have been fully observed. The contents of this thesis are original
and have not been presented anywhere else for the award of a Ph.D.
degree.
(Dr Leena Sinha) (Prof. U. D. Misra)
Associate Professor Professor & Head
Department of Physics Department of Physics
University of Lucknow University of Lucknow
Lucknow – 226007 Lucknow- 226007
C E R T I F I C A T E
This is to certify that the work contained in this thesis entiled “DFT
STUDY OF SMALL MOLECULES/CLUSTER” by Vijay Narayan has
been carried out under my supervision and that this work has not been
submitted anywhere else for Ph. D degree.
(Dr Leena Sinha)
Associate Professor
Department of Physics
University of Lucknow
Lucknow - 226007
Words of Gratitude
Pursuing a Ph.D. was a magnificent as well as challenging experience to
me. It opened the doors to another world, a beautiful one, and gave me the
chance to grow, not only scientifically but also as a human being. The one
who made all this possible was Dr. Leena Sinha. I wish to thank my
supervisor (Dr Leena Sinha) for giving me the chance to join your
workgroup and pursue the Ph.D. degree in field of Quantum Chemistry. I
am very grateful for the confidence that she showed in me and her
extraordinary support. Every time I knocked at her door, she was there
with a smile on her face and a solution to my problems.
My gratitude also extends to Prof. Onkar Prasad who deserves
special thanks as this thesis work would not have been possible without
his support and encouragement. His constant support when I encountered
difficulties inspired me all through. His understanding, encouraging
suggestions and personal guidance have provided a good basis for the
present work.
I would also like to thank Prof. K. Klinch, Industrial Research Limited,
Lower Hutt, New Zealand for providing me sample for the running of FT-
IR & FT-RAMAN spectra.
I am thankful to the Head, Prof. U.D. Misra, Department of Physics,
University of Lucknow, Lucknow, for his kind support.
Also, Special thanks go to my seniors Dr. Jitendra Pathak, Dr. Anoop
Kumar Pandey and Dr. S. A. Siddiqui, Mr. Amrendra Kumar, Mr.
Naveen Saxena, Mr. Rajesh Shrivastava, Mr. H. N. Mishra, Mr.
Satish Chand, without their help, I would have never come so far.
I am also thankful to my friends from S. R. M. G. P. C. Lucknow Ms.
Ankita Pandey, Ms. Monika Singh, Mr. Atul Shukla, Mr. Bhagwati
Prasad and Mr. Shailesh Kumar Mishra for their lovely and joyful
company and cooperation throughout my research work.
I would like to extend my special thanks to my friends Mr. Upkar Verma
from IIT Kanpur and Mr. Ajit Kumar Katiyar from IIT Kharagpur, Mr.
Subodh Kumar Pandey, for their consistent support throughout my
work.
It was a time with many “vibrations” exactly like in a Raman spectrum, I
would never have managed to withstand without the support of my family
and my good friends. I would like to show my gratitude to my wonderful
parents; Shri. R. A. Mishra & Smt. Vidya Devi who always encouraged
me to go on with my studies and showed to me how to become a better
person. Also, personal thanks to my sister, Smt. Kumud Mishra and my
Elder brother and bhabhi ji Mr. H. N. Mishra & Mrs. Nisha Mishra for
their incessant support.
(Vijay Narayan)
LIST OF PUBLISHED / COMMUNICATED PAPERS
1. Monomeric and Dimeric structures, electronic properties and
vibrational spectra of azelaic acid by HF and B3LYP methods,
Journal of Molecular Structure, Vol. 1022, 81-88, (2012).
2. Electronic structure, electric moments and vibrational analysis of 5-
nitro 2- furaldehyde semicarbazone: A D.F.T. study.
Computational and Theoretical Chemistry. Vol. 973, 20-27,
2011.
3. Raman, FT-IR spectroscopic analysis and first-order
hyperpolarizability of 3-benzoyl-5- chlorouracil by first principles.
Molecular Simulation. Vol. 37, No. 2, 153–163, 2011.
4. Electronic structure, electric moments and vibrational analysis of 3-
(2- methoxyphenoxy) propane-1,2-diol by ab initio and density
functional theory. J. At. Mol. Sci. Vol. 2, No. 3, pp. 212-224, 2011.
5. Molecular Geometry and Polarizability of small Cadmium Telluride
Cluster using ab initio and Density functional theory. L. J.of
Science, Vol. 8,(2011), 550-553
6. Molecular structure, Electronic properties, NLO analysis and
spectroscopic characterization of Gabapentin with experimental
(FT-IR and FT-Raman) techniques and quantum chemical
calculations. Spectrochimica Acta Part-A, (communicated)
PAPERS PRESENTED IN NATIONAL AND INTERNATIONAL
CONFERENCES
1. Molecular Polarizability, HOMO-LUMO and Molecular Electrostatic
Potential Surface of Tranexamic acid, National Seminar on Advances
in Laser, Spectroscopy and Nono-materials, held at Physics
Department, Nehru Gram Bharti University, Allahabad, March 5-7,
2011.
2. Comparative Electronic, non Linear optical and vibrational properties
of ortho and meta- Fluorobenzaldehyde, Meghnad Saha Memorial
International conference –cum-workshop on Laser Induced
Breakdown Spectroscopy, 80, December 21-23, 2010.
3. Electronic structure and vibrational analysis of Imidacloprid using
Density Functional Theory. 97th
Indian Science Congress,
Thiruvananthapuram, JD11, P111, January 3-7, 2010.
4. Structure and Electronic properties of 2-Phenyl-1H-1,3(2H)-Dione.
Symposium on recent trends in Biophysics organized by Department
of Physics, B.H.U., Varanasi. P-71, February 13-16, 2010.
5. Electronic properties and Molecular Electrostatic Potential Surface of
2-Hydroxy-3-(2-MethoxyPhenoxy) Propyl Carbamate. Symposium on
recent trends in Biophysics organized by Department of Physics,
B.H.U., Varanasi. P-72, February 13-16, 2010.
6. Study on Frontier Orbitals, Electron Density and Molecular
Electrostatic Potential Surfaces of Oxygen Nano Cluster O8 by First
Principles, 73-75, Proceedings of 2nd
National Conference on
Nanomaterials and Nanotechnology, Department of Physics,
University of Lucknow, December 21 -23, 2009.
7. DFT Study of Isoelectronic Amino acids, Conference on Mesogenic
and Ferroic materials (CMFM 09), held at B.H.U. Varanasi, 74,
January 9-11, 2009.
8. DFT Studies of p-Cymene and Carvacrol, Conference on Mesogenic
and Ferroic materials (CMFM 09), held at B.H.U. Varanasi, 75,
January 9-11, 2009.
TABLE OF CONTENTS
Page Number
Chapter 1: Introduction 1-20
1.1 Prime Methods for the Study of Electronic Structure
1.2 Vibrational Analysis: Key Approches
1.2.1 Infrared-Spectroscopy 1.2.2 Raman Spectroscopy
References
Chapter 2: Theoretical Approach 21-50
2.1 Introduction
2.2 The Born–Oppenheimer Approximation
2.3 The Hartree-Fock (HF) Method
2.4 Basis Set
2.5 Purturbation theory
2.6 Density Functional Theory
2.7 Gauss Veiw
References
Chapter 3: Raman, FTIR spectroscopic analysis and 51-76
first order hyperpolarizability of 3-benzoyl
-5-chlorouracil
3.1 Introduction
3.2 Experimental
3.3 Results and Discussion
3.3.1 Electronic Properties
3.3.2 Electric Moment
3.3.3 Vibrational Analysis
3.3.3.1 Chloro-substituted uracil (CSU) ring vibrations
3.3.3.2 C=O group vibrations
3.3.3.3 Phenyl ring vibrations
3.3.4 NLO activity and its vibrational correlation
3.4 Conclusions
References
Chapter 4: Molecular structure, Electronic 77-101
properties, NLO analysis and spectroscopic
characterization of Gabapentin
4.1 Introduction
4.2 Results and Discussion
4.2.1 Molecular Geometry
4.2.2 Vibrational Assignements
4.2.3 Electronic Properties
4.2.4 NLO Properties
4.2.5 Thermodynamic Properties
4.3 Conclusions
References
Chapter 5: Molecular geometry, polarizability 102-121
and reactivity descriptors of small cadmium
Telluride clusters
5.1 Introduction
5.2 Theoretical Approach
5.3 Result and Discussion
5.3.1 Binding Energy and HOMO-LUMO analysis
5.3.2 Global reactivity Descriptors
5.3.3 Global electrophilicity index
5.4 Conclusions
References
Chapter 6: Conclusions 122-128
CHAPTER 1
INTRODUCTION
1
1. Introduction
After the decades of theoretical evolution, algorithm improvement, and
computational advances, the theoretical investigations of the electronic structure
of matter now, offer computational simulation of new materials, a better
understanding of the structure, formed by the atoms of materials, in addition to
describing the great variety of phenomena observed. Comprehensive
considerate of the electronic properties of a solid system has become an
indispensable part of materials research nowadays, for the fundamental
electronic structure, affects the materials properties in a substantial way. There
has been a major attention in solving chemical problems like molecular
geometries, spectroscopic signatures, transition states, and various
thermodynamic properties using the tools of Quantum Chemistry over the last
three decades
[1-5], Quantum chemistry is a branch of theoretical chemistry which applies
quantum mechanics and to address problems in chemistry. Quantum chemistry
lies on the border between chemistry and physics. Thus, significant
contributions have been made by scientists from both fields. It has a strong and
active overlap with the field of atomic physics and molecular physics, as well as
physical chemistry.
Quantum chemistry can be thought of describing efforts in achieving a
microscopic understanding of the interrelationships between composition,
2
structure, and various materials properties using quantum mechanics. Detailed
simulations based on the principles of quantum mechanics play an ever
increasing role in signifying, guiding, and explaining experiments in chemistry
and materials science. Quantum chemists today are involved in both developing
and applying these methods. Solving the equations governing the properties of
molecules is very complex, and it cannot be done exactly. A hierarchy of
approximate methods has therefore been developed that allow quantum
chemists to select the method most appropriate for a given problem. Which
methods are practicable depends on the computational cost of applying each
method to a particular problem. The least computationally expensive methods
also tend to be the least accurate methods. Density functional theory method is
one of the most popular Quantum Chemical methods because of a good balance
between computational cost and accuracy.
Some of the almost limitless properties that can be calculated with tools of
quantum chemistry are - i) Optimized ground state and transition-state
structures ii) Vibrational frequencies, IR and Raman Spectra iii) Dipole and
quadrapole moments, polarizabilities, and hyperpolarizabilities etc.
iv) Electronic excitations and UV spectra v) NMR spectra vi) Reaction rates and
cross sections vii) Thermodynamical data. Fig 1.1 illustrates some results
obtained from quantum Chemical methods for a variety of molecules.
3
Optimized molecule of 5-nitro 2- furaldehyde
semicarbazoneby quantum chemical DFT study[6].
Study of reaction mechanism using quantum chemical
method.
Experimental and Theoretical IR Spectra (4000 - 400 cm-1)
spectra of Acenaphthenequinone as obtained by density
functional theory [7].
HOMO- LUMO orbitals, corresponding energy gap and
MEP surface for 5-nitro 2- furaldehydesemicarbazoneby
quantum chemical study[6].
UV-Vis spectra for 5-nitro 2- furaldehydesemicarbazoneby
quantum chemical study[6].
Fig. 1.1 Showing various applications of Quantum Chemical methods
4
1.1 Prime Methods for the Study of Electronic Structure
In the beginning, attempts to solve the time-independent Schrodinger equation
for the electronic structure of a system were carried out through approximation
techniques. One of the first methods used was called ab initio, "from the
beginning" calculations [8]. A typical study using ab initio methods begins with
a tentative molecular structure for a system that may or may not be known.This
method commences with the Schrodinger equation and makes approximations
to construct Hamiltonians that can be solved. Fig1.2 shows different types of ab
initio calculations and their basic characteristics. The foundation of quantum
chemical models starts with the Hartree-Fock approximation, which when
applied to the many-electron Schrödinger equation, not only leads directly to a
significant class of quantum chemical models but also provides the base for
both simpler and more complex models. In-effect, the Hartree-Fock
approximation replaces the true description of electron motions by a depiction
in which the electrons behave in effect as independent particles. Hartree-Fock
model was first tried out in the 1950’s, and there is now a great deal of
experience with their successes and failures. Hartree-Fock model provide good
descriptions of equilibrium geometries conformations, and also perform well for
many kinds of thermochemical comparisons [9], except where transition metals
are involved. However, Hartree-Fock model costs poorly in accounting for the
5
The simplest ab initio
calculation
electron correlation is
not taken into consideration.
Improves on the
Hartree-Fock
method
electron
correlation effects
added
use ofRayleigh–
Schrödinger
perturbation
theory
system is described via
its density and not via its
many-body wave function
uses a variational wave
function that is a linear
combination of
configuration state
functions built from spin
orbitals
Fig.1.2 Different types of ab initio methods and their basic characteristics
Different Types of ab initio
Calculations
Hartree
Fock
(HF)
Møller-Plesset
Perturbation Theory
Density Functional
Theory (DFT)
Configuration
Interaction (CI)
6
thermochemistry of reactions concerning explicit bond making or bond
breaking. The failures of Hartree-Fock model can be traced to an incomplete
description of the way in which the motion of one electron affects the motions
of all the other electrons (electron correlation). Two fundamentally different
approaches for improvement of Hartree-Fock model have come out. One
approach is to construct a more supple description of electron motions in terms
of a combination of Hartree-Fock descriptions for ground and excited states –
examples are Configuration interaction (CI) and Møller-Plesset (MP) models.
The so called second-order Møller-Plesset model (MP2) is the most rational and
widely employed. It generally provides excellent descriptions of equilibrium
geometries and conformations, as well as thermochemistry, including the
thermochemistry of reactions where bonds are broken and formed [10]. An
alternative approach to improve upon Hartree-Fock model involves including an
explicit term to account for the way in which electron motions affect each other.
In practice, this account is based on an exact solution for an idealized system,
and is introduced using empirical parameters. As a class, the resulting models
are referred to as density functional models.In the sixties it was recognized that
a system of interacting electrons is completely characterized by the electron
density ρ(r) in the ground state. With the density as a basic variable one only
has to find a function of 3 variables, independently of the number of electrons in
the system. Unfortunately the equations for determining the density are not
7
known so that one has to work with approximate equations. The success of
density functional theory is based on the fact that very good approximations
have been found and on the availability of computers of ever increasing speed.
This allows practical calculations of numerous physical properties for vast
classes of molecules and solids. In 1965, Kohn and his student Liu Ju Sham
further modified the theory, with the addition of Kohn-Sham equations. These
K-S equations [11] depend on mathematical implements called exchange-
correlation potentials to account for the forces electrons have on each other as
they move around the atomic nucleus. At present, there are many such
potentials in use to describe the electronic properties of matter. These
achievements were recognized with the 1998 Nobel Prize in Chemistry to
Walter Kohn.
Density functional model has proven to be successful for determination of
equilibrium geometries and conformations [12-18], and are almost as successful
as MP2 models for establishing the thermochemistry of reactions where bonds
are broken or formed [19-20]. The Hartree-Fock approximation also presented
the basis for what are now commonly referred to as semi-empirical models.
These introduce additional approximations as well as empirical parameters to
greatly simplify the calculations, with minimal adverse effect on the results.
While this objective has yet to be fully realized, several useful schemes have
resulted, including the popular AM1 and PM3 models. Semi-empirical models
8
have proven to be successful for the calculation of equilibrium geometries,
including the geometries of transition-metal compounds [21]. They are,
however, not satisfactory for thermochemical calculations or for conformational
assignments.
The work presented in this thesis is primarily based on the calculation of
molecular properties of small molecules/cluster using density functional theory.
Density functional theory (DFT) is primarily a theory of electronic ground state
structure, couched in terms of the electronic density distribution ρ(r). Since its
birth, it has become increasingly useful for the understanding and calculation of
the ground state density, ρ(r). and ground state energy E of molecules, clusters,
and solids - any system consisting of nuclei and electrons - with or without
applied static perturbations. It is an alternative, and complementary, approach to
the traditional methods of quantum chemistry which are couched in terms of the
many electron wave function ψ(ρ1,... ρN). Both Thomas – Fermi and Hartree –
Fock – Slater methods can be regarded as ancestors of DFT. In any quantum
chemical calculation the first step requires optimization of the molecular
geometry. Mostly this is done on an isolated molecule, assumed to be in the gas
phase. A sensible starting point for geometry optimization is to use
experimental data i.e. the X-Ray diffraction data of the molecules whenever
possible [22], The energy and wave functions are computed for the initial guess
of the geometry, which is then modified iteratively until (I) an energy minimum
9
has been identified and (II) forces within the molecules are zero. This can often
be difficult for non-rigid molecules, where there may be several energy minima,
and some effort may be required to find the global minimum. In addition to
molecular properties like dipole moment, polarizability, electron affinity and so
forth, the vibrational modes can also be calculated [23] by computing the
second derivative of the energy with respect to the pairs of the atomic cartesian
coordinates. In addition to simulation of infrared and Raman spectra [24],
which also require computation of dipole and polarizability derivatives,
determination of force constants provides a useful check on the geometry
optimization. Since an optimized geometry should result in zero forces within
the molecule, all principle force constants must be positive and therefore not
result in any imaginary vibrational frequencies.
1.2 Vibrational analysis: Key approaches
Vibrational spectroscopy has been used to make significant contribution in
many areas of physics and chemistry as well as in other areas of science. Its
important applications are in the study of intra molecular and inter molecular
forces, molecular structure determination, computation of degree of association
in condensed phases, elucidation of molecular symmetries, identification and
characterization of new molecules, deducing thermodynamical properties of
molecular system, etc.
10
1.2.1 Infrared- spectroscopy
Infrared spectroscopy directly measures the natural vibrational frequencies of
the atomic bonds in molecules. These frequencies depend on the masses of the
atoms involved in the vibrational motion (i.e. on their elemental and isotopic
identity), on the strengths of the bonds, and on the resting bond lengths and
angles - in other words, on all the parameters that constitute the structure of the
molecule. For this reason, infrared spectroscopy is a powerful technique for the
identification, quantification and structural analysis of small molecules, and has
been established for many decades as an indispensible tool in organic chemistry,
polymer chemistry, pharmaceuticals, forensic science, and many other areas. IR
spectroscopy is the measurement of the wavelength and intensity of the
absorption of midinfrared light by a sample. Mid-infrared light (2.5 - 50 cm-1
,
4000 - 200 cm-1
) is energetic enough to excite molecular vibrations to higher
energy levels.
IR radiation does not have enough energy to induce electronic transitions as
seen with UV and visible light. Absorption of IR is restricted to excite
vibrational and rotational states of a molecule. Even though the total charge on a
molecule is zero, the nature of chemical bonds is such that the positive and
negative charges do not necessarily overlap in this case. Such molecules are
said to be polar because they possess a permanent dipole moment. For a
molecule to absorb IR, the vibrations or rotations within a molecule must cause
11
a net change in the dipole moment of the molecule. The alternating electrical
field of the radiation interacts with fluctuations in the dipole moment of the
molecule. If the frequency of the radiation matches the vibrational frequency of
the molecule then radiation will be absorbed, causing a change in the amplitude
of molecular vibration. The result of IR absorption is heating of the matter since
it increases molecular vibrational energy. Molecular vibrations give rise to
absorption bands throughout most of the IR region of the spectrum.
An infrared spectrum is commonly obtained by passing infrared radiation
through a sample and determining what fraction of the incident radiationis
absorbed at a particular energy. The energy at which any peak in an absorption
spectrum appears corresponds to the frequency of a vibration of a part of a
sample molecule [25], like a fingerprint no two unique molecular structures
produce the same infrared spectrum. This makes infrared spectroscopy useful
for several types of analysis. FT-IR, Fourier Transform Infrared [26] is one of
the preferred methods of infrared spectroscopy. Fourier Transform Infrared (FT-
IR) spectrometry was developed in order to overcome the limitations
encountered with dispersive instruments. The main difficulty was the slow
scanning process. A method for measuring all of the infrared frequencies
simultaneously, rather than individually, was needed. The solution resulted in
the development of FT-IR spectrometer. It produces a unique type of signal
which has all of the infrared frequencies “encoded”into it. The signal can be
12
.
Fig 1.3 : Basic Components of FTIR Spectrometer.
Source Interferometer
Sample
Detector
Amplifier Analog to Digital Converter
Computer
13
measured very quickly, usually of the order of one secondor so. Thus, the time
element per sample is reduced to a matter of a few seconds rather than several
minutes. Fourier-transform infrared (FTIR) spectroscopy is based on the idea of
the interference of radiation between two beams to yield an interferogram. The
latteris a signal produced as a function of the change of path length between the
two beams. The two domains of distance and frequency are interconvertible by
The mathematical method of Fourier-transformation. The basic components of
an FTIR spectrometer are shown schematically in Fig 1.3. The radiation
emerging from the source is passed through an interferometer to the sample
before reaching a detector. Upon amplification of the signal, in which high-
frequency contributions have been eliminated by a filter, the data are converted
to digital form by an analog-to-digital converter and transferred to the computer
for Fourier-transformation [27]
1.2.2 Raman spectroscopy
Raman spectroscopy has long been accepted as a precious research technique in
theyears since the phenomenon was first observed by Dr. C. V. Raman in 1928.
Recently Raman spectroscopy has emerged as an important analytical tool
across a number of industriesand applications.Raman spectroscopy is the
measurement of the wavelength and intensity of in-elastically scattered light
from molecules. The Raman scattered light occurs at wavelengths that are
14
Fig. 1.4 Block diagram of laser Raman Spectrophotometer
Sample
Laser
Source Power
Supply
L
E
N
S
s
Monochromator Photo-
Multiplier
Power
Supply
Amplifier
Recorder
15
shifted from the incident light by the energies of molecular vibrations. The
mechanism of Raman scattering is different from that of infrared absorption,
and Raman and IR spectra provide complementary information. Typical
applications are in structure determination, multicomponent qualitative analysis,
and quantitative analysis.
Raman spectroscopy can also provide exquisite structural insights into small
molecule because it involves an intimate interplay between atomic positions,
electron distribution and intermolecular forces [28]. The FT-Raman
spectroscopy has made possible the study of materials that was previously
impossible because of fluorescence [29]. Raman spectroscopy is a spectroscopic
technique rooted in the inelastic scattering of monochromatic light, generally
from a laser source (Fig 1.4). Inelastic scattering implies that the frequency of
photons in monochromatic light changes upon interaction with a sample.
Photons of the laser light are absorbed by the sample and then reemitted.
Frequency of the reemitted photons is either shifted up or down in comparison
with original monochromatic frequency, which is called the Raman effect. The
difference in frequency/energy is made up by change in the rotational and
vibrational energy of the molecule and gives information on its energy levels.
The Raman effect is based on molecular deformations in electric field E
determined by molecular polarizability α. Raman spectroscopy can be used to
study solid, liquid and gaseous samples.By combination of Raman and IR we
16
have found a lot of information about symmetry and asymmetry of molecule
nature of bond.
The work presented in the thesis has been divided into two partsThe first part
deals with the investigation ofmolecular, structural, vibrational and energetic
data analysis of 3-benzoyl-5-chlorouracil,and Gabapentin which are biologically
and pharmaceutically important molecules, using Quantum Chemical methods.
The structure and the ground state properties of the molecules under
investigation has been analysed employing Density functional theory (DFT). In
order to obtain a complete description of molecular dynamics, vibrational
frequency calculations have been carried out at the DFT level. The vibrational
analysis also yields the detailed information about the intramolecular vibrations
in the molecular fingerprint region. The reported geometries, molecular
properties such as equilibrium energy, dipole moment and vibrational
frequencies along with the electrostatic potential maps, have also been used to
understand the activity of the molecules. The second part involves the
investigation of properties of CdTe clusters. Study of physical and chemical
properties of clusters is one of the most active and emerging frontiers in
physics, chemistry and material science. In the last decade or so, there has been
a substantial progress in generation, characterization and understanding of
clusters. Clusters of varying sizes, ranging from a few angstroms to nano-
meters, can be produced using a variety of techniques such as sputtering,
17
chemical vapour deposition, laser vaporization, supersonic molecular beam etc.
Their electronic, magnetic, optical and chemical properties are found to be very
different from their bulk form and depend sensitively on their size, shape and
composition. Thus, clusters form a class of materials different from the bulk and
isolated atoms/molecules. Looking at the mass distribution of clusters, some are
found to be much more abundant than others. These clusters are therefore more
stable and are called magic clusters. They act like superatoms and can be used
as building blocks or basis to form a cluster assembled solid. It is these kinds of
developments that add new frontiers to material science and offer possibilities
of designing new materials with desirable properties by assembling suitably
chosen clusters. To calculate the properties of clusters, we treat them as
molecules and use existing molecular orbital theories such as density functional
theory for the purpose. This approach can be used to calculate the actual
geometric and electronic structure of small metal clusters. The molecular orbital
approach is also able to account for the dependence of the binding energy and
ionization energy on the number of atoms in the cluster.
18
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20. K.J.H. Giesbertz, E.J. Baerends, and O.V. Gritsenko, PRL101, (2008)
033004.
21. K. Chaitanya, Spectrochimica Acta Part A 86 (2012) 159– 173.
22. G.J. Gainsford and K. Clinch.3-Benzoyl-5-chlorouracil, Acta Cryst. E65
(2009), o342.
23. N. Oliphant, R. J. Bartlett J. Chem. Phys. 100, 6550 (1994).
24. P. Vandenabeele, D.M. Grimaldi, H.G.M. Edwards and L. Moean,
Spectrochim Acta Part A (2003), 59, 2221.
25. H.G.M. Edwards and D.W. Farwell ,Spectrochim Acta Part A (1996), 52,
1119.
26. R.H. Brody and H.G.M. Edwards, Spectrochim Acta Part A (2001), 57,
1325.
27. Introduction to Fourier Transform Infrared Spectrometry- Thermo Nicolet,
2001, Thermo Nicolet corporation
28. J. Mink, Cs. Ne´meth,, L. Hajba,, M. Sandstro, P.L. Goggin Journal of
Molecular Structure 661-662 (2003) 141–150.
20
29. Y. Fujimura, H. Kono, T. Nakajima, S. H. Lin, J. Chem. Phys. 75, 99
(1981).
CHAPTER 2
THEORETICAL
APPROACH
21
2.1 Introduction
This chapter will give a short glance of quantum chemical methods which is based
mainly on the article “Short Introduction to Quantum ωhemistry Methods” by
Holger Naundorf (2005). Electronic structure methods use the law of quantum
mechanics as the basis for their computations. Quantum mechanics states that the
energy and other related properties of a molecule can be obtained by solving the
Schrodinger equation:
molH = E ----(2.1)
Which describes a many body system consisting of nuclei and electrons. An
analytical solution for this problem is only possible for very few simple systems
[1], e.g. the harmonic oscillator or the Hydrogen atom. To solve this for more
complicated systems one has to apply several approximations before a solution of
Eq. (1) is possible. The most important among them is the Born–Oppenheimer
approximation, used to separate the motion of the heavy nuclei from that of the
light electrons.
However, exact solutions to the Schrodinger equation are not pragmatic. Electronic
structure methods are characterized by their various mathematical approximations
to their solutions. There are two major classes of electronic structure methods:
22
Semi - empirical methods use a simpler Hamiltonian than the correct
molecular Hamiltonian and use a parameter whose values are adjusted to fit
the experimental data. That means they solve an approximate form of the
Schrodinger equation that depends on having approximate parameters
available for the type of chemical system in question. There is no unique
method for the choice of parameter. Ab initio force fields provide solutions
to these problems.
Ab initio methods use the correct Hamiltonian and does not use
experimental data other than the values of the fundamental physical
constants (i.e., c, h, mass and charges of electrons and nuclei). Moreover it is
a relatively successful approach to perform vibrational spectra.
The basis of most of the numerical solutions for the electronic system is the Hatree
–Fock self-consistent field approach. This can be refined via perturbation theory
based on the work of Møller and Plesset. Another approach to solve the electronic
problem of the molecules is density functional methods.
2.2 The Born–Oppenheimer Approximation
The Born–Oppenheimer approximation [2] is used to separate the motion of the
heavy nuclei of a molecule from the much faster dynamics of the electrons. The
complete molecular Hamiltonian of a system consisting of Nnuc atoms with nuclear
charges Z1, . . . ,ZNnuc , Cartesian positions Rn and momenta Pn and Nel electrons
23
with positions and momenta written as rn and pn, respectively, is generally given in
the form
nucelnucnucnucelelelmol VVTVTH ˆˆˆˆˆˆ ------ (2.2)
The single terms are the kinetic energy for the electrons, elT , and for the nuclei,
nucT , as
elN
j e
j
elm
pT
1
2
2ˆ
and
nucN
j j
jnuc
M
pT
1
2
2ˆ
Where me is the electron mass and Mj is the mass of the jth nucleus. The interaction
between these particles via the Coulomb force results in the potential terms for the
electron–electron interaction elelV ˆ the nucleus–nucleus interaction nucnucV
ˆ and for
the electron–nucleus interaction nucelV ˆ , as
ji ji
elelrr
eV
2
2
1ˆ ,
ji ji
ji
nucnucRR
eZZV
2
2
1ˆ and
ji ji
j
nucelRr
eZV
,
2
ˆ
The solution of the Schrodinger equation for many body problem is then simplified
by the application of the Born–Oppenheimer approximation, which assumes that
the electrons move in the electro-static field generated by a fixed geometry of the
nuclei. This is motivated by the fact, that due to the large mass difference between
electrons and nuclei the electrons will be able to respond instantaneously to any
24
change in the nuclear configuration. Therefore it is possible to represent the
electronic Hamiltonian in a form, which only depends parametrically on the
nuclear coordinates R:
nucelelelelel VVTRH ˆˆˆ)(ˆ ------ (2.3)
The solution of the stationary Schrodinger equation Eq. (1) with this electronic
Hamiltonian is the objective of quantum chemistry programs. It results in
electronic energies and wave functions , which will depend
parametrically on the nuclear geometry:
).()(),(ˆ RrRERrH n
nl
nnel , ------(2.4)
The solution of the electronic part of the Schrodinger equation for different nuclear
coordinates R results in the potential hyper surface V(R) when the inter-nuclear
repulsion is added. This part of the potential is constant with respect to the
electronic coordinates. Here we have neglected a potential term, which results
from the non-adiabatic coupling operator, and describe the interaction between the
different electronic states [3], a single adiabatic potential energy surface, can be
written as:
nucnuc
el
nn VRERV ˆ)()( ----(2.5)
25
If the electronic states of the molecule are well separated from each other this
approach is justified. The elimination of the non-adiabatic electronic coupling is
the core of the Born–Oppenheimer approximation, which leads to a nuclear
Schrodinger equation
)()()](ˆ[)(ˆ RERRVTRH n
nuc
nnnnucnnuc -----(2.6)
This describes the geometry of the nuclei in the average field generated by the fast
moving electrons. It is to be noted, that there will be a different nuclear potential
for each electronic state. The dynamics of the nuclei is described reasonably well
with the nuclear potential V(R) within the Born–Oppenheimer approximation, as
long as the potential surfaces belonging to different states stay well separated.
2.3 The Hartree–Fock (HF) Method
While dealing with Born–Oppenheimer approximation it was noted that the
potential hyper surface and therefore the nuclear dynamics is mainly determined by
the solution of the electronic Schrodinger equation (4) for a fixed nuclear
configuration. While this problem is easier to solve than the complete molecular
Hamiltonian, it is still not possible to calculate the electronic orbitals and energies
exactly for anything but the most simple systems. To evaluate more complicated
molecules, it is again necessary to resort to some approximations. One of the oldest
methods, which is also the basis of other, more refined theories, is the Hartree–
26
Fock self-consistent field method (HF-SCF) [4]. This method gives an approximate
solution of the electronic Schrodinger equation (4) using the Hamiltonian elH as
obtained from the Born–Oppenheimer approximation.
The HF method is a non-relativistic approach, in which the single electrons are
described by single particle functions (x) consisting of a product of a spatial
orbital (r), depending on the position of the electron and a spin orbital α( ) or
β( ) depending only on the spin coordinate:
)()()(),()(
rrx nn ------ (2.7)
The total electronic wave function of the Nel electron molecular system can then be
described – at least within the HF approximation – as a single, anti-symmetric
Slater determinant:
)()()(
)()()(
)()()(
!
1)(
21
2221
11211
1
elNel
N
N
el
el
xxx
xxx
xxx
Nx
elel
el
el
------(2.8)
The single particle functions (x) are then determined by minimizing the
functional for the energy expectation value:
elel
elelel
elel
HE
ˆ ---(2.9)
27
To perform this minimization it is convenient to split the electronic Hamiltonian
Hel Eq. (3) into a sum of single electron operators )(ˆ irh , which affect only the ith
electron and the non-separable interaction potential elelV ˆ between all electrons:
ji jii
ielrr
erhH
2
2
1)(ˆˆ ------(2.10)
Where
elel
e
j
i Vm
prh ˆ
2)(ˆ
2
------ (2.11)
In addition the orthonormality of the single particle functions is
assumed. After performing the variational optimization, one obtains the Hartree–
Fock equations for the single particle spin orbitals (x) :
)()(ˆ xxF nnn ------- (2.12)
with the Fock operator F . It consists of the single particle operator h and the so
called Coulomb and exchange operators J and K , respectively :
'
'
''*
2'
'
''*
2 )()()(
)()()(
)(ˆ)(ˆ drxrr
xxexdr
rr
xxexhxF
elel N
j
i
jjN
j
i
ji
ii
)(ˆ xJ i )(ˆ xK i
= )(xii . ---- (2.13)
28
This form can be interpreted as a single particle operator consisting of the basic
operator h for one electron with an additional effective Hartree–Fock potential
term
elN
i
ii
HFxKxJexV )](ˆ)(ˆ[)( 2 ------(2.14)
which can be written in the simple form
)()()](ˆ[ xxxVh iii
HF -------(2.15)
The interpretation for the Coulomb part of this potential is straight forward, it just
describes the interaction of one electron with the charge of all other electrons
located in all the other single particle orbitals. The exchange part on the other hand
has no classical counterpart and is a purely quantum mechanical effect, caused by
the anti-symmetric ansatz of the wave function. The energy of the HF molecular
orbital is then calculated via
EHF = --------(2.16)
With iiii hh ˆ and the Coulomb and correlation energies as derived from the
corresponding operators
------(2.17)
29
------(2.18)
To solve these equations an iterative method has to be employed, as the operator
generating the single particle functions (x) itself depends on these functions via
the Hartree –Fock potential VHF (x). Therefore it is necessary to start with an
initial guess of the (x) use them to calculate an approximate VHF (x) and from
this the Fock operator F , recalculate the (x) with this operator and repeat this
procedure until the single particle functions converge to a stable solution.
2.4 Basis Sets
In modern quantum chemical methods, calculations are typically performed within
a finite set of basis functions [5]. Gaussian 09 [6] and other ab initio electronic
structure programs use Gaussian type atomic functions as basis functions. A basis
set is the mathematical description of the orbitals within a system (which in turn
combine to approximate the total electronic wave functions) used to perform
theoretical calculation.
To further simplify the problem and reduce the numerical effort the standard
quantum chemistry programs represent the spatial part of the single particle
functions (r) from which the total molecular wave function is built as a linear
combination of fixed basis functions:
30
Fig. 2.1 Flow diagram of program used in the quantum chemical calculations
Graphical input of geometry
Or
Input files as recommended by computer program
ab initio geometry Optimizations including offset forces
Cartesian gradient, Force constant,
Dipole moment and Polarizablity
Transformation of Force Constant, Dipole moment, and
Polarisabilty derivatives, Normal Coordinates Analysis
Theoretical Frequencies and IR, Raman
intensities in the form of graphical display
31
(r) = -------- (2.19)
The wave functions under consideration are all represented as vectors, the
components of which correspond to coefficients in a linear combination of the
basis functions in the basis set used. The operators are then represented as
matrices, in this finite basis. When molecular calculations are preformed, it is
common to use basis composed of a finite number of atomic orbitals, centered at
each atomic nucleus within the molecule. Initially, atomic orbitals were typically
slater orbital, which corresponded to a set of functions, which decayed
exponentially with distance from the nuclei. These Slater-type orbitals could be
approximated as linear combinations of Gaussian orbitals.
Historically this linear combinations were built from atomic orbitals or from a
linear combination of Slater–type orbitals (STOs) in the form
------ (2.20)
which are centered on each atom. This approach is named linear combination of
atomic orbitals (LCAO), and leads to an equation for the coefficients of the
molecular orbitals (Roothaan equation).The solution of these equations for larger
molecules requires an evaluation of three and four center integrals (i.e. integrals
over basis functions centered on up to four different atoms), which is very time
consuming for STOs. In modern quantum chemistry programs the atomic or
32
Slater–type orbitals normally are not used. Instead a collection of square integrable
functions, usually easy to integrate Gaussians, are used. A typical Cartesian
Gaussian basis function is defined as
-------(2.21)
where i, j and k are non-negative integers, is a positive orbital exponent and x, y
and z are Cartesian coordinates centered on a nucleus. For i + j + k = 0 this results
is a s-type gaussian, for i + j + k = 1 is three p-type Gaussians, and so forth. The
fact that the radial component of these functions varies with and not with the
correct exponential factor is compensated by choosing a linear combination of
these Gaussian functions for each orbital. Different sets of these linear
combinations, the so called contracted Gaussian type functions (CGTF), are used
to build up the atomic orbitals of the system. Sets of these CGTF for the atoms are
called the basis sets of the calculation.
The most common addition to minimal basis sets is the addition of polarization
functions, denoted by an asterisk*. Two asterisks** indicate that polarization
functions are also added to light atoms (hydrogen and helium). When polarization
is added to this basis set, a p-function is added to the basis set. This adds some
additional needed flexibility within the basis set, effectively allowing molecular
orbitals involving the hydrogen atoms to be more asymmetric about the hydrogen.
33
Similarly, d-type functions can be added to a basis set with valance p orbitals, and
f-functions to a basis set with d-type orbitals and so on [7]. The precise notation
indicates exactly which and how many functions are added to the basis set, such as
(d,p) Another common addition to basis sets is the addition of diffuse functions,
denoted by a plus sign, +. Two plus signs indicate that diffuse functions are also
added to light atoms (hydrogen and helium). These additional basis functions can
be important when considering anions and other large, soft molecular system.
2.5 Perturbation Theory
The Hartree–Fock approximation has one serious shortcoming – even with an
infinite number of single particle functions in the so called HF–limit a single
determinant is not able to represent the electron density accurately. The main
problem is that the electrons are allowed to approach closer to each other than the
true quantum mechanical description of the correlated movement of the electrons
would allow. To overcome this problem one naturally has to move away from
the HF description toward a model using not one but several Slater determinants to
describe the total molecular wavefunction. One possible approach is described in
the theory by Møller and Plesset [8]. This approach includes the additional
determinants via a perturbation scheme using the original spin orbitals generated
by the HF method and is not variational itself. The so called Møller–Plesset (MP)
34
perturbation theory starts by dividing the Hamiltonian into a main, unperturbed
part, and an additional perturbation operator. In this case the unperturbed operator
is defined as the Hartree–Fock operator (the sum overall single particle Fock
operators):
i
i
HF
i
i
i
HFxVxhxFHH )]()(ˆ[)(ˆˆˆ 0 -------(2.22)
while the perturbation operator is set to the difference between this operator and
the exact electronic Hamiltonian:
i
i
HF
elelel VVHHH )(ˆˆˆˆ 01 -------(2.23)
As the Hartree–Fock potential already gives a quite good approximation of the true
electron–electron interaction (typically around 99%), the energy correction
generated by this perturbation operator is relatively small. The additional Slater
determinants used to describe the molecular orbitals are generated by replacing one
or two of the occupied single particle functions from the ground state HF
determinant with unoccupied, so called virtual, orbitals. These determinants are
called singly or doubly excited, as they represent molecular orbitals in a higher
energy state. An important property of this approximation is, that in first order it
just reproduces the result of the Hartree–Fock calculations. To achieve any
refinement one has to calculate the corrections in second and higher orders. The
35
method is labeled according to the order of the perturbation treatment used. The
MP2 method mostly used in this work therefore is the Møller–Plesset perturbation
theory in second order.
2.6 Density Functional Theory
The density functional theory (DFT) offers a completely different approach to the
calculation of molecular potentials. In contrast to the perturbation methods this
theory is not based on the refinement of a result obtained via Hartree–Fock, but
takes a different route to calculate the molecular energies [9, 10].
The DFT methods derive these from a charge density ρ(r), which depends only on
the coordinates x, y and z. The proof that this much simpler quantity indeed
provides enough information to calculate the molecular energies was found by
Hohenberg and Kohn and presented in their famous paper from 1964, which
started the whole field of DFT methods [11]. In it the first Hohenberg–Kohn
theorem is proven, which states that “The external potential Vext(r) (i.e. the
complete molecular potential) is (to within a constant) a unique functional of ρ(r);
since, in turn Vext(r) fixes H we see that the full many particle ground state is a
unique functional of ρ(r)”. Therefore, instead of using a Slater determinant of spin
orbitals, by virtue of this theorem it is possible to calculate the total energy via the
36
minimization of the charge density functional which depends on the
electron density
. ------- (2.24)
This is stated in the second Hohenberg–Kohn theorem, which proves that the
energy obtained from a trial density represents an upper bound to the true ground
state energy, as obtained from the exact ground state density . The energy in the
DFT approach is not given as the expectation value of an operator, like in the HF
approach (Eq. (16)), but as a sum of energy functionals depending on the electron
density:
EDFT (ρ) = T(ρ) + V (ρ) + U(ρ) + EXC(ρ), ----------(2.25)
where T(ρ) describes the kinetic energy of the electrons, V (ρ) the interaction with
the nuclei, U(ρ) the Coulomb repulsion between the electrons and EXC(ρ) the
effects generated by the electron correlation which have no classical counterpart.
This so called exchange-correlation energy is used to collect all parts of the energy
which cannot be handled exactly. According to the second Hohenberg–Kohn
theorem the total energy given by Eq. (25) obeys the relation:
--------(2.26)
37
where E0 is the true ground state energy. The equality holds only, if the density
inserted into Eq. (25) is the exact ground state density. Similar to the HF equations
(13) the Kohn–Sham approach leads to a set of one-electron equations, which have
to be solved iteratively. The difference to Eq. (15) lies in the form of the effective
potential, which now is of course no longer given by , but by an effective DFT
potential defined by:
= ---- (2.27)
where the first term is equivalent to the Coulomb–term of the HF equations, while
VXC is the potential due to the non-classical exchange-correlation energy EXC. This
is simply defined via the functional derivative of EXC:
---- (2.28)
If the exact form of the exchange-correlation energy EXC were known, the solution
of the Kohn–Sham equation would generate the correct energy eigenvalue of the
total Hamiltonian of the Schrodinger equation. So while the HF model started with
the approximation that the total wave function can be described by a single Slater
determinant, and therefore cannot result in an exact solution, the Kohn–Sham
approach is in principle exact. Unfortunately the correct form of EXC is not known,
so the art of DFT calculations is to find good functional forms for this energy.
38
A commonly used pair of functionals is ψecke’s 1988 exchange functional (ψ88 or
B) [12] and the Lee–Yang–Parr (LYP) [13] correlation functional, or the so called
Becke3LYP (B3LYP) hybrid functional, which combines the B88 and LYP
functionals via three parameters (indicated by the 3) with three additional
functionals. The parameters in these functionals are determined by fitting the
results of the calculations for small molecular test systems to well established
experimental molecular data.
In computer based calculations DFT methods, for which the numerical effort is of
the same order of magnitude as that of the bare HF calculation, will normally
deliver results much faster than advanced methods based on HF theory, which
require the calculation of additional determinants and their correlation via
perturbation or variational methods. The drawbacks are that one cannot be certain
that a given functional used for the exchange-correlation energy will produce good
results with any given molecule, so that it is normally necessary to cross check the
results with other data.
2.7 Gauss View
Gaussview is an affordable, full-featured graphical user interface for Gaussian 09.
With the help of Gaussview, one can prepare input for submission to Gaussian and
to examine graphically the output that Gaussian produces. The first step in
producing a Gaussian input file is to build the desired molecule. The bond lengths,
39
bond angles, and dihedral angles for the molecule will be used by Gaussview to
write a molecular structure for the calculation. Gaussview incorporates an excellent
Molecule Builder. One can use it to rapidly sketch in molecules and examine them
in three dimensions. Molecules can be built by atom, ring, group, amino acid and
nucleoside. Gaussview is not integrated with the computational module of
Gaussian, but rather is a front-end/back-end processor to aid in the use of
Gaussian. Gaussview can graphically display a variety of Gaussian calculation
results, including the following:
• Molecular orbitals
• Atomic charges
• Surfaces from the electron density, electrostatic potential, NMR shielding
density, and other properties. Surfaces may be displayed in solid, translucent and
wire mesh modes.
• Surfaces can be colored by a separate property.
• Animation of the normal modes corresponding to vibrational frequencies.
• Animation of the steps in geometry optimizations, potential energy surface scans,
intrinsic reaction coordinate (IRC) paths.
40
2.8 Application of Quantum Chemical Methods
2.8.1 Geometry Optimization
Geometry Optimization is the name for the process thar attempts to find the
configuration of minimum energy of the molecule. A sensible starting point for
geometry optimization is to use experimental data i.e. the X-Ray diffraction data of
the molecules whenever possible. The energy and wave functions are computed
for the initial guess of the geometry, which is then modified iteratively until (I) an
energy minimum has been identified and (II) forces within the molecules are zero.
This can often be difficult for non-rigid molecules, where there may be several
energy minima, and some effort may be required to find the global minimum. But
in those cases where molecules have unknown or unconfirmed structures,
geometry optimization can also be used to locate minima on a potential energy
surface (PES) and can predict the equilibrium structure of the molecule in question.
A point on a PES where the forces are zero is called a stationary point and these
are the points generally located during an optimization. Whether these points are
local or global minima, or even transition states, is another matter. An input
geometry is provided for geometry optimization and the calculation proceeds to
move across the PES. At each point the energy and the gradient are calculated and
41
Fig.2.2 A three-dimensional potential energy curve that shows global minima,
transition state and local minima
42
the distance and direction of the next step are determined. The force constants are
usually estimated at each point and these constants specify the curvature of the
surface at that point; this provides additional information useful to determining the
next step. Convergence criteria about the forces at a given point and the
displacement of the next step determine whether a stationary point has been found.
To determine whether the geometry optimization has found a minimum or a
transition state (TS), it is necessary to perform frequency calculations. A TS is a
point that links two minima on the PES, and is characterized by one imaginary
frequency. The eigenvector from the Hessian force constant matrix determines the
nature of the imaginary frequency and indicates a possible reaction coordinate. A
minimum structure will have no imaginary frequencies.
2.8.2 Frequency Calculations
IR and Raman spectra of molecules can be predicted for any optimized molecular
structure. The position and relative intensity of vibrational bands can be gathered
from the output of a frequency calculation. This information is independent of
experiment and can therefore be used as a tool to confirm peak positions in
experimental spectra or to predict peak positions and intensities when experimental
data is not available. Calculated frequencies are based on the harmonic model,
43
while real vibrational frequencies are anharmonic. This partially explains
discrepancies between calculated and experimental frequencies.
The total energy of a molecule comprising N atoms near its equilibrium structure
may be written as
ji
eqi j ji
eq
i
i qqqq
VVqV
3
1
3
1
23
1
2
2
1 …. (2.29)
Here the mass-weighted cartesian displacements, qi, are defined in terms of the
locations Xi of the nuclei relative to their equilibrium positions Xi’eq and their
masses Mi,
ieqiiiq 21 …. (2.30)
Veq is the potential energy at the equilibrium nuclear configuration, and the
expansion of a power series is truncated at second order [14]. For such a system,
the classical-mechanical equation of motion takes the form
i
i
iji qfQ
3
1
, j = 1, 2, 3 …3N. …. (2.31)
The fij term quadratic force constants are the second derivatives of the potential
energy with respect to mass-weighted Cartesian displacement, evaluated at the
equilibrium nuclear configuration, that is,
44
eqji
ijqq
Vf
2
…. (2.32)
The fij may be evaluated by numerical second differentiation,
jiji Vqq
V
V
2
…. (2.33)
By numerical first differentiation of analytical first derivatives,
i
j
ji q
qV
V
2
…. (2.34)
or by direct analytical second differentiation, Eq. (2.89). The choice of procedure
depends on the quantum mechanical model employed, that is, single-determinant
or post-Hartree-fock, and practical matters such as the size of the system.
Equation (2.86) may be solved by standard methods [15] to yield a set of 3N
normal-mode vibrational frequencies. Six of these (Five for linear molecules) will
be zero as they correspond to translational and rotational (rather than vibrational)
degrees of freedom. Normal modes of vibration are simple harmonic oscillations
about a local energy minimum, characteristic of a system's structure and its energy
function for a purely harmonic potential any motion can be exactly expressed as a
45
superposition of normal modes. In the present work the computed vibrational
wavenumbers, their IR and Raman intensities and the detailed description of each
normal mode of vibration are carried out in terms of the potential energy
distribution. The DFT calculated wavenumbers, for the majority of the normal
modes, are typically slightly higher than that of their experimental counterpart and
thus proper scaling factors [16,17] are employed to have better agreement with the
experimental wavenumbers.
The Raman intensities were calculated from the Raman activities (Si) obtained with
the Gaussian 09 program, using the following relationship derived from the
intensity theory of Raman scattering [18,19]
Ii = [f(ν0 – ν i)4 Si] / [ν i{1- exp(-hc ν i/kT)}] ….[2.35]
Where ν0 being the exciting wavenumber in cm-1, νi the vibrational wave number
of ith normal mode, h, c and k universal constants and f is a suitably chosen
common normalization factor for all peak intensities.
2.8.3 Calculation of dipole moment and polarizability
The Gaussian 09 program was used to calculate the dipole moment (µ) and
polarizability (α) of the molecules, based on the finite field approach. Following
46
ψuckingham’s definitions [20], the total dipole moment and the mean
polarizability in a Cartesian frame is defined by
µ = (µx2 + µy
2 +µz2)1/2 ..…[2.36]
<α> = 1/3 [αxx + αyy + αzz ] ……..[2.37]
2.8.4 Calculation of Thermodynamical Properties
Heat capacity Cp and entropy S were calculated using DFT and were obtained
from the output of Gaussian programs. The equations used for calculating the
absolute entropy of a molecule are as follows [21,22]
vibrottrans SSSS …. (2.38)
where Strans, Srot and Svib are translational, rotational and vibrational entropy,
respectively, which can be calculated by the following equations-
2/5)/ln()/2ln(2/3 2 PkThmkTRStrans
2/3))8/)(8/)(8//(ln()2/1()/ln( 22222232/1
kIhkIhkIhTRS zyxrrot
63
1
)}/exp(1ln{)}1)//(exp()/{(N
i
vib kThvikTihkTihRS
where N is the number of atoms in a molecule, R is the gas constant, m is the
molecular mass, k is the ψoltzmann constant, h is Planck’s constant, T is the
47
temperature, P is the pressure, σr is the symmetry number for rotation, I is the
moment of inertia, and υ is the vibrational frequency.
The heat capacity at constant pressure was calculated using the equation-
63
1
2
})1)/exp()/()/exp()2/3()2/5( /({N
i
vibrottransp kTihkTihkTihRRRCCCC
…. (2.39)
where Ctrans, Crot and Cvib are contribution to heat capacity due to translation,
rotational motion, and vibrational motion respectively.
48
References
1. J. A. Pople and D. L. Beveridge , Approximate Molecular Orbital
Theory, McGraw-Hill, New York, (1970).
2. M. Born and R. Oppenheimer. Zur Quantentheorie der Molekeln. Ann.
Phys., 84,(1927) 457.
3. V. May and O. K¨uhn. Charge and Energy Transfer Dynamics in Molecular
Systems. Wiley-VCH, Berlin, 2000.
4. D. R. Hartree. Proc. Cambridge Phil. Soc., 24,(1928)111.
5. J. B. Foresman and A. Frisch, Exploring Chernistry with Electronic
Structure Methods, Gaussian Inc., Pittsburgh, (1993).
6. M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R.
Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G.A. Petersson, H.
Nakatsuji, M. Caricato, X. Li, H.P. Hratchian, A.F. Izmaylov, J. Bloino, G.
Zheng, J.L. Sonnenberg,M. Hada, M. Ehara, K. Toyota, R. Fukuda, J.
Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T.
Vreven, J.A. Montgomery Jr., J.E. Peralta, F. Ogliaro, M. Bearpark,
J.J. Heyd, E. Brothers, K.N. Kudin, V.N. Staroverov, R. Kobayashi, J.
Normand, K. Raghavachari, A. Rendell, J.C. Burant, S.S. Iyengar, J.
Tomasi, M. Cossi, N. Rega, J.M.Millam,M. Klene, J.E. Knox, J.B.
Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R.E. Stratmann, O.
Yazyev, A.J. Austin, R. Cammi, C. Pomelli, J.W. Ochterski, R.L.
Martin, K. Morokuma, V.G. Zakrzewski, G.A. Voth, P. Salvador, J.J.
Dannenberg, S. Dapprich, A.D. Daniels, Ö. Farkas, J.B. Foresman,
J.V. Ortiz, J. Cioslowski, D.J. Fox, Gaussian 09, Revision A.1, Gaussian,
Inc., Wallingford CT (2009).
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density functionals.Rev. Mod. Phys., 71 , (1999) 1253.
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136(1964) 864.
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13. C. Lee, W. Yang, and R. G. Parr.. Phys. Rev. B, 37:785, 1988.
14. Bernhard Schrader, Infrared & Raman Spectroscopy, VCH Pub., Inc.,
New York, (1995).
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Chem. Soc., 105 (1983) 7037.
18. G. Keresztury, S. Holly, J. Varga, G. Besenyei, A. Y. Wang, and J. R.
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19. G. Keresztury, in Raman Spectroscopy: Theory-Handbook of Vibrational
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20. A. D. Buckingham, Adv. Chem. Phys., 12 (1967) 107.
21. D.A. McQuarrie and J. D. Simon, Molecular Thermodynamics, (University
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Molecular orbital Theory, (New York: Wiley. 1986)
CHAPTER 3
Raman, FTIR spectroscopic analysis and first order hyperpolarizability of
3-benzoyl-5-chlorouracil
51
3.1 Introduction
A variety of systems including inorganic materials, organic materials,
organometallics, and polymers have been investigated in the recent years, as
highly prospective materials for various optical devices on account of their non
linear optical activity. Organic molecules have received immense attention due
to the combination of molecular design flexibility, chemical tenability and
choice of synthetic strategies. 3-benzoyl-5-chlorouracil [systematic name: 3-
benzoyl-5-chloro-pyrimidine-2,4(1H,3H)-dione], a biologically active synthetic
molecule was prepared for incorporation into potential thymidine phosphorylase
inhibitor [1]. 3-benzoyl-5-chlorouracil (3B5CU) contains a bicyclic system,
composed of a heterocyclic aromatic chlorouracil ring and a phenyl ring,
bridged through a carbonyl group (Fig. 3.1). The crystallographic data of
3B5CU confirms that 8 molecules of 3B5CU exist per unit cell (z=8) as shown
in Figure 3.2. 3B5CU crystallizes in a space group C2/c. The crystal belongs to
monoclinic system with the lattice parameters a=21.936 A0, b=5.402 A0,
c=19.964 A0, β = 113.2º. Its unit cell volume being 2174.89 [Å]3 respectively.
The crystal packing is dominated by centro symmetric hydrogen bonding
(shown with green colour in Figure 3.2) that plays a significant role in the
stability of the crystal structure [1].
52
The present chapter deals with the investigation of the structural, electronic and
vibrational properties of 3B5CU. The structure and harmonic wavenumbers
have been determined and analyzed at DFT level employing the basis set 6-
311++G(d,p). The optimized geometry of 3B5CU and its molecular properties
such as equilibrium energy, frontier orbital energy gap, molecular electrostatic
potential energy map, dipole moment, polarizability, and first static
hyperpolarizability have been calculated and discussed. The NLO activity of
3B5CU has been reported for the first time and the first static
hyperpolarizability is found to be almost 15 times higher than urea. A complete
vibrational analysis of the molecule has been performed by combining the
experimental Raman, FTIR spectroscopic data and the quantum chemical
calculations. Both Raman and IR spectroscopic methods being the traditional
methods of vibrational analysis are particularly useful in non-destructive
characterization of chemical systems [2,3]. Density functional theory based
calculations provide not only the qualitative also the quantitative
understanding of energy distribution of each vibrational mode on the basis of
potential energy distribution (PED) and lead to an additional interpretation of
the vibrational spectroscopic data as demonstrated in studies conducted by
various groups [4-6].
3.2 Experimental
The pure single crystal of the sample was obtained from Prof. K. Clinch [1] and
was used as such for the spectroscopic measurements. FTIR spectra was
53
recorded on a Bruker FT-IR spectrometer with a spectral resolution of 4 cm-1 in
the region 400–4000 cm-1. KBr pellet of solid sample was prepared from
mixture of KBr and the sample in 400:1 ratio using a hydraulic press. The
Raman spectra was recorded on SNOM/CONFOCAL/MICRRAMAN/ WITec
alpha 300 series microscope, using a 514.75 nm laser line as the exciting
wavelength for recording the Raman spectra in the region 400–4000 cm-1
with spectral resolution of 4 cm-1. Theoretical and Experimental IR and Raman
are shown in Fig. 3.3.
3.3 Results and Discussion
The ground state optimized parameters and the hyperpolarizability of 3B5CU
are reported in Table 3.1 and Table 3.2 respectively. The dihedral angle
between the planes of two aromatic rings in the title compound is calculated to
be almost 900 which is close to the value reported in XRD data [1]. The
heterocyclic uracil ring is found to be deformed in its plain as the calculated
endohedral angles vary largely in the range 113.40 - 127.20. The decrease in the
endohedral angle N7-C8-N5 to 113.50 and increase in endohedral angle N7-C8-
O2 to 123.90 from the usual 120.00, is attributed to the repulsion between O2 and
O4 atoms. Moreover reduction in endohedral angle N7-C9-C10 to 113.40 and
enhancement in the exohedral angle O3-C9-C10 to 125.90 from 120.00 has also
been observed in quantum chemical calculations. The electron cloud of
chlorine atom is shifted towards the ring and results in almost neutral potential
54
Fig. 3.1 Displacement ellipsoids (ORTEP view) at 50% probability level with the optimized structure of 3-benzoyl-5-chlorouracil
55
Fig. 3.2 Unit cell Structure of 3-benzoyl-5-chlorouracil showing hydrogen bonding
56
Table 3.3. Comparison of optimized interatomic distances (Bond Lengths in A0) of 3-Benzoyl 5-
chlorouracil at B3LYP/6-311++G(d,p) level with X-Ray data
Interatomic distance
B3LYP Bond length
X-Ray Data
Interatomic distance
B3LYP Bond length
X-Ray Data
Cl-C10 1.735 1.718 N7-C13 1.498 1.498
O2-C8 1.211 1.222 N9-C10 1.468 1.453
O3-C9 1.210 1.209 C10-C11 1.347 1.336
O4-C13 1.196 1.192 C13-C14 1.476 1.468
N5-H6 1.009 0.870 C14-C15 1.400 1.394
N5-C8 1.391 1.364 C14-C23 1.403 1.383
N5-C11 1.373 1.366 C15-C17 1.391 1.379
N7-C8 1.392 1.378 C17-C19 1.394 1.371
N7-C9 1.417 1.404 C21-C23 1.388 1.382
Table 3.1. Theoretically computed ground state
optimized parameters
Parameters 3B5CU B3LYP/
6-311++G(d,p)
5CU B3LYP/
6-311++G(d,p)
Energy (in Hartree) -1219.01612 a.u.
-874.55977 a.u.
Frontier orbital energy gap (in
Hartree)
0.17418 a.u 0.18958 a.u.
Dipole moment (in Debye)
4.75 4.16
Polarizability / a.u. 161.784 78.984
Table 3.2. All β components and β total
of 3-Benzoyl- 5-chlorouracil
B3LYP/6-311++G(d,p)
βXXX 142.6732
βXXY 122.0162
βXYY 69.2520
βYYY 24.9418
βXXZ 182.2957
βXYZ 50.9231
βYYZ -30.1287
βXZZ 49.2772
βYZZ 54.7263
βZZZ -35.7325
βTOTAL 2.93 x 10-30 e.s.u.
57
Table 3.4. Comparison of optimized bond angles in degrees of 3B5CU at B3LYP/ 6-
311++G(d,p) level with X-Ray data
Bond Angles B3LYP Bond Angles
X-Ray Data
Bond Angles B3LYP Bond Angles
X-Ray Data
C9-N7-C7 116.4 116.9 C21-C23-H24 121.1 120.0
O2-C8-N5 122.6 123.4 C14-C23-H24 118.9 120.0
O2-C8-N7 123.9 121.4 C19-C21-C23 120.0 119.5
N5-C8-N7 113.5 115.3 C19-C21-H22 120.1 120.2
O3-C9-N7 120.7 120.7 C23-C21-H22 120.0 120.2
O3-C9-C10 125.9 126.4 C17-C19-C21 120.2 120.8
N7-C9-C10 113.4 113.0 C17-C19-H20 119.9 119.6
C11-C10-C9 120.6 121.2 C21-C19-H20 119.9 119.6
C11-C10-Cl 1 121.5 121.5 C19-C17-C15 120.0 120.2
C9-C10-Cl 1 117.9 117.2 C19-C17-H18 120.1 119.9
C10-C11-N5 121.2 121.1 C15-C17-H18 119.9 119.9
C10-C11-H12 122.5 123.4 C15-C17-C14 120.1 119.5
N5-C11-H12 116.4 115.4 C17-C15-H16 119.7 120.2
O4-C13-C14 126.0 127.0 C14-C15-H16 120.2 120.2
O4-C13-N7 117.9 117.2 C2-N3-C4 127.2 126.4
C14-C13-N7 116.1 115.5 C2-N3-C7 116.0 116.3
C23-C14-C15 119.7 119.9 C21-C23-C14 120.1 120.0
58
around the chlorine atom as discussed later in the next section. This charge
transfer leads to the reduction of Cl1-C10-C9 angle to 117.90 from 120.00. The
structure of 3B5CU molecule is stabilized by inter as well as intra molecular
hydrogen bonding. Hydrogen bonding influences the bond stiffness and so
alters the wavenumber of vibration. According to the calculations, the angles
C24-C14-C15 and C15-C14-C13 decrease and increase by 2.30 and 2.60
respectively from the usual 120.00, and this asymmetry in exohedral reveals the
probable interaction between bridge carbonyl and phenyl ring. The reported
intermolecular [1] and calculated intra-molecular hydrogen bonding between
N5-H6……O2 (2.473 A0) is also reflected in the overestimation of the
calculated N-H wavenumber. The calculated C-Cl bond length is 1.735 A0 and
is smaller than the usual C-Cl bond length (1.766 -1.850 A0), again due to the
shifting of electron cloud from the Cl atom to the ring. The C=O bond lengths
lie within the standard range 1.196 to 1.211 A0 [7,8]. The C-C and C-H bond
lengths in the phenyl ring vary in the range 1.388 – 1.403 A0 and 1.082 – 1.084
A0 respectively. In general optimized parameters agree very well with the
experimental XRD data (refer to Table 3.3 and Table 3.4). According to our
calculations all the carbonyl oxygen atoms carry net negative charges, with the
O2 atom carrying maximum negative charge.
3.3.1 Electronic properties
The frontier orbitals, HOMO and LUMO determine the way a molecule
interacts with other species. The frontier orbital gap helps characterize the
59
chemical reactivity and kinetic stability of the molecule. Small frontier orbital
gap makes a molecule more polarizable and is generally associated with a high
chemical reactivity, low kinetic stability [9]. The electronic properties of
3B5CU have been compared with the electronic properties of 5-chlorouracil
(5CU) molecule [10-14], computed quantum chemically at the same level of
theory and basis set. The frontier orbital gap in case of 3B5CU is found to be
0.41901 eV lower than the 5CU molecule indicating that the substitution of
benzoyl ring/ moiety on 5CU can lead to the higher chemical activity of end
product 3B5CU[1]. The 3D plots of the atomic frontier orbitals HOMO and
LUMO composition and the molecular electrostatic potential surface map
(MESP) for 3B5CU molecule are shown in Figure 3.4. It can be seen from the
Figure 3.4 that, the HOMO is distributed uniformly almost over the heterocyclic
aromatic ring. HOMO shows considerable anti bonding character. The LUMO
is found to be spread over the entire phenyl ring, carbonyl group and a part of
chloro-substituted uracil (CSU) ring. The nodes in HOMO’s and LUMO’s are
placed almost symmetrically. The MESP simultaneously displays molecular
shape, size and electrostatic potential values and has been plotted for 3B5CU.
MESP mapping is very useful in the investigation of the molecular structure
with its physiochemical property relationships [15-21]. The MESP of 3B5CU
shows clearly the three major negative potential regions characterized by
yellowish red colour around three oxygen atoms and one of the two nitrogen
atoms (N5), the other nitrogen atom N7 and hydrogen atoms of heterocyclic
60
ring exert a positive potential while the chlorine atom seems to have almost
neutral electrostatic potential. The predominance of green region in the MESP
surfaces corresponds to a potential halfway between the two extremes red and
dark blue colour. The MESP map has been used to explain the intra-charge
transfer path in the NLO activity section.
3.3.2 Electric moments
The calculated value of dipole moment in case of 3B5CU is found to be 14 %
higher than the 5CU. According to the present calculations, the mean
polarizability of 3B5CU (refer to Table 3.1) is found significantly higher than 5-
CU (78.984/ a.u. calculated at the same level of theory as well as same basis
set). This is related very well to the smaller frontier orbital gap of 3B5CU as
compared to 5CU. The first static hyperpolarizability β calculated value is
found to be appreciably higher in case of 3B5CU (2.930 x 10-30 e.s.u., Table
3.2) as compared to 5CU (0.808 x 10-30 e.s.u.). In addition, β values seem to
follow the same trend as α does, with the frontier orbital energy gaps. It may
thus be concluded that the high values of first order hyperpolarizability,
polarizability and dipole moment make the 3B5CU molecule a potential
candidate for non linear optical communication applications [ 22-24].
3.3.3 Vibrational analysis
61
Fig. 3.3 Theoretical and Experimental IR and Raman Spectra
62
The optimized molecular conformation exhibits no special symmetries and
consequently all the 66 fundamental vibrations of the molecule are both IR and
Raman active and are spread over the functional and Fingerprint regions. The
calculated Raman and IR spectral intensities have been used to convolute all the
predicted vibrational modes using a pure Lorentzian line shape with a FWHM
bandwith of 10 cm-1, to simulate the spectra. Vibrational spectral assignments
have been performed on the recorded Raman and FTIR spectra in conjunction
with the theoretically predicted wavenumbers computed at the B3LYP level
with the triple split valence basis set 6-311++G(d,p), on the basis of relative
intensities, line shape and potential energy distribution. The assigned
wavenumbers of the calculated vibrational modes along with their PED are
given in Table 3.5.The calculated harmonic wavenumbers are usually higher
than the corresponding experimental quantities because of the combination of
electron correlation effects and basis set deficiencies. These discrepancies are
taken care of, either by computing anharmonic corrections explicitly or by
introducing scalar field or even by direct scaling of the calculated
wavenumbers with a proper scaling factor. The comparison of the scaled
wavenumbers with experimental values reveals that the B3LYP method shows
very good agreement with the experimentally observed spectra. The DFT
method predicts vibrational spectra with high accuracy and is applicable to a
large number of compounds, except for the cases where the effect of dispersion
forces is significant. Also, the vibrational spectra calculated with appropriate
63
functionals are often in good agreement with the observed wavenumbers when
the calculated wavenumbers are uniformly scaled with only one scaling factor
[25,26]. Experimental and calculated (scaled) Raman and IR spectra of 3B5CU
are shown in Figure 3.3. The title compound 3B5CU consists of a phenyl rings
and a heterocyclic aromatic ring bridged by a carbonyl group and hence for its
complete vibrational analysis, the vibrational modes are discussed under three
heads-(i) chloro-substituted uracil (CSU) ring (ii) carbonyl group and (iii)
phenyl ring.
3.3.3.1 Chloro-substituted uracil (CSU) ring vibrations
The ring stretching vibrations are very important in the spectrum of uracil and
its derivatives, and are highly characteristic of the aromatic ring itself. The
aromatic C–H stretching vibrations are observed as multiple bands in the region
3000–3100 cm-1. The heterocyclic aromatic ring has single C–H bond. The C-H
stretching vibration of the CSU ring calculated at 3114 cm-1 is assigned to a
strong peak 3120 cm-1 in the Raman and to a medium intensity peak at 3090cm-1
in FTIR Spectra. The C-H stretching vibrations in the aromatic rings are
usually strong in both Raman and IR spectra. The contribution of this C-H
stretching mode to the total PED is found to be 99%. The CH in-plane bending
mode of the CSU ring appears as a mixed mode with major contribution from
C10=C11 stretch and is assigned at very strong peak 1613 cm-1 in the
Raman spectrum. The wavenumber of C-H out-of plane motion is calculated to
64
be 882 cm-1 as a pure mode and is assigned to a weak band at 899 cm-1 in the
Raman spectrum.
The C-Cl stretching wavenumber generally appears in 800-1000 cm-1 in the
derivatives of uracil containing a chlorine atom [27-29] but in the present case
this wavenumber is found to be higher due to the shorter C-Cl bond length than
the usual. A medium intensity peak observed at 1097 cm-1 in the Raman and at
1082 cm-1 in FTIR, match well with the calculated band at 1081 cm-1 and are
identified as (C-Cl) stretching mode. The other stretching modes of CSU ring
are complicated combination of C-C, C-N and C=C vibrations and appear as
mixed modes, spreading all around in the wavenumber range 1000 to 1500
cm-1. Assigning C-N stretching wavenumber is a rather difficult task since they
appear as mixed modes. Silverstein et. al. [30] has assigned C-N mode in the
region 1382 – 1266 cm-1 for aromatic amines. Sunderganeshan et. al. [31] has
assigned the C-N stretching absorption at 1381 cm-1 in case of 2 amino-5-
iodopyridine. In the present case also, this mode appears as mixed modes at
1342, 1211, 1167 and 1128 cm-1 in calculation, out of these modes the mode
with 1128 cm-1 wavenumber has the maximum contributions to its total PED
(65%). The wavenumber of the stretching mode (C=C) is calculated to be 1618
cm-1 and is assigned to very strong peak at 1613 cm-1 in the Raman spectrum
and 1634 cm-1 in FTIR. The torsional modes of the CSU ring are calculated to
be 528 and 403 cm-1.
65
The band observed at 3514 cm-1 in calculation has been identified as N-H
stretching mode of CSU ring and is assigned to 3423 cm-1 / 3454 cm-1 in
Raman/ FTIR spectra. The discrepancy in the relatively higher calculated and
lower experimental N-H stretching wave number is indicative of the fact that
this group is involved in weak H- bonding with other adjacent molecules in
condensed phase. The C-N-H in-plane bending mode of the CSU ring which
contribute 85% to the PED, is calculated to be 1443 cm-1 and corresponds to the
observed peak at 1446 cm-1 in both the spectra. The mode calculated at 537 cm-
1 (93% PED contribution) is identified as almost the pure N-H wagging mode
and is assigned well with the peak appearing at 549 cm-1 in Raman spectra.
The ring trigonal deformation is calculated at 1081 cm-1 and is observed at
1097/ 1082 cm-1 in the Raman/FTIR spectra.
3.3.3.2 C=O group vibrations
The appearance of strong bands in FTIR and weak bands in Raman spectra
(less polarizability resulting due to highly dipolar carbonyl bond) around 1650
to 1800 cm-1 in aromatic compounds, shows the presence of carbonyl group and
is due to the C=O stretching motion. The wavenumber of the stretch due to
carbonyl group mainly depends on the bond strength which in turn depends
upon inductive, conjugative, field and steric effects. The three strong bands in
the IR spectra at 1765, 1710 and 1672 cm-1 are due to C=O stretching
vibrations corresponding to the three C=O groups at C(13), C(8) and C(9)
positions respectively. These bands are calculated at 1765, 1724 and 1689 cm-1
66
and appear as coupled modes and have been assigned well with the
corresponding experimentally observed peaks. The corresponding peaks in
Raman spectra are found to be weak due to the less polarisable C=O bond. A
very interesting pattern of the relative contributions of the three carbonyl groups
to the total PED has been observed. The contribution of one carbonyl group
increases at the expense of other two carbonyl groups as evident from PED
table. The small discrepancy between the calculated and the observed
wavenumbers may be due to the intermolecular hydrogen bonding [1].
The in and out-of-plane C=O bending vibrations in case of 5-chlorocytosin has
been assigned at 630 and 400 cm-1 by Rastogi et. al. [32], whereas Nowek and
others [33] have identified in-plane C=O bending vibration at 437 cm-1. In full
conformity with these work the bands calculated at 647, 570 cm-1 / 590 cm-1 are
identified as C=O out-of-plane/ in-plane bending modes respectively and
assigned with the bands at 648/ 659 cm-1, 579 cm-1 and 610/ 590 cm-1 in
Raman/ FTIR spectra respectively.
3.3.3.3 Phenyl ring vibrations
The phenyl ring spectral region predominantly involves the C-H, C-C, C=C
stretching and C-C-C as well as H-C-C bending vibrations. The bands due to the
ring C-H stretching vibrations are observed as group of partially overlapping
absorptions in the region 3000 to 3100 cm-1. The calculated CH stretching
modes are at 3103, 3101, 3089, 3080 and 3068 cm-1 wavenumbers. Vibrations
involving C–H in-plane bending are found throughout the region 1000–1700
67
Fig. 3.4 Plots of HOMO-LUMO and MESP of 3-benzoyl-5-chlorouracil
68
cm-1. The computed bands at 1472 cm-1 and 984 cm-1 are due to semicircle
stretching and trigonal ring deformation respectively. The dominant H-C-C in-
plane bending of the phenyl ring with more than 70% contribution to the total
PED are calculated to be 1160 and 1148 cm-1 and correspond to the peaks at
1150 cm-1 and 1135 cm-1 in the Raman. The C-H wagging mode starts
appearing at 982 cm-1 and has contributions up to 590 cm-1 and is assigned well
in the spectra. The torsional modes appear in general in the low wavenumber
regions. In the present case the calculated normal modes below 550 cm-1
wavenumbers are mainly the torsional modes. The phenyl ring torsional modes
with more than 50% contribution are found at 427, 421 and 399 cm-1 and are
matched well with peaks in the FTIR spectra.
3.3.4 NLO activity and its vibrational correlation
Organic molecules have recently attracted much attention due to their wide and
varied NLO applications. The vibrational spectroscopy has emerged as a
potential tool to investigate and characterize the structural features responsible
for the NLO properties in the charge conjugated systems, where presence of
electron donating as well as electron withdrawing groups around the aromatic
moieties enhance the optical non-linearity [34,35]. The existence of larger
intra-molecular charge transfer path depends on the efficiency of electron
charge transfer mechanism through the donor and acceptor groups.
In the present communication the atomic charges, MESP surfaces calculated on
the basis of density functional theory are being used to explain the large intra-
69
molecular charge transfer path. Due to the inductive effect of the phenyl ring
(donor), the electron cloud gets transferred from it to the bridge carbonyl group
(acceptor). The CSU ring also acts as donor and its electron cloud is also
transferred to the bridge carbonyl group via transfer of lone pair of electrons
from nitrogen atom (N7). The same lone pair of electrons is also shared with
adjacent carbonyl groups as a consequence of resonance. The electron cloud/
charge is found to resonate between both the carbonyl oxygen of the CSU ring
and the bridge carbonyl oxygen. The charge transfer from the phenyl ring and
CSU ring to the carbonyl groups is further corroborated by the previously
discussed MESP surface (under electronic property section), which predicts
correctly the accumulation of electron cloud over the carbonyl groups and the
depletion of electron charge/ cloud above and below the phenyl ring plane as
well as over some part of the CSU ring also. The appearance of nitrogen atom
(N7) as positively charged species in MESP supports the donation of its lone
pair of electrons and enabling the electron resonance. The involvement of the
intra-molecular charge transfer from donor (phenyl and CSU rings) to acceptor
(bridge carbonyl group), thus gives rise to a large fluctuation / variation in the
dipole moment and polarizability and results in a simultaneous good infrared
and Raman activity for the vibrational modes in question. The strong bands
observed at 3454, 1634, 1229 1119 and 590 cm-1 in FTIR and .and their
counterpart at 3423, 1613, 1233, 1135 and 610 cm-1 in Raman show that the
relative intensities in IR and Raman spectra are comparable, and results due to
70
Table 3.5. : Calculated and Experimental vibrational wave numbers (in cm-1
) and their assignments
for 3B5CU Experimental Theoretical (B3LYP/6-311++G(d,p) )
Intensity Assignment with PEDa
FTIR RAMAN unscaled scaled
(cm-1) (cm-
1) (cm-
1) (cm-
1) IR Raman
3454 bb
- 3631 3514 124.94 24.86 ν(N5-H6)(100)
3090 m 3120 s 3217 3114 1.18 25.41 ν(C11-H12)(99) 3090 m 3120 s 3206 3103 3.38 51.05 νs(C-H)R1(92) 3090 m 3120 s 3204 3101 7.91 4.97 νas(C-H)R1(89) 3079 m - 3191 3089 13.98 32.44 νas(C-H)R1(91) 3079 m - 3182 3080 6.88 27.11 νas(C-H)R1(89) 3079 m 3004 s 3170 3068 0.26 12.60 νas(C-H)R1(97) 1765 s 1765 w 1824 1765 346.40 80.63 ν(C13=O4) (66)+ ν(C8-O2) (16)+ ν(C9-O3) (10) 1710 s 1742 w 1781 1724 384.35 24.73 ν (C8-O2) (43) + ν (C13-O4) (24) + ν (C9-O3) (14) 1672 s 1689 w 1745 1689 678.45 11.51 ν (C9-O3) (75)+ ν (C8-O2) (10) + β (H6-N5-C8) (10) 1634 s 1613 vs 1672 1618 93.48 31.80 ν (C10=C11) (63) + β (H12-C11-C10) (27)
1595 sh 1580 s 1640 1587 41.32 83.19 ν(C-C)R1(53)+ β(H-C- C)R1(20) - 1545 w 1621 1569 6.87 4.76 ν(C-C)R1(45)+ β(C-C-C)R1(11)+ β(H-C- C)R1(10)
1497 m 1469 s 1521 1472 0.77 1.10 ν(C-C)R1(51)+ β(H-C- C)R1(40) 1446 m 1446 w 1491 1443 48.87 6.80 β(C11-N5-H6)(85)+ ν(C8-O2)(10) 1416 s 1446 w 1480 1432 16.48 2.53 β(H-C- C)R1(54)+ ν(C-C)R1(13) 1335 m 1339 w 1386 1342 193.88 2.11 ν(N5-C8)(14)+ ν(N7-C8)(13)+ β(H12-C11- C10)(11)+
β(C9-N7-C13)(11)+ β(H6-N5-C11)(10)+ ν(C9-C10)(10) 1315 m - 1354 1311 4.74 3.63 β(H-C- C)R1(46)+ ν(C-C)R1(34)
- - 1343 1299 24.33 16.94 β(H-C- C)R1(41)+ ν(C-C)R1(14)+ β(H12-C11-N5)(12)
1250 vs - 1337 1294 26.35 5.18 β(H-C- C)R1(26)+ ν(C-C)R1(20)+ β(H12-C11-N5)(11)+ν(N5-C8)(10)
1229 vs 1233 vs 1251 1211 303.84 36.48 ν(C13-C14)(38)+ ν (N7-C9)(17)+ν(C-C)R1(11)+ β(C-C-C)R1 (10)+ ν(N7-C13)(10)
1176 s 1180 vw 1206 1167 132.08 3.23 ν (N7-C8)(26)+β(H6-N5-C8)(20)+β(H12-C11-C10)(20) 1159 s 1150 w 1198 1160 63.21 6.83 β(H-C- C)R1(73)+ β(H6-N5-C8)(20)
- 1135 m 1186 1148 1.22 5.65 β(H-C- C)R1(76)+ ν(C-C)R1(10) 1119 s 1135 m 1165 1128 19.13 3.99 ν (N5-C11)(37)+ ν(N7-C9)(28)+β(H6-N5-C11)(10)+ β(H-C- C)R1(10) 1082 w 1097 m 1117 1081 93.85 4.92 β(C10-C11-N5)(26)+ ν(Cl1-C10)(20)+ β(N5-C8-N7)(14)+ν (N7-
C13)(10) 1067 w 1074 w 1108 1073 19.49 2.64 β(H-C- C)R1(36)+ ν(C-C)R1(29) 1024 w 1043 vs 1070 1036 1.15 6.88 β (C9-N7-C13)(20)+ ν(N5-C8)(15) +β (H12-C11-C10)(11)+
β(C11-N5-C8)(10) - 1013 m 1047 1013 2.45 19.47 ν(C-C)R1(40)+ β(H-C- C)R1(14)+ β(C-C-C)R1(10)
1001 w 990 w 1017 984 3.20 50.49 β(C-C-C)R1(48)+ ν(C-C)R1(13) - 990 w 1015 982 0.03 0.30 C-H ring wag(73) + βout (C-C-C)R1(12) - - 998 966 0.70 0.04 C-H ring wag(69) + βout (C-C-C)R1(13)
928 sh 936 s 957 926 38.13 5.12 C-H ring wag(51) + βout (C-C-C)R1(10)+β (N7-C13-C14)(10) 906 w 914 w 952 921 77.88 9.84 C-H ring wag(21)+ β (O-C-C)(13)+ β(C-C-C)R1 (11)
- 899 w 911 882 12.85 1.54 (C11-H12) wag (81) 806 s 808 w 857 829 0.81 0.06 C-H ring R1 wag(92) 789 s - 814 788 63.91 1.10 βout (O4-C13-N7)(16)+ βout (C23-C14-C13)(13) +C-H ring R1 wag(12)+
βout(C-C-C)R1(11) 764 s - 793 768 13.92 4.64 C-H ring R1 wag (20)+ Ʈ (N7-C13-C14-C23)(20) + β(N5-C11-10)(15) 733 w 754 m 772 747 20.35 18.55 βout (N7-C9-C10)(28)+ βout (N7-C8-N5)(20)+ βout (C9-C10-C11)(15)+
C-H ring R1 wag(12) 733 w - 763 739 7.67 5.77 βout (N7-C9-C10)(39)+ βout (N7-C8-N5)(22)+ βout (C9-C10-C11)(18)+
C-H ring R1 wag(17)
71
Table 3.5.(continued)
Experimental Theoretical (B3LYP/6-311++G(d,p) )
Intensity Assignment with PEDa
FTIR RAMAN unscaled scaled
(cm-1) (cm-
1) (cm-
1) (cm-
1) IR Raman
700 m 731 w 750 726 12.20 2.25 βout (N7-C8-N5)(74)+ C-H ring R1 wag(10)
- - 706 683 27.24 12.07 C-H ring R1 wag(41)+ βout (O4-C13-N7)(21)
679 vs 678 m 696 674 27.24 2.73 C-H ring R1 wag(64)
659 vs 648 m 668 647 27.07 4.48 βout (N7-C13-O4)(23)+ β (N7-C8-N5)(14)+ β (N7-C13-C14)(13)+
β(C-C-C)R1(11)
- 610 s 631 611 69.51 14.17 β(C-C-C)R1(77)
590 s 610 s 610 590 0.71 17.39 β (O2-C8-N5)(48)+ β (O3-C9-C10)(26)+ C-H ring R1 wag(10)
- 579 m 589 570 1.20 14.49 βout (N7-C13-C14)(22)+ β out (O2-C8-N5)(13)+ β out (O3-C9-
N7)(11)+ β out (O4-C13-N7)(11) + β(C-C-C)R1(10)
542 s 549 w 555 537 15.02 0.54 (N5-H6)wag(93)
- - 545 528 71.85 8.62 Ʈ(C9-N7-C13-C14)(26)+ Ʈ(C8-N5-C11-H12)(25)+
β(O4-C13-C14)(16)
422 m - 441 427 23.80 14.28 Ring R1 torsion (54)+ β (O2-C8-N5)(14)+ β (O4-C13-C7)(14)+
β (O3-C9-C10)(12)
412 m - 435 421 3.10 5.57 Ring R1 torsion (51)+ Ʈ(O4-C13-N7-C8)(22)
412m - 416 403 1.44 7.08 Uracil ring Torsion (56)+ Ʈ(O4-C13-N7-C8)(17)
412m - 412 399 8.64 0.05 Ring R1 torsion (82)
Abbreviations: ν-stretching, νs – symmetric stretching, νas –asymmetric stretching, β- in-plane angle
bending, βout - out-of-plane bending, Ʈ -torsion , R1- phenyl ring, bb- broad band, s-strong, vs-very strong, m-medium,w-weak, sh-shoulder band. aOnly contributions larger than 10% are given.
72
the electron cloud movement through conjugation framework from electron
donor groups to electron acceptor group.
3.4 Conclusions
The equilibrium geometry and harmonic wavenumbers of 3B5CU molecule
under investigation have been analyzed at DFT/ 6-311++G(d,p) level. In
general, a good agreement between experimental and calculated normal modes
of vibrations has been observed. The frontier orbital gap, dipole moment,
molecular electrostatic potential surface and first static hyperpolarizability of
3B5CU have been calculated and compared with 5CU. The strong vibrational
modes contributing towards the NLO activity, involving the whole charge
transfer path have been identified and analyzed. The present study of 3B5CU,
in general may lead to the better understanding of the relationship between the
molecular architecture/ structure and non linear response in terms of
hyperpolarizability and its vibrational modes and may help in designing and
synthesizing new efficient materials for technological applications.
73
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pp. 508-519
CHAPTER 4
Molecular structure,Electronic properties, NLO analysis and
Spectroscopic Characterization of Gabapentin
77
4.1 Introduction
Neuropathic pain involves a range of chronic pain syndromes caused by injury
or disease of the peripheral or central nervous system [1,2] and is characterized
by distinctive clinical symptoms and signs such as spontaneous pain, allodynia,
hyperalgesia, and pain summation [3]. Neuropathic pain is often considered to
be poorly responsive to conventional analgesic medications, including
nonsteroid antiinflammatory drugs and opioid analgesics. Gabapentin [1-
(aminomethyl)cyclohexane acetic acid], a –aminobutyric acid (GABA)
molecule joined to a lipophilic cyclohexane ring, initially introduced in 1994 as
an antiepileptic drug (AED), particularly for partial seizures, was soon found to
be promising in treating neuropathic pain associated with postherpetic neuralgia
(PHN) [4,5], postpoliomyelitis neuropathy [6], and reflex sympathetic
dystrophy [7]. Placebo-controlled clinical trials also have indicated a role of
Gabapentin (GP) in treating pain related to diabetic neuropathy (DNP) [8] and
PHN [9]. Recent studies also shows that, GP may help treat alcohol
dependence [10].
As it is well known that amino acids exist as zwitterions as well as in the neutral
form depending on the environment (solvent, pH etc.) and that GP is a , -
disubstituted γ amino acid residue, we analysed molecular properties of both
the zwitterionic and neutral form of GP. The X ray crystallographic data
suggests that GP exists in zwitterionic form in solid state [11]. To the best of
78
our knowledge, neither quantum chemical calculations, nor the vibrational
analysis study of GP has been reported, yet. The ground state properties of both
zwitterionic and neutralform of GP have been calculated employing
DFT/B3LYP level of theory. A complete assignment of the vibrational modes
has been performed on the basis of the total energy distribution (TED) values
and using the scaled quantum mechanics method. The theoretical data
(molecular parameters, IR and Raman spectra) are compared to the results of
the experimental studies performed in the solid state. The polarizability and first
static hyperpolarizability of both zwitterionic and neutral form have also been
calculated and compared.
4.2 Results and Discussion
4.2.1 Molecular Geometry
The X-ray diffraction data of GP [11] was used to optimize the structure. X-
ray structural data shows that GP exists in zwitterionic form (Z) in solid state
(Table 4.1). Its crystal structure involves intensive hydrogen bonding between
NH3+ and COO- groups of neighbouring molecules[11]. The structural analysis
of both the neutral and zwitterionic form of GP has been performed at
B3LYP/6-311++G(d,p). The optimized Geometry has been used as inputs for
further calculations at the B3LYP level.
79
Fig 4.1 Optimized Molecular Geomtry of zwitterionic and neutral Gabapentine.
80
The final optimized geometry calculated using the Gaussian 09 program [12]
is shown in Figure 4.1. GP consists of a 1,1 – disubstituted cyclohexane ring
which can exist in two different conformation in which amino methyl and
carboxy methyl sustituents interconvert between axial and equitorial
orientations. Our theoretical calculation on both the neutral and zwitterionic
form confirms amino methyl substituent in axial while carboxy methyl
substituents in equitorial position. The energy of neutral GP is found to be lower
than zwitterionic form by an amout 0.31153 hartree (Table 4.2 ), which is quite
obvious as the zwitterion charge separation is not stabilized by the environment
in gas phase. The cyclohexane ring is found to be in a slightly strained chair
conformation with C-C-C angles varying in the range 109.2 - 113.9, while
endocyclic torsion angles lying in the range 50.9 to 55.3. The dihedral for
axial amino methyl substituent is deviated by 0.6 from standard value of 120.
The two C=O bond lengths are slightly different (1.250 Å and 1.223 Å) due to
the charge delocalization as compared to neutral form having one single and one
double C=O bond, the long bond involves an O atom that forms two N-HO
bonds and the short bond involves an O atom that forms only one N-HO bond
[11]. Likewise the two N-H bond lengths are same at 1.022 Å and one longer N-
H bond is at 1.0534 Å.
A significant feature of the zwitterionic GP is the presence of a 1,1-disubstituted
cyclohexane ring, with the NH3+ and methylene groups at axial and
81
Table 4.1. The optimized geometric parameters of GP and comparison with experimental results, bond lengths in angstrom (Å), bond angles and selected dihedral angles in degrees (◦).
Bond Lengths Exp. a,b B3LYP Bond Angles Exp. a,b B3LYP
O1-C29 1.272 1.223 N3-C23-C7 114.0 113.8
O2-C29 1.252 1.250 C7-C26-C29 119.7 114.1
N3-C23 1.499 1.516 O1-C29-O2 123.5 134.3
C7-C8 1.544 1.553 O1-C29-C26 115.6 119.4
C7-C20 1.552 1.564 O2-C29-C26 120.9 106.3
C7-C23 1.535 1.546 Dihedral Angles
C7-C26 1.545 1.550 C20-C7-C8-C11 -54.0 -52.2
C8-C11 1.533 1.537 C23-C7-C8-C11 67.3 68.4
C11-C14 1.528 1.533 C26-C7-C8-C11 -177.0 -166.7
C14-C17 1.524 1.533 C8-C7-C20-C17 54.7 50.9
C17-C20 1.525 1.540 C23-C7-C20-C17 -63.7 -67.7
C26-C29 1.528 1.611 C26-C7-C20-C17 176.3 168.6
Bond Angles
C8-C7-C23-N3 179.7 165.4
C8-C7-C20 109.5 109.2 C20-C7-C23-N3 -61.0 -75.1
C8-C7-C23 108.2 107.7 C26-C7-C23-N3 62.1 43.2
C8-C7-C26 110.6 109.8 C8-C7-C26-C29 -62.9 -79.1
C20-C7-C23 111.5 111.0 C20-C7-C26-C29 174.1 163.6
C20-C7-C26 106.5 104.9 C26-C7-C26-C29 58.2 42.0
C23-C7-C26 110.6 114.1 C7-C8-C11-C14 56.1 55.3
C7-C8-C11 112.7 113.8 C8-C11-C14-C17 -54.6 -55.1
C8-C11-C14 111.4 111.2 C11-C14-C17-C20 53.7 54.5
C11-C14-C17 110.5 111.4 C14-C17-C20-C7 -54.3 -53.4
C14-C17-C20 111.1 112.0 C7-C26-C29-O1 -65.3 -69.0
C7-C20-C17 114.0 113.5 C7-C26-C29-O2 117.0 111.8 aJames A. Ibers, Acta Cryst. (2001). C57, 641-643 b M. Wenger , J. Bernstein, Crystal Growth & Design, 8, 2008, 1595-1598
82
carboxylate COO- and methylene groups at equatorial positions. GP with 29
atoms has 81 normal modes of vibrations. The calculated wave number for each
mode along with their Raman intensities and their corresponding total energy
distribution of each normal mode of vibration of GP are given in Table 4.3(a).
It is generally known that hydrogen bonding between the proton donor and
acceptor alters the characteristics of adjacent bonds, and as a consequence there
is alteration in the characteristic vibrational wavenumbers. In GP, there is
extensive hydrogen bonding between the NH3+ + and COO- groups of
neighboring molecules, some prominent differences between theoretical spectra
and experimental spectra have been observed. The two moderately intense
bands (3358 cm-1 and 3304 cm-1) predicted by DFT calculations are assigned to
N-H asymmetric and symmetric stretching modes of cationic amino group NH3.
As expected this mode is pure stretching mode as it is evident from TED
column, contributing 100%. The theoretical wavenumber has a positive
deviation of 44 cm-1/72 cm-1 for asymmetric stretch and 52 cm-1/48 cm-1 for
symmetric stretch with the experimental FTIR/Raman wavenumber which may
be due to the intermolecular hydrogen bonding in the molecular packing
structure. The corresponding wavenumbers for N-H stretch in case of neutral
GP are far more off with the corresponding experimental values [Table 4.3(b)].
The spectral region 2960-2870 cm-1 in the FT-IR and FT-Raman contains strong
83
5.2.1 Vibrational assignments
Fig 4.2 (a) Theortical IR and RAMAN spectra
84
Fig 4.2(b) Experimental IR and RAMAN spectra
85
Table 4. 2 Ground state optimized parameters
Basic set B3LYP/6-311++G(d,p)
Zwitterionic Neutral
SCF Energy (a.u) -558.27665 -558.58818 Zero point Energy (kcal mol-1) 162.11023 163.05272 Rotational Constants (GHz) A B C
1.54314 0.63105 0.54332
1.54680 0.62859 0.53793
Total Energy 169.745 170.392
Specific heat at constant Volume ( Cv) (cal mol-1 K-1) 48.111 46.743
Entropy(S) (cal mol-1 K-1) 107.950 104.541
Dipole moment (Debye) 6.0988 6.7844
86
Table 4.3(a). FT-IR, FT-Raman spectral data and computed vibrational wavenumbers along with the assignments of vibrational modes based
on TED results.
No
Exp. FTIR
Exp. FT-Raman
Unscaled
Scaled IIR SARa IRa Assignments (TED ≥10%)
1 - - 61 60 5.20 0.72 0.00 t CO2 (56) + CCCO (26)
2 - - 80 78 3.31 5.76 0.01 t CO2 (89)
3 - - 115 113 2.71 1.77 0.00 CCCCring (55)
4 - - 157 154 6.20 1.98 0.00 r (CH2-NH3) (γ6) + CCCCring (14)
5 - - 197 194 24.26 12.21 0.01 r (CH2-NH3) (56)
6 - - 234 230 39.98 9.90 0.01 CCCO (68) + C7C26C29 (31)
7 - - 257 253 1.42 1.18 0.00 CCCCring (54)
8 - - 277 272 38.14 8.96 0.01 C26C29 (γ6) + CCCCring (β9) + C7C26C29 (18)
9 - - 298 293 10.20 2.14 0.00 r (CH2-NH3) (49)
10 - - 320 314 2.10 0.64 0.02 r (CH2)ring (γ6) + C26C29 (13)
11 - - 354 348 9.42 37.94 1.00 CO2 (74)
12 - - 389 382 5.78 5.93 0.13 r (CH2)ring (ββ) + C=O of CO2 (11)
13 - - 395 388 10.70 4.87 0.10 τ CH3 (55) + ρ CO2 (17)
14 - - 401 394 3.32 30.37 0.61 r C-CO2 (40)
15 403 - 436 428 0.57 1.64 0.03 CCCCring (β6) + CCCring (19) + CCCO (16)
16 447 - 469 461 2.02 21.53 0.31 CCCring (25)
17 507 - 498 489 2.31 2.98 0.04 CCCring (19) + C7C23N3 (16)
18 540 559 551 542 4.34 1.50 0.01 C7C26 (11) + w CO2 (10)
19 618 584 613 603 24.79 25.62 0.20 C26C29 (γ6) + CO2 (22)
20 708 698 682 671 12.10 5.67 0.03 CCring (γ1) + sym C26C7C29 (ββ) + C23C7 (16)
21 748 734 755 742 18.85 8.58 0.04 CCCO (59)
22 - 772 783 770 3.27 1.45 0.01 CCring (16) + r (CH2)ring (13)
23 782 806 813 799 10.91 8.68 0.04 ring breathing (56)
24 820 818 830 816 12.64 2.12 0.01 CCring (20)
25 - 829 854 839 0.86 4.38 0.02 CCring (39)
26 851 863 870 855 18.53 46.31 0.16 CCring (β0) + sym C23C7C26 (14)
27 892 892 917 901 4.98 81.83 0.25 CCring (41)
28 - 910 927 911 6.08 9.70 0.03 CH2-NH3 (24)
29 922 930 938 922 19.16 55.88 0.16 CH2-NH3 (γ7) + sym C20C7C26 (12)
30 929 948 954 938 6.52 3.61 0.01 CCring (10) + CH of (CH2)ring (10)
31 976 982 1003 986 1.38 23.56 0.06 C7-C23 (15) + CH2-NH3 (12)
32 - 994 1023 1005 1.63 43.68 0.10 CCring (48)
33 1020 1013 1037 1020 2.73 146.55 0.33 CCring (46)
34 1040 1026 1047 1029 13.37 14.45 0.03 sym C8C7C26 (20) + r NH3 (18)
35 1064 1044 1085 1067 5.73 45.27 0.09 CCring (74)
36 1080 1084 1097 1078 44.42 2.72 0.01 sym CO2 (γ0) + CH of (CH2- CO2) (16) + NH of NH3 (12)
37 1091 1107 1121 1102 15.19 1.88 0.00 CH of {(CH2)ring + NH3 + CH2- NH3} (24)
38 1119 1133 1153 1133 2.65 33.78 0.06 sym CO2 (β8) + CH of (CH2-CO2) (17)
39 1133 1165 1173 1153 28.35 141.67 0.24 CH of (CH2)ring (21) + t (CH2- CO2) (18)
87
40 1165 - 1177 1157 5.22 20.26 0.03 t NH2 of NH3 (24) + t (CH2- NH3) (10)
41 1195 1181 1203 1182 17.43 166.10 0.26 sym C23C7C26 (16)
42 1211 1213 1236 1215 14.96 95.98 0.14 CH of (CH2- CO2) (β6) + υasym CCCring (11)
43 1258 1263 1282 1260 0.88 12.54 0.02 t (CH2)ring (49)
44 1274 - 1295 1273 12.10 61.93 0.08 w (CH2- CO2) (γ5) + sym CO2 (13)
45 - 1287 1307 1285 4.28 8.38 0.01 t (CH2)ring (41)
46 1300 1306 1321 1298 4.85 4.44 0.01 t (CH2)ring (21)
47 1327 1317 1349 1326 0.70 40.00 0.05 w (CH2)ring (43)
48 1338 1330 1364 1341 16.77 8.26 0.01 t (CH2- NH3) (β8) + CH of (CH2)ring (11)
49 1347 1343 1366 1343 2.55 88.40 0.10 t (CH2- NH3) (β1) + CH of (CH2)ring (21)
50
- 1357 1381 1357 5.65 10.15 0.01 w (CH2)ring (40)
51 - 1364 1387 1364 2.59 35.13 0.04 w (CH2)ring (56)
52 1363 1374 1389 1366 10.00 28.74 0.03 w (CH2)ring (β9) + CH of (CH2)ring (15)
53 1400 1388 1423 1398 2.89 3.05 0.00 w (CH2- NH3) (63)
54 1422 1415 1468 1443 24.60 1.72 0.00 ρ (CH2- CO2) (69)
55 1448 1426 1480 1455 110.20 61.28 0.06 NH3 umbrella (38)
56 1455 1457 1489 1464 5.58 22.02 0.02 ρ (CH2)ring (47)
57 - 1479 1490 1465 10.08 7.78 0.01 ρ (CH2)ring (55)
58 1465 - 1493 1467 100.33 11.91 0.01 NH3 umbrella (β9) +ρ (CH2)ring (15)
59 - - 1501 1476 26.76 2.45 0.00 ρ (CH2)ring (46)
60 - 1489 1510 1485 2.24 36.29 0.03 ρ (CH2)ring (60)
61 1475 1503 1514 1488 59.44 14.40 0.01 ρ (CH2- NH3) (56)
62 1545 1602 1642 1614 28.72 59.83 0.04 ρ NH2 of NH3 (83)
63 - 1657 1698 1669 80.21 24.88 0.02 NH of NH3 (80)
64 1615 1633 1712 1640 224.44 279.08 0.17 asym CO2 (78)
65 2809 - 2943 2820 447.21 320.67 0.03 υ NH of NH3 (97)
66 2861 2865 2998 2872 32.17 82.68 0.01 CH of (CH2)ring (92)
67 2896 2882 3010 2884 33.20 159.59 0.02 CH of (CH2)ring (84) + sym (CH2)ring (11)
68 - 2893 3015 2888 7.34 92.73 0.01 CH of (CH2)ring (95)
69 - - 3026 2899 9.99 32.64 0.00 sym (CH2)ring (94)
70 - 2913 3028 2901 32.97 36.06 0.00 sym (CH2)ring (93)
71 2929 - 3036 2909 9.27 97.85 0.01 sym (CH2)ring (99)
72 - 2933 3055 2927 12.83 108.62 0.01 asym (CH2)ring (8β) + CH of (CH2)ring (15)
73 2954 - 3065 2936 15.32 52.54 0.00 asym (CH2)ring (91)
74 - - 3071 2942 15.92 496.33 0.04 asym (CH2)ring (8β) + CH of (CH2)ring (16)
75 - - 3080 2950 14.34 339.49 0.03 asym (CH2)ring (68) + CH of (CH2)ring (30)
76 - 2952 3082 2952 25.31 102.06 0.01 asym (CH2)ring (97)
77 2975 2970 3099 2969 2.74 50.96 0.00 sym (CH2- NH3) (99)
78 - 3009 3142 3010 5.23 35.78 0.00 asym (CH2- CO2) (100)
79 - 3025 3156 3024 0.69 33.56 0.00 asym (CH2- NH3) (100)
80 3252 3256 3449 3304 69.58 89.59 0.01 υsym NH2 of NH3 (100)
81 3314 3286 3505 3358 74.54 34.19 0.00 υasym NH2 of NH3 (100)
IIR, IRa—IR and Raman Intensity , SARa—Raman activity, sym—symmetric stretchingν asym— asymmetric stretchingν —in-plane bendingν —out-of-plane bendingν ρ—scissoring; t— twisting; r—rockingν ω—waggingν τ—torsion.
88
CH2 asymmetric, symmetric and C-H stretching vibrational modes of the
cyclohexane ring. The calculated wave numbers 2952, 2950, 2942, 2936, 2927,
2909, 2901, 2899, 2888, 2884 and 2872 cm-1 agree quite well with the observed
frequencies and literature values [13]. The CH2 scissoring for cyclohexane ring
is calculated at 1476, 1465 and 1464 cm-1 and matches well with the FTIR/FT-
Raman band at 1455/1457 cm-1. In addition to the CH2 groups of cyclohexane
there are two methylene groups (bridge group) – one between NH3+
group and
the cyclohexane ring and another between COO- group and the cyclohexane
ring. All the vibrational modes for methylene bridge (C23H2) are found to be at
higher wavenumbers than for the corresponding modes of (C26H2) group. This
can be attributed to the higher percentage of s character in the hybridized carbon
C23 as compared to carbon C26 atom, which further results in an increase of
bond strength and decrease in C-H bond length and hence higher wavenumbers
for the former. The asymmetric stretching vibration of the anionic carboxyl
group is typically found in the region 1650-1600 cm-1 [14]. The strong band in
the theoretical spectrum of neutral GP at 1739 cm-1 due to asymmetric C=O
stretch is shifted to 1640 cm-1 in the zwitterionic form. In the experimental FT-
IR spectra this band is assigned at 1615 cm-1, confirming that carboxylic group
in solid phase of GP is in zwitterionic form. A mixed vibration of symmetric
C=O stretch and methylene bend is calculated at 1133 cm-1, the corresponding
experimental values in FT-IR and FT-Raman spectra are at 1119 cm-1 and 1133
89
cm-1. Asymmetric N-H bending of NH3+ group with 80 % TED is calculated at
1669 cm-1 while the symmetric bending vibration of NH3+ group is calculated at
1467 cm-1. These calculated modes match well with the experimental values.
The 1300-600 cm-1 range in theoretical IR is more or less same for neutral as
well as zwitterionic form, as the bands due to COO- and NH3+ groups do not
occur in this region.
Below 1450 cm-1 region CH2 modes of rotator origin (“wagging”, “twisting”,
“rocking”) are observed [15].The skeletal vibrations of cyclohexane ring are
\prominent in the region below 1100 cm-1. A strong ring breathing mode at 802
cm-1 characteristic of chair-form cyclohexane, calculated at 799 cm-1 is assigned
to the band 782 cm-1/806 cm-1 in FT-IR/Raman spectra.
5.2.2 Electronic Properties
The 3D plots of the frontier orbitals HOMO, LUMO and the Molecular
electrostatic potential map (MESP) figures for the GP are shown in Fig. 4.3 and
Fig. 4.4. The system analysed is an open-shell molecular system, hence the
unrestricted formalism (UB3LYP) was used. Energetically, the true HOMO-
LUMO gap in an S = 1/2 system within a spin-unrestricted formalism is
typically the -HOMO- -LUMO gap [16]. The -HOMO orbital (MO = 47)
at -12.04649 eV (gas phase) is almost spread over entire molecule and exhibit
large amount of π character, whereas the -LUMO at -9.39475 eV lies
mainly over COO- and adjacent CH2 group.
90
Table 4.3(b). FT-IR, FT-Raman spectral data and computed vibrational wavenumbers of neutral form of GP
along with the assignments of vibrational modes based on TED results. No Unscaled Scaled IIR SARa IRa Assignments (TED ≥6%)
1 69 68 2.05 0.32 0.01 CCCO (85) 2 89 87 6.96 1.30 0.04 τ COOH (64) + (C1C8C9) (15) 3 117 115 1.43 0.26 0.01 CCCring (54) + (C1C8C9) (10) 4 165 162 1.35 0.32 0.00 CCCring (βγ) + CCCO (17) + (C2,6C8C9) (7) 5 207 203 6.94 0.46 0.01 CCCN (41) + CCCO (β9) + (C2,6C8C9) (11) 6 230 226 0.87 0.60 0.01 CCCO (45) + (C1C8C9) (14) 7 265 261 1.91 0.33 0.00 r C-NH2 (βγ) + CCCring (9) + CCN (7) 8 278 274 0.66 1.13 0.01 (CCN + CCC + CCO10) (40) + CCCO (32) 9 306 301 4.72 1.52 0.75 CCCN (β7) + CCCring (14) + r NH (7) 10 327 321 1.72 0.66 0.28 CCCring (10) 11 382 376 19.55 0.25 0.08 τ NH2 (59) 12 397 391 0.78 0.87 0.25 CCCring (43) 13 435 428 1.75 1.31 0.30 CCCring (β1) + CCring (β6) + CCCring (8) 14 443 435 2.14 0.95 0.21 r COOH (γ6) + CCCring (9) + r (CH2- COOH) (7) 15 482 474 2.72 0.40 0.07 r COOH (γγ) + CCCring (8) + r (CH2- COOH) (7) 16 513 504 4.53 2.19 0.35 CCCring (14) + CCN (11) + CCring (6) 17 548 539 5.75 1.41 0.20 C1C8 (13) 18 626 615 3.56 1.15 0.12 OCO (47) + C8C9 (9) 19 682 670 3.21 11.76 1.00 CCring (β6) + OCO (β0) + C1C7 (15) + C1C8 (11) 20 780 766 0.42 1.73 0.11 CCring (14) + CCOH (7) 21 790 777 0.78 1.14 0.07 CCring (8) + C1C7 (6)
22 819 805 0.51 5.25 0.29 CCring (40) + C1C7 (13)
23 848 834 8.01 1.70 0.09 CCring (24) + ω NH2 (21)
24 853 839 5.01 1.13 0.06 CCring (23) + r (CH2)ring (18)
25 878 863 4.12 5.02 0.24 CCring (β7) + C-OH (15) + C8C9 (1β) + C1C7 (8)
26 895 880 16.38 0.79 0.04 ω NH2 (γ0) + CCring (15) + C8C9 (9)
27 932 916 4.90 1.85 0.08 C8C9 (14) + CCring (1γ) + C1C8 (1β) + C-OH (8) 28 940 924 6.80 1.85 0.07 r (CH2)ring (ββ) + CCring (11) 29 956 940 2.13 0.82 0.03 CCring (22) 30 981 965 152.54 2.56 0.09 OH (74) 31 986 969 14.37 3.82 0.14 C-N (17) + C1C8 (6) 32 1010 993 23.86 2.68 0.09 r (CH2- NH2) (β0) + NH of NH2 (7) 33 1039 1022 0.57 7.17 0.22 CCring (47) + C-N (10) + CHring (7) 34 1059 1041 8.79 3.60 0.11 C-N (5γ) + C1C7 (11) 35 1078 1060 1.32 8.43 0.24 CCring (30) + t NH2 (8) 36 1092 1074 2.02 0.47 0.01 CCring (68) 37 1114 1095 10.61 2.42 0.06 C1C8 (8) + C-OH (6) 38 1133 1114 0.33 0.50 0.01 t (CH2)ring (23) + t NH2 (21) 39 1164 1144 37.24 5.22 0.12 t (CH2- COOH) (17) + C-OH (1β) + C1C8 (8) 40 1184 1164 1.93 2.73 0.06 t (CH2)ring (26) + t NH2 (9) 41 1215 1195 11.51 6.03 0.13 C1C7 (6) + C-OH (5) + CH of (CH2)ring (6) 42 1247 1226 33.31 1.46 0.03 t NH2 (β0) + C-OH (11) + CCring (10) 43 1283 1261 46.08 2.28 0.04 CH of (CH2- COOH) (ββ)+ C-OH (16) 44 1287 1265 3.21 12.32 0.22 t (CH2)ring (34) 45 1304 1281 1.15 6.71 0.12 t (CH2)ring (46) 46 1317 1294 2.55 1.95 0.03 t (CH2- NH2) (48) 47 1327 1304 4.14 1.23 0.02 CH of (CH2- COOH) (24) 48 1352 1329 6.07 0.59 0.01 ω (CH2)ring (19) + ω (CH2- COOH) (14)
91
49 1358 1335 4.33 0.88 0.01 ω (CH2)ring (26) 50 1371 1347 0.65 0.72 0.01 ω (CH2)ring (41) 51 1380 1357 0.19 0.52 0.01 ω (CH2)ring (58) 52 1389 1365 0.24 1.46 0.02 ω (CH2)ring (27) 53 1392 1368 0.25 2.36 0.03 ω (CH2)ring (37) 54 1425 1401 4.77 0.88 0.01 ω (CH2- NH2) (63) + r NH2 (13) 55 1464 1439 225.69 3.36 0.04 OH (80) 56 1482 1457 2.29 5.13 0.06 ρ (CH2)ring (41) 57 1487 1461 0.87 11.51 0.14 ρ (CHβ)ring (5β) 58 1492 1466 5.24 14.09 0.17 ρ (CHβ)ring (γ1) 59 1493 1468 11.98 1.56 0.02 ρ (CH2)ring (32) 60 1498 1473 16.50 0.56 0.01 ρ (CH2)ring (48) 61 1509 1484 3.34 2.36 0.03 ρ (CH2)ring (61) 62 1528 1502 3.98 2.88 0.03 ρ (CH2- NH2) (87) 63 1654 1626 39.77 4.25 0.04 ρ NH2 (86) 64 1815 1739 384.98 16.56 0.12 C=O (82) 65 3000 2874 18.53 90.84 0.12 sym (CH2)ring (95) 66 3003 2877 22.49 144.39 0.19 sym (CH2)ring (93) 67 3008 2881 23.73 20.24 0.03 sym (CH2)ring (97) 68 3013 2886 13.28 82.66 0.11 sym (CH2)ring (90) 69 3018 2892 17.23 36.05 0.05 sym (CH2)ring (96) 70 3032 2905 42.24 124.56 0.16 sym (CH2- NH2) (88) 71 3034 2906 38.65 53.62 0.07 asym (CH2)ring (93) 72 3041 2914 19.92 107.20 0.14 sym (CH2-COOH) (98) 73 3050 2922 60.08 156.18 0.20 asym (CH2)ring (96) 74 3053 2925 46.71 194.71 0.25 asym (CH2)ring (93) 75 3055 2927 25.08 68.50 0.09 asym (CH2)ring (86)+ asym (CH2- NH2) (10) 76 3063 2935 69.30 42.80 0.05 asym (CH2)ring (93)
77 3068 2939 25.94 79.13 0.10 asym (CH2- NH2) (94)
78 3106 2976 16.22 50.54 0.06 asym (CH2-COOH) (100)
79 3286 3148 676.56 89.69 0.08 OH (99)
80 3496 3350 0.58 132.78 0.10 sym NH2 (100) 81 3567 3417 6.93 55.31 0.04 asym NH2 (100)
IIR, IRa—IR and Raman Intensity (Kmmol−1), SARa—Raman scattering activity (A4amu-1), sym—symmetric stretching; asym— asymmetric stretchingν —in-plane bendingν —out-of- plane bendingν ρ—scissoring; t— twisting; r—
rockingν ω—waggingν τ—torsion. The out-of-plane banded atoms were underlined.
92
Fig 4.3 HOMO-LUMO plot of molecule in gas phase
Fig 4.4 MESP plot of Gabapentine
93
The different values of the electrostatic potential at the surface are represented
by different colors. The color code of these maps is in the range between -0.020
a.u. (deepest red) to 0.299 a.u. (deepest blue) in compound. As can be seen from
the MESP map of the title molecule, the regions having negative potential are
over the electronegative atom (Oxygen atoms), the regions having the positive
potential are over the hydrogen atoms (NH3 group). From the MESP plot, we
can say that the H atoms are sites for electrophilic attraction and O atoms are
sites for nucleophilic activity. The cyclohexane ring reveals almost neutral
potential.
5.2.4 NLO properties
Dipole moment is one of the important quantities which are of fundamental
importance in structural chemistry. It can be used as a descriptor to illustrate the
charge movement across the molecule. The direction of the dipole moment
vector in a molecule depends on the centres of positive and negative charges.
The dipole moment of GP (zwitterionic) is calculated to be 6.0988 Debye with
maximum contribution from y. In X and Z directions, dipole moment is
practically negligible. Polarizability is the quantity by which the induced dipole
moment of a molecule is related to the external electric field that is providing
the perturbative knock on the electron density. According to the present
calculations, the mean polarisability of zwitterionic/neutral GP (refer to
94
Table 4.4 Components of polarizability and hyperpolarizability Neutral Zwitterionic Neutral Zwitterionic
a.u esu(×10−24
) a.u esu(×10−24
) a.u esu × 10−33)
a.u. esu (×10−33)
αxx 104.4859 15.4848 152.440 22.5916 xxx 43.0903 372.2704 -3561.0041 -30764.5827 αxy 4.4027 0.6525 10.203 1.5121 xxy 7.2687 62.7967 -803.8848 -6945.0020 αyy 125.1174 18.5424 118.907 17.6220 xyy 8.3025 71.7275 -253.6204 -2191.1027 αxz -1.9057 -0.2824 3.718 0.5510 yyy 61.9768 535.4359 -147.1452 -1271.2315 αyz -5.1303 -0.7603 0.891 0.1320 xxz 1.7662 15.2585 -25.8499 -223.3250 αzz 124.9442 18.5167 97.793 14.4929 xyz 20.6309 178.2365 -54.9720 -474.9196 αtotal 118.1825 17.5146 123.0466 18.2355 yyz 20.0645 173.3428 16.5493 142.9744 ∆α 23.8772 3.5386 51.3267 7.6066 xzz 14.1624 122.3531 -26.3274 -227.4503 µx 0.4889 0.1135 yyz 0.3988 3.4456 9.7683 84.3913 µy 2.6059 6.0692 zzz -13.1347 -113.4750 22.7304 196.3747 µz -0.3081 0.1135 tot 96.0387 829.7072 3954.6258 34165.1987 µ 2.6692 6.0988
95
Fig 4.5 (a) Plot between Heat Capacity Vs Temperature
Fig 4.5 (b) Plot between Entropy Vs Temperature
96
Table-4.4) is found to 123.0466 a.u./ 118.1825 a.u.. The first static
hyperpolarisability value follows the same trend as mean polarizability
and is found to be appreciably higher 3954.6258 a.u.( 34165.1987 x10-33 e.s.u.)
in zwitterionic form than the neutral form 96.0387 (829.7072 x10-33 e.s.u.)
(Table-4.6). The hyperpolarizability is dominated by the longitudinal
component xxx, whereas the medium values of are noticed for XXY, XYY
and YYY directions. Our calculations clearly indicate that the
hyperpolarizabilities are increased by the proton transfer.
4.2.5 Thermodynamic Properties
On the basis of vibrational analysis, the statistical thermodynamic functions:
heat capacity (C), enthalpy changes (ΔH) and entropy (S) for GP in zwitterionic
and neutral form were obtained from the theoretical harmonic frequencies and
listed in Table-4.3. From the Table-4.5, it can be observed that these
thermodynamic functions increase with temperature ranging from 100 to 700 K
due to the fact that the molecular vibrational intensities increase with
temperature. The thermodynamic functions of the zwitterionic and neutral form
are not very much different. The correlation equations between heat capacity,
enthalpy, entropy changes and temperatures for the zwitterionic form were
fitted by quadratic formulas and the corresponding fitting factors (R2) for these
thermodynamic properties are 0.9993, 1.0000 and 0.9999 respectively. The
97
Table 4.5 Variation of Thermodynamic Parameters with temperature
T(K) C(cal mol-1 K-1) S(cal mol-1 K-1)
Zwitterionic Neutral Zwitterionic Neutral
100 18.085 17.400 72.612 70.571
200 33.057 31.580 91.190 88.375
300 48.403 47.043 108.261 104.849
400 63.934 62.956 124.906 121.155
500 77.797 77.135 141.146 137.212
600 89.470 89.016 156.756 152.722
700 99.213 98.887 171.608 167.514
98
corresponding fitting equations are as follows and the correlation graphics of
those shown in Figs. 4.5(a)-4.5(b).
)9993.0(100.61833.04987.0 225 RTTC
)0000.1(100.31901.0104.54 225 RTTS
All the thermodynamic data supply helpful information for the further
study on the Gabapentin. They can be used to compute the other
thermodynamic energies according to relationships of thermodynamic functions
and estimate directions of chemical reactions according to the second law of
thermodynamics in thermochemical field. It is to be noted that all
thermodynamic calculations were done in gas phase.
5.3 Conclusions
Quantum chemical calculations of energies, geometrical structure and
vibrational wavenumbers of zwitterionic and neutral form of GP have been
performed using density functional (DFT/B3LYP) method with 6-311++G(d,p)
basis set. The energy of neutral GP is found to be lower than zwitterionic form
form by an amout 0.31153 hartree, which is not surprising as the zwitterion
charge separation is not stabilized by the environment in gas phase. The spectral
characterization studies such as FT-IR, FT-Raman for GP have been carried out
for the first time. A good agreement between experimental and calculated
normal modes of vibrations has been observed. The true HOMO-LUMO gap ie.
-HOMO- -LUMO gap for GP with S = 1/2 has been calculated as 2.65174 eV.
The dipole moment, polarizability and first static hyperpolarisability value are
99
found to be appreciably higher in zwitterionic form than the neutral form. The
correlations between the thermodynamic functions and temperature are also
obtained for both the forms of GP. It is seen that the heat capacities, entropies
and enthalpies increase with the increasing temperature owing to the intensities
of the molecular vibrations increase with increasing temperature. The present
quantum chemical study may lead to the diversification in the activity of GP,
with a hope to have many more medicinal uses of it.
100
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CHAPTER 5
Molecular geometry, Polarizability and reactivity descriptors of small
Cadmium Telluride clusters
102
5.1 Introduction
Semiconductor nanocrystals, frequently known as quantum dots [1], have
been used widely for a varied range of applications in bio-imaging and bio-
sensing. These quantum dots (QDs) are generally composed of atoms from
groups II and VI or groups III and V of the periodic table. The diameters of
QDs typically are between 1 and 10 nm, and each dot contains a relatively
small number of atoms in a discrete cluster [2]. Cadmium telluride (CdTe)
is a crystalline compound formed from cadmium and tellurium with a zinc
blende (cubic) crystal structure. In the bulk crystalline form it is a direct
band gap semiconductor. Recently Zhang Yun et. al. [3] have used
cadmium telluride quantum dots as a proton flux sensor and have
successfully used it to detect H9 avian influenza virus. Sander F. Wuister
et. al. [4] have used efficiently luminescing colloidal CdTe quantum dots
(QDs) for the preparation of mono-dispersed and mixed size QD solids. In
recent years, quantum dots (QDs) have emerged as an attractive alternative
to traditional fluorescent organic dyes for biological labeling owing to their
unique, size-tunable spectral properties and excellent photostability[5,6].
One challenge in the application of QDs, however, is their stability and
biocompatibility in biological systems. As an important kind of visible light
emitting, CdTe QDs have been widely used in biological labeling, such as
103
living-cell imaging [7,8] and cancer marker targeting [9,10]. Structurally,
QDs also possess large surface areas for the attachment of multiple
diagnostic and therapeutic agents [11,12]. Earlier a brief study of structure
and energetics on CdTe cluster by ab initio theory has been carried out[13].
With the increasing interest in Cadmium Telluride nano crystals as non
linear optical devices, quantum dots and nanosensors [3,4], the present
chapter deals with the calculation of molecular geometry, dipole moment
electric polarizability and DFT based reactivity descriptors such as
molecular chemical potential, chemical hardness, global electrophilcity
index, as well as homo lumo energies of Cadmium Telluride clusters
(CdTe)n, n=1-8 in gas phase using HF and density functional theory based
methods. It is necessary to explore the possible relationships of these
reactivity descriptor with cluster size.
Theoretical Background
Parr et.al and Chhatraj et.al [14,15] have interpreted that chemical potential
(μ) could be written as the partial derivative of the system’s energy with
respect to the number of electrons at a fixed external potential v(r) :
μ = (∂E/∂N)v(r) ----(1)
Iczkowski and Margrave [16] proposed to define electronegativity as
ζ = - (∂E/∂N)v(r) -----(2)
104
Fig 5.1 Molecular Geometries of (CdTe)n cluster( n= 1- 8) at B3LYP/
LANL2DZ basis set.
105
for a fixed nuclear charge.
The working formulas in DFT for calculating chemical potential (μ),
electronegativity (ζ) and hardness (η) are as follows:
μ ≈ −(I+A)/2 ; ζ ≈ (I+A) / 2 ; η ≈ (I−A) / 2 ------(3)
The ionization potential and electron affinity can be replaced by the HOMO
and LUMO energies, respectively, using Koopmans’ theorem [17] within a
Hartree-Fock scheme yielding
ζ = - (εHOMO + εLUMO )/2 -----(4)
and so on.The ionization potential and electron affinity may be better
expressed as:
I ≈ E(N-1) –E(N) --------(5a)
A ≈ E(N) –E(N+1) --------(5b)
Parr et al. [14] have introduced the global electrophilicity index (ω ) as a
measure of energy lowering due to maximal electron flow between a donor
and an acceptor in terms of the chemical potential and the hardness as
ω = µ2/2η ---------(6)
Binding energy of the cluster be also defined as given below:
binding energy per atom{Eb}= {-E(CdTe)n + n(Cd) +n (Te)}/2n
106
Results and Discussion-
The calculated molecular geometries for the CdTe and its clusters are shown
in Fig. 5.1. These geometries lie on true minima. The HOMO and LUMO of
(CdTe)n; n=1,3,5,7 and(CdTe)n; n=2,4,6,8 are shown in Fig. 5.2 and Fig.5.3.
The calculated values of dipole moment, homo and lumo energies, and
chemical potential, chemical hardness mean, polarizability, global
electrophilcity index and binding energy are listed in Table 5.1, Table 5.2,
Table 5.3 and Table 5.4.
Binding energy and HOMO LUMO analysis:
The binding energy curve for CdTe cluster is shown in Fig. 5.4 for different
basis set with cluster size. The binding energy per atom of the cluster is
defined with respect to free atoms follow the mathematical equation: Eb=-
[Ecluster- n(ECd)- n (ETe)]/2n where E cluster, ECd, ETe are optimized of cluster,
free cadmium and free tellurium atom. The stability of the compound is
usually measured in terms of binding energy, bond length, bond dissociation
energy,frontier orbital energy and their gap. Frontier orbital energy band
gap has been used to evaluate stability. It is found that binding energy per
atom with cluster size monotonically increases and dimer, tetramer hexamer
and octamer are more stable than monomer, trimer, pentamer and heptamer.
107
Fig 5.2 HOMO and LUMO of CdTe Clusters monomer, trimer, pentamer
and heptamer.
Fig 5.3 HOMO and LUMO of CdTe Clusters dimer, tetramer hexamer and
octamer.
108
Table : 5.1 Parameters for odd values of n (1,3,5,7) for (CdTe)n with LANL2DZ basis set
Clu
ster
met
ho
d
LANL2DZ
Dipole
moment d
in Debye
Homo in
eV
Lumo in
eV
Chemical
potential
μ in e.v.
Hardness
η in eV
Mean α in a. u.
ω in eV Binding
energy in
eV
Mo
no
mer
HF
6.4892 -7.6192 -1.6055 -4.613 -3.006 87.99 -3.54 -0.545
B3
LY 5.3258 -5.4967 -4.2450 -4.87 -0.626 79.14 -15.559 -0.830
B3
PW
9
5.7277 -5.5512 -4.2178 -4.89 -0.667 89.27 -17.925 -0.955
Tri
mer
HF
0.0002 -8.2451 -0.3538 -4.300 -3.551 197.64 -2.603 -1.767
B3
LY 0.0052 -6.0410 -2.9116 -4.477 -1.564 227.21 -6.407 -1.875
B3
PW
91
0.0004 -6.1498 -2.7756 -4.463 -1.687 221.21 -5.903 -2.09
Pen
tam
er
HF
2.6318 -7.2927 -0.5442 -3.9185 -3.374 343.559 -2.2683 -3.768
B3
LY
P
3.5295 -5.4695 -3.2654 -4.3675 -1.102 386.816 -8.6540 -3.706
B3
PW
91
0.9033 -5.6056 -3.2110 -4.4083 -1.197 378.877 -8.1154 -4.192
Hep
tam
er
HF
4.3212 -7.7009 -0.5986 -4.1498 -3.551 482.264 -2.4247 -4.026
B3
LY
P
4.2178 -5.7416 -3.5103 -4.6260 -1.115 551.931 -9.5903 -3.858
B3
PW
91
4.0563 -5.7961 -3.5375 -4.7620 -1.129 531.428 -10.0401 -4.344
109
Table:5.2 Parameters for even values of n (2,4,6,8) for (CdTe)n with LANL2DZ basis set C
lust
er
met
ho
d
LANL2DZ
Dipole
moment
in Debye
Homo in
eV
Lumo in
eV
Chemical
potential μ in eV
Hardness
η in eV
Mean α in a. u.
ω in eV Binding
energy in
eV
Dim
er
HF
7.2138 -7.1839 -1.1429 -4.164 -3.020 161.40 -2.870 -1.01
B3
LY
P
0.0116 -5.0886 -3.5103 -4.300 -0.789 172.27 -11.717 -1.3775
B3
PW
91
0.0035 -5.0341 -3.5919 -4.313 -0.721 169.53 -12.900 -1.5375
Tet
ram
er
HF
0.0006 -8.1907 -0.2177 -4.2042 -3.9865 275.98 -2.2169 -4.215
B3
LY
P
0.7442 -6.0410 -2.8300 -4.4355 -1.6055 322.618 -6.1270 -3.850
B3
PW
91
0.8332 -6.2042 -2.7484 -4.4763 -1.7280 312.639 -5.7978 -4.275
Hex
am
er
HF
0.0002 -8.0274 -0.6259 -4.3266 -3.700 387.738 -2.5292 -4.172
B3
LY
P
1.9340 -6.1498 -3.1021 -4.6260 -1.524 444.209 -7.0219 -4.073
B3
PW
91
1.8859 -6.2887 -2.9389 -4.5988 -1.659 431.137 -6.3706 -4.592
Oct
am
er
HF
0.0020 -8.0546 -0.5714 -4.3130 -3.7416 535.242 -2.4858 -4.283
B3
LY
P
2.5036 -6.1770 -3.1293 -4.6532 -1.5238 623.0997 -7.1047 -4.078
B3
PW
91
2.4570 -6.3131 -2.9933 -4.6532 -1.6599 602.755 -6.5222 -4.584
110
Table:5.3 Parameters for odd values of n (1,3,5,7) for (CdTe)n with LANL2MB basis set C
lust
er
met
ho
d
LANL2MB
Dipole
moment in
Debye
Homo in
eV
Lumo in
eV
Chemical
potential
μ in eV
Hardness
η in eV
Mean α in a. u.
ω in eV Binding
energy in
eV
Mo
no
mer
HF
5.0194 -7.7553 -1.5238 -4.64 -3.115 86.37 -3.456 -0.260
B3
LY
P
4.6491 -5.6327 -4.4899 -5.062 -0.571 70.72 -22.437 -0.525
B3
PW
91
4.9917 -5.6872 -4.5171 -5.102 -0.585 71.34 -22.248 -0.620
Tri
mer
HF
0.0002 -8.2723 -0.8708 -4.572 -3.700 190.35 -2.824 -1.168
B3
LY
P
0.0008 -6.1770 -3.3742 -4.776 -1.401 214.20 -8.140 -1.406
B3
PW
91
0.0005 -6.3131 -3.3198 -4.816 -1.496 207.99 -7.752 -1.59
Pen
tam
er
HF
2.6318 -7.2927 -0.5442 -3.9185 -3.3742 343.559 -2.2683 -3.768
B3
LY
P
3.2693 -5.8504 -3.5647 -4.7076 -1.1429 352.601 -9.6953 -2.976
B3
PW
91
3.1819 -5.9321 -3.5103 -4.7212 -1.2109 340.423 -9.2038 -3.393
Hep
tam
er
HF
4.3212 -7.7009 -0.5986 -4.1498 -3.5511 482.264 -2.4247 -4.026
B3
LY
P
3.7799 -6.0682 -3.7280 -4.8991 -1.1701 513.416 -10.2519 -3.086
B3
PW
91
3.63132 -6.2042 -3.7824 -4.9933 -1.2109 493.366 -10.2953 -3.504
111
Table : 5.4 Parameters for even values of n (2,4,6,8) for (CdTe)n with LANL2MB basis set C
lust
er
met
ho
d
LANL2MB
Dipole
moment
in Debye
Homo in
eV
Lumo in
eV
Chemical
potential μ in eV
Hardness
η in eV
Mean α in a. u.
ω in eV Binding
energy in eV
Dim
er
HF
7.0837 -7.2111 -1.7143 -4.463 -2.748 163.72 -3.624 -0.645
B3
LY
P
5.1197 -5.2246 -4.1634 -4.694 -0.530 166.91 -20.786 -1.09
B3
PW
91
5.4977 -5.2791 -4.1089 -4.694 -0.612 164.05 -18.001 -1.225
Tet
ram
er
HF
0.0000 -8.2723 -0.5987 -4.4355 -3.8368 273.211 -2.5638 -3.024
B3
LY
P
0.5634 -6.2315 -3.0205 -4.6260 -1.6055 309.666 -6.6446 -2.958
B3
PW
91
0.5646 -6.3675 -2.9933 -4.6804 -1.6871 300.006 -6.4922 -3.282
Hex
am
er
HF
0.0002 -8.0274 -0.6259 -4.3266 -3.7007 387.738 -2.5292 -4.172
B3
LY
P
1.6704 -6.4491 -3.5919 -5.0205 -1.4286 402.344 -8.8217 -3.252
B3
PW
91
1.6206 -6.5852 -3.5103 -5.0478 -1.5374 387.507 -8.2868 -3.695
Oct
am
er
HF
0.0020 -8.0546 -0.5714 -4.3130 -3.7416 535.242 -2.4858 -4.283
B3
LY
P
2.1644 -6.4764 -3.5647 -5.0205 -1.4558 582.369 -8.6569 -3.248
B3
PW
91
2.1071 -6.6124 -3.4831 -5.0478 -1.5647 559.581 -8.1422 -3.681
112
0 1 2 3 4 5 6 7 8 9
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
Bin
din
g E
ne
rgy
Cluster Size
B3LYP(LANl2DZ)
B3PW91(LANL2DZ)
B3LYP(LANL2MB)
B3PW91(LANL2MB)
Fig 5.4 Variation of Binding Energy with cluster size n=1-8.
113
The Eb values are listed in Table 5.1, Table 5.2, Table 5.3, Table 5.4 and a
graph between Eb and cluster size is given in Fig 5.4. The maximum binding
energy is obtained as 4.584 eV per atom for (CdTe)8. Fukui et al. [18]
described the eminent role played by HOMO and LUMO as a governing
parameter of chemical reaction. Several studies show that band gap E homo-
lumo is a very important stabilty index of molecules [19,20]. A large band
gap implies high stability where as a small band gap implies lower stability.
Variations of HOMO LUMO composition is also shown in Fig.(5.2,5.3). It
decreases with cluster size from 6.0137 eV to 2.3846 eV for hartee fock
theory (Fig. 5.5) whereas it increases for DFT functional with cluster size
from 1.2517 eV to 2.3946 eV.
Global Reactivity Descriptors:
Basic reactivity descriptors play a very important role in rationalizing
molecular structure and chemical reaction . DFT has provided the basis for
calculation of reactivity descriptors. The chemical potential (µ)
characterizes the escaping tendency of electrons from equilibrium. The
hardness (η) can be seen as resistance to charge transfer and softness (S) has
been quantitatively related to polarizabilty of system. The value of these
descriptors are listed in Table 5.1, Table 5.2, Table 5.3, Table 5.4 and their
variation with respect to cluster size are shown in Fig. 5.6, Fig. 5.7, Fig. 5.8.
114
It has been found that tetramer , hexamer and octamer are more harder
(more stable) than neighbouring cluster. In Fig. 5.7 plot of chemical
hardness has been shown with the lowest value of 0.530 eV and 3.9865 eV
as maximum value. A harder molecule means it is hard to react or more
stable. As hardness and softness are important factors of the charge transfer
resistance and inversaly proportional to each other [14]. For small chemical
systems the softness is readily related with polarizabilty.The polarizability
(α) measures the distortion of the electron density of the molecules in the
response of the molecule to the external electric field. As shown in Fig 5.8
the mean polarisability monotonically increases with cluster size for both
even and odd cluster size and have maximum value 623.0997 a.u. for
octamer.
The chemical potential (μ) characterizes the tendency of
electron to escape from the molecule in the equilibrium state. Koopman’s
theorem has been used to calculate μ of the molecules [17]. In present
calculation the chemical potential varies with size but it increase for even n
values of cluster ( Fig 5.6), a reverse trend for odd n has been observed
except for heptamer.
115
Fig 5.5 Variation of Frontier Orbital energy gap with cluster size n=1-8.
116
0 1 2 3 4 5 6 7 8 9
4.2
4.4
4.6
4.8
5.0
5.2
5.4
Ch
em
ica
l p
ote
nti
al
cluster size
B3LYP(LANl2DZ)
B3PW91(LANL2DZ)
B3LYP(LANL2MB)
B3PW91(LANL2MB)
Fig5.6 Variation of Chemical Potential with cluster size n=1-8.
0 1 2 3 4 5 6 7 8 9
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
Ch
emic
al H
ard
nes
s
cluster size
B3LYP(LANl2DZ)
B3PW91(LANL2DZ)
B3LYP(LANL2MB)
B3PW91(LANL2MB)
Fig 5.7 Variation of Chemical Hardness with cluster size n=1-8.
117
0 1 2 3 4 5 6 7 8 9
0
100
200
300
400
500
600
Mea
n P
ola
riza
bil
ity
Cluster Size
B3LYP(LANl2DZ)
B3PW91(LANL2DZ)
B3LYP(LANL2MB)
B3PW91(LANL2MB)
Fig 5.8 Variation of Mean Polarizability with cluster size n=1-8.
0 1 2 3 4 5 6 7 8 9
6
8
10
12
14
16
18
20
22
24
Glo
bal e
lect
rofic
ity In
dex
Cluster Size
B3LYP(LANl2DZ)
B3PW91(LANL2DZ)
B3LYP(LANL2MB)
B3PW91(LANL2MB)
Fig 5.9 Variation of Global Electrofilcity Index with cluster size n=1-8.
118
Global electrophilicity index:
The generalized concept of philicity was proposed by Chattaraj et. al. [20].
The group concept of philicity is very useful in unraveling reactivity of
various molecular system. The condense philicity summed over a group of
relevant atoms is defined as the group philicity. It can be expressed as:
ω = µ2/2η
In the present work it is seen that the global
electrophilicity index first decreases with cluster size and is minimum for
trimer and then rises slowly for both n even and odd values (Fig. 5.9).
Conclusions
According to the present calculations on CdTe clusters (n=1-8), we observed
that with change in cluster size binding energy increases, the even n
clusters i.e. dimer, tetramer, hexamer and octamer have more binding
energy than preceding odd n clusters monomer, trimer, pentamer and
heptamer. It has also been found that mean polarisability increases with
cluster size, whereas dipole moment does not follow any trend. Calculation
of chemical hardness and homo – lumo gap also confirms the greater
reactivity of odd n, CdTe clusters. The present quantum chemical study
119
may further play an important role in understanding in the use of CdTe
clusters in various devices.
120
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4973.
CHAPTER 6
CONCLUSIONS
122
Quantum chemistry is the field in which solutions to the Schrödinger equation
are used to predict the properties of molecules and solve chemical problems. Its
arrival and popularity have paralleled improvements in computing power during
the last several decades. Introduction of high speed computers made the
electronic structure calculation an imperative element of theoretical and
experimental chemical researchers. The electronic structure of materials, in
general sense determines all the molecular properties accurately by ab initio
calculations i.e. from fundamental quantum theory. The simplest type of ab
initio electronic structure calculation is the Hartree–Fock (HF) method but
Density Functional Theory (DFT) has become a widely used class of quantum
chemical methods because of its ability to predict relatively accurate molecular
properties with relatively less computational cost [1-5]. The work reported in
this thesis is based on the calculation of ground state properties and the
vibrational analysis of finite molecules using DFT method.
In the preceding chapters, calculation of molecular properties and vibrational
analysis of two small molecules of different type namely 3-benzoyl 5-
chlorouracil and Gabapentin have been reported. Chapter 3 involves the
investigation of molecular structural, vibrational and energetic data analysis of
3-Benzoyl-5-chlorouracil (3B5CU), a biologically active synthetic molecule, at
DFT/6-311++G(d,p) level and reported for the first time as a potential candidate
for nonlinear optical (NLO) applications. The frontier orbital energy gap,
123
dipole moment, polarisability and first static hyperpolarisability have been
calculated. The first static hyperpolarisability is found to be almost 15 times
higher than that of urea. The high value of first static hyperpolarisability (2.930
× 10-30
e.s.u.) due to the intra-molecular charge transfer in 3B5CU has been
discussed using first principles. A complete vibrational analysis of the molecule
has been performed by combining the experimental Raman, FT-IR spectral data
and the quantum chemical calculations. In general, a good agreement of
calculated modes with the experimental ones has been obtained. The strong
vibrational modes contributing towards NLO activity, involving the whole
charge transfer path, have been identified and analysed. Chapter 4 deals with
the calculation of ground state properties of both zwitterionic and neutral form
of Gabapentin (GP) employing DFT/B3LYP level of theory. A complete
assignment of the vibrational modes has been performed on the basis of the total
energy distribution (TED) values and using the scaled quantum mechanics
method. The theoretical data (molecular parameters, IR and Raman spectra) are
compared to the results of the experimental studies performed in the solid state.
The polarizability and first static hyperpolarizability of both zwitterionic and
neutral form have also been calculated and compared. In Chapter 5, the
calculation of molecular geometry, dipole moment, electric polarizability and
DFT based reactivity descriptors such as molecular chemical potential, chemical
hardness, global electrophilcity index, as well as homo lumo energies of
124
Cadmium Telluride clusters (CdTe)n, n=1-8 in gas phase has been done using
HF and density functional theory based methods.
The work reported in the thesis is primarily based on the calculation of
molecular properties using DFT method. All these studies are based on certain
assumptions and as such have their own limitations. The experimental data,
which have been used, also have their dependability within certain limits.
Density functional theory (DFT) calculations are the most common type of
calculations, though they are subject to limitations in the accuracy of the
functional employed, and the ability to chemically interpret the result. These are
briefly discussed as follows - DFT methods are not systematically improvable
like wavefunction based methods and so it is impossible to assess the error
associated with the calculations without reference to experimental data or other
types of calculation. The choice of functionals is intimidating and can have a
real impact on the calculations. The geometric differences between the
optimized molecules and the molecule in solid state are due to the fact that
the molecular conformation in the gas phase is different from that in the solid
state, where inter molecular interactions play an important role in
stabilizing the crystal structure. Although DFT is enjoying ever increasing
popularity in Solid State Physics and Quantum Chemistry but it is generally
known that HF overestimates the HOMO-LUMO gap whereas DFT/ B3LYP
underestimates it [6,7]. Hence methods like MP2 should be used to get a better
125
estimate of HOMO-LUMO gap. This has not been used as it is very
computationally costly and beyond the scope of the present work.
In the present work one of the important limitations in the evaluation of
spectroscopic data lies in the fact that an isolated model has been used in place
of three dimensional systems. This leads to a shift of few wave numbers in the
calculated frequencies. Calculations on a three dimensional system together
with intermolecular interactions will fully interpret the vibrational modes, but
the calculation with three dimensional system becomes computationally very
costly and cumbersome.
Most of the work reported here is based on the FT-IR and FT-Raman
spectra. It is to be noted that the FT-IR and FT-Raman spectra have their own
limitations. Their interpretation may not be simple. Sometimes, fluorescence of
impurities or of the sample itself can hide the Raman spectrum. In case of bands
separated by small energy, the information contained in them may be masked
by overlapping. Other features which limit the information can be because of
over tones and shifting of bands due to structural features.
Unlike Infrared or Raman study, neutron scattering does not involve
electromagnetic interaction [8, 9] and there is no restriction on selection rules.
Thus it can give information on the entire range of vibrational spectra of a
molecule besides giving density-of-states directly. It is specially suitable in the
low frequency spectral region for lattice modes and chain vibrations.
126
The future research scope involves the quantum chemical study of a series of
derivatives of 3B5CU, so that the trend in electronic properties may be used to
interpret the dynamics of such compounds and their use as NLO materials. UV
and NBO analysis can be done through quantum chemical methods to have a
better understanding of action and activity of the drug.
The present work can also be extended for time-dependent density functional
theory (TDDFT) studies. TDDFT is a quantum mechanical method to
investigate the properties of many-body systems beyond the ground state
structure. It is an extension of density functional theory (DFT) to the time-
dependent domain as a method to describe such systems when a time dependent
perturbation is applied and as DFT, it is becoming one of the most popular and
versatile methods available in condensed matter physics, computational physics
and computational chemistry [10].
127
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