An Introduction to Computational Chemistry

Computational ChemistryCHM 425/525 Fall 2011 Dr. Martin

Solution

Theory Experiment

Computation

What is Computational Chemistry?

Use of computers to aid chemical inquiry, including, but not limited to:– Molecular Mechanics (Classical Newtonian Physics)– Semi-Empirical Molecular Orbital Theory– Ab Initio Molecular Orbital Theory– Density Functional Theory– Molecular Dynamics– Quantitative Structure-Activity Relationships– Graphical Representation of Structures/Properties

Levels of Calculation

Molecular mechanics...quick, simple; accuracy depends on parameterization.

Semi-empirical molecular orbital methods...computationally more demanding, but possible for moderate sized molecules, and generally more accurate.

Ab initio molecular orbital methods...much more demanding computationally, generally more accurate.

Levels of Calculation...

Density functional theory…more efficient and often more accurate than ab initio calc.

Molecular dynamics…solves Newton’s laws of motion for atoms on a potential energy surface; temperature dependent; can locate minimum energy conformations.

QSAR…used to predict properties of new structures or predict structures that should have certain properties (e.g., drugs)

Relative Computational “Cost”

Molecular mechanics...cpu time scales as square of the number of atoms...

Calculations can be performed on a compound of ~MW 300 in a minute on a pc, or in a few seconds on a parallel computer.

This means that larger molecules (even large peptides) and be modeled by MM methods.

Relative Computation “Cost”

Semi-empirical and ab initio molecular orbital methods...cpu time scales as the third or fourth power of the number of atomic orbitals (basis functions) in the basis set.

Semi-empirical calculations on ~MW 300 compound take a few minutes on a pc, seconds on a parallel computer (cluster).

Molecular Mechanics

Employs classical (Newtonian) physics

Assumes Hooke’s Law forces between atoms (like a spring between two masses)

EEstretchstretch = k = kss (l - l (l - loo))22

graph: graph: C-CC-C; ; C=OC=O

Bond Stretching Energy

0

50

100

150

200

250

300

350

0 1 2 3

Internuclear Distance

En

erg

y, k

cal/m

ol

Molecular Mechanics...

Similar calculations for other deviations from “normal” geometry (bond angles, dihedral angles)

Based on simple, empirically derived relationships between energy and bond angles, dihedral angles, and distances

Ignores electrons and effect of systems! Very simple, yet gives quite reasonable,

though limited results, all things considered.

Properties calculated by MM:

“Steric” or Total energy = sum of various artificial energy components, depending on the program...not a “real” measurable energy.

Enthalpy of Formation (sometimes) Dipole Moment Geometry (bond lengths, bond angles, dihedral

angles) of lowest energy conformation.

Molecular Mechanics Forcefields

MM2, MM3 (Allinger) MMX (Gilbert, in PCModel) MM+ (HyperChem’s version of MM2) MMFF (Merck Pharm.) Amber (Kollman) OPLS (Jorgensen) BIO+ (Karplus, part of CHARMm) (others)

Semi-Empirical Molecular Orbital Theory Uses simplifications of the Schrödinger

equation to estimate the energy of a system (molecule) as a function of the geometry and electronic distribution.

The simplifications require empirically derived (not theoretical) parameters (or fudge factors) to allow calculated values to agree with observed values.

Properties calculated by molecular orbital methods: Energy (enthalpy of formation) Dipole moment Orbital energy levels (HOMO, LUMO,

others) Electron distribution (electron density) Electrostatic potential Vibrational frequencies (IR spectra)

Properties calculated by molecular orbital methods... HOMO energy (Ionization energy) LUMO energy (electron affinity) UV-Vis spectra (HOMO-LUMO gap) Acidity & Basicity (proton affinity) NMR chemical shifts and coupling

constants others

Semi-Empirical MO Theory Types

Hückel (treats electrons only) CNDO, INDO, ZINDO MINDO/3 MNDO AM1, PM3 (currently most widely used)

Collections of these are found in AMPAC, MOPAC, HyperChem, Spartan, Titan, etc.

Ab Initio Molecular Orbital Theory

Uses essentially the same (Schrödinger) equation as semi-empirical MO calculation

Introduces fewer approximations, therefore needs fewer parameters (“fudge factors”)

Is more “pure” in relation to theory; if theory is correct, should give more accurate result.

Takes more cpu time because there are fewer approximations.

Variations of Ab Initio Theory

HF (Hartree-Fock)– electron experiences a ‘sea’ of other electrons

Moller-Plesset perturbation theory– includes some electron correlation; MP2, MP3

Configuration Interaction– QCISD, QCSID(T)

All of the above involve choices of basis sets:– STO-3G, 3-21G, 6-31+G, 6-311G**, etc. (many)

Basis Sets

STO-3G (Slater-type orbitals approximated by 3 Gaussian functions)

Split Basis Sets...

Use two sizes of Gaussian functions to approximate orbitals:

3-21, 6-31, 6-311 (large and small orbitals) additional features which can be added to any

basis set:– polarization functions (mixes d,p with p,s orbitals)– e.g., 6-31G** [= 6-31G(d,p)]– diffuse functions + (allows for distant interactions)

Molecular Geometry

Molecular geometry can be described by three measurements:– bond length (l)– bond angle ()– dihedral angle ()

C C

H

H

H

HH

Hl

H H

HH H

H

Bond length

Distance between nuclei of adjacent atoms that are covalently bonded (can also describe distance between non-covalently bonded, or non-bonded atoms)

But atoms are in constant motion, even at absolute zero! How do we define the “distance” between them?

Measurements of bond length

X-ray crystallography– distances in crystalline solid; only ‘heavy’ atoms– geometry may differ from solution phase

Gas Phase electron diffraction– weighted average distances in gas phase– not a single conformation; solvent effects ignored

Neutron diffraction– only heavy atoms included

Equilibrium bond length

Molecules exist in an ensemble of energy states which depends on T.

Several vibrational and rotational states are populated for each electronic state.

Geometry optimization computations determine the equilibrium bond length.

v1v2v3

v0

r0, r1, r2...

Energy

Distance between atomseq. bond length

zero point energy

Units of Measurement

Bond lengths are usually reported in Angstroms (1Å = 10-10 m = 100 pm); this is not an SI unit, but it is convenient because most bond lengths are of 1 to 2 Å.

Angles are measured in degrees. Potential energy is usually measured in

kcal/mol (1 kcal/mol = 4.184 kJ/mol).

Some Applications...

Calculation of reaction pathways & energies Determination of reaction intermediates and

transition structures Visualization of orbital interactions (forming

and breaking bonds as a reaction proceeds) Shapes of molecules, including large

biomolecules Prediction of molecular properties

…more Applications

QSAR (Quantitative Structure-Activity Relationships)

Remote interactions (those beyond normal covalent bonding distance)

Docking (interaction of molecules, such as pharmaceuticals with biomolecules)

NMR chemical shift prediction

Modeling Charge-Transfer Complexation of Amines with Singlet Oxygen

N-O “bond” distance = 1.55 ÅqN = +0.35esu qOdistal = -0.33 esu

Modeling Aggregation Effects on NMR Spectra N-Phenylpyrrole has a

concentration-dependent NMR spectrum, in which the protons are shifted upfield (shielded) at higher concentrations.

We hypothesized that aggregation was responsible.

Modeling Aggregation Effects on NMR Spectra...

p

mean dimer (calc'd.)

m o

pmean monomer (calc'd.)

m o

8.2 8.0 7.8 7.6 7.4 7.2 7.0 6.8

7.8 7.6 7.4 7.2 7.0 6.8

Two monomers were modeled in different positions parallel to one another, and the energywas plotted vs. X and Y. The NMR of the minimum complex was calculated.

Orbital Perturbations

Proximity of orbitals results in perturbation.

This shows methane with one H 2.0Å above the middle of the bond of ethene

This leads to alterations in the magnetic field, which affects the NMR chemical shift

Magnetic Shielding Surfaces