employing dft methods for designing molecules with ultra...

Employing DFT methods for designing molecules with ultra-strong dipole moments

George Papamokos

Heraklion, September 2015

Motivation: Organic molecules with large dipole moments

• Why are we interested in?

Potential applications in:

Ferroelectrics

Non-linear optics (NLO)

Incorporation of strong dipoles can lead to improved charge separation at the interface of the donor- and the acceptor- phase in bulk heterojunction solar cells

Architecture of an organic photovoltaic device.

• The negative electrode is aluminum

• Indium tin oxide (ITO) is a common transparent electrode, and the substrate is glass.

• A bulk heterojunction (BHJ) active layer where the donor and acceptor blend forms phase segregated domains within the active layer.

• The structure of the BHJ is critical to the performance of the solar device.

A schematic energy diagram of a D–A interface.

Each material has a HOMO (IP) and a LUMO (EA). The difference between the energy of HOMO and LUMO is the band gap. The difference between the HOMO of the donor and the LUMO of the acceptor is the open circuit voltage Voc. The differences in EA and IP of the two materials set up electrostatic forces at the D–A interface. Progress in Polymer Science 38 (2013) 1929– 1940

Polymer solar cells

A higher dielectric constant may lead to a higher efficiency.

The relative permittivity of a substance is large if its molecules are polar or highly polarizable.

Electric properties: Definitions

• An electric dipole consists of two electric charges +Q and −Q separated by a distance R.

μ= Q R

• Units: coulomb*metre (Cm), or debye, D 1 D = 3.335 64 Χ 10−30 Cm

• A polar molecule is a molecule with a permanent

electric dipole moment.

• The resultant μres of two dipole moments μ1 and μ2 that make an angle θ to each other is approximately

μres ~(μ12 +μ2

2 + 2μ1μ2 cosθ)1/2

Atkins P. 2010

Electric properties: Definitions

Atkins 2010 9th edition

Electric dipole moments

• Relative permittivity is a function of the electric properties of the molecules

Polar diluted systems Debye Equation

Non Polar systems Clausious Mossotti equation

Polar systems Onsager Equation

Polar systems Kirkwood Fröhlich Equation short range interactions

Idea

• Exchange of hydrogen in benzene with highly polarizing substituents bearing opposing electron affinities lead to electron donors or electron acceptors.

• By adding substituents on opposing ends of a conjugated system, permanent dipole moments can be generated.

• Creation of a large dipole on a conjugated system requires

careful selection of functional groups on opposing ends. • The stronger the electron-tug on the acceptor side and the

electron-pull on the donor side, the higher the total dipole moment.

Idea

Electon Withdrawing Groups vs Electron Donating Groups

• Cyano- group is one of the most electron-withdrawing groups, with the strongest counterpart being the amino-group.

• Thus the combination of amino- and cyano-groups can generate dipole moments with values exceeding 10 debye.

Choice of donors and acceptors

An entirely different synthetic approach in benzene chemistry

Design strategy:

Successful combination of two donors and four acceptors in a fully substituted benzene resulted to:

The strongest dipole moments reported for hexasubstituted benzenes with promising applications as NLOs.

Benzene is kept non-charged

Synthesis and Characterization

Characterization and physicochemical properties

• UV/Vis-spectra have been recorded for all compounds in THF solutions (concentration 10-5 mol/L) to determine the respective optical gaps.

• X-Ray

• Further characterization via cyclic voltammetry to determine electron affinities and compare them to the calculated LUMO-values was not possible due to the small range given by oxidation/reduction of the possible solvents.


Comparison of the UV/Vis-spectra in THF solutions (c=10-5 mol/L) of all

compounds.

300 400 500 6000

4000

8000

12000

(l

mo

l-1 c

m-1)

Wavelength (nm)

5a

3 complex with DMAC

3

2

1

4a


Crystal structure of molecule 3 (with DMAC) and packing within the crystal

Experimental methods

• Experimental dipole moments were evaluated from dielectric spectroscopic measurements performed at 25 oC using a Novocontrol Alpha frequency analyzer (frequency range from 10-2 to 107 Hz).

• Measurements of the dielectric permittivity were made with a BDS 1308 liquid parallel plate sample cell.

Experimental methods

• Dilute solutions in THF

• For molecule 5b solutions in chloroform were prepared and the dielectric permittivity was measured as a function of solute concentration.

Electric properties: Equations For polar solute and solvent - our case - we used the modified

Onsager equation according to Böttcher:1-3

• Following the formalism of Böttcher and • Assuming ideal solution of the two components the dipole moment

of the solute can be obtained from the derivative of ε12 with respect to concentration in the limit of infinite dilution.

• C.J.F. Böttcher; Rec. Trav. Chim. 1943, 62, 119-133. 1. H.A. Rizk, I.M. Elanwar; Can. J. Chem. 1968, 46, 507-513. 2. C.W.N. Cumper, P.G. Langley; Trans. Faraday Soc. 1971, 67, 35-43.

Electric properties: Equations

• where Ni is the number of molecules of type i per cc of the solution, • ε∞ square of refractive index of component i, • μi dipole moment of type i in the vapor state, and • ai, radius of the hypothetical spherical molecule containing the point

dipole, pi, • the subscript 12 being for the solution. • Ni is related to Ci, which is the number of gram molecules of

component i per liter of solution, by the equation

Onsager's equation in a modified form can be written without taking association into consideration, in Bottcher's expression as:


• Let’s assume that the hypothetical volume of Na spherical molecules in a gram-molecule of component i is equal to the molar volume, Vi, Then we have:

Electric properties: Equations • Let’s Substitute for Ni in eq. [1] from eqs. [2] and

put:

Then we get:

Electric properties: Equations • Assume ideal solution of two components

• Designate the polar solute by subscript 2 and the polar solvent by subscript 1

• Then the volume additivity is given by

Electric properties: Equations • Substitution of C1

0 = 1000 x (d1/M1) for the molar concentration of pure solvent and

• V2 = M2/(1000 x d2) for the molar volume

• (in liters) of pure solute gives:

For a binary system eq 6 can be written as:

Electric properties: Equations • Substituting C1 from eq [8] to equation [9] and

taking the derivative of e12 with respect to C2 we obtain:

Electric properties: Equations • Solving for the square of the dipole moment we get

equation [10]:

Where A’ and B’ are the derivatives of A and B with respect

to C2

Electric properties: Equations • Now we substitute A1’, A2’ B1’ B2’ from equation [11] to

equation [10] and put:

• Taking the slope dε12/dC2 in the limit of C2 approaching zero, the terms can be calculated using the dielectric constant of the solvent ε1 instead that of the solution ε12.

Results

Dielectric permittivity as a function of concentration for molecules 1-5b in THF (red symbols) and for 5b in chloroform (blue symbols) solutions. The highest concentrations refer to the solubility limit for each compound. Lines represent linear fits to the ε'(c) data. From the slopes the respective dipole moments were calculated.

Computational Methods

• DFT-B3LYP level of theory with the aug-cc-pVTZ basis set • The above combination has been shown recently to produce very accurate

results with respect to dipole moments and polarizabilities.

• In a subsequent calculation the methyl groups of 5a were replaced with n-heptyl chains in all-trans conformation and the new molecule 5b was optimized at the DFT-B3LYP level of theory and the 6-311++G(d,p) basis set.

• Gaussian 09 was employed for all calculations.

Results Table 1: Molecular structures, calculated HOMO-LUMO (eV), experimental optical gap (eV), calculated and measured dipole moments (D)

and calculated polarizabilities of the molecules studied in this work. Level of theory: DFT-B3LYP, basis set: aug-cc-pVTZ for molecules 1-5a

and 6-311++G(d,p) for molecule 5b. Arrows represent the direction of dipole moment (not proportional to its magnitude). Experimental

dipole moments were measured in THF. Molecule 5b was also measured in chloroform solution

No/

Chem. Formula

1/

C8N4H4Br2

2/

C8N4H6

3/

C10N6H4

4a/

C11N4H8Br2

5a/

C11N6H8

5b/

C25N6H30

Calc. LUMO (eV) -2.4 -2.0 -3.4 -2.3 -3.0 -2.9

Calc. HOMO (eV) -6.8 -6.6 -7.4 -6.3 -6.8 -6.6 Calc. ΔE

(HOMO- LUMO)

(eV)

4.4 4.6 4.0 4.0 3.8 3.7

Exp. Optical Gap

(eV) 3.4 3.5 3.0 3.0 3.0 2.9

Calc. Dipole Moment

(D) 9.6 10.0 9.6 11.5 12.3 12.7

Calc. Total Mol.

Polarizability

(× 10-40 C2m2J-1)

29.2 21.9 27.9 35.3 34.2 57.9

Exp. Dipole Moment

(D) 12.3 ± 0.4 10.5 ± 0.2 14.1 ± 0.7* 12 ± 1 10.9 ± 0.3

12.2 ± 0.3

11.9 ± 0.2**

* The higher dipole moment reflects complex formation with DMAC

**Measured in chloroform solution

Conclusions

• New hexasubstituted benzenes - the smallest neutral molecular species with the highest dipole moments as determined by dielectric spectroscopy and DFT methods.

• Based on the preparation of 4,5-diamino-3,6-dibromophthalonitrile (1), combined with a novel method to synthesize dihydrobenzimidazoles, these benzene derivatives have dipole moments in excess of 10 debye.

• Such dipole moments are desirable in ferroelectrics, non-linear optics and in organic photovoltaics.

Acknoledgements Jakob Wudarczyk

Prof. Klaus Müllen

Max Planck Institute for Polymer Research, Mainz, Germany

Dr. Dieter Schollmeyer

Institute of Organic Chemistry, University of Mainz, Germany

Vasilis Margaritis -

undergraduate student

Prof. George Floudas

Department of Physics, University of Ioannina, Greece.

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