Hendrik F. Hameka

Theoretical studies of the methyl rotational barrier in toluene

Abstract We report computations of the rotational barrier of the methyl group in toluene. The computations are based on the use of the gaussian 92 Program Package with the 6-311G∗∗ basis set. The results are 2.69 wavenumbers at the HF level of approximation and 5.02 wavenumbers at the MP2 level. These results compare favorably with the experimental value of 4.9 wavenumbers. It is shown that inclusion of the vibrational zero-point energy in the calculations is necessary for obtaining satisfactory results.

Interaction Effects on Lifetimes of Atomic Excitations

The apparent lifetime of an excited atom in a p state is investigated when another atom, in an s ground state, is present. The dependence of the lifetime on the distance RAB between the two atoms is obtained. It is found that the results for a p0 state differ somewhat from those for the p±1 states. (The axis of quantization is taken as the line joining the two atoms.)

THEORETICAL STUDIES OF THE INFRARED AND RAMAN SPECTRA OF PERYLENE

Abstract We present computations of the structure and vibrational frequencies of perylene at the Hartree–Fock and B3LYP (DFT) levels of theory using the standard 6-31G* basis set. A detailed analysis of the normal vibrational modes of perylene along with assignments of both symmetry and molecular motion are also presented. Empirical correction factors for all computational data are calculated and presented. The large size and high symmetry of the perylene make it an interesting candidate for a detailed study of vibrational normal modes of the molecule.

On the Use of Green Functions in Atomic and Molecular Calculations. I. The Green Function of the Hydrogen Atom

It is customary to derive the quantum‐mechanical theory of quasifree particles by means of Green‐function techniques, making use of the Green function of a free particle. It is pointed out here that similar techniques can be used in atomic and molecular calculations if use is made of the Green function of the hydrogen atom, rather than the Green function of a free particle. The Green function of the hydrogen atom is derived by means of contour integrations in the complex plane, following previous work by Meixner. We also derive a slightly modified Green function which is adapted to perturbation calculations of the ground state. Both of these Green functions are obtained as expansions in terms of spherical harmonics; the radial functions are expressed in terms of confluent hypergeometric functions.

Calculation of linear and nonlinear electric susceptibilities of conjugated hydrocarbon chains

We calculated the π electron contributions to the linear and nonlinear static electric susceptibilities of a linear conjugated hydrocarbon chain. We started from the Huckel equations for the π electrons in the presence of an electric field, and we expanded the equation in terms of the electric field by using perturbation theory. We solved the successive perturbation equations analytically, and we derived exact analytical expressions for the energy perturbations up to fourth order. We used these energy perturbations to derive values for χ(1)XX, χ(2)XXX, and χ(3)XXYY where the X axis is along the chain. We found that the molar linear susceptibility χ(1)XX is roughly proportional to the 2.8 power of N and that the nonlinear susceptibility χ(3)XXXX is roughly proportional to the 5.3 power of N. For larger values of N the π electron contributions to the susceptibilities become much larger than the σ electron contributions.

Theoretical studies of the infrared and Raman spectra of cubane

Abstract We present computations of the structure and of the vibrational frequencies of the cubane molecule at the Hartree-Fock and the MP2 levels of theory with the 6-311G ∗ basis set. We also present empirical correction factors for all computational data. The agreement between the corrected theoretical and the experimental data is satisfactory.

Born—Oppenheimer Approximation and the Calculation of Infrared Intensities

In evaluating transition moments it is customary to transform from the momentum representation to the dipole representation by making use of the commutator relations between the Hamiltonian and the particle coordinates. In the present paper we show that in the case of infrared, vibrational transitions it makes quite a difference whether we introduce the Born—Oppenheimer approximation before or after this transformation. In the first case the transition moment depends on the nuclear contribution to the molecular dipole moment and in the second case on the total dipole moment of the molecule. In order to dissolve this discrepancy we calculated the first‐order correction to the Born—Oppenheimer approximation. We introduced this correction in the transition moment calculations and we found that the correction terms bring the two different results into agreement with each other. It was found that the correction is quite small in the case where the Born—Oppenheimer approximation is introduced after the momentum...

Calculations of the energies, geometries and vibrational frequencies of the ground and first excited singlet states of toluene and p-cresol

Abstract We attempt to interpret the fluorescence of toluene and p -cresol from ab initio calculations on the ground state and the lowest excited singlet state of each molecule. We determine the energy minima and the optimized geometries of the ground states and of the lowest excited singlet states from 4 in 4 CASSCF computations using a 6–31G basis set. We also compute the vibrational frequencies of both molecules in the two states.

Improved calculation of nonlinear electric susceptibilities of conjugated hydrocarbon chains

We calculated the three relevant tensor components of the third‐order electric susceptibilities of conjugated hydrocarbon chains in order to determine the space fixed third‐order electric susceptibilities χxxxx–. We found that the space fixed susceptibility χxxxx differs significantly from the molecular parameter χXXXX.

Correlation of structure and vibrational spectra of the zwitterion L-alanine in the presence of water: an experimental and density functional analysis.

Infrared vibrational spectra were collected along with the vibrational circular dichroism (VCD) spectra for the zwitterions alpha-D-alanine, alpha-L-alanine, alpha-D-mannose and alpha-L-mannose as potassium bromide (KBr) pressed samples. VCD for D- and L-alanine dissolved in water was also measured and compared against the spectra resulting from KBr pressed samples. The experimental data were compared against the ab initio B3LYP/6-31G* optimized geometry. The zwitterion structure of alpha-L-alanine was stabilized by the addition of water molecules. Computationally, beta-L-mannose was studied and resulting expected VCD bands assigned. We present the molecular structures resulting VCD spectra and infrared vibrational spectra from experimentation as compared with the computed results.