Coupled calculation of vibrational frequencies and intensities

The combination of normal coordinate analysis with intensity calculations gives quantitative information about molecular force fields and the assignments of vibrational frequencies. Calculations of vibrational intensities by means of a standard CNDO/2 version give rise to satisfactory results for the IR intensities. However, the calculated Raman intensities often differ strongly from the experimental data. Inclusion of 2p-polarization functions on hydrogen in the usually used valence basis set is quite successful to obtain improved molecular polarizabilities as well as Raman intensities.     

Temperature dependence of the bandwidths and frequencies of some anthracene phonons. High-resolution Raman measurements

Using a coupled interferometer—spectrometer with a resolution of 0.02 cm^?1 we have measured the Raman band profiles of the four low-frequency anthracene phonons ω₁(a_g), ω₂(a_g), ω₆(b_g) and ω₇(b_g) in the temperature range 2–70 K. These phonons possess very narrow bandwidth at low temperature which are convinently measured under high resolution. In particular the two lowest-frequency phonons ω₁(a_g) and ω₆(b_g) have a bandwidth at 2 K of 0.045 cm^?1. The other two phonons ω₇(b_g) and ω₂(a_g) have bandwidths at 2 K of 0.165 and 0.4 cm^?1, respectively. A detailed analysis of the bandwidth variation with temperature was made in terms of three-phonon decay processes. The exrerimental variation of the bandwidth with temperature was correctly reproduced assuming a single down-and up-process. The following results were obtained: ω₁(a_g): 49.45 cm^?1 = 2×24.72 cm^?1, 49.45 cm^?1 = 98.45 cm^?1 ?49.0 cm^?1; ω₆(b_g): 57.50 cm^?1 = 2×28.75 cm^?1, 57.50 cm^?1 = 108.50 cm^?1 ?51.0 cm^?1; ω₇(b_g): 71.20 cm^?1 = 2×35.6 cm^?1, 71.20 cm^?1 = 120.20 cm^?1 ?49.0 cm^?1: ω₂(a_g): 82.40 cm^?1 = 57.50 cm^?1 +24.9 cm^?1, 82.40 cm^?1 = 138.4 cm^?1 ?56 cm^?1. The efficiency of the down- and up-processes is discussed in terms of the two-phonon density of states. The bandwidths at 2 K follows very closely the variation of the two-phonon sum density of states, whereas the relative importance of the up-processes follows well the two-phonon difference density of states. The anharmonic frequency shifts are corrected for the thermal expansion of the crystal using the Grüneisen single-phonon parameters and the thermal expansion coefficients given in the literature. This permits an estimation of the variation of the anharmonic shifts in the temperature range studied.     

Overtone intensities in resonance Raman scattering

A model calculation of resonance Raman scattering tensors has been carried out for a diatomic molecule with a harmonic potential for the ground state and a linear repulsive potential for the excited state. Expressions for scattering tensors have been obtained by using a series of recurrence formulas induced from the Green function of the nuclear hamiltonian of the repulsive potential of the excited state and nuclear wavefunctions for the harmonic potential. The relative scattering intensities of overtones depend on the gradient of the repulsive potential curve and are interpreted in terms of the overlap integrals between nuclear wavefunctions of upper and lower states.     

Coupled calculations of vibrational frequencies and intensities. III. IR and Raman spectra of ethylene oxide and ethylene sulfide

The experimental IR and Raman spectra of ethylene oxide have been reinvestigated with particular attention to the intensities. The absolute IR intensities have been measured for the gaseous state. The spectra have been simulated by using a normal coordinate analysis coupled with a CNDO determination of the intensities. The intensity calculation using polarization functions appears to be more reliable than the standard version. Furthermore, the force field has been extended for ethylene sulfide.     

Evaluation of range-separated hybrid density functionals for the prediction of vibrational frequencies, infrared intensities, and Raman activities

We present an assessment of different density functionals, with emphasis on range-separated hybrids, for the prediction of fundamental and harmonic vibrational frequencies, infrared intensities, and Raman activities. Additionally, we discuss the basis set convergence of vibrational properties of H2O with long-range corrected hybrids. Our results show that B3LYP is the best functional for predicting vibrational frequencies (both fundamental and harmonic); the screened-PBE hybrid (HSE) density functional works best for infrared intensities, and the long-range corrected PBE (LC-omegaPBE), M06-HF, and M06-L density functionals are almost as good as MP2 for predicting Raman activities. We show the predicted Raman spectrum of adenine as an example of a medium-size molecule where a DFT/Sadlej pVTZ calculation is affordable and compare our results against the experimental spectrum.     

Vibronic coupling and Raman intensities of pyrazine

The fluorescence spectrum of pyrazine vapour and the Raman spectra of liquid pyrazine excited at various wavelengths were observed. The appearance of the long progression of the hydrogen bending vibration ν₅ (b_2g) in the fluorescence spectrum and a remarkable preresonance effect of the Raman line of the same vibration confirm the theoretical prediction given by Albrecht.     

Conformational flexibility in open chain molecules: chiral and achiral alkanes

Conformational partition functions of chiral and achiral alkanes have been computed by using a continuum approach (instead of rotational isomeric state approximations). The accessible conformational space per bond depends upon the structure of the compound and is only in the range of 5–13% of the maximum accessible range. In order to partly overcome the intrinsic ambiguity of the term “conformational flexibility”, the distinction between number flexibility (a measure of the number of accessible energy minima) and space flexibility (a measure of the total allotted space) is proposed. Further, the conformational versatility of each bond of a molecule is evaluated in terms of the a priori probability density function of that bond, and it is shown that the use of this function permits a comparison of the relative conformational flexibilities of the individual bonds, which is particularly useful for molecules having more than two rotation angles (where the conventional energy maps cannot be used). Optical rotations are calculated for a series of chiral alkanes by combining the continuum approach for conformational analysis and a recent optical activity calculation scheme. Contributions of single bonds to the molar optical rotation are evaluated and discussed. The influence of temperature upon conformational and chiral properties is evaluated.     

Induced changes in stimulated Raman scattering intensities

The stimulated Raman scattering (SRS) intensity of neat liquids and of binary liquid mixtures was measured as a function of the power of the pump field and of an additional radiation field at the Stokes frequency. In neat p-xylene SRS intensity transfer, form one vibrational mode to another, was observed. In benzene/nitrobenzene mixtures it was found possible, at various concentrations, to selectively generate SRS from one component in the mixture, including the minor one. Implications of the results for the selective excitation by the SRS process of a single species in a mixture are discussed.     

Vibrational frequencies and infrared absorption intensities of 1,2-dibromoethane

Infrared and Raman spectra of 1,2-dibromoethane CH₂BrCH₂Br and CD₂BrCD₂Br were observed in the liquid state, and the fundamental frequencies were determined by comparison with those of related molecules. Infrared absorption intensities of fundament bands were measured in the liquid state, and the intensity data were interpreted on the basis of the valence-optical theory. From the converged value of a population ratio, the energy difference between the trans and gauche isomers was determined, which was in good agreement with the value obtained from the temperature effect of the IR spectrum.     

Solvent dependence of electronic transition intensities

Most of the research on solvent effects on the electronic spectra of organic molecules has been concerned with frequency shifts. Solvent induced intensity changes, however, have not received much attention. At present there is no simple, general theory that relates: (a) the solvent induced changes in electronic transition intensities to (b) the macroscopic properties of the solvent. In this article we derive an equation that provides a quantitative interpretation for the changes in the absorption intensities. We show that solvent induced intensity changes are related to van der Waals constants for solvent and solute. Absorption data, some from previous investigations, are presented to show the usefulness and limitations of the theory.     

Ab initio simulation of benzene Raman intensities

C₆H₆ Raman scattering activities calculated from harmonic model ab initio Hartree–Fock 6–311 ++ G(d, p) polarizability derivatives (and harmonic force fields calculated at the same level) accurately simulate experiment (to within 1% for the a_1g modes). Accurate predictions are also made for the e_2g modes (to within 5% for ν₇ and ν₉, and more poorly for ν₆ and ν₈ [in Fermi resonance with ν₆ + ν₁]) and for the e_1g out-of-plane mode, ν₁₀. Only the ν₆ in-plane CCC bending mode scattering activity is found to be anomalous. Systematic variation of the basis set indicates that the benzene scattering activities and depolarization ratios are strongly dependent on inclusion of both carbon and hydrogen atom diffuse functions in the basis set. Predictions are also made for ¹²C₆D₆ and for unmeasured intensities in ¹³C₆H₆. Measurements of a_1g mode scattering activities in the latter molecule are predicted to be useful in testing the harmonic Hartree–Fock Raman intensity model.     

Conformational dependence of charges in protein simulations

We have studied the conformational dependence of molecular mechanics atomic charges for proteins by calculating the charges fitted to the quantum mechanical (QM) electrostatic potential (ESP) for all atoms in complexes between avidin and seven biotin analogues for 20 snapshots from molecular dynamics simulations. We have studied how various other charge sets reproduce those charges. The QM charges, even if averaged over all snapshots or all residues, in general have a larger magnitude than standard Amber charges, indicating that the restraint toward zero in the restrained ESP method is too strong. This has a significant influence on the electrostatic conformational energies and the interaction energy between the biotin ligand and the protein, giving a difference between the QM and Amber charges of 43 and 8 kJ/mol for the negatively charged and neutral biotin analogues, respectively (3-4%). However, this energy difference is strongly reduced if the solvation energy (calculated by the Poisson-Boltzmann or Generalized Born methods) is added, viz., to 7 kJ/mol for charged and 3 kJ/mol for uncharged ligand. In fact, charges need to be recalculated with a QM method only for residues within 7 or 4 A of the ligand, if the error should be less than 4 kJ/mol. Unfortunately, the QM charges do not give significantly better MM/PBSA estimates of ligand-binding affinities than standard Amber charges.     

Coupled calculation of vibrational frequencies and intensities: VII. Absolute intensities of methane and deuterated derivatives

The absolute IR and Raman intensities of methane and deuterated derivatives are calculated with a CNDO method. Discrepancies with the experiment are discussed and scale factors proposed.     

The effect of absorbancy upon Raman intensities in solutions

Reasonable agreement is obtained in the relationship between intensities of Raman lines as measured experimentally and as calculated from an equation derived on the basis of absorbancy laws. A direct relationship between Raman intensity and concentration exists with excitation outside an absorption band, and an inverse relationship over some or all concentration ranges is found with excitation within an absorption band.     

Polarized Raman spectra and intensities of aliphatic amino acids

Raman spectra of aliphatic α-l-amino acids, glycine, alanine, and valine were re-investigated both in aqueous solution and deuterium oxide solution. The spectra were taken of the zwitterionic and of the completely deprotonated form of the amino acids. Spectra of leucine and isoleucine were studied in water at the isoelectric point. Spectra were recorded both with parallel and perpendicular polarization and the isotropic and anisotropic scattering components were isolated.The integrated intensities of CH stretch, CC stretch and carboxylate bend vibrations are discussed. Linear relations between the number of CC and CH bonds and the total scattered intensity in the appropriate spectral regions are observed. The sum over the carboxylate modes shows characteristic intensities for the first three members of the aliphatic amino acids.An increase of isotropic scattering of ϱ_co2 near 510 cm⁻¹ with increasing chain length of the amino acid (or with increasing concentration) is interpreted as the result of micelle formation.     

Raman intensities of ethylene and deuterated derivatives in the gas phase

Experimental gas phase Raman scattering differential cross sections and depolarization ratios of ethylenes C₂H₄, C₂H₃D, C₂H₂D₂-a, C₂HD₃ and C₂D₄ are reported. An interpretation of these data is accomplished using the bond polarizability model. Within constraints imposed to the first order parameters, the CH bond polarizability derivatives here obtained compare quite well with the values reported for the same bond in other hydrocarbons. The CC bond electrooptical properties are found to be between those of the CC in ethane and CC in acetylene.     

Conformational dependence of intramolecular vibrational redistribution in methanol

Previous state-selected spectra of methanol in the 5nu(1) OH stretch overtone region [O. V. Boyarkin, T. R. Rizzo, and D. S. Perry, J. Chem. Phys. 110, 11346 (1999)] revealed a structure indicating an intramolecular vibrational redistribution on three time scales. Whereas in that work, methanol in the 5nu(1) bright state was prepared close to the staggered conformation, methanol in the "partially eclipsed" conformation is prepared here by double resonance excitation through a torsionally excited intermediate state. The excited molecules are detected by infrared laser assisted photofragment spectroscopy. In partially eclipsed methanol, the strong coupling of the nu(1) OH stretch to the nu(2) CH stretch becomes weaker, but the coupling responsible for the widths of the narrowest features becomes stronger.     

Temperature dependence of lattice distortions in polyethylene

Summary Melt-crystallized samples of polyethylene show a reversible change of the line-width in X-ray wide angle scattering. The width increases with decreasing temperature, the largest changes occur in the temperature ranges of the- and-relaxation processes. Fourier analyses of the line profiles using the method of Warren and Averbach are indicative of strain variances which can be attributed to stress variances over larger domains in the semi-crystalline superstructure. An explanation for this effect is found in the stress parallel to the planes of the lamellae produced by the differences of the thermal expansion coefficients of the crystalline and amorphous domains in the lamellar two-phase systems. The magnitude of the stress is determined by the difference of the thermal expansion coefficients as well as the Young's moduli of the domains whereas the stress variances are related to the statistics of the lamellar thicknesses.With 23 figures and 3 tables