Coupled-cluster calculations of vibrational Raman optical activity spectra

We present the first calculations of Raman optical activity spectra at the coupled-cluster level of theory. Calculations are presented for (S)-methyloxirane and compared to recent experimental gas-phase measurements as well as the results obtained at the Hartree-Fock and density functional level of theory using the popular B3LYP functional. For the experimentally relevant frequency region of 400-1600 cm(-1), the Hartree-Fock, B3LYP and coupled-cluster spectra are very similar when the same force field is used, and the results also agree well with experiment. For high-frequency vibrational modes, differences in the ROA difference parameters are observed and are analyzed. The new coupled-cluster ROA code will allow for critical benchmarking of the accuracy of modern exchange-correlation functionals in the calculation of ROA spectra.     

A frequency-weighted sum rule for vibrational Raman optical activity

The sums of frequency-weighted vibrational Raman optical activity (ROA) intensities of isotopic molecules are shown to be related through the elements of the inverse force constant matrix. These relations could be used to determine force constants from experimental ROA intensities.     

A combined theoretical and experimental study of the structure and vibrational absorption, vibrational circular dichroism, Raman and Raman optical activity spectra of the L-histidine zwitterion

A combined theoretical and experimental study of the vibrational absorption (VA)/IR, vibrational circular dichroism (VCD), Raman and Raman optical activity (ROA) spectra of l-histidine in aqueous solution has been undertaken to answer the questions (i) what are the species present and (ii) which conformers of the species are present under various experimental conditions. The VA spectra of l-histidine have been measured in aqueous solution and the spectral bands which can be used to identify both species (cation, zwitterion, anion) and conformer of the species have been identified and subsequently used to identify the species (zwitterion) and conformer (gauche minus minus, gauche minus plus for the side chain dihedral angles) present in solution at pH 7.6. The VCD spectral intensities have been used subsequently in combination with further theoretical studies to confirm the conclusions that have been arrived at by only analyzing the VA/IR spectra. Finally a comparison of measured Raman and ROA spectra of l-histidine with Raman and ROA spectral simulations for the conformers and species derived from the combined VA/IR and VCD experimental and theoretical work is presented as a validation of the conclusions arrived at from VA/IR and VCD spectroscopy. The combination of VA/IR and VCD with Raman and ROA is clearly superior and both sets of experiments should be performed.     

Relevance of the electric-dipole--electric-quadrupole contribution to Raman optical activity spectra

We examine the importance of the electric-dipole--electric-quadrupole polarizability tensor in the intensity theory of Raman optical activity (ROA) spectra. Using density functional theory, ROA spectra of organic cyclic compounds, alanine, oligoalanines, and examples from the literature are analyzed in detail, and a statistical investigation is performed. It is found that the contribution of the electric-dipole--electric-quadrupole tensor is often small, except for some special cases that involve C-H stretching vibrations.     

Experimental and ab initio theoretical vibrational Raman optical activity of alanine

The vibrational Raman optical activity (ROA) spectra of l-alanine in water, 1 N NaOH and 1 N HCl between 720 and 1500 cm⁻¹ measured in backscattering are reported. Unlike the associated vibrational circular dichroism (VCD), the main ROA features are relatively insensitive to pH changes. Ab initio Raman and ROA intensities were evaluated using 6-31G and 6-31G* basis sets and found to agree remarkably well with the experimental parameters in the lower-frequency region.     

Conformational analyses of peptides and proteins by vibrational Raman optical activity

Recent developments of vibrational Raman optical activity (ROA) spectroscopy enabled the detailed analyses of the backbone and side chain conformations of peptides and proteins in solution phases. ROA can be used as a powerful analytical technique for determining not only the structures of conformers, but also their populations even for systems in fast conformational equilibria where NMR spectroscopy is difficult to be applied. ROA enabled the monitoring of the secondary structures of denatured or unfolded proteins, such as an amyloid fibril and its prefibril intermediates.     

Ab initio derivative calculation of vibrational circular dichroism

The recent formalism of Stephens for the calculation of rotational strength in vibrational circular dichroism has been implemented, exploiting the analytical derivative technique for ab initio Hartree-Fock wavefunctions.     

Basis set and density functional dependence of vibrational Raman optical activity calculations

We present an extensive investigation of the dependence of the scattering intensity difference of right and left circularly polarized light observed in vibrational Raman optical activity (VROA) on the choice of basis set and exchange-correlation functional. These dependencies are investigated for five molecules for which accurate experimental data are available: (S)-methyloxirane, (R)-epichlorhydrin, (S)-glycidol, (M)-spiro[2,2]pentane-1,4-diene, and (M)-sigma-[4]-helicene. Calculations are presented using the SVWN exchange-correlation functional (LDA), the BLYP exchange-correlation functional, and the B3LYP hybrid functional, using six different basis sets: the cc-pVDZ, cc-pVTZ, aug-cc-pVDZ, aug-cc-pVTZ, Sadlej's polarized basis set, and a minimal VROA basis set recently proposed by Zuber and Hug. It is demonstrated that results from pure gradient-corrected and hybrid functionals are comparable and that the aug-cc-pVDZ and aug-cc-pVTZ basis sets yield similar results. Furthermore, the combination of the small basis set by Zuber and Hug with an accurate force field represents the best compromise between computational accuracy and computational efficiency.     

Experimental and ab initio theoretical vibrational Raman optical activity of tartaric acid

The vibrational Raman optical activity (ROA) spectra of (2R,3R)-(+) tartaric acid-d₀ in H₂O and (2R,3R)-(+) tartaric acid-d₄ in D₂O between 300 and 1800 cm⁻¹ measured in backscattering are reported. Ab initio Raman intensifies were evaluated using basis sets at 6-31G, 6-31G* and double zeta plus polarization (DZP) levels. Ab initio ROA intensities were obtained at two levels: in one calculation both the normal coordinates and the polarizability and optical activity tensor derivatives were evaluated with the 6-31G basis set; in a second calculation normal coordinates obtained with the DZP basis set were used to evaluate the normal coordinate derivatives of polarizability and optical activity tensors from the corresponding Cartesian derivative tensors obtained with the 6-31G basis set. Sufficiently good correlation was found between many of bands in the theoretical and experimental Raman and ROA spectra for both the -d₀ and -d₄ species to confirm that the absolute configuration of the ( + )-enantiomer is indeed (2R,3R) and to suggest that the trans COOH and trans COOD conformations are dominant. Tartaric acid-d₄ shows very similar ROA to tartaric acid itself in the range 300–800 cm⁻¹ but quite different in the range 800–1450 cm⁻¹, which provides insight into the influence of normal mode composition on ROA spectra. It was found that the normal mode compositions are much more sensitive to the level of basis set used than the polarizability and optical activity tensor derivatives.     

The vibrational Raman spectra of selenium trioxide ag

The vibrational Raman spectra of selenium trioxide have been observed in the solid and vapour phases for the same sample. The spectrum of the vapour phase, which essentially arises from the monomeric species SeO₃, has provided for the first time values of the Raman-active ν₁, ν₃ and ν₄ wavenumbers of SeO₃. The spectrum of the solid phase represents an improvement on previous work and has enabled a partial assignment of the tetrameric species (SeO₃)₄ to be made.     

Far IR and Raman vibrational spectra of nitramines

Vibrational spectra of several nitramines in the long-wave region (50–450 cm⁻¹) were studied. The frequencies of intra- and intermolecular vibrations were separated and a tentative assignment of the frequencies of self-associative complexes was performed. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 11, pp. 2241–2244, November, 1998.     

Theoretical determination of the vibrational Raman optical activity signatures of helical polypropylene chains.

Raman and vibrational Raman optical activity (VROA) spectra of helical conformers of polypropylene chains are simulated using ab initio methods to unravel the relationships between the vibrational signatures and the primary and secondary structures of the chains. For a polypropylene chain containing three units, conformational effects are shown to lead to more acute signatures for VROA than for Raman spectra. In addition to regular polypropylene chains, which can display right and left helicities with the same probability, chirality and therefore helicity are enforced by substituting one chain end with a phenyl group. The simulations predict that the threefold helical structures, which correspond to (TG)(N) conformations of the backbone, have a specific VROA backward signature in the form of an intense couplet around 1100 cm(-1). This couplet is associated with collective wagging and twisting motions, while most of its intensity comes from the anisotropic invariants combining normal coordinate derivatives of the electric dipole-electric dipole polarizability and of the electric dipole-magnetic dipole polarizability. A similar signature has already been found in model helical polyethylene chains, whereas it is very weak in forward VROA.     

Resonance vibrational Raman optical activity: a time-dependent density functional theory approach

We present a method to calculate both on- and off-resonance vibrational Raman optical activities (VROAs) of molecules using time-dependent density functional theory. This is an extension of a method to calculate the normal VROA by including a finite lifetime of the electronic excited states in all calculated properties. The method is based on a short-time approximation to Raman scattering and is, in the off-resonance case, identical to the standard theory of Placzek. The normal and resonance VROA spectra are calculated from geometric derivatives of the different generalized polarizabilites obtained using linear response theory which includes a damping term to account for the finite lifetime. Gauge-origin independent results for normal VROA have been ensured using either the modified-velocity gauge or gauge-included atomic orbitals. For the resonance VROA only the modified-velocity gauge has been implemented. We present some initial results for H(2)O(2) and (S)-methyloxirane and compare with predictions from a simple two-state approximation.     

Electronic and vibrational resonance Raman spectra of octamethyluranocene

The Raman spectrum of bis(tetramethylcyclo-octatetraene)uranium (U(TMCOT)₂), excited in resonance with its visible charge-transfer transitions shows an anomalously polarized electronic band at 473 cm^?1, twice as broad as the analogous band of uranocene, at 466 cm^?1. The broadening is attributed to crystal-field splitting associated with the lowered symmetry introduced by the methyl group, and/or a distribution of rotamer populations. Totally symmetric vibrational modes are observed at 879, 750, 580, 513 and 95 cm^?1; possible assignments are discussed.     

Quantum chemical calculation of vibrational spectra of large molecules--Raman and IR spectra for Buckminsterfullerene

In this work we demonstrate how different modern quantum chemical methods can be efficiently combined and applied for the calculation of the vibrational modes and spectra of large molecules. We are aiming at harmonic force fields, and infrared as well as Raman intensities within the double harmonic approximation, because consideration of higher order terms is only feasible for small molecules. In particular, density functional methods have evolved to a powerful quantum chemical tool for the determination of the electronic structure of molecules in the last decade. Underlying theoretical concepts for the calculation of intensities are reviewed, emphasizing necessary approximations and formal aspects of the introduced quantities, which are often not explicated in detail in elementary treatments of this topic. It is shown how complex quantum chemistry program packages can be interfaced to new programs in order to calculate IR and Raman spectra. The advantages of numerical differentiation of analytical gradients, dipole moments, and static, as well as dynamic polarizabilities, are pointed out. We carefully investigate the influence of the basis set size on polarizabilities and their spatial derivatives. This leads us to the construction of a hybrid basis set, which is equally well suited for the calculation of vibrational frequencies and Raman intensities. The efficiency is demonstrated for the highly symmetric C(60), for which we present the first all-electron density functional calculation of its Raman spectrum.     

Solvent effects on Raman optical activity spectra calculated using the polarizable continuum model

The integral equation formulation of the polarizable continuum model (IEFPCM) has been extended to the calculation of solvent effects on vibrational Raman optical activity spectra. Gauge-origin independence of the differential scattering intensities of right and left circularly polarized light is ensured through the use of London atomic orbitals. Density functional theory (DFT) calculations have been carried out for bromochlorofluoromethane, methyloxirane, and epichlorhydrin. The results indicate that solvent effects on the ROA differential scattering intensities can be substantial, and vary in sign and magnitude for different vibrational modes. It is demonstrated that both direct and indirect effects are important in determining the total solvent effects on the ROA differential scattering intensities. Local field effects are shown to be in general small, whereas electronic nonequilibrium solvation has a profound effect on the calculated solvent effects compared to an equilibrium solvation model. For molecules with several conformations, the changes in the relative stability of the different conformers also lead to noticeable changes in the ROA spectra.     

Quantum chemical calculation of force constants and vibrational spectra

As a result of the development of direct derivative methods and improved computational facilities, ab initio quantum chemical calculations have become an increasingly important source of information for the determination of molecular force constants. Within the Hartree-Fock (H-F) SCF model and using moderate size basis sets such calculations are now economically feasible for molecules of up to 2o–3o atoms. At this level of theory, harmonic diagonal force constants are overestimated by 1o–3o%, corresponding to 5–15% in the frequencies. However, the largely systematic errors can be accounted for by simple empirical corrections. The resulting SQM (Scaled Quantum Mechanical) force fields are probably the most reliable ones available at present for larger molecules. Calculated infrared intensities are semi-quantitatively correct. Beyond the H-F model, large scale calculations including electron correlation give great improvements in the force constants, but there are still residual errors of a few percent.     

Improved DFT calculation of Raman spectra of silicates

Very accurate vibrational spectra of silicates are obtained from DFT calculations if the appropriate Hamiltonian is used. Theoretical considerations suggest that the Hartree-Fock component of ACM1 hybrid functionals should be 1/6 instead of 1/4 for this class of compounds. When applied to the PBE functional this removes the scaling error of the calculated vibrational frequencies. Calculations using this PBE(n = 6) functional in combination with optimized Gaussian basis sets result in very small remaining deviations between observed and calculated Raman shifts, with standard uncertainties of ≈3.5 cm⁻¹, maximum deviations of ≈10 cm⁻¹, and no significant systematic trends. This has been confirmed for a wide range of silicate structures, for which high-quality Raman spectra have been published: forsterite α-Mg₂SiO₄ (nesosilicate), γ-Y₂Si₂O₇ (sorosilicate), K₂Ca₃Si₃O₁₀ (oligosilicate), K₂Ca₄Si₈O₂₁ (phyllosilicate), and α-quartz SiO₂ (tectosilictae).     

Theoretical calculation of the vibrational spectra of some XHn type molecules

The potential function of some molecules of type XH_n has been obtained by a priori calculations of the total energy, within the Born Oppenheimer approximation, for several geometrical configurations. These functions have been used to calculate the simply excited vibrational levels. The calculated values of the electric dipole moment for the different geometrical configurations has enabled the computation of its derivative with respect to the nuclear coordinates. The results reported are critically discussed and some explanations are presented to justify the discrepancies found with the experimental data.

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Zusammenfassung Mittels einer apriorischen Berechnung der Gesamtenergie nach der Born-Oppenheimer-Methode ist die Potentialfunktion für einige Moleküle der Art XH_n in verschiedenen Konfigurationen erhalten worden. Diese Funktionen sind für die Berechnung der monoerregten SchwingungszustÄnde gebraucht worden. Die berechneten Werte des elektrischen Dipolmoments für verschiedene Geometrien haben die Berechnung der Ableitungen des Dipolmoments nach den Kernkoordinaten erlaubt. Die erhaltenen Resultate werden diskutiert und einige ErklÄrungen vorgeführt, um die gefundenen Unterschiede von den experimentellen Ergebnissen zu klÄren.

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Résumé La fonction potentiel de quelques molécules XH_n a été obtenue par le calcul a priori de l'énergie moléculaire, dans l'approximation de Born et Oppenheimer, pour plusieures configurations géométriques. Ces fonctions ont été utilisées pour calculer les vibrations monoexcitées. Les valeurs calculées du moment de dipole électrique pour différentes configurations donnent la possibilité de calculer ses dérivées par rapport aux coordonées nucléaires. On donne des justifications a l'accord peu satisfaisant entre les résultats et l'expérience.