Calculation of absolute Raman scattering cross-sections using vibrational self-consistent field/vibrational configuration interaction wave functions.

In the present study, the differential scattering cross-sections, depolarization ratios and Raman shifts of small molecular systems are obtained from configuration iteration wave functions of vibrational self-consistent field (VSCF) states. The transition polarizabilities were modeled using the Placzek approximation, neglecting those contributions not arising from the electric dipole mechanism. This theoretical approach is considered a good approximation for samples that absorb in the UV range if the excitation radiation falls in the visible region, as is the case of the molecules selected for the present study, namely: water, methane, and acetylene. Potential energy and electronic polarizability surfaces are calculated by the CCSD(T) and CC3 methods with aug-cc-p(C)V(T,Q,5)Z basis sets. The vibrational Hamiltonian includes the vibrational angular momentum contribution of the Watson kinetic energy operator. As expected, due to the variational nature of the VSCF and vibrational configuration interaction (VCI) methods, the Raman transition wavenumbers are substantially improved over the harmonic predictions. Surprisingly, the scattering cross-sections obtained using the harmonic approximation or the VSCF method better agrees with the experimental values than those cross-sections predicted using VCI wave functions. The more significant deviations of the VCI results from the experimental reference may be related to the significant uncertainties of the measured cross-sections. Still, it may also indicate that the VCI Raman transition moments may require a more accurate description of the electronic polarizability surface. Finally, the depolarization ratios calculated for H2 O and C2 D2 using harmonic and VCI wave functions have similar accuracy, whereas, for C2 H2 and C2 HD, the VCI results are more accurate.

AC/DC Analysis: Broad and Comprehensive Approach to Analyze Infrared Intensities at the Atomic Level.

We present a complete theoretical protocol to partition infrared intensities into terms owing to individual atoms by two different but related approaches: the atomic contributions (ACs) show how the entire molecular vibrational motion affects the electronic structure of a single atom and the total infrared intensity. On the other hand, the dynamic contributions (DCs) show how the displacement of a single atom alters the electronic structure of the entire molecule and the total intensity. The two analyses are complementary ways of partitioning the same total intensity and conserve most of the features of the total intensity itself. Combined, they are called the AC/DC analysis. These can be further partitioned following the CCTDP (or CCT) models according to the population analysis chosen by the researcher. The main conceptual features of the equations are highlighted, and representative numerical results are shown to support the interpretation of the equations. The results are invariant to rotation and translation and can readily be extended to molecules of any size, shape, or symmetry. Although the AC/DC analysis requires the choice of a charge model, all charge models that correctly reproduce the total molecular dipole moment can be used. A fully automated protocol managed by the Placzek program is made available, free of charge and with input examples.

Fully Anharmonic Vibrational Resonance Raman Spectrum of Diatomic Systems.

A study is presented on the resonance Raman (RR) spectrum based on fully anharmonic wave functions and energies obtained from ab initio multireference potential energy curves of diatomic systems. The vibrational problem is numerically solved using a variational stochastic method or the Cooley-Numerov method, as implemented in Le Roy's LEVEL program. Anharmonic Franck-Condon and Herzberg-Teller integrals are numerically evaluated, and the RR polarizability is calculated within the time-independent framework of the RR theory. At the harmonic level, the differential cross sections show faster convergence with respect to the number of intermediate vibrational states than what is obtained from anharmonic wave functions. Twice as many intermediate states are required to achieve the same convergence in the RR intensities as observed within the harmonic model. The anharmonic spectra evaluated for H2, C2, and O2 molecules show that RR intensities are strongly affected by anharmonic effects. They differ from their harmonic counterparts not only in the position of the peaks but also in the absolute and relative intensities.

Can the Resonance Raman Optical Activity Spectrum Display Sign Alternation?

The monosignate character of resonance Raman optical activity (RROA) spectra has been often taken as granted in experimental and computational approaches, on the basis of basic theoretical approximations only considering resonance with a single electronic state of the molecule and the scattering process to be governed by the Franck-Condon mechanism. We show in this letter for the first time that, by resorting to a fully quantum mechanical (QM) methodology able to take into account all terms entering the general definition of RROA, and which considers excited state interference and Herzberg-Teller effects, sign alternation and at the same time intensity enhancement in RROA spectra is obtained. Such features constitute an important milestone toward the exploration of RROA of a wide range of chiral biological molecules.

Characteristic infrared intensities of carbonyl stretching vibrations.

The experimental infrared fundamental intensities of gas phase carbonyl compounds obtained by the integration of spectral bands in the Pacific Northwest National Laboratory (PNNL) spectral database are in good agreement with the intensities reported by other laboratories having a root mean square error of 27 km mol(-1) or about 13% of the average intensity value. The Quantum Theory of Atoms in Molecules/Charge-Charge Transfer-Counterpolarization (QTAIM/CCTCP) model indicates that the large intensity variation from 61.7 to 415.4 km mol(-1) is largely due to static atomic charge contributions, whereas charge transfer and counterpolarization effects essentially cancel one another leaving only a small net effect. The Characteristic Substituent Shift Model estimates the atomic charge contributions to the carbonyl stretching intensities within 30 km mol(-1) or 10% of the average contribution. However, owing to the size of the 2 × C × CTCP interaction contribution, the total intensities cannot be estimated with this degree of accuracy. The dynamic intensity contributions of the carbon and oxygen atoms account for almost all of the total stretching intensities. These contributions vary over large ranges with the dynamic contributions of carbon being about twice the size of the oxygen ones for a large majority of carbonyls. Although the carbon monoxide molecule has an almost null dipole moment contrary to the very polar bond of the characteristic carbonyl group, its QTAIM/CCTCP model is very similar to those found for the carbonyl compounds.

Origin invariance in vibrational resonance Raman optical activity.

A theoretical investigation on the origin dependence of the vibronic polarizabilities, isotropic and anisotropic rotational invariants, and scattering cross sections in Resonance Raman Optical Activity (RROA) spectroscopy is presented. Expressions showing the origin dependence of these polarizabilities were written in the resonance regime using the Franck-Condon (FC) and Herzberg-Teller (HT) approximations for the electronic transition moments. Differently from the far-from-resonance scattering regime, where the origin dependent terms cancel out when the rotational invariants are calculated, RROA spectrum can exhibit some origin dependence even for eigenfunctions of the electronic Hamiltonian. At the FC level, the RROA spectrum is completely origin invariant if the polarizabilities are calculated using a single excited state or for a set of degenerate states. Otherwise, some origin effects can be observed in the spectrum. At the HT level, RROA spectrum is origin dependent even when the polarizabilities are evaluated from a single excited state but the origin effect is expected to be small in this case. Numerical calculations performed for (S)-methyloxirane, (2R,3R)-dimethyloxirane, and (R)-4-F-2-azetidinone at both FC and HT levels using the velocity representation of the electric dipole and quadrupole transition moments confirm the predictions of the theory and show the extent of origin effects and the effectiveness of suggested ways to remove them.

Core-valence correlation effects on IR calculations: the BF3 and BCl3 cases.

The first theoretical results of core-valence correlation effects are presented for the infrared wavenumbers and intensities of the BF3 and BCl3 molecules, using (double- and triple-zeta) Dunning core-valence basis sets at the CCSD(T) level. The results are compared with those calculated in the frozen core approximation with standard Dunning basis sets at the same correlation level and with the experimental values. The general conclusion is that the effect of core-valence correlation is, for infrared wavenumbers and intensities, smaller than the effect of adding augmented diffuse functions to the basis set, e.g., cc-pVTZ to aug-cc-pVTZ. Moreover, the trends observed in the data are mainly related to the augmented functions rather than the core-valence functions added to the basis set. The results obtained here confirm previous studies pointing out the large descrepancy between the theoretical and experimental intensities of the stretching mode for BCl3.

Algorithms for computer detection of symmetry elements in molecular systems.

Simple procedures for the location of proper and improper rotations and reflexion planes are presented. The search is performed with a molecule divided into subsets of symmetrically equivalent atoms (SEA) which are analyzed separately as if they were a single molecule. This approach is advantageous in many aspects. For instance, in those molecules that are symmetric rotors, the number of atoms and the inertia tensor of the SEA provide one straight way to find proper rotations of any order. The algorithms are invariant to the molecular orientation and their computational cost is low, because the main information required to find symmetry elements is interatomic distances and the principal moments of the SEA. For example, our Fortran implementation, running on a single processor, took only a few seconds to locate all 120 symmetry operations of the large and highly symmetrical fullerene C720, belonging to the Ih point group. Finally, we show how the interatomic distances matrix of a slightly unsymmetrical molecule is used to symmetrize its geometry.

Quantum theory of atoms in molecules charge-charge flux-dipole flux models for the infrared intensities of X(2)CY (X = H, F, Cl; Y = O, S) molecules.

The molecular dipole moments, their derivatives, and the fundamental IR intensities of the X2CY (X = H, F, Cl; Y = O, S) molecules are determined from QTAIM atomic charges and dipoles and their fluxes at the MP2/6-311++G(3d,3p) level. Root-mean-square errors of +/-0.03 D and +/-1.4 km mol(-1) are found for the molecular dipole moments and fundamental IR intensities calculated using quantum theory of atoms in molecules (QTAIM) parameters when compared with those obtained directly from the MP2/6-311++G(3d,3p) calculations and +/-0.05 D and 51.2 km mol(-1) when compared with the experimental values. Charge (C), charge flux (CF), and dipole flux (DF) contributions are reported for all the normal vibrations of these molecules. A large negative correlation coefficient of -0.83 is calculated between the charge flux and dipole flux contributions and indicates that electronic charge transfer from one side of the molecule to the other during vibrations is accompanied by a relaxation effect with electron density polarization in the opposite direction. The characteristic substituent effect that has been observed for experimental infrared intensity parameters and core electron ionization energies has been applied to the CCFDF/QTAIM parameters of F2CO, Cl2CO, F2CS, and Cl2CS. The individual atomic charge, atomic charge flux, and atomic dipole flux contributions are seen to obey the characteristic substituent effect equation just as accurately as the total dipole moment derivative. The CH, CF, and CCl stretching normal modes of these molecules are shown to have characteristic sets of charge, charge flux, and dipole flux contributions.