Abstract
In this paper, we show that the standard second-order vibrational perturbation theory (VPT2) for Abelian groups can be used also for non-Abelian groups without employing specific equations for two- or threefold degenerate vibrations but rather handling in the proper way all the degeneracy issues and deriving the peculiar spectroscopic signatures of non-Abelian groups (e.g., -doubling) by a posteriori transformations of the eigenfunctions. Comparison with the results of previous conventional implementations shows a perfect agreement for the vibrational energies of linear and symmetric tops, thus paving the route to the transparent extension of the equations already available for asymmetric tops to the energies of spherical tops and the infrared and Raman intensities of molecules belonging to non-Abelian symmetry groups. The whole procedure has been implemented in our general engine for vibro-rotational computations beyond the rigid rotor/harmonic oscillator model and has been validated on a number of test cases.
Highlights
Among the different approaches available to go beyond the rigid rotor/harmonic oscillator approximation,[11−35] those based on perturbation theory applied to the expansion of the nuclear Hamiltonian in the power series of products of vibrational and rotational operators are appealing for their remarkable cost/performance ratio, at least for semi-rigid molecular systems
generalized VPT2 (GVPT2) is built on top of deperturbed VPT2 (DVPT2) by adding a final step to calculate the anharmonic energies as eigenvalues of a variational matrix, whose diagonal elements are the DVPT2 energies, discussed in the previous section, and the off-diagonal elements represent the corrective terms to Fermi resonances, complemented by Darling− Dennison interactions, evaluated over the basis of the canonical harmonic-oscillator wave functions
The absence of Fermi and 1−1 Darling−Dennison resonances implies that the anharmonic fundamentals do not vary going from VPT2 to DVPT2 or GVPT2 schemes
Summary
The reliability of quantum chemical (QC) models to support experimental findings is related from one side to their accuracy and from the other side to their feasibility, robustness, and ease of use.[1,2] Concerning the accuracy, electronic structure computations of energies, geometries, and force fields are nowadays able to rival high-resolution spectroscopy for small systems and to help assignments and interpretation of all kinds of spectra for larger molecular systems, provided that nuclear motions and environmental effects are taken into proper account.[3−8] In the present contribution, we will be concerned with molecular vibrations, which are directly sampled by different conventional [infrared (IR), Raman] and chiral (VCD, ROA) spectroscopies,[2,9] but tune the outcomes of other spectroscopies (e.g., distortion constants in microwave spectroscopy[4] or line shapes in electronic spectroscopies[10]). The current implementation is intricate due to the constant case switch depending on the symmetry and degeneracy of the modes in the calculation of the quantities of interest for the vibrational energies It requires the use of complex algebra in the variational treatment, which leads to complex eigenvectors of the variational matrix, and the transition moments, even if the final intensities remain, real. A general and robust framework can be set for the calculation of both IR and Raman intensities for all point groups without any need of complex algebra This has convinced us to follow a different route, that is, to employ the asymmetric-top formulation for the other cases, handling in the proper way all the degeneracy issues and deriving the customary spectroscopic signatures of non-Abelian groups (e.g., S-type doubling) by a posteriori transformations of the eigenvectors. The main results, remaining challenges, and perspectives are shortly outlined in the concluding section
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