Abstract
We present the first computational treatment of the complete second-order vibrational perturbation theory applied to hyper-Raman scattering spectroscopy. The required molecular properties are calculated in a fully analytic manner using a recently developed program [Ringholm, Jonsson and Ruud, J. Comp. Chem., 2014, 35, 622] that utilizes recursive routines. For some of the properties, these calculations are the first analytic calculations of their kind at their respective levels of theory. We apply this approach to the calculation of the hyper-Raman spectra of methane, ethane and ethylene and compare these to available experimental data. We show that the anharmonic corrections have a larger effect on the vibrational frequencies than on the spectral intensities, but that the inclusion of combination and overtone bands in the anharmonic treatment can improve the agreement with the experimental data, although the quality of available experimental data limits a detailed comparison.
Highlights
Hyper-Raman scattering was predicted in the late 1950s1 and observed experimentally in the mid-1960s.2 It is a process which complements the infrared (IR) and conventional Raman spectroscopies because the vibrational transition moments involve the molecular first hyperpolarizability instead of the dipole moment or polarizability tensors that govern IR and Raman spectroscopy, respectively
We present the first computational treatment of the complete second-order vibrational perturbation theory applied to hyper-Raman scattering spectroscopy
Spectroscopies involving molecular vibrations have been simulated ab initio for a long time, and the stage was set by early developments that allowed for the calculation of geometric derivatives of the molecular energy
Summary
Hyper-Raman scattering was predicted in the late 1950s1 and observed experimentally in the mid-1960s.2 It is a process which complements the infrared (IR) and conventional Raman spectroscopies because the vibrational transition moments involve the molecular first hyperpolarizability instead of the dipole moment or polarizability tensors that govern IR and Raman spectroscopy, respectively. The calculation of the properties needed for anharmonic corrections can be done by numerical or analytic methods through the use of response theory, but as is well known and as demonstrated in recent work for IR and Raman spectroscopy, calculations involving numerical methods can be prone to errors and it can be difficult to identify when these errors have occurred. The implementation uses recursive routines to ensure generality and open-endedness, and we have already used it for the first analytic calculations of many properties of relevance to vibrational spectroscopies at the density-functional theory (DFT) level This includes the first reported analytic DFT quartic force constants and geometric first derivatives of the hyperpolarizability for hyper-Raman scattering in the doubleharmonic approximation..
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