Hyper Raman spectra calculated in a time-dependent Hartree–Fock method

Abstract

Hyper Raman scattering (HRS) of the benzonitrile (BN) and 1,3,5-trinitro-1,3,5-triazacyclohexane (RDX) molecules is studied by means of ab initio calculations. The computational procedure employs a recently developed methodology for the analytic calculations of frequency-dependent polarizability gradients of arbitrary order, including perturbation dependent basis sets. The result are compared to normal Raman scattering (NRS) and coherent anti-Stokes Raman scattering (CARS) that previously have been studied using the same technology. It is found that some suppressed or silent modes in CARS and NRS spectra are clearly seen in HRS, and that although under general excitation conditions the HRS intensities are much lower than for CARS and NRS, HRS provides complementary information useful for target identification.

Analytic calculations of hyper-Raman spectra from density functional theory hyperpolarizability gradients

“…5,[8][9][10] As the main difference between DFT and HF will be in the evaluation of the exchangecorrelation contributions, we will here follow our earlier exposition of the analytic evaluation of the gradients of the first hyperpolarizability at the HF level, 5 providing an outline of the general energy-derivative theory framework but with the main focus given to the new and nontrivial exchangecorrelation contributions. However, in order to establish the notation and provide the background for the quantities we need to evaluate, we first give a brief introduction to the expressions for the HRS cross sections.…”

“…In earlier theoretical studies of hyper-Raman spectra, 5,8,9 with the exception of one study in which also the (static) first hyperpolarizability gradients were calculated at the Møller-Plesset (MP) level of theory, 10 HRS spectra have been calculated using gradients of the first hyperpolarizability calculated at the HF level. We here extend these earlier studies to evaluate the importance of electron correlation effects on the hyper-Raman scattering cross sections as described by DFT, presenting the first analytic implementation of the first hyperpolarizability gradient at the DFT level.…”

“…The scattering process and the involvement of the first hyperpolarizability in HRS allow for the enhancement of other vibrational modes than those observed, for instance, in infrared absorption or Raman spectroscopy. [3][4][5] Furthermore, HRS is well suited for the study of low-frequency vibrational modes, which has traditionally been a difficult region for other spectroscopies because of instrumental limitations, although we note that these limitations are gradually being lifted in the case of (chiroptical) Raman spectroscopy. 6 Hyper-Raman scattering is not as well known or frequently used as, e.g., infra-red (IR) or Raman spectroscopy, mainly because the signal is significantly weaker than the corresponding Raman signal due to its multiphoton nature (it is typically several orders of magnitude weaker than nonresonant Raman scattering 7 ).…”

“…More recently, Ågren and co-workers have also presented theoretical studies of HRS. 5 However, all analytic calculations of the hyperpolarizability gradients in previous studies have been restricted to the Hartree-Fock (HF) level of theory.…”

Gauge-origin independent calculations of electric-field-induced second-harmonic generation circular intensity difference using London atomic orbitals

“…[38] The method has been shown to be amendable to the use of recursive programming routines, thereby making it fully open-ended with respect to the order of the applied perturbations, [39] as long as the perturbation ansatz remains valid for the interaction of the electronic density with the applied perturbations. We have recently used this program to calculate various high-order properties, such as anharmonic force fields [40], anharmonic infrared and Raman spectra [41], hyperRaman spectra [42] as well as a variety of multiphoton absorption processes. [43,44].…”