Analytic ab initio calculations of coherent anti-Stokes Raman scattering (CARS)

Abstract

We present a theory for the analytic calculation of frequency-dependent polarizability gradients, and apply the methodology to the calculation of coherent anti-Stokes Raman scattering (CARS). The formalism used is based on an open-ended theory for the calculation of frequency-dependent molecular response properties of arbitrary order, also including contributions from perturbation-dependent basis sets. An important feature of our approach is the close connection between the formalism--which is fully matrix-based in an atomic orbital basis--and the implementation, allowing for the rapid implementation of higher-order molecular properties. Care is taken to allow the formalism to be utilized with linearly-scaling Hartree-Fock and density-functional theory codes. By avoiding the evaluation of responses due to geometry distortions, only 9 response equations need to be solved for the calculation of the CARS intensities, independent of the size of the molecular system. The theory is illustrated by calculations on a set of polyaromatic hydrocarbons using a DFT/B3LYP force field and Hartree-Fock polarizability gradients. Good agreement with the experimental CARS spectra of these compounds is obtained.

Modeling Coherent Anti-Stokes Raman Scattering with Time-Dependent Density Functional Theory: Vacuum and Surface Enhancement.

“…Throughout the paper the label HF attached to a spectrum indicates that it was generated with HF polarizability derivatives calculated along the normal modes emerging from a B3LYP calculation, ie: the procedure which was previously available. 13 Although note that in that work χ (3) NR = χ (3) e , whereas in this work it's approximated as the product of dynamic polarizabilities described above. No subsequent scaling of the vibrational frequencies of DFT has been performed.…”

“…Comparing against the spectra from ref. 13 and knowing that the perylene has a low-lying first excited state at roughly 24,000 cm −1 26 these are likely artifacts of our approximation to the NR signal.…”

“…13,14 HF theory's neglect of electron-electron interaction is especially unphysical for systems with sig-nificant correlation, like metals. For this reason, we replace HF for the calculation of CARS on metal cluster models.…”

Atomic orbital-based cubic response theory for one-, two-, and four-component relativistic self-consistent field models

“…The code has so far been used to study higher-order frequency-dependent properties such as coherent anti-Stokes Raman Scattering (CARS) [18], pure vibrational contributions to (hyper)polarizabilities [19], hypermagnetizabilities using London atomic orbitals [20] and electric field gradient-induced birefringence, also using London orbitals [21]. The formalism is furthermore expressed fully in the AO basis, allowing us in the nonrelativistic framework to take advantage of recent advances in linear scaling self-consistent field theory [22][23][24][25][26][27].…”

“…In order to calculate the (hyper)polarizabilities, we thus need to determine the first-, second-, and third-order perturbed densities for different sets of frequencies. The strategy for obtaining these perturbed densities has been described previously [17,18], but we will outline the main features of the approach in the next subsection, emphasizing how we can obtain these densities from an existing relativistic linear response solver in the molecular orbital basis.…”