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

• 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.

Nyckelord

density-functional theory

frequency-dependent polarizabilities

polycyclic aromatic-hydrocarbons

dynamic dipole polarizabilities

cluster response theory

hartree-fock schemes

perturbation-theory

excitation-energies

quasi-energy

hyperpolarizabilities

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