Frequency-dependent first hyperpolarizability tensors

Our present focus is on correlated electronic structure methods for describing molecular systems interacting with a structured environment where the electronic wavefunction for the molecule is given by a multiconfigurational self-consistent field wavefunction. Using the MCSCF structured environment response method it is possible to determine molecular properties such as (i) frequency-dependent polarizabilities, (ii) excitation and deexcitation energies, (iii) transition moments, (iv) two-photon matrix elements, (v) frequency-dependent first hyperpolarizability tensors, (vi) frequency-dependent polarizabilities of excited states, (vii) frequency-dependent second hyperpolarizabilities (y), (viii) three-photon absorptions, and (ix) two-photon absorption between excited states. 

Table 1 Static and frequency-dependent (m in a.u.) SHG first hyperpolarizability tensor components (in a.u.) of the CH and CH2 ( Ai) molecules calculated at different levels of CC theory (from ref. 18)... 

Heterogeneous dielectric media models have included the developments of Jprgensen et al. [7-9] (reviewed here) and Corni and Tomasi [52,53], Generally, the number of methods for determining frequency-dependent molecular electronic properties, such as the polarizability or first- and second hyperpolarizability tensors of heterogeneously solvated molecules, is very limited. 

The PCM calculation are performed by using the CPHF formalism [51] for the static case, and to the TD-CPHF formalism for the frequency dependent case [52]. There are also calculations at higher levels of the QM theory which have not been fully analyzed. The formulas are quite complex, and we refer the interested readers to the two source papers. What is worth remarking here is that (hyper)polarizability values are quite sensitive to the cavity errors. In passing from 7I ) (i.e. a, the polarizability tensor) to 7 1 (i.e. /9, the first hyperpoljirizability) and to 7 (i.e. 7, the second hyperpolarizability) the problem of cavity errors become worse and worse. 

An interesting application of the first case (i.e., an external oscillating field) is the study of the nonlinear properties of molecules in condensed matter. Once the approximate solutions of the corresponding time-dependent SchrOdinger equation are found, the frequency-dependent electric response functions (polarizability and hyperpolarizabilities tensors) of the molecular solute are easily calculated. 

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