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Theory and computational methods for studies of nonlinear phenomena in laser spectroscopy. II. Calculations of steady‐state wave functions
Author(s) -
Roos Bjöurn O.,
Dmitriev Yuri Yu.,
Hotokka Matti
Publication year - 1984
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560260105
Subject(s) - hyperpolarizability , polarizability , wave function , steady state (chemistry) , molecular orbital , fourier transform , atomic orbital , nonlinear system , chemistry , physics , function (biology) , quantum mechanics , atomic physics , molecular physics , classical mechanics , molecule , electron , evolutionary biology , biology
Methods will be developed for variational calculations of steady‐state wave functions and the corresponding quasienergies. These functions appear as solutions to the time‐dependent Schrödinger equation for a molecule interacting with an oscillating electromagnetic field. A variation principle is used to obtain coupled equations for each Fourier component ( FC ) of the steady‐state wave function. The FC s are expanded in configuration state functions using the structure of the complete active space ( CAS ) SCF approach. Two methods are outlined, one which is based on a common set of molecular orbitals for all FC s and one based on an individual optimization of both CI coefficients and molecular orbitals for each FC . The latter method leads to molecular orbital sets for the different FC s which are mutually nonorthogonal. Formulas are derived for the calculation of higher‐order dynamic susceptibilities for steady states. An application is made to the H 2 molecule, and results are presented for the frequency‐dependent polarizability and hyperpolarizability along the molecular axis. The static values obtained are α = 6.413 (6.387) and γ = 676 (674) atomic units, with exact numbers within parentheses.