(e, 2e) [AM83b, TMC84]. (n−) [MOT83]. (N − 1) [Mor89]. + [AM82, BNK86, Bow86, ES81, GT86, GT87a, GM86a, KU80, KS89b, KM89b, LB83, RBL84, SBE87, SS84b, SS87, YKZ89]. 1/Z [PS84]. $104.75 [Pic83b]. 12 [KU80]. 14 [SST84]. $15.00 [Mår80]. 1s [NMK84, Ten88b]. 1s2pJp ′ jJ [ST84]. 1s2s [DS80a]. 1s2s2pjJ [ST84]. 1s2s 2 [ST84]. 1s2s [DS81c]. 2 [BW85, MOT83, MK83, ddF86]. $26.25 [Wol81]. $28.50 [Pic83a]. 2′ [LMG85, SP82a]. 2: 1 [GP83a]. 3 [BW85, ddF86]. 3′ [KG80]. 3d [WS80b]. $49.00 [Sie83a]. 4L [FEKC84]. 4L+ 2 [FEKC84]. 4× 4 [Lin81a]. $59.00 [Gos80]. 5d [CPGP83]. $85.00 [LM81]. $88.00 [Mår82]. $9.95 [Lun82]. < pu|∂/∂v|s > [JL85]. < r−1 12 > [BB81a]. < r−1 1 > [BB81a]. = [Dat82, KU80, PXLC86, PFLB83, WBK86]. + [CEB86, CLM80, CD89a, CC82b, Con87, DF89, DLVÖ84, EY82, ESKG83, GLLOB88, GP82, JŻ85, Kog84, Kun86, LPS83b, NMK84, PC83b, Sch80a,

A Bibliography of Publications in The International Journal of Quantum Chemistry: 1980{1989

A CI program is described for the evaluation of two‐photon electronic transitions, based on time dependent second order perturbation theory. The expression of the transition amplitudes is obtained by directly solving first order perturbation equations over the CI components, avoiding the second order expression with summation over the full set of the intermediate CI eigenstates. The procedure has been implemented as part of a general CI program for ab initio computations of these properties. To test the program, the relative intensities of the ‘‘hot’’ vibronic components of the A1g→B2u transition of the benzene molecule have been evaluated on a minicomputer and compared to the experiment.

A configuration interaction (CI) procedure for the evaluation of two‐photon electronic transition probabilities. Program implementation with application to the A1g→B2u transition of benzene

Nonlinear optical properties of organic molecules: a theoretical study with semi-empirical methods

The standard formalism of the perturbation theory for time-dependent perturbations follows from the assumption that the exact solution of the unperturbed time-independent problem is known. The consequences of this assumption are analyzed.



Particular attention is given to the methods used for the evaluation of transition intensities. It is shown that the traditional intensity formula in most cases violates the assumptions underlying its derivation. It is shown that for the given ansatz concerning the form of the approximate wave function, the transition intensities should be determined from the variation treatment of the corresponding time-dependent problem. The wave functions of both states involved in the transition should be given the same amount of variation flexibility. This condition is satisfied if the transition intensity expression follows from the complete timedependent perturbation treatment of the perturbed system.

Time‐dependence of wave functions and the calculation of transition intensities

At the moment, the most efficient method to compute the state of a periodically driven quantum system is using Floquet theory and the Floquet eigenbasis. The wide application of this basis set method is limited by a lack of unique ordering of the Floquet eigenfunctions, an ambiguity in their definition at resonance, and an instability against infinitesimal perturbation at resonance. We address these problems by redefining the eigenbasis using a revised definition of the average energy as a quantum number. As a result of this redefinition, we also obtain a Floquet-Ritz variational principle, and justify the truncation of the Hilbert space.

Defining a well-ordered Floquet basis by the average energy

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 Schrodinger 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 FCs 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 FCs 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 FCs which are mutually nonorthogonal. Formulas are derived for the calculation of higher-order dynamic susceptibilities for steady states. An application is made to the H2 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.

Bjöurn O. Roos

Papers

Theory and computational methods for studies of nonlinear phenomena in laser spectroscopy. II. Calculations of steady‐state wave functions