Premium
Equations de Hartree–Fock dependant du temps
Author(s) -
Smet F.,
Tillieu J.,
Van Groenendael Et A.
Publication year - 1980
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.560170313
Subject(s) - equivalence (formal languages) , monochromatic color , atomic orbital , hartree–fock method , nonlinear system , lagrange multiplier , physics , mathematical physics , mathematics , mathematical analysis , quantum mechanics , optics , pure mathematics , electron
The time‐dependent Hartree–Fock ( TDHF ) equations are derived up to the second order when the system is perturbed by a monochromatic plane wave. The solutions of the equations are subjected to the orthonormalization conditions satisfied by the orbitals. In the equations, these conditions are expressed by the appearing of coefficients λ jk n ,ϵplaying the part of Lagrangian multipliers. Relations between the coefficients λ jk n ,ϵare established. These relations are equivalent to the above‐mentioned orthonormalization conditions. This equivalence enables us to substitute for the solution of an integrodifferential equation system subject to constraint conditions, that of a free system. The TDHF equations obtained determine the first‐ and second‐order orbital perturbations, which no doubt verify the orthonormalization conditions. These orbitals can be used in the calculation, up to second order, of different nonlinear optical effects.