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New algorithm for high‐order time‐dependent hartree–fock theory for nonlinear optical properties
Author(s) -
Sekino Hideo,
Bartlett Rodney J.
Publication year - 1992
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.560430111
Subject(s) - hyperpolarizability , formalism (music) , fock space , hartree–fock method , coupled cluster , chemistry , perturbation theory (quantum mechanics) , perturbation (astronomy) , nonlinear system , nonlinear optical , computational chemistry , algorithm , quantum mechanics , statistical physics , physics , mathematics , molecule , art , musical , visual arts
A new formalism and algorithm is developed for solving the general ‐ order time‐dependent Hartree–Fock (TDHF) problem. It is shown that for any order a generalization of the TDHF equations can be derived where all lower‐order solutions constitute a constant term. This makes it very easy to obtain high‐order solutions. As the space required for the mapping of density matrices to Fock matrices in a problem of a giver order is largely reduced, we can perform the most time‐consuming steps within the core memory of the machine and easily manipulate vector products via optimum routines. The second hyperpolarizability γ is obtained from the secondorder TDHF solution via a 2 n rule. The formalism also allows for expressing all terms in the equation diagrammatically, which provides additional physical insight and a more systematic evaluation of terms. To illustrate the method, TDHF results are presented for trans ‐butadiene and carbon monoxide for several optical processes, including correlation corrections to their static hyperpolarizabilities obtained via coupled cluster (CCSD) and many‐body perturbation theory. The hybrid TDHF/CCSD method provides excellent agreement with the DC–SHG experiments (χ|| (2) = 11.4 x 10 −32 esu/mol compared to 12.9 ± 11.4 × 10 −32 esu/mol and χ|| (3) = 149 compared to 144 ± 4 × 10 −39 esu/mol).