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Quadratically convergent simultaneous optimization of wavefunction and geometry
Author(s) -
HeadGordon Martin,
Pople John A.,
Frisch Michael J.
Publication year - 2009
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.560360833
Subject(s) - quadratic growth , wave function , convergence (economics) , scaling , energy minimization , mathematics , linear scale , order (exchange) , hartree–fock method , physics , geometry , mathematical analysis , quantum mechanics , geodesy , finance , geography , economics , economic growth
Abstract A second‐order (quadratically convergent) method is presented for simultaneously optimizing the molecular wavefunction and geometry within the finite basis Hartree–Fock model. Due to inclusion of exact second derivative information, its convergence properties are greatly superior to first‐order optimization schemes, while its cost only scales as the fourth power of the molecular size, like conventional first‐order optimizations. By contrast, a conventional second‐order geometry optimization (in which the wavefunction is constrained to be optimal), involves a step scaling as the fifth power. The performance of the new method relative to a conventional geometry optimization is illustrated by calculations on ( S )‐α‐formylaminopropanamide, CHO—NH—CHCH 3 —CO—NH 2 .