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Approximately spin‐projected Hessian for broken symmetry method and stretching frequencies of F 2 and singlet O 2
Author(s) -
Kitagawa Yasutaka,
Saito Toru,
Nakanishi Yasuyuki,
Kataoka Yusuke,
Shoji Mitsuo,
Koizumi Kenichi,
Kawakami Takashi,
Okumura Mitsutaka,
Yamaguchi Kizashi
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.22407
Subject(s) - hessian matrix , singlet state , spin (aerodynamics) , symmetry (geometry) , ultra high frequency , energy (signal processing) , molecule , chemistry , projection (relational algebra) , order (exchange) , atomic physics , molecular physics , physics , quantum mechanics , mathematics , excited state , geometry , algorithm , thermodynamics , telecommunications , computer science , finance , economics
An approximate spin projection (AP) method is applied to a second derivative of energy (Hessian) of the broken‐symmetry (BS) method in order to eliminate a spin contamination error. Stretching frequencies of F 2 ( X 1 ∑ g + ) and singlet molecular oxygen ( a 1 Δ g ) are calculated by using the spin‐projected Hessian (AP Hessian). In case of F 2 molecule, a potential curve of an unrestricted Hartree‐Fock (UHF) method does not have an energy minimum but the stretching frequency can be calculated by the AP UHF method. The difference in the calculated stretching frequencies between a restricted HF (RHF) and the AP UHF methods is 650–700 cm −1 , and indicates that a static correlation correction is a crucial to consider the frequency. On the other hand, we cannot find a significant difference in calculated frequencies of RHF and AP‐BS HF in case of 1 O 2 molecule within the HF method. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009