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The first and second derivative matrices in the random phase approximation scheme by using the Lagrangian technique
Author(s) -
Gotoh Masashi,
Tachikawa Masanori,
Ryuo Kotaro,
Sasagane Kotoku,
Suzuki Kazunari,
Mori Kazuhide,
Nakamura Shinichiro
Publication year - 2005
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.20695
Subject(s) - lagrangian , scheme (mathematics) , singlet state , formaldehyde , derivative (finance) , matrix (chemical analysis) , random phase approximation , second derivative , phase (matter) , excited state , mathematics , quantum mechanics , physics , chemistry , mathematical analysis , organic chemistry , chromatography , financial economics , economics
We have presented the explicit formulas for first and second derivatives of A and B matrices, appearing in the random phase approximation (RPA), with the aid of Lagrangian technique. Owing to the 2 n + 1 rule, the Lagrangian approach is more efficient than the conventional approach to evaluate the higher‐order matrix elements. We have confirmed the validity of our formulation by demonstrating the geometry optimization of the first‐excited singlet states of formaldehyde, ethylene, and 1‐amino‐3‐propenal molecules. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005