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Augmented Lagrangian method for spin‐coupled wave function
Author(s) -
Sumita Masato,
Yoshikawa Naruki
Publication year - 2021
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.26746
Subject(s) - eigenfunction , wave function , eigenvalues and eigenvectors , atomic orbital , augmented lagrangian method , ground state , spin (aerodynamics) , quantum mechanics , physics , mathematics , algorithm , thermodynamics , electron
We applied augmented Lagrangian method coupled with derivative‐free methods to optimize molecular wave function based on non‐orthogonal orbitals, that is called spin‐coupled generalized valence bond (SCGVB), for its ground‐state energy. In contrast to the orthogonal‐orbital‐based electronic structure theory, the SCGVB includes spin eigenfunctions to satisfy the eigenstates as the operator of the square of the spin. To obtain the ground‐state energy of SCGVB, therefore, it is necessary to optimize the orbital and the spin‐coupling coefficients simultaneously. In this study, we validated feasibility of the derivative‐free augmented Lagrangian method for optimizing the spin‐coupling and the orbital coefficients with the constraint of normality of the wave function. We employed this SCGVB method to compute dissociative potential energy curves (PECs) of H 2 , H 2 − , He 2 + , and LiH. The obtained PECs by the SCGVB method are close to these by full configuration interaction theory. These results indicate that the augmented Lagrangian method is effective to optimize the wave function of SCGVB.