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Stability properties of closed‐shell restricted Hartree–Fock solutions for electronic systems in the framework of the projected Hartree–Fock method and their utilization
Author(s) -
Karadakov Peter,
Castan̄o Obis
Publication year - 1983
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.560240504
Subject(s) - hartree–fock method , open shell , singlet state , operator (biology) , stability (learning theory) , projection (relational algebra) , spin (aerodynamics) , electronic structure , eigenvalues and eigenvectors , chemistry , quantum mechanics , mathematics , computational chemistry , physics , thermodynamics , computer science , excited state , algorithm , biochemistry , repressor , machine learning , transcription factor , gene
Abstract This paper contains a derivation of stability conditions for closed‐shell restricted Hartree–Fock ( RHF ) solutions in the framework of the projected Hartree–Fock ( PHF ) method. It is shown that for any projection operator whose choice is consistent with the symmetry of the RHF solution, one obtains four stability subproblems (one “singlet” and three “nonsinglet”). The stability conditions are specialized to several particular choices of the projection operator, including Löwdin's spin projection operator for the singlet case (this choice corresponds to the celebrated spin‐ PHF method). The stability of closed‐shell RHF solutions for alternat π‐electronic systems in the framework of the alternant molecular orbital ( AMO ) method is also discussed. The theoretical considerations are illustrated by PPP calculations for several closed‐shell π‐electronic models. The results for even alternant conjugated hydrocarbons show that the AMO construction is suggested by the structure of the eigenvector pointing into the direction of steepest descent from the pertinent RHF solution in the framework of the spin‐ PHF method. The minimization of the spin‐ PHF energy expectation value in this direction in a number of cases allows that value to approach rather closely the energy values obtained in a fully variational spin‐ PHF treatment and thus provides either a one‐parameter variational method which is shown to be superior to the one‐parameter AMO method or a convenient initial approximation to the solution of the spin‐ PHF equations.