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Efficient generation of Heisenberg Hamiltonian matrices for VB calculations of potential energy surfaces
Author(s) -
Tokmachev A. M.,
Robb M. A.
Publication year - 2008
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.21815
Subject(s) - atomic orbital , valence bond theory , hamiltonian (control theory) , modern valence bond theory , generalized valence bond , chemistry , excited state , quantum mechanics , ionic bonding , complete active space , hamiltonian matrix , valence electron , electron , molecular orbital theory , physics , atomic physics , ion , mathematics , mathematical optimization , eigenvalues and eigenvectors , symmetric matrix
The spin‐Hamiltonian valence bond theory relies upon covalent configurations formed by singly occupied orbitals differing by their spin counterparts. This theory has been proven to be successful in studying potential energy surfaces of the ground and lowest excited states in organic molecules when used as a part of the hybrid molecular mechanics—valence bond method. The method allows one to consider systems with large active spaces formed by n electrons in n orbitals and relies upon a specially proposed graphical unitary group approach. At the same time, the restriction of the equality of the numbers of electrons and orbitals in the active space is too severe: it excludes from the consideration a lot of interesting applications. We can mention here carbocations and systems with heteroatoms. Moreover, the structure of the method makes it difficult to study charge‐transfer excited states because they are formed by ionic configurations. In the present work we tackle these problems by significant extension of the spin‐Hamiltonian approach. We consider (i) more general active space formed by n ± m electrons in n orbitals and (ii) states with the charge transfer. The main problem addressed is the generation of Hamiltonian matrices for these general cases. We propose a scheme combining operators of electron exchange and hopping, generating all nonzero matrix elements step‐by‐step. This scheme provides a very efficient way to generate the Hamiltonians, thus extending the applicability of spin‐Hamiltonian valence bond theory. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009