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Nonlinear wave function expansions: A progress report
Author(s) -
Shepard Ron,
Minkoff Michael,
Brozell Scott R.
Publication year - 2007
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.21503
Subject(s) - wave function , eigenfunction , hamiltonian (control theory) , basis function , nonlinear system , density matrix , mathematics , quantum mechanics , statistical physics , mathematical analysis , physics , quantum , eigenvalues and eigenvectors , mathematical optimization
Some recent progress is reported for a novel nonlinear expansion form for electronic wave functions. This expansion form is based on spin eigenfunctions using the Graphical Unitary Group Approach and the wave function is expanded in a basis of product functions, allowing application to closed and open shell systems and to ground and excited electronic states. Each product basis function is itself a multiconfigurational expansion that depends on a relatively small number of nonlinear parameters called arc factors. Efficient recursive procedures for the computation of reduced one‐ and two‐particle density matrices, overlap matrix elements, and Hamiltonian matrix elements result in a very efficient computational procedure that is applicable to very large configuration state function (CSF) expansions. A new energy‐based optimization approach is presented based on product function splitting and variational recombination. Convergence of both valence correlation energy and dynamical correlation energy with respect to the product function basis dimension is examined. A wave function analysis approach suitable for very large CSF expansions is presented based on Shavitt graph node density and arc density. Some new closed‐form expressions for various Shavitt Graph and Auxiliary Pair Graph statistics are presented. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007