Optimization of nonlinear wave function parameters

Abstract

AbstractAn energy‐based optimization method is presented for our recently developed nonlinear wave function expansion form for electronic wave functions. This expansion form is based on spin eigenfunctions, using the graphical unitary group approach (GUGA). The wave function is expanded in a basis of product functions, allowing application to closed‐shell and open‐shell systems and to ground and excited electronic states. Each product basis function is itself a multiconfigurational function that depends on a relatively small number of nonlinear parameters called arc factors. The energy‐based optimization is formulated in terms of analytic arc factor gradients and orbital‐level Hamiltonian matrices that correspond to a specific kind of uncontraction of each of the product basis functions. These orbital‐level Hamiltonian matrices give an intuitive representation of the energy in terms of disjoint subsets of the arc factors, they provide for an efficient computation of gradients of the energy with respect to the arc factors, and they allow optimal arc factors to be determined in closed form for subspaces of the full variation problem. Timings for energy and arc factor gradient computations involving expansion spaces of >1024 configuration state functions are reported. Preliminary convergence studies and molecular dissociation curves are presented for some small molecules. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006