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388. ANO:A Program for the Determination of
Approximate External Natural Orbitals
by Clifford E. Dykstra, Department of Chemistry, University of Illinois, Urbana, Illinois 61801 ANO utilizes an operator structure to calculate Hamiltonian matrix elements between a reference wavefunction and doubly substituted configurations. The reference wavefunction may be either an SCF configuration or a Generalized Valence Bond/Perfect Pairing wavefunction. The spin states may be closed- shell singlets, or singlets with two open-shell electrons, or states with parallel open-shell electrons (doublets, triplets, quartets,...). Orbital energies are used with the Hamiltonian matrix elements to find a first-order perturbationtheory wavefunction, represented by pair coefficient matrices given directly in terms of the basis functions. The external part of the first-order reduced-density matrix is found using the pair coefficient matrices. Diagonalization of this matrix yields a transformation among the external orbitals, or orbitals unoccupied in the reference wavefunction, which produces approximate natural orbitals (ANOs). In some test cases, ANOs are very similar to NOs obtained from configuration interaction (CI) wavefunctions and thus may be a useful orbital set for selected CI methods. Computation times for this procedure are similar to SCF. That is, one operator is constructed for each internal pair of electrons. (For N occupied orbitals, one may include double substitutions from up to N(N+1)/2 internal pairs.) The construction of each operator is equivalent to the construction of one Fock operator matrix. The other manipulations in the ANO procedure that follow the operator construction step are of minor computational expense. A program write-up outlining the theory, program organization, input data, etc., accompanies the program. FORTRAN IV (CDC) Lines of Code: 1260 Recommended Citation: C. E. Dykstra, QCPE 13, 388 (1981). |