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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).
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