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International Journal of Quantum Chemistry

The antisymmetrized geminal power approximation to the excitation propagator

Brian Weiner, Henry A. Kurtz

Published Jun 1, 1985• 5 citations
Publisher

Abstract

Abstract A consistent propagator approximation, denoted as the excitation propagator, is introduced. This propagator describes excitations between N‐particle states and its approximation has properties required of consistent random phase approximation schemes. Several properties of this propagator are explored when based on a generalized antisymmetrized geminal power wavefunction. How singularities in the metric occur and how to remove them is discussed in detail. The excitation propagator is also contrasted with the principal (polarization) propagator.

DOI
10.1002/qua.560270611

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Physical Review A•Jan 1, 1983•29 citations
Abstract A consistent propagator approximation, denoted as the excitation propagator, is introduced. This propagator describes excitations between N‐particle states and its approximation has properties required of consistent random phase approximation schemes. Several properties of this propagator are explored when based on a generalized antisymmetrized geminal power wavefunction. How singularities in the metric occur and how to remove them is discussed in detail. The excitation propagator is also contrasted with the principal (polarization) propagator.
The generalized antisymmetrized geminal-power (GAGP) function, shown to be the ground state for the oneparticle-hole propagator, can be computed using the rather simple properties of its reduced density matrices and the properties of unitary transformations. The practical procedure involves limited storage notwithstanding the rather large number of configurations with which the GAGP function can be associated. Using the stability properties previously derived for this function, we construct the self-consistent one-particle-hole propagator.
Self-consistent polarization-propagator approximations (i.e., those based on a proper vacuum) are compared to conventional time-dependent Hartree-Fock --- random-phaseapproximation ones, with special attention to the fulfillment of the fff-sum rule. The effect on the properties of the consistent propagator, based on a general-antisymmetrizedgeminal-power vacuum, when degeneracies occurring in the first-order reduced-density matrix of this vacuum are examined. The foregoing analysis shows that low-lying electronic states can be expected to become degenerate with the vacuum in conjunction with superphenomena in extended systems and oscillator-strength anomalies in finite ones.
Abstract The properties of the n‐electron wave functions equation image with symplectic symmetries have been discussed. These functions are built up with two kinds of geminals. The well‐known antisymmetrized geminal power (AGP) function is only a special case of them. The first‐ and second‐order reduced density matrices and the natural expansions of these functions have been given, and the uniform expressions for system energies in the states corresponding to these functions have been deduced. It has been shown that the special case equation image is probably another consistent ground state for the particle‐hole propegator or random‐phase approximation (RPA) besides the AGP function.
Some of the difficulties encountered in the approximation of Green's functions are reviewed with particular emphasis on the self-consistent polarization propagator. Some new basic theorems are presented, involving a general procedure, which lead to both a derivation and alternate prescriptions for the computations. As demonstrated by Linderberg and Öhrn the ground state is an AGP (antisymmetrized geminal power). An energy optimized AGP ( E AGP ) in a Brueckner orbital representation can be used to generate a manifold of excited states| K ⟩ = O K + |AGP⟩, O K |AGP⟩ = 0 with the excitation operators, O + K , and killers, O K , being combinations of particle-hole and hole-particle operators. The SCPP can be expressed then as ⟨⟨ X, Y ⟩⟩ E = - ⟨AGP| XT 0 (- E + E AGP ) Y + YT 0 ( E + E AGP ) X |AGP⟩ in terms of the resolvent T 0 ( ) = P ( - PHP ) -1 with P spanned by the states| K ⟩⟨ K |, in the sense of Löwdin. Our results establish a natural relationship between hermiticity, completeness, non-redundance of operator manifolds with stationarity and killer conditions.
Strong pairing correlations are responsible for superconductivity and off-diagonal long-range order in the two-particle density matrix. The antisymmetrized geminal power wave function was championed many years ago as the simplest model that can provide a reasonable qualitative description for these correlations without breaking number symmetry. The fact remains, however, that the antisymmetrized geminal power is not generally quantitatively accurate in all correlation regimes. In this work, we discuss how we might use this wave function as a reference state for a more sophisticated correlation technique such as configuration interaction, coupled cluster theory, or the random phase approximation.