doi:10.1016/j.cplett.2004.10.075
Copyright © 2004 Elsevier B.V. All rights reserved.
Extraction of ionization energies from the ground-state two-particle reduced density matrix
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John D. Farnum and David A. Mazziotti
, 
Department of Chemistry, James Franck Institute, The University of Chicago, Chicago, IL 60637, USA
Received 3 September 2004;
revised 20 October 2004.
Available online 11 November 2004.
Abstract
Two methods for extracting ionization energies from the two-particle reduced density matrix (2-RDM) are explored: (i) diagonalization of the Hamiltonian in the basis of a single annihilation operator applied to the ground-state wave function |Ψg
and (ii) diagonalization of the Hamiltonian in the basis of two annihilation and one creation operators applied to the ground-state |Ψg
. While the second basis set is more accurate, its Hamiltonian matrix elements depend upon the 3- and 4-RDMs. Using cumulant theory, however, we can approximate the 3- and 4-RDMs as functionals of the 2-RDM. Both methods are illustrated with calculations on a series of atoms and molecules.
Table 1.
Cumulant expansion formulas for the 3- and 4-RDMs are shown where the RDMs are normalized as in second quantization

Table 2.
The error in the ionization energies in comparison with full configuration interaction (FCI) are reported in atomic units for 2-RDM methods and a variety of wavefunction methods

‘Simple’ – RDM calculation in the basis of single ionizations only; ‘cumulant’ – RDM calculation in the a†aa|Ψg
basis where third- and fourth-order connected pieces are equal to zero (i.e. the electrons are unconnected); ‘NY’ – same as ‘cumulant’ except the connected pieces are approximated with the Nakatsuji–Yasuda correction; ‘Koop’ – Koopmann’s approximation to ionization energies; ‘OVGF’ – outer valence Green’s function solutions; ‘MP2’, ‘MP3’, and ‘MP4’ – perturbation calculations; ‘Full CI’ – full configuration interaction calculations; ‘Exp’ – experimental values.
Experimental values are included to show the relative accuracy of the FCI basis set [23].

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