Journal
PHYSICAL REVIEW A
Volume 80, Issue 2, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevA.80.022507
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Funding
- NSF [0644888]
- Henry-Camille Dreyfus Foundation
- David-Lucile Packard Foundation
- Microsoft
- Division Of Chemistry
- Direct For Mathematical & Physical Scien [0644888] Funding Source: National Science Foundation
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Direct calculation of the ground-state two-electron reduced density matrix (2-RDM) and its energy has recently been achieved for many-electron atoms and molecules by solving the anti-Hermitian part of the contracted Schrodinger equation (ACSE) [D. A. Mazziotti, Phys. Rev. Lett. 97, 143002 (2006)]. In this paper the ACSE method is extended to computing the 2-RDMs and energies of excited states without the many-electron wave function. The contracted Schrodinger equation (CSE) is an important ingredient for excited-state 2-RDM methods because it is a stationary-state condition for both ground and excited states. We develop the theoretical framework for the ACSE as a stationary-state condition through its connections to the CSE and the Schrodinger equation. As in previous ground-state calculations, the indeterminacy of the ACSE is removed by reconstructing its 3-RDM as a functional of its 2-RDM through a cumulant theory for RDMs [D. A. Mazziotti, Chem. Phys. Lett. 289, 419 (1998)]. We calculate the initial 2-RDM from a multiconfiguration self-consistent-field calculation that includes multireference electron correlation, which can be especially important for excited states. The excited-state ACSE method is applied to computing absolute excited-state energies and vertical excitation energies of the molecules HF, H2O, and N-2 as well as ground and excited potential-energy curves of HF. Comparisons are made to traditional multireference methods as well as full configuration interaction. Computed excited-state 2-RDMs nearly satisfy necessary N-representability conditions.
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