AntiHermitian part of the contracted Schroedinger equation for the direct calculation of twoelectron reduced density matrices
Abstract
A recent advance in the theory of the contracted Schroedinger equation (CSE), in which only the antiHermitian part of the equation is solved, permits the direct determination of groundstate twoelectron reduced density matrices (2RDM's) that yield 95%100% of the correlation energy of atoms and molecules [D. A. Mazziotti, Phys. Rev. Lett. 97, 143002 (2006)]. Here we discuss in detail the antiHermitian contracted Schroedinger equation (ACSE) and its comparison to the CSE with regard to cumulant reconstruction of RDM's, the role of Nakatsuji's theorem, and the structure of the wave function. The ACSE is also formulated in the Heisenberg representation and related to canonical diagonalization. The solution of the ACSE is illustrated with a variety of molecules including H{sub 2}O, CH{sub 2}, NH{sub 4}{sup +}, HF, and N{sub 2}, and potential energy and dipolemoment surfaces are computed for boron hydride in a polarized double{zeta} basis set. The computed 2RDM's very closely satisfy known Nrepresentability conditions.
 Authors:
 Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637 (United States)
 Publication Date:
 OSTI Identifier:
 20982104
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevA.75.022505; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 74 ATOMIC AND MOLECULAR PHYSICS; ATOMS; BORON HYDRIDES; CATIONS; DENSITY MATRIX; DIPOLE MOMENTS; ELECTRON CORRELATION; ELECTRONS; GROUND STATES; HEISENBERG PICTURE; HERMITIAN MATRIX; HYDROFLUORIC ACID; MATHEMATICAL SOLUTIONS; MOLECULES; NITROGEN COMPOUNDS; ORGANIC COMPOUNDS; POTENTIAL ENERGY; SCHROEDINGER EQUATION; SURFACES; WATER; WAVE FUNCTIONS
Citation Formats
Mazziotti, David A. AntiHermitian part of the contracted Schroedinger equation for the direct calculation of twoelectron reduced density matrices. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVA.75.022505.
Mazziotti, David A. AntiHermitian part of the contracted Schroedinger equation for the direct calculation of twoelectron reduced density matrices. United States. doi:10.1103/PHYSREVA.75.022505.
Mazziotti, David A. Thu .
"AntiHermitian part of the contracted Schroedinger equation for the direct calculation of twoelectron reduced density matrices". United States.
doi:10.1103/PHYSREVA.75.022505.
@article{osti_20982104,
title = {AntiHermitian part of the contracted Schroedinger equation for the direct calculation of twoelectron reduced density matrices},
author = {Mazziotti, David A.},
abstractNote = {A recent advance in the theory of the contracted Schroedinger equation (CSE), in which only the antiHermitian part of the equation is solved, permits the direct determination of groundstate twoelectron reduced density matrices (2RDM's) that yield 95%100% of the correlation energy of atoms and molecules [D. A. Mazziotti, Phys. Rev. Lett. 97, 143002 (2006)]. Here we discuss in detail the antiHermitian contracted Schroedinger equation (ACSE) and its comparison to the CSE with regard to cumulant reconstruction of RDM's, the role of Nakatsuji's theorem, and the structure of the wave function. The ACSE is also formulated in the Heisenberg representation and related to canonical diagonalization. The solution of the ACSE is illustrated with a variety of molecules including H{sub 2}O, CH{sub 2}, NH{sub 4}{sup +}, HF, and N{sub 2}, and potential energy and dipolemoment surfaces are computed for boron hydride in a polarized double{zeta} basis set. The computed 2RDM's very closely satisfy known Nrepresentability conditions.},
doi = {10.1103/PHYSREVA.75.022505},
journal = {Physical Review. A},
number = 2,
volume = 75,
place = {United States},
year = {Thu Feb 15 00:00:00 EST 2007},
month = {Thu Feb 15 00:00:00 EST 2007}
}

Twoelectron reduced density matrices (2RDMs) have recently been directly calculated by solving the antiHermitian contracted Schroedinger equation (ACSE) to obtain 95100 % of the groundstate correlation energy of atoms and molecules with the accuracy increasing with the size of the oneelectron basis set [Mazziotti, Phys. Rev. Lett. 97, 143002 (2006).] In this paper, the ACSE method is extended to treat strong multireference correlation effects that are often important at nonequilibrium molecular geometries. While previous ACSE calculations have employed an initial 2RDM from the HartreeFock method, we initialize the solution of the ACSE with a 2RDM guess from a multiconfiguration selfconsistentmore »

Enhanced computational efficiency in the direct determination of the twoelectron reduced density matrix from the antiHermitian contracted Schrödinger equation with application to ground and excited states of conjugated πsystems
Determination of the twoelectron reduced density matrix (2RDM) from the solution of the antiHermitian contracted Schrödinger equation (ACSE) yields accurate energies and properties for both ground and excited states. Here, we develop a more efficient method to solving the ACSE that uses secondorder information to select a more optimal step towards the solution. Calculations on the ground and excited states of water, hydrogen fluoride, and conjugated π systems show that the improved ACSE algorithm is 1020 times faster than the previous ACSE algorithm. The ACSE can treat both single and multireference electron correlation with the initial 2RDM from a completeactivespacemore » 
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Differing perspectives on the accuracy of threeelectron reduceddensitymatrix (3RDM) reconstruction in nonminimal basis sets exist in the literature. This paper demonstrates the accuracy of cumulantbased reconstructions, developed by Valdemoro (V) [F. Colmenero et al., Phys. Rev. A 47, 971 (1993)], Nakatsuji and Yasuda (NY) [Phys. Rev. Lett. 76, 1039 (1996)], Mazziotti (M) [Phys. Rev. A 60, 3618 (1999)], and ValdemoroTelPerezRomero (VTP) [Manyelectron Densities and Density Matrices, edited by J. Cioslowski (Kluwer, Boston, 2000)]. Computationally, we extend previous investigations to study a variety of molecules, including LiH, HF, NH{sub 3}, H{sub 2}O, and N{sub 2}, in Slatertype, doublezeta, and polarized doublezetamore » 
Solution of the 1,3contracted Schroedinger equation through positivity conditions on the twoparticle reduced density matrix
Correlation energies and reduced density matrices (RDMs) of atoms and molecules are directly computed by solving the 1,3contracted Schroedinger equation (1,3CSE). The solution of the 1,3CSE synthesizes two optimization strategies recently employed for the direct determination of the 2RDM: (i) variational minimization of the energy with respect to a 2RDM constrained by positivity conditions [D. A. Mazziotti, Phys. Rev. A 65, 062511 (2002)] and (ii) the contracted power method for solving the 2,4CSE [D. A. Mazziotti, J. Chem. Phys. 116, 1239 (2002)]. While both the 3 and the 4RDMs in the 2,4CSE are reconstructed from the 2RDM by cumulant expansions,more » 
Strongly correlated mechanisms of a photoexcited radical reaction from the antiHermitian contracted Schroedinger equation
Photoexcited radical reactions are critical to processes in both nature and materials, and yet they can be challenging for electronic structure methods due to the presence of strong electron correlation. Reduceddensitymatrix (RDM) methods, based on solving the antiHermitian contracted Schroedinger equation (ACSE) for the twoelectron RDM (2RDM), are examined for studying the strongly correlated mechanisms of these reactions with application to the electrocyclic interconversion of allyl and cyclopropyl radicals. We combine recent extensions of the ACSE to excited states [G. Gidofalvi and D. A. Mazziotti, Phys. Rev. A 80, 022507 (2009)] and arbitrary spin states [A. E. Rothman, J. J.more »