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Title: N-representability-driven reconstruction of the two-electron reduced-density matrix for a real-time time-dependent electronic structure method

Abstract

Propagating the equations of motion (EOM) for the one-electron reduced-density matrix (1-RDM) requires knowledge of the corresponding two-electron RDM (2-RDM). We show that the indeterminacy of this expression can be removed through a constrained optimization that resembles the variational optimization of the ground-state 2-RDM subject to a set of known N-representability conditions. Electronic excitation energies can then be obtained by propagating the EOM for the 1-RDM and following the dipole moment after the system interacts with an oscillating external electric field. For simple systems with well-separated excited states whose symmetry differs from that of the ground state, excitation energies obtained from this method are comparable to those obtained from full configuration interaction computations. Although the optimized 2-RDM satisfies necessary N-representability conditions, the procedure cannot guarantee a unique mapping from the 1-RDM to the 2-RDM. This deficiency is evident in the mean-field-quality description of transitions to states of the same symmetry as the ground state, as well as in the inability of the method to describe Rabi oscillations.

Authors:
Publication Date:
OSTI Identifier:
22413260
Resource Type:
Journal Article
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 141; Journal Issue: 21; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9606
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; COMPARATIVE EVALUATIONS; CONFIGURATION INTERACTION; DENSITY MATRIX; DIPOLE MOMENTS; ELECTRIC FIELDS; ELECTRONIC STRUCTURE; ELECTRONS; EQUATIONS OF MOTION; EXCITATION; EXCITED STATES; GROUND STATES; OPTIMIZATION; OSCILLATIONS; TIME DEPENDENCE; VARIATIONAL METHODS

Citation Formats

Jeffcoat, David B., and DePrince, A. Eugene, E-mail: deprince@chem.fsu.edu. N-representability-driven reconstruction of the two-electron reduced-density matrix for a real-time time-dependent electronic structure method. United States: N. p., 2014. Web. doi:10.1063/1.4902757.
Jeffcoat, David B., & DePrince, A. Eugene, E-mail: deprince@chem.fsu.edu. N-representability-driven reconstruction of the two-electron reduced-density matrix for a real-time time-dependent electronic structure method. United States. https://doi.org/10.1063/1.4902757
Jeffcoat, David B., and DePrince, A. Eugene, E-mail: deprince@chem.fsu.edu. 2014. "N-representability-driven reconstruction of the two-electron reduced-density matrix for a real-time time-dependent electronic structure method". United States. https://doi.org/10.1063/1.4902757.
@article{osti_22413260,
title = {N-representability-driven reconstruction of the two-electron reduced-density matrix for a real-time time-dependent electronic structure method},
author = {Jeffcoat, David B. and DePrince, A. Eugene, E-mail: deprince@chem.fsu.edu},
abstractNote = {Propagating the equations of motion (EOM) for the one-electron reduced-density matrix (1-RDM) requires knowledge of the corresponding two-electron RDM (2-RDM). We show that the indeterminacy of this expression can be removed through a constrained optimization that resembles the variational optimization of the ground-state 2-RDM subject to a set of known N-representability conditions. Electronic excitation energies can then be obtained by propagating the EOM for the 1-RDM and following the dipole moment after the system interacts with an oscillating external electric field. For simple systems with well-separated excited states whose symmetry differs from that of the ground state, excitation energies obtained from this method are comparable to those obtained from full configuration interaction computations. Although the optimized 2-RDM satisfies necessary N-representability conditions, the procedure cannot guarantee a unique mapping from the 1-RDM to the 2-RDM. This deficiency is evident in the mean-field-quality description of transitions to states of the same symmetry as the ground state, as well as in the inability of the method to describe Rabi oscillations.},
doi = {10.1063/1.4902757},
url = {https://www.osti.gov/biblio/22413260}, journal = {Journal of Chemical Physics},
issn = {0021-9606},
number = 21,
volume = 141,
place = {United States},
year = {Sun Dec 07 00:00:00 EST 2014},
month = {Sun Dec 07 00:00:00 EST 2014}
}