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

• Published in: The Journal of chemical physics Vol. 141; no. 21; p. 214104
• Main Authors: Jeffcoat, David B., DePrince, A. Eugene
• Format: Journal Article
• Language: English
• Published: United States American Institute of Physics 07.12.2014
• Subjects: COMPARATIVE EVALUATIONS; CONFIGURATION INTERACTION; Density; DENSITY MATRIX; DIPOLE MOMENTS; ELECTRIC FIELDS; ELECTRONIC STRUCTURE; ELECTRONS; EQUATIONS OF MOTION; EXCITATION; EXCITED STATES; Ground state; GROUND STATES; INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; OPTIMIZATION; OSCILLATIONS; Physics; Symmetry; TIME DEPENDENCE; VARIATIONAL METHODS
• ISSN: 0021-9606; 1089-7690; 1089-7690
• DOI: 10.1063/1.4902757

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.