Time-dependent density-matrix-functional theory
Abstract
Although good progress has been made in the calculation of correlation energies from total energy expressions which are implicit functionals of the one-particle reduced density matrix, and explicit functionals of the natural orbitals (NOs) and their occupation numbers, a formulation of the calculation of excitation energies in this so-called density-matrix-functional theory (DMFT) is still lacking. In this paper we propose a time-dependent density-matrix-functional theory (TDDMFT). It is based on the equation of motion (EOM) for the 1-matrix P(s)(t) in the representation of the stationary NOs. In the final form of the EOM, the rate of change of the P(s)(t) , ∂P(s)(t)/∂t , is determined by the commutator of the generalized time-dependent Fock matrix F(s)(t) with P(s)(t) plus an additional term D(s)(t) . The matrix F(s)(t) determines the evolution of the NOs in the time-dependent one-electron Schrödinger equations, while D(s)(t) determines the time evolution of the NO occupations. With the neglect of the electron Coulomb correlation, the time-dependent one-electron equations for the NOs reduce to those for the Hartree-Fock (HF) orbitals of time-dependent HF (TDHF) theory. The coupled-perturbed equations of TDDMF response theory (TDDMFRT) are derived for the linear response of the 1-matrix δP(s)(t) to a time-dependent perturbation δvext(t) of the external potential. The frequency-dependent changes δP(s),ij(ω) and δP(s),kl(ω) are coupled through the coupling matrix Kijkl(ω) , which is produced with the derivatives of F(s)(t) and D(s)(t) with respect to Pkl(t') . Based on the response equations, TDDMFRT eigenvalue equations are derived for the electron excitations ωq .
- Publication:
-
Physical Review A
- Pub Date:
- January 2007
- DOI:
- 10.1103/PhysRevA.75.012506
- Bibcode:
- 2007PhRvA..75a2506P
- Keywords:
-
- 31.15.Ew;
- 31.70.Hq;
- Density-functional theory;
- Time-dependent phenomena: excitation and relaxation processes and reaction rates