Time-dependent exchange-correlation current density functionals with memory

Abstract

Most present applications of time-dependent density functional theory use adiabatic functionals, i.e. the effective potential at time t is determined solely by the density at the same time. This paper discusses a method that aims to go beyond this approximation, by incorporating "memory" effects: the potential will depend not only on present behavior but also on the past. In order to ensure the derived potentials are causal, we formulate the action on the Keldysh contour for electrons in electromagnetic fields, from which we derive suitable Kohn-Sham equations. The exchange correlation action is now a functional of the electron density and velocity field. A specific action functional is constructed which is Galilean invariant and yields a causal vector potential term to the Kohn-Sham equations that incorporates causal memory effects. We show explicitly that the exchange-correlation Lorentz force is zero. The potential is consistent with known dynamical properties of the homogeneous electron gas (in the linear response limit).

Tuned Range-Separated Hybrids in Density Functional Theory

“…The inclusion of memory is next to impossible with local TDXC approximations to TDDFT because Galilean invariance and the 0-force conditions cannot be imposed (107)(108)(109) as there is no stationary principle for nonadiabatic functionals in TDDFT (110). These problems prompted KS-like developments within time-dependent current-density functionals (109,111,112), metric or deformation tensor functionals (106,(113)(114)(115)(116), and potential-adaptation methods (117,118). Another problem with adiabatic semilocal functionals within TDKS theory is that they predict too low excitation energies for long-range charge-transfer excitations (CTEs) (38,45,52,119,120).…”

Quantum memory effects in the dynamics of electrons in gold clusters

“…leads to a dependence of XC v at time t on the density at a later time. It was however shown that a TI action can still be obtained if one considers a mathematical device called the Keldysh contour 34 .…”

“…Extending this approach to real-time and beyond linear response applications is complicated and has been done only in 1-dimensional cases 26,33 . The basic problem is that imposition of TC usually warrants a Lagrangian system of coordinates 23,26,28,34 , as opposed to the normally used Eularian (fixed) coordinate system. In three dimensions, this is a great impediment since the numerical methods for solving the Schrödinger equation in a Lagrangian frame are still not developed and robust enough to serve a basis for a general TDDFT program.…”

Adapting approximate-memory potentials for time-dependent density functional theory

“…f GK is determined using the Kramers Kroning relations (see Appendix D of ref. 7 for the details). By definition, the linear response around the ground state of a homogeneous electron gas gives:…”

“…These laws are derived from the fundamental notions of classical mechanical description of space and time, since the era of Galileo and Netwon. A complete treatment of this problem leads one to the realm of time-dependent current-density functional theory (TDCDFT) [6][7][8][9] . However, the problems can also be treated within TDDFT 5 , 10, 11 .…”