Memory in Time-Dependent Density Functional Theory

Neepa Maitra
Hunter College, CUNY

Most applications of TDDFT utilize the adiabatic approximation, where the instantaneous density is inserted into a ground-state approximation for the exchange-correlation potential. In such a calculation, the exchange-correlation functional depends only on the instantaneous density, however the exact functional is known to depend on the history of the density as well as the initial interacting state and the choice of initial Kohn-Sham state. An exact condition relates the two sources of memory. By defining an "adiabatically-exact" functional, one can isolate errors that are due exclusively to making the adiabatic approximation in contrast to errors arising from the choice of ground-state functional. Several examples will be given which demonstrate memory-dependence, and the exact functional will be compared with the adiabatically-exact.

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