Excited-state forces within time-dependent density-functional theory: A frequency-domain approach

We introduce a frequency-domain formalism for computing excited-state forces using linear response theory within the framework of time-dependent density-functional theory. We present an implementation of the formalism within a real-space computational framework. We demonstrate the validity and usefulness of the approach by comparing its results to those obtained with a Green’s function approach using the GW+Bethe-Salpeter-equation method, for the simple case of the CO molecule. We expect the method to be advantageous for computing excited-state dynamics in large systems.

Figure 1

(Color online) (a) Energies and (b) forces for the CO molecule as a function of bond length. Ground-state calculations ($X{}^1\Sigma ^{+}$, circles) were performed with LDA. First singlet excited-state $\left(A{}^1\Pi \right)$ calculations were performed with both time-dependent LDA (TDLDA) (squares) and $\mathrm{GW}-\mathrm{BSE}$ (triangles). The dashed lines in the energy curves are a guide to the eye. The dashed lines in the force curves are the “exact” forces computed by taking finite-difference numerical derivatives of the ground- and excited-states energy curves.