A joint time-dependent density-functional theory for excited states of electronic systems in solution

TL;DR

This paper introduces a new joint time-dependent density-functional theory for accurately modeling excited states of solute-solvent systems in time-dependent external fields, enabling better understanding of solvatochromic effects.

Contribution

It develops a systematic approach to eliminate solvent degrees of freedom from quantum-mechanical functionals, leading to an exact and coarse-grained description that improves upon existing embedding theories.

Findings

Derived a novel approximate action functional for solute-water systems.

Successfully computed the solvatochromic shift of formaldehyde's excited state in water.

Results agree well with experimental data.

Abstract

We present a novel joint time-dependent density-functional theory for the description of solute-solvent systems in time-dependent external potentials. Starting with the exact quantum-mechanical action functional for both electrons and nuclei, we systematically eliminate solvent degrees of freedom and thus arrive at coarse-grained action functionals which retain the highly accurate \emph{ab initio} description for the solute and are, in principle, exact. This procedure allows us to examine approximations underlying popular embedding theories for excited states. Finally, we introduce a novel approximate action functional for the solute-water system and compute the solvato-chromic shift of the lowest singlet excited state of formaldehyde in aqueous solution, which is in good agreement with experimental findings.