Natural Charge-Transfer Analysis: Eliminating Spurious Charge-Transfer States in Time-Dependent Density Functional Theory via Diabatization, with Application to Projection-Based Embedding

For
many types of vertical excitation energies, linear-response
time-dependent density functional theory (LR-TDDFT) offers a useful
degree of accuracy combined with unrivaled computational efficiency,
although charge-transfer excitation energies are often systematically
and dramatically underestimated, especially for large systems and
those that contain explicit solvent. As a result, low-energy electronic
spectra of solution-phase chromophores often contain tens to hundreds
of spurious charge-transfer states, making LR-TDDFT needlessly expensive
in bulk solution. Intensity borrowing by these spurious states can
affect intensities of the valence excitations, altering electronic
bandshapes. At higher excitation energies, it is difficult to distinguish
spurious charge-transfer states from genuine charge-transfer-to-solvent
(CTTS) excitations. In this work, we introduce an automated diabatization
that enables fast and effective screening of the CTTS acceptor space
in bulk solution. Our procedure introduces “natural charge-transfer
orbitals” that provide a means to isolate orbitals that are
most likely to participate in a CTTS excitation. Projection of these
orbitals onto solvent-centered virtual orbitals provides a criterion
for defining the most important solvent molecules in a given excitation
and be used as an automated subspace selection algorithm for projection-based
embedding of a high-level description of the CTTS state in a lower-level
description of its environment. We apply this method to an ab initio molecular dynamics trajectory of I–(aq) and report the lowest-energy CTTS band in the absorption spectrum.
Our results are in excellent agreement with the experiment, and only
one-third of the water molecules in the I–(H2O)96 simulation cell need to be described with
LR-TDDFT to obtain excitation energies that are converged to <0.1
eV. The tools introduced herein will improve the accuracy, efficiency,
and usability of LR-TDDFT in solution-phase environments.