Analytical Gradients for Nuclear-Electronic Orbital Time-Dependent Density Functional Theory: Excited State Geometry Optimizations and Adiabatic Excitation Energies

TL;DR

This paper develops and implements analytical gradients for the nuclear-electronic orbital time-dependent density functional theory, enabling accurate excited state geometry optimizations and excitation energy calculations that include nuclear quantum effects.

Contribution

It introduces the derivation and implementation of analytical gradients for NEO-TDDFT and NEO-TDA, advancing excited state calculations with nuclear quantum effects.

Findings

NEO-TDDFT improves excitation energy accuracy over conventional methods.

Geometry optimizations reveal stronger hydrogen bonds in excited states.

The approach facilitates nonadiabatic dynamics simulations of proton transfer.

Abstract

The computational investigation of photochemical processes often entails the calculation of excited state geometries, energies, and energy gradients. The nuclear-electronic orbital (NEO) approach treats specified nuclei, typically protons, quantum mechanically on the same level as the electrons, thereby including the associated nuclear quantum effects and non-Born-Oppenheimer behavior into quantum chemistry calculations. The multicomponent density functional theory (NEO-DFT) and time-dependent DFT (NEO-TDDFT) methods allow efficient calculations of ground and excited states, respectively. Herein, the analytical gradients are derived and implemented for the NEO-TDDFT method and the associated Tamm-Dancoff approximation (NEO-TDA). The programmable equations for these analytical gradients, as well as the NEO-DFT analytical Hessian, are provided. The NEO approach includes the anharmonic zero-point energy and density delocalization associated with the quantum protons, as well as vibronic mixing, in geometry optimizations and energy calculations of ground and excited states. The harmonic zero-point energy associated with the other nuclei can be computed via the NEO Hessian. This approach is used to compute the 0-0 adiabatic excitation energies for a set of nine small molecules with all protons quantized, exhibiting slight improvement over the conventional electronic approach. Geometry optimizations of two excited state intramolecular proton transfer systems are performed with one and two quantized protons, respectively. The NEO calculations for these systems produce electronically excited state geometries with stronger intramolecular hydrogen bonds and similar relative stabilities compared to conventional electronic methods. This work provides the foundation for nonadiabatic dynamics simulations of fundamental processes such as photoinduced proton transfer and proton-coupled electron transfer.