Lagrangian Formulation of Nuclear-Electronic Orbital Ehrenfest Dynamics with Real-time TDDFT for Extended Periodic Systems

TL;DR

This paper develops a Lagrangian-based method combining nuclear-electronic orbital theory with real-time TDDFT to simulate proton transfer in extended periodic systems, capturing both quantum and classical nuclear dynamics.

Contribution

It introduces a Lagrangian formulation for NEO Ehrenfest dynamics with RT-TDDFT in periodic systems, enabling more accurate simulations of proton transfer and solvation effects.

Findings

Validated on proton transfer in o-hydroxybenzaldehyde with water

Highlighted the role of solvation dynamics in proton transfer

Demonstrated the method's applicability to complex condensed systems

Abstract

We present a Lagrangian-based implementation of Ehrenfest dynamics with nuclear-electronic orbital (NEO) theory and real-time time-dependent density functional theory (RT-TDDFT) for extended periodic systems. In addition to a quantum dynamical treatment of electrons and selected protons, this approach allows for the classical movement of all other nuclei to be taken into account in simulations of condensed matter systems. Furthermore, we introduce a Lagrangian formulation for the traveling proton basis approach and propose new schemes to enhance its application for extended periodic systems. Validation and proof-of-principle applications are performed on electronically excited proton transfer in the o-hydroxybenzaldehyde molecule with explicit solvating water molecules. These simulations demonstrate the importance of solvation dynamics and a quantum treatment of transferring protons. This work broadens the applicability of the NEO Ehrenfest dynamics approach for studying complex heterogeneous systems in the condensed phase.