Orbital-Based Correlated Electron–Nuclear Dynamics for Extended Systems with Exact Factorization

In this work, we introduce a practical orbital-based
framework
for simulating correlated electron–nuclear dynamics in extended
systems within the exact factorization (XF) formalism. Building on
our earlier derivation of time-dependent Kohn–Sham (TDKS) equations
that merge real-time time-dependent density functional theory with
XF, we apply the classical path approximation and incorporate pairwise
XF-derived decoherence corrections in the Kohn–Sham basis.
This leads to a new efficient algorithm capable of treating nonadiabatic
processes involving thousands of atoms. As a demonstration, we perform
nonadiabatic dynamics simulations of two spiro-type hole-transport
materials under periodic boundary conditionsthe first application
of XF-based methods to extended systems. While hole dynamics without
decoherence yield unphysical, persistent coherences, the inclusion
of XF-derived decoherence produces physically consistent relaxation
from lower to higher bands.