Conical Intersections in Solution with Polarizable Embedding: Integral-Exact Direct Reaction Field

A common strategy to exploring the
properties and reactivity of
complex systems is to use quantum mechanics/molecular mechanics (QM/MM)
embedding, wherein a QM region is defined and treated with electronic
structure theory, and the remainder of the system is treated with
a force field. Important to the description of electronic excited
states, especially those of charge-transfer character, is the treatment
of the coupling between the QM and MM subsystems. The state of the
art is to use a polarizable force field for the MM region and mutually
couple the QM wavefunction and MM induced dipoles, in addition to
the usual electrostatic embedding, yielding a polarizable embedding
(QM/MM-Pol) approach. However, we showed previously that current popular
QM/MM-Pol approaches exhibit issues of root flipping and/or incorrect
descriptions of electronic crossings in multistate calculations [J. Chem. Theory Comput. 14, 2137 (2018)]. Here,
we demonstrate a solution to these problems with an integral-exact
reformulation of the direct reaction field approach of Thole and Van
Duijnen (QM/MM-IEDRF). The resulting embedding potential includes
one- and two-electron operators and many-body dipole-induced dipole
interactions and thus includes a natural description of the screening
of electron–electron interactions by the MM induced dipoles.
Pauli repulsion from the environment is mimicked by effective core
potentials on the MM atoms. Inherent to the DRF approach is the assumption
that MM dipoles respond instantaneously to the positions of the QM
electrons; therefore, dispersion interactions are captured approximately.
All electronic states are eigenfunctions of the same Hamiltonian,
while the polarization induced in the environment and the associated
energetic stabilization are unique to each state. This allows for
a consistent definition of transition properties and state crossings.
We demonstrate QM/MM-IEDRF by exploring the influence of a (polarizable)
inert xenon matrix environment on the conical intersection underlying
the photoisomerization of ethylene.