Multistate, Polarizable QM/MM Embedding Scheme Based on the Direct Reaction Field Method: Solvatochromic Shifts, Analytical Gradients and Optimizations of Conical Intersections in Solution

We recently introduced
a polarizable embedding scheme based on
an integral-exact reformulation of the direct reaction field method
(IEDRF) that accounts for the differential solvation of ground and
excited states in QM/MM simulations. The polarization and dispersion
interactions between the quantum-mechanical (QM) and molecular-mechanical
(MM) regions are described by the DRF Hamiltonian, while the Pauli
repulsion between explicitly treated QM electrons and the implicit
electron density around MM atoms is modeled with effective core potentials.
A single Hamiltonian is used for all electronic states so that Born–Oppenheimer
states belonging to the same geometry are orthogonal and state crossings
are well-defined. In this work, we describe the implementation of
the method using graphical processing unit acceleration in TeraChem,
where it is combined with multiple electronic structure methods, including
Hartree–Fock, time-dependent density functional theory, and
complete active space self-consistent field. In contrast with older
implementations of the DRF method, integrals of the polarization operators
are evaluated exactly. Expressions for ingredients needed to construct
analytical gradients and nonadiabatic coupling vectors are derived
and tested by optimizing a conical intersection between two excited
states in the presence of a polarizable solvent shell. The method
is applied to estimate the solvent shifts of absorption energies of
a series of donor–acceptor dyes having low-lying charge-transfer
states. Even for a nonpolar solvent such as n-hexane,
the inclusion of its static polarizability leads to non-negligible
shifts that improve the agreement to essentially quantitative levels
(0.03 eV) with full-system calculations. Good agreement with the positions
of the experimental absorption maxima measured in solution is also
observed.