Embedding methodology such as QM/MM is a powerful approach to modelling the properties and dynamics of complex systems, wherein electronic structure theory is applied to an “active” Quantum Mechanical (QM) region, with the remainder of the system treated with Molecular Mechanics (MM) forcefields. Building on the long history of QM/MM approaches to ground-state dynamics, there has been a recent rise in applying QM/MM to simulate the excited-state dynamics of complex systems, by evolving the QM/MM Hamiltonian with a nonadiabatic propagation of the nuclear trajectories, e.g. with ab initio multiple spawning or surface hopping. To achieve high accuracy, two approaches are typically followed: 1) increasing the size of the QM region to convergence; 2) using a polarizable MM (MM-Pol) forcefield and mutually coupling the QM and MM-Pol induced dipoles. In the context of solution-phase excited-state dynamics, both approaches introduce problems: 1) the boundary between QM- and MM-treated solvent molecules must dynamically adapt in the course of the simulation to avoid mixing of QM and MM regions; 2) QM/MM-Pol introduces problems of root flipping and/or incorrect descriptions of electronic crossings in multistate calculations.[<i>J. Chem. Theory Comput.</i> <b>14</b>, 2137 (2018)] To address these issues, we have developed two complementary approaches. The first method is Flexible Boundary Layer using Exchange (FlexiBLE), which adds a biasing potential to the system that maintains QM and MM separation while leaving ensemble averages and even dynamical properties unaltered. The second method is Many-Body Polarization/Dispersion embedding (QM/MM-MBPD). The new 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. In addition, since the MM dipoles are entangled with the QM system, dispersion interactions between the QM and MM subsystems are approximately recovered. Furthermore, since the embedding operator has no explicit state dependence, root-flipping issues are avoided and the method correctly describes electronic state crossings. We demonstrate the methods on challenging condensed-phase systems, including photosynthetic complexes and the hydrated electron, an excess electron embedded in liquid water.

Developments in QM/MM for condensed-phase ground- and excited-state dynamics

ACS Spring 2022

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