A popular strategy to exploring the molecular 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 forcefield. Equally important to the level of electronic structure theory and quality of forcefield is the treatment of the coupling between the QM and MM subsystems, i.e. how the QM region is embedded in the MM system. The state-of-the-art is to use a polarizable forcefield 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, extensions to electronic excited states are less well developed, and we showed previously that current QM/MM-Pol approaches have problems of root flipping and/or incorrect descriptions of electronic crossings in multistate calculations. 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. In addition, since the MM dipoles are entangled with the QM system, state-dependent QM-MM polarization interactions are captured, and the method correctly describes electronic state crossings. We describe a graphical processing unit implementation of the method and its analytical gradients that enables application to systems of hundreds of QM and MM particles at the HF, DFT, CIS, TDDFT, CASCI, and CASSCF levels. We furthermore demonstrate that QM/MM-IEDRF correctly predicts asymmetry in the charge-transfer pathways of the purple bacteria reaction center (A-branch versus B-branch), and that protein polarization plays a dominant role in selecting the A-branch.

Multistate polarizable QM/MM embedding scheme: Integral-exact direct reaction field

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