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Electrostatic potential fitting method (ESPF) is a powerful way of definingatomic charges derived from quantum density matrices fitted to reproduce aquantum mechanical charge distribution in the presence of an externalelectrostatic potential. These can be used in the Hamiltonian to define arobust and efficient electrostatic embedding QM/MM method. The originalformulation of ESPF QM/MM contained two main approximations, namely, theneglect of grid derivatives and the non-conservation of the total QM charge.Here, we present a new ESPF atomic charge operator which solves these drawbacksat virtually no extra computational cost. The new charge operators employatom-centered grids and conserve the total charge when traced with the densitymatrix. We present an efficient and easy-to-implement analytic form for theenergy, gradient, and hessian that scale linearly with the MM subsystem size.We show that grid derivatives and charge conservation are fundamental topreserve the translational invariance properties of energies and itsderivatives and exact conditions to be satisfied by the atomic chargederivatives. As proof of concept, we compute the transition state that leads tothe formation of hydrogen peroxide during cryptochrome's reoxidation reaction.Last, we show that the construction of the full QM/MM hessian scales linearlywith the MM subsystem size.

journal of chemical theory and computation

Analytic energy, gradient, and hessian of electrostatic embedding QM/MM  based on electrostatic potential fitted atomic charges scaling linearly with  the MM subsystem size