Ab initio quantum mechanics/molecular mechanics method with periodic boundaries employing Ewald summation technique to electron-charge interaction: Treatment of the surface-dipole term.

We have developed a combined quantum mechanics/molecular mechanics (QM/MM) method with periodic boundary condition (PBC) treatment of explicit electron-charge interactions in a theoretically rigorous manner, for an accurate description of electronic structures for molecules in the condensed phase. The Ewald summation technique is employed for the calculation of the one-electron Hamiltonian in an ab initio framework. We decompose the Coulomb interactions into two components: those within the same cell and those between different cells. The former is calculated in the same way as the conventional QM/MM calculation for isolated systems; this article focuses on our novel method for calculating the latter type of Coulomb interactions. The detailed formulation of the Hamiltonian of this new QM/MM-PBC method, as well as the necessary one-electron integrals and their gradients, is given. The novel method is assessed by applying it to the dilute water system and a system with a coumarin molecule in water solvent; it successfully reproduces the electronic energies, frontier orbital energies, and Mulliken population charge of the real-space limit calculated by QM/MM using large isolated systems. We investigated the contribution from each term of the Hamiltonian and found that the surface-dipole term in the Ewald summation technique is indispensable for QM/MM-PBC calculations. The newly developed QM/MM-PBC method is promising for tackling chemical reactions and excited states of molecules in the condensed phase.