Simple minimum principle to derive a quantum-mechanical/molecular-mechanical method.

We propose a minimum principle to derive a QM/MM (quantum-mechanical/molecular-mechanical) method from the first principle. We approximate the Hamiltonian of a spectator substituent as the structure-dependent effective Hamiltonian in a least-squares sense. This effective Hamiltonian is expanded with the orthogonal operator set called the normal-ordered product. We determine the structure-dependent energy that corresponds to the classical MM energy and the extra one-electron potential that takes account of the interface effects. This QM/MM method is free from the double-counting problem and the artificial truncation of the localized molecular orbitals. As a numerical example we determine the one-electron effective Hamiltonian of the methyl group. This effective Hamiltonian is applied to the ethane and CH(3)CH(2)X molecules (X=CH(3), NH(2), OH, F, COOH, NH(3) (+), OH(2) (+), and COO(-)). It reproduced the relative energies, potential energy curves, and the Mulliken populations of the all-electron calculations fairly well.