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

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Abstract

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 CH3CH2X 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.

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