Quantum mechanical/quantum mechanical methods. I. A divide and conquer strategy for solving the Schrödinger equation for large molecular systems using a composite density functional–semiempirical Hamiltonian

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Abstract
Herein we describe a new combined quantum mechanical/quantum mechanical (QM/QM) method for solving the Schrödinger equation for large molecular systems. The new method uses the divide and conquer (D&C) strategy to partition a large molecular system into subsystems and a composite density functional theory (DFT)–semiempirical (SEM) Hamiltonian to describe the molecular interactions. The DFT and SEM subsystems are coupled through the chemical potential and are equilibrated by exchanging electronic charge. Calculations performed with the DFT,SEM, and composite (DFT/SEM) methods on diatomic, triatomic, and polyatomic molecules show that as one moves away from the QM/QM boundary region the Mulliken charges converge to the values that would be obtained using the “pure” Hamiltonian. In other words, we find that the quality of each SEM and DFTwave function is largely conserved, which strongly suggests that this type of approach could be applied to study chemical reactivity much in the same way combined quantum mechanical/molecular mechanical (QM/MM) methods are presently utilized.

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