Constrained Møller–Plesset perturbation theory for charge transfer states

We propose a constrained Møller-Plesset second-order perturbation theory (CMP2) that incorporates electron correlation into the constrained Hartree-Fock (CHF) framework. In CMP2, the CHF solution is employed as the reference state, and a common Lagrange multiplier is introduced for both the zeroth-order and constraint Hamiltonians, enabling the inclusion of correlation effects with minimal modification to existing MP2 implementations. Two schemes are developed for determining the Lagrange multiplier: (i) CMP2-i (iterative), which iteratively updates the multiplier until the MP2 electron density satisfies the constraint, and (ii) CMP2-s (single-shot), which performs a single MP2 calculation using a CHF reference that satisfies the constraint at the Hartree-Fock level. The methods are applied to an intramolecular charge-transfer reaction of the 1,3-dinitrobenzene anion radical. CMP2-s significantly reduces computational cost while reproducing relative energy profiles comparable with CMP2-i. In addition, adiabatic energy profiles obtained with configuration interaction calculations based on CMP2 (CMP2-CI) are in good agreement with those from extended multistate complete active space second-order perturbation theory (XMS-CASPT2), demonstrating that the present approach provides a practical and efficient extension of constrained electronic structure methods to the post-Hartree-Fock level.