Analytical first-order derivatives for second-order Møller–Plesset perturbation theory with pair-natural orbitals using localized virtual molecular orbitals: electronic response properties

Accelerating analytical energy derivative calculations for large systems remains challenging within wave function-based quantum chemistry frameworks. The pair-natural orbital (PNO) method provides a powerful approach to reduce computational costs while maintaining accuracy. The authors recently reported a fully analytical nuclear gradient theory for the second-order Møller–Plesset perturbation theory using orthogonal localized virtual molecular orbital-based PNOs. This paper provides an overview of the theoretical framework and describes its extension to electronic response property calculations.