The orbital picture of the first dipole hyperpolarizability from many-body response theory

We present an approach for obtaining a molecular orbital picture of the first dipole hyperpolarizability (β) from correlated many-body electronic structure methods. Ab initio calculations β rely on quadratic response theory, which recasts sum-over-all-states expression into closed-form by calculating handful first- and second-order states; resonantly enhanced β, damped theory is used. These states are then used to construct reduced one-particle density matrices (1PDMs), which, upon visualization in terms natural orbitals (NOs), facilitate rigorous black-box mapping underlying with β. explain interpretation different components 1PDMs corresponding NOs within both undamped framework. illustrate utility this new tool deconstructing cis-difluoroethene, para-nitroaniline, hemibonded OH· + H2O complex, computed framework coupled-cluster singles doubles range frequencies.