We present an approach for obtaining a molecular orbital picture of the first dipole hyperpolarizability from correlated many-body electronic structure methods. Ab initio calculations of β rely on quadratic response theory, which

recasts the sum-over-all-states expression of β into a closed-form expression by calculating a handful of first- and

second-order response states; for resonantly enhanced β , damped response theory is used. These response states are

then used to construct second-order response reduced one-particle density matrices (1PDMs), which, upon visual-

ization in terms of natural orbitals (NOs), facilitate a rigorous and black-box mapping of the underlying electronic

structure with β. We explain the interpretation of different components of the response 1PDMs and the corresponding

NOs within both the undamped and damped response theory framework. We illustrate the utility of this new tool by

deconstructing β for cis-difluoroethene, para-nitroaniline, and hemibonded OH . +H 2 O complex, computed within the

framework of coupled-cluster singles and doubles response theory, in terms of the underlying response 1PDMs and

NOs for a range of frequencies.

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The Orbital Picture of the First Dipole Hyperpolarizability from Many-Body Response Theory

1 results in Keywords: first dipole hyperpolarizability