Theoretical study on the spin state and open-shell character dependences of the second hyperpolarizability in hydrogen chain models

Spin state and open-shell character dependences of the static second hyperpolarizability (γ) are theoretically investigated using hydrogen chain models H2n(1≤n≤3) at the full configuration interaction level of approximation. The variation in γ is examined as a function of changing the spin state for a variety of open-shell characters ranging from the closed-shell to pure open-shell states. It is found that (i) in the nearly ground-state closed-shell region, higher-spin states exhibit much larger γ values than the singlet state; (ii) in the intermediate and large open-shell character regions, the singlet state presents the largest γ and γ decreases with the spin multiplicity; and (iii) in the pure open-shell region, all the spin states exhibit negligible γ values. The summation-over-states approach enables rationalizing these findings by considering the primarily contributing excited states. These results reveal that there are two types of molecular design guidelines for enhancing γ values: (a) for nearly closed-shell systems, increasing the spin multiplicity; and (b) for open-shell singlet systems, tuning the open-shell character to the intermediate region.