Full configuration interaction calculations of the second hyperpolarizabilities of the H₄ model compound: Summation-over-states analysis and interplay with diradical characters

The second hyperpolarizability (γ) of the one-dimensional H4 model compoundhas been calculated at the full configuration interaction level to describe its relationships with the diradical characters yi [the occupation numbers of the lowest unoccupied natural orbital (LUNO) + i] and the geometry. It is found that the system with intermediate y0 ( = 0.527) and small y1 ( = 0.178) exhibits the largest γ value [enhanced by a factor of 9 compared to that of a nearly closed-shell H4 analog (y0 = 0.099, y1 = 0.029)], where both the outer H–H distances are slightly larger than the inner one. These results provide a molecular design guideline for enhancing and controlling the third-order nonlinear optical properties of singlet multiradical linear molecular systems such as multiradical organic aggregates, supermolecular systems, and extended metal atom chains.