The hyperpolarizability of Li 1s22s2S: a test case for advanced theories of electronic properties

From the existing calculations of the hyperpolarizability, gamma , of Li 1s 2 2s 2 S, it is evident that this quantity is very difficult to obtain reliably. The authors present a state-specific approach for the computation of linear and non-linear polarizability of polyelectronic ground or excited states and apply it to the prototypical He 1 S and Li 2 S states. The problem is formulated as one of searching for the complex eigenvalue of a non-Hermitian matrix, H, constructed from multidimensional function spaces, Q and P, which are chosen according to the spectral features and electronic structure of the system under investigation. For example, in the present case, singly and selected doubly excited states are included, representing valence and core-valence electron correlation and field-induced excitations. On the other hand, for reasons of economy the pair correlation of the K-shell electrons in Li is neglected. The results, alpha (He) = 1.389 au, gamma (He) = 42.78 au and alpha (Li) = 164.9 au, gamma (Li) = 3.7 x 10 4 au are compared with previous ones, obtained from methods using fixed basis sets or r ij -dependent expansions. For gamma (Li), the observed discrepancy suggests that additional theoretical and certainly experimental information would be very useful.