Origin of the Enhancement of the Second Hyperpolarizabilities of Metal-Carbon Bonds

The spin-unrestricted coupled-cluster method was employed to investigate the origin of the second hyperpolarizabilities (I³) in model systems involving metal-carbon bonds with various bond lengths as a function of their diradical character (y) and charge transfer (CT). These systems exhibit unique features: (i) σ electrons give the dominant contribution to I³, (ii) the Ï€ electrons contribution to I³ is negative, (iii) when the bond length increases, I³ exhibits two positive extrema, which are associated with the CT nature and the intermediate diradical character, respectively, (iv) and one negative extremum corresponding to intermediate CT and diradical character, and (v) in the bond stretching process, the maximum I³ amplitude per σ bond is about 7 times larger than that per Ï€ bond. These features are significantly different from those observed in pure organic systems.