Structure−Property Correlation on Second Hyperpolarizabilities of Symmetric One-Center and Three-Center Radicals

In order to elucidate the features of the second hyperpolarizabilities ( γ ) for n -center radical systems ( n, integer), we investigate the γ of symmetric one-center radical models, i.e., BH 3 -, CH 3, and NH 3 +, and three-center radical models, i.e., BH(CH 2 ) 2 -, CH(CH 2 ) 2, and NH(CH 2 ) 2 +, by various electron-correlation and a density functional methods using extended basis sets. Since these models are isoelectronic systems involving 9 and 23 electrons, respectively, the γ values are expected to reflect the features of their charge density distributions. It is actually found that the γ values for the isoelectronic systems sensitively depend on their charged states. For instance, the one-center radicals exhibit positive γ values at high-order electron correlation level using sufficiently large basis sets, while, for the three-center radicals, only NH(CH 2 ) 2 + is found to possess negative γ . These features are analyzed using γ density plots, which can provide a local view of spatial contributions of electrons to the γ, and are discussed in relation to our structure-property correlation rule.