Second hyperpolarizabilities of 1-center radicals
Abstract We study the second hyperpolarizabilities ( γ) for 1-center radicals, i.e. , BH 3 − , CH 3 and NH 3 + . It is found that magnitudes of γ( ¦γ¦) of the radicals are sensitively influenced by features of each charged state. It is also found that electron-correlation dependence of γ can be related to the resonance structure contributing to the ground state of the molecules
Abstract Using order statistics, we prove Gauss' 2F1 identity probabilistically. As a consequence, we show that Gauss' 2F1 summation formula is related to an inverse Polya distribution. We observe that a relationship exists between WZ-pairs and our probabilistic approach.