Rare gas atomic number dependence of the hyperpolarizability for rare gas inserted fluorohydrides, HRgF (Rg = He, Ar, and Kr).

The three structures of rare gas inserted fluorohydrides HRgF (Rg = He, Ar, and Kr) with all real frequencies are obtained at the QCISD(T)/aug-cc-pVTZ level. The static first hyperpolarizabilities (beta(0)) at the QCISD/aug-cc-pVQZ level are 8 a.u. (HF), 384 a.u. (HHeF), 737 a.u. (HArF), and 465 a.u. (HKrF). The beta(0) value remarkably increases by about 50-90 times from 8 a.u. (HF) to 384-737 a.u. (HRgF) due to the inserted rare gas (Rg). The Rg atomic number dependence of beta(0) for HRgF (Rg = He, Ar, and Kr) is found at the first time. The order of beta(0) is unmonotonic to be HHeF<HArF>HKrF, but not monotonic (HHeF<HArF<HKrF). Why? The Rg atomic number dependence of beta(0) relates to both the geometric effect (expanded H...F distance by Rg) and the electronic effect of Rg. From HHeF to HArF and from HArF to HKrF, the preponderant effect on beta(0) is variational. From HHeF to HArF, the geometric effect is preponderant and the beta(0) value increases; from HArF to HKrF, the electronic effect of Rg is preponderant and the beta(0) value decreases. Thus, the rare gas atomic number dependence of beta(0) is unmonotonic. Furthermore, as the order of beta(0) is consistent with that of the difference between the ground and excited-state dipole moments (Deltamu), the Deltamu may be one mainly controlling factor of beta(0). The nature of H-Rg bond is also explored that special short H-He bond of 0.811 A is only a half single bond due to its Wiberg bond index of 0.51, while the long H-Ar and H-Kr bonds are almost single bond with the Wiberg bond index of about 0.8.