A Dependence on the Petal Number of the Static and Dynamic First Hyperpolarizability for Electride Molecules: Many-Petal-Shaped Li-Doped Cyclic Polyamines

Doping Li atom into higher flexible cyclic polyamines with many amine unit petals (ethyleneimine) forms the n-petal-shaped Li-doped cyclic polyamines (n = 3-5). Three structures, referred to as three-petal-shaped Li-[9]aneN(3), four-petal-shaped Li-[12]aneN(4), and five-petal-shaped Li-[15]aneN(5), with all-real frequencies are obtained at the MP2/6-31+G(d) level. Because the chemical doping with Li and the deformation of the complexant produce more diffuse excess electron, the three molecules with the excess electrons exhibit considerably large static first hyperpolarizabilities (beta(0)) at the MP2 level. Additionally, the beta(0) value increases with increasing the petal number (n) as follows: 52292 (n = 3) < 65505 (n = 4) < 127617 au (n = 5). This shows a new complexant effect on beta(0), that is, a dependence on the petal number (n) of beta(0) owing to the flexibility of the complexants increasing with the petal number. The MP2 frequency-dependent beta values are estimated by using the multiplicative approximation. The frequency dispersion is Found to be strong. For the MP2 frequency-dependent beta values, the more pronounced dependence on the petal number (n) of beta (-2 omega; omega, omega) and beta (-omega; omega, 0) are shown.