Coupled-cluster calculation of hyperpolarizabilities and polarizabilities for Be

The dipole-dipole-quadrupole (B) and second-dipole (γ) hyperpolarizabilities and the dipole (${\alpha }_1$) and quadrupole (${\alpha }_2$) polarizabilities are calculated for the ground state of the beryllium atom. The results are based on finite-field energies computed using the coupled-cluster double-excitation model (commonly known as CCD), corrected by fourth-order contributions from single and triple excitations computed with CCD amplitudes. The final values are ${\alpha }_1$ =37.30$e^2$ $a_0^2$ $E_H^{\mathrm{-}1}$, ${\alpha }_2$ =298.8$e^2$ $a_0^4$ $E_H^{\mathrm{-}r1\mathrm{}}$, B=-2102$e^3$ $a_0^4$ $E_H^{\mathrm{-}2}$, and γ=3.15 ×${10}^4$ $e^4$ $a_0^4$ $E_H^{\mathrm{-}3}$.