Dipole and quadrupole polarizabilities and shielding factors of beryllium from exponentially correlated Gaussian functions

Abstract

Dynamic dipole and quadrupole polarizabilities as well as shielding factors of the beryllium atom in the ground state were computed at real frequencies by using the variation-perturbation method. The zeroth-and the first-order wave functions were expanded in many-electron basis of exponentially correlated Gaussian functions. The 1600-term expansion of the unperturbed wave function yielded the ground-state energy accurate to 1 cm Ϫ1 . The first-order wave functions were expanded in very large bases ͑4800 and 4400 terms͒. The nonlinear parameters of the first-order correction functions were optimized with respect to both the static and dynamic polarizabilities, and with respect to the excited-state energies. The procedure employed ensures a high accuracy of determination of dynamic properties in a wide range of frequencies and correct positions of the transition poles. Test calculations, performed on He and Li, confirmed the ability of this method to obtain the atomic properties with very high accuracy. The final values of the static properties of Be were 37.755e 2 a 0 2 E H Ϫ1 and 300.96e 2 a 0 4 E H Ϫ1 for the dipole and quadrupole polarizabilities, respectively, and 1.4769 for the quadrupole shielding factor. The convergence of the atomic properties with the size of the expansion of both the zerothand first-order functions was checked. Thanks to very high accuracy of the unperturbed wave function and the efficient method of construction of the first-order wave functions, the dynamic polarizability results presented in this work are of benchmark quality. As a by-product of this project, a set of the most accurate upper bounds to the energies of 1 P and 1 D states of Be was obtained.

Lithium electric dipole polarizability

“…At the leading (nonrelativistic) order, the ground-state polarizability of the lithium atom has already been calculated with high numerical precision to be α 0 = 164.112(1) [23]. The result α 0 = 164.1117 of comparable accuracy has also been obtained with explicitly correlated Gaussian (ECG) functions [24]. Calculations beyond the leading order have never been performed so far, probably due to high complexity.…”

Polarizabilities of the beryllium clock transition

“…It is less than 0.05 a.u. smaller than the close to exact determination using a basis of explicitly correlated Gaussians (ECGs) [17]. Similarly, the relativistic configuration interaction plus many-body perturbation theory (CI + MBPT) values of Porsev and Derevianko [18] lie within 0.05 a.u.…”

“…There have been some previous investigations of the beryllium polarizabilities [9][10][11][12][13][14][15][16][17][18][19][20][21]. These have mainly focused on the ground state and only a few calculations have been performed for any of the excited states [10,14,19].…”

The three-electron harmonium atom: The lowest-energy doublet and quadruplet states

“…The primitives (13) do not correspond to any particular value of L, except for the case when all the vectors {R Ip } vanish (which yields L = 0). In principle, the multiplication of these primitives by either respective angular functions 23 or polynomials in {x p }, {y p }, and {z p } (p = 1, 2, 3) 32 would produce their counterparts pertaining to higher angular momenta. However, the lobe primitives are numerically expedient and efficient when the energies are minimized with respect to all the variational parameters {C I ,…”