Ground state of Li andBe+using explicitly correlated functions

Abstract

We compare the explicitly correlated Hylleraas and exponential basis sets in the evaluations of ground state of Li and Be + . Calculations with Hylleraas functions are numerically stable and can be performed with the large number of basis functions. Our results for ground state energies −7.478 060 323 910 10(32), −14.324 763 176 790 43(22) of Li and Be + correspondingly, are the most accurate to date. When small basis set is considered, explicitly correlated exponential functions are much more effective. With only 128functions we obtained about 10 −9 relative accuracy, but the severe numerical instabilities make this basis costly in the evaluation.

Explicitly correlated Gaussian calculations of the 2P o Rydberg spectrum of the lithium atom

“…The basis set optimization has been carried out separately for each of the nine 2 P o states considered in this work. As mentioned, it was only done for the 7 Li isotope and then the 7 Li basis sets were reused in the 6 Li and ∞ Li calculations without reoptimization of the nonlinear parameters (i.e., the L k matrix elements and the i k electron indices were kept the same for all isotopes). Our previous experience suggests that readjusting the linear expansion coefficients is sufficient to account for the small variation of the total wave function resulting from the change of the nuclear mass.…”

“…[1][2][3][4][5][6][7][8][9] We have also contributed to this effort. [10][11][12] 13 basis functions because they are capable of very well describing the medium and long range electron correlations.…”

“…The calculations, which involve generating an ECG basis for each studied state, are first performed for the most abundant lithium isotope, 7 Li. Subsequently, the basis sets generated for the nine 2 P o states of 7 Li are used in the calculations for 6 Li, as well as in the calculations of the lithium atom with an infinite nuclear mass ( ∞ Li). The purpose of the latter set of calculations is to generate energies that can be directly compared with the results obtained in conventional nonrelativistic calculations, which are usually performed with the infinite-nuclear-mass approach (i.e., by assuming the Born-Oppenheimer approximation).…”

“…where n is the number of electrons, r i is the vector connecting the nucleus with the ith electron, r i is its length, r ij is the distance between electrons i and j, m 0 is the nucleus mass (12 786.3933m e for 7 Li and 10 961.898m e for 6 Li, where m e = 1 is the electron mass), q 0 = 3 is its charge, q i = −1 are electron charges, and μ i = m 0 m i /(m 0 + m i ) are electron reduced masses. The prime indicates the matrix/vector transpose.…”

Assessment of the accuracy the experimental energies of the 1P o 1s22s6p and 1s22s7p states of 9Be based on variational calculations with explicitly correlated Gaussians

“…For two-and three-electron atomic systems, such as the helium and lithium atoms, the explicitly correlated Hylleraas-type basis functions have provided the highest accuracy level in the calculations. [3][4][5][6] The wave functions constructed from Hylleraas-type functions can satisfy the Kato cusp conditions, 7 which is a desirable feature in very accurate calculations. Unfortunately, the applicability of Hylleraas-type basis functions is limited to atoms with no more than three electrons due to unresolved issues in calculating the Hamiltonian matrix elements (at least for the general form of the basis functions).…”