Accurate Analytical Self-Consistent Field Functions for Atoms. IV. Ground States and Several Excited States for Atoms and Ions of Al and Cu

Abstract

Self-consistent field calculations by the expansion method were carried out for the ground states and several excited states of atoms and ions of Al and Cu. The results for the total energies of the states computed represent very accurately the absolute Hartree-Fock solutions. The wave functions were calculated with the requirement to satisfy identically the cusp condition so that they can be considered to be particularly accurate in the immediate vicinity of the nucleus. Comparison with experiment is carried out in particular for the calculated energy levels.

Wave-functions overlap in stoichiometric lanthanide laser crystals

“…Analytical six-term (6-t) SCF wave functions for the lowest states of Nd 3 þ , namely 4 I, 4 F, 4 G, and 4 D [18], and for the ground state of Pr 3 þ [24] have been converted into their unnormalized form by means of the following notation [25]: (3), and considering Eq. (4), the following relationship between both types of expansion coefficients can be obtained:…”

Quadrupole antishielding factors for ions and atomic states

“…The core wave functions (including 3d) used in the present calculations were the Hartree-Fock functions obtained by Hartree [30]. For the 4p electron in the excited 3d1°4p state, we used a modification of the Hartree-Fock wave function obtained by Synek [31]. The modification consisted in using a slightly more internal wave function which would reproduce the experimental value of ( Y -~)~, = 1.276us3, as deduced by Elbel from the measured fine structure [28].…”

An extended Wolfsberg-Helmholz calculation on CuF6-4

“…It was, therefore, investigated how these differences influenced the values of the overlap integrals. The wavefunctions which were used are the Synek [3] and Watson [4,5] functions for Cu and the Clementi et al [6] and Clementi and McLean [7] functions for F. Other useful wavefunctions include the Cu functions in [8] and [9] and the F orbitals in [10][11][12][13]. The numerical values of the overlap integrals were evaluated by means of an ' Algol' programme [14] on a ' GIER' computer.…”