Electron-momentum densities of singly charged ions

Abstract

Spherically averaged electron momentum densities ⌸( p) are constructed by the numerical Hartree-Fock method for 54 singly charged atomic cations from He ϩ ͑atomic number Zϭ2) to Cs ϩ (Zϭ55) and 43 anions from H Ϫ (Zϭ1) to I Ϫ (Zϭ53) in their experimental ground state. As in the case of neutral atoms, the Hartree-Fock momentum densities for all these ions can be classified into three types; 28 cations and 10 anions have a unimodal density with a maximum at pϭ0, 22 cations and 21 anions have a unimodal density with a maximum at pϾ0, and 4 cations and 12 anions have a bimodal density with a primary maximum at pϭ0 and a secondary maximum at pϾ0.

Electron-pair densities of group 14, 15, and 16 atoms in their low-lying multiplet states

“…25-27͒ atoms, explicit examination of the spherically-averaged h(u) and radial H(u) electron-pair intracule densities, where u denotes the relative distance between any pair of electrons, showed that the Fermi hole effect in high spin states appears only in a very small u region, and high spin states have a greater probability of finding a pair of electrons at smaller u than low spin states. The same has been confirmed recently 27 to be true for all the group 2 atoms up to Ra (Zϭ88), where Z stands for atomic number.…”

“…In other words, a pair of electrons in a low energy state is more likely to be on opposite sides of the nucleus than in a high energy state, as observed for the 1 P Ϫ 3 P differences in the He atom 21 and the group 2 atoms. 27 This trend works to reduce the increase in the electron repulsion, observed in the analysis of intracule densities and moments, in a high energy state. The differences in the extracule moments ͗R k ͘ summarized in Table II are consistent with ⌬D(R); for all the five atoms, the moments ͗R k ͘ with k Ͼ0 increase while ͗R k ͘ with kϽ0 decrease in the order of the 3 P, 1 D, and 1 S states, with a sole exception for ͗R Ϫ2 ͘ of the C atom.…”

“…9, 11-16͒ and 1 P/ 3 P ͑Refs. 9, 11, 12, 16-21͒ multiplets of the He atom, the 1 P/ 3 P multiplets of the Be atom, [22][23][24][25][26][27] and the 1 ⌸ u / 3 ⌸ u states of the H 2 molecule, 28,29 all the studies have a common conclusion that a state with a higher spin or orbital angular momentum is more tight in the relevant valence orbital, and a lower total energy E of the state is generally due to the decrease in the electron-nucleus attraction energy V en which is greater in magnitude than the increase in the electron-electron repulsion energy V ee . Neither simple perturbation theoretic considerations based on the exchange integral in the Hartree-Fock theory nor naïve anticipation of the effect of Fermi hole in high spin states was found to be valid.…”

Exponentially correlated Gaussian functions in variational calculations. Momentum space properties of the ground state helium dimer

“…[29][30][31][32][33][34] There are many reasons which make the momentum space properties so attractive. One surely comes from the fact that many of them is accessible from measurements.…”

Structural properties of reciprocal form factor in neutral atoms and singly charged ions

“…[11][12][13][14] T. Koga and coworkers have studied that according to ⌸(p) modalities the atoms that have been studied in this work can be separated into three distinct categories: 13,14 • Type A. Atoms with a unimodal ⌸(p) with its maximum located at the origin (p max ϭ0); i.e., a monotonically decreasing momentum density.…”