Unified interpretation of Hund’s first and second rules for 2p and 3p atoms

Abstract

A unified interpretation of Hund's first and second rules for 2p (C, N, O) and 3p (Si, P, S) atoms is given by Hartree-Fock (HF) and multiconfiguration Hartree-Fock (MCHF) methods. Both methods exactly satisfy the virial theorem, in principle, which enables one to analyze individual components of the total energy E(=T+V(en)+V(ee)), where T, V(en), and V(ee) are the kinetic, the electron-nucleus attraction, and the electron-electron repulsion energies, respectively. The correct interpretation for each of the two rules can only be achieved under the condition of the virial theorem 2T+V=0 by investigating how V(en) and V(ee) interplay to attain the lower total potential energy V(=V(en)+V(ee)). The stabilization of the more stable states for all the 2p and 3p atoms is ascribed to a greater V(en) that is caused by contraction of the valence orbitals accompanied with slight expansion of the core orbitals. The contraction of the valence orbitals for the two rules is a consequence of reducing the Hartree screening of the nucleus at short interelectronic distances. The reduced screening in the first rule is due to a greater amount of Fermi hole contributions in the state with the highest total spin-angular momentum S. The reduced screening in the second rule is due to the fact that two valence electrons are more likely to be on opposite sides of the nucleus in the state with the highest total orbital-angular momentum L. For each of the two rules, the inclusion of correlation does not qualitatively change the HF interpretation, but HF overestimates the energy difference ∣ΔE∣ between two levels being compared. The magnitude of the correlation energy is significantly larger for the lower L states than for the higher L states since two valence electrons in the lower L states are less likely to be on opposite sides of the nucleus. The MCHF evaluation of ∣ΔE∣ is in excellent agreement with experiment. The present HF and MCHF calculations demonstrate the above statements that were originally given by Katriel [Theor. Chem. Acta 23, 309 (1972); 26, 163 (1972)]. We have, for the first time, analyzed the correlation-induced changes in the radial density distribution for the excited LS terms of the 2p and 3p atoms as well as for the ground LS term.

Origin of Hund’s multiplicity rule in singly excited helium: Existence of a conjugate Fermi hole in the lower spin state

“…Following Davidson's paper a number of studies evaluated one-electron and two-electron energies with improved accuracy confirming Davidson's conclusion for neutral atomic species [30,31] and provided additional insight into the problem. The same nature of the one-and two-electron components in the singlet and triplet excited states of He was shown to hold even when correlation effects are accounted for [18,32]. Recently, a very thorough study of these effects has been carried out by Oyamada et al [32] to which we refer the reader for an excellent overview of the literature concerning this problem.…”

“…The same nature of the one-and two-electron components in the singlet and triplet excited states of He was shown to hold even when correlation effects are accounted for [18,32]. Recently, a very thorough study of these effects has been carried out by Oyamada et al [32] to which we refer the reader for an excellent overview of the literature concerning this problem.…”

“…The first Hund rule states that among the different spin states belonging to the same orbital configuration it is the highest spin state that has the lowest energy. In the intervening years since the formulation of these rules numerous authors endeavored to provide their theoretical underpinning [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]. More recently, similar attention has been paid to the role of Hund rules in quantum dots or artificial atoms [33,34].…”

Activity of cladribine combined with cyclophosphamide in frontline therapy for chronic lymphocytic leukemia with 17p13.1/TP53 deletion

“…Several other discussions of these issues appeared during the intervening years, some of which provide further or more detailed analysis, for example, Oyamada et al27, where an excellent review of related work can be found. A study of 2392 spectroscopic terms of 170 electronic configurations arising in 80 different neutral atoms confirmed that the lower energy term tends to have a higher interelectronic repulsion28.…”

One and two body densities for excited states of the helium confined atom

“…This property, V ee greater for the triplet than for the singlet, has been observed for a great number of neutral atoms. [11,12] But the study of atomic isoelectronic sequences shows that the interelectronic repulsion reaches greater values for the singlet states than for the corresponding triplet ones as the nuclear charge of the ion increases. [13,14] This same happens when the atoms are confined, that is, the interelectronic repulsion energy for the singlet becomes greater than for the triplet as the confinement radius decreases.…”