TY - JOUR
T1 - Unified interpretation of Hund's first and second rules for 2p and 3p atoms
AU - Oyamada, Takayuki
AU - Hongo, Kenta
AU - Kawazoe, Yoshiyuki
AU - Yasuhara, Hiroshi
N1 - Funding Information:
The authors are grateful to Dr. Mark A. Watson for his fruitful comments and Dr. Soh Ishii and Dr. Hannes Raebiger for their valuable discussions. The authors wish to express their gratitude to the referees for pointing out several pertinent issues about the traditional interpretation of Hund’s rules and suggesting some changes to make the manuscript more readable and clearer. One of the authors (T.O.) would like to express his appreciation to Professor Hirohiko Kono and Professor Tsuyoshi Kato for their encouragement. This work has been supported by the Grant-in-Aid for Japan Society for the Promotion of Science (JSPS) research fellows (Grant No. 20⋅6432). K.H. is grateful for a JSPS Postdoctoral Fellowship for Research Abroad. The computation in this work has been performed using SR11000 supercomputer and the facilities of the Center for Computational Materials Science of the Institute for Materials Research, Tohoku University.
PY - 2010/10/28
Y1 - 2010/10/28
N2 - 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+ Ven + Vee), where T, Ven, and Vee 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 Ven and Vee interplay to attain the lower total potential energy V (= Ven + V ee). The stabilization of the more stable states for all the 2p and 3p atoms is ascribed to a greater Ven 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.
AB - 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+ Ven + Vee), where T, Ven, and Vee 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 Ven and Vee interplay to attain the lower total potential energy V (= Ven + V ee). The stabilization of the more stable states for all the 2p and 3p atoms is ascribed to a greater Ven 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.
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U2 - 10.1063/1.3488099
DO - 10.1063/1.3488099
M3 - Article
C2 - 21033781
AN - SCOPUS:78149402391
VL - 133
JO - Journal of Chemical Physics
JF - Journal of Chemical Physics
SN - 0021-9606
IS - 16
M1 - 164113
ER -