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

 Takayuki Oyamada, Kenta Hongo, Yoshiyuki Kawazoe, and Hiroshi Yasuhara

 

 Received 22 April 2010; accepted 17 August 2010; published online 29 October 2010

 

 A unified interpretation of Hund’s first and second rules for 2pC, N, Oand 3pSi, P, Satoms isgiven by Hartree–FockHFand multiconfiguration Hartree–FockMCHFmethods. Both methodsexactly satisfy the virial theorem, in principle, which enables one to analyze individual componentsof the total energyE=T+Ven+Vee, whereT,Ven, andVeeare the kinetic, the electron-nucleusattraction, and the electron-electron repulsion energies, respectively. The correct interpretation foreach of the two rules can only be achieved under the condition of the virial theorem 2T+V=0 byinvestigating howVenandVeeinterplay to attain the lower total potential energyV=Ven+Vee. Thestabilization of the more stable states for all the 2pand 3patoms is ascribed to a greaterVenthat iscaused 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 Hartreescreening of the nucleus at short interelectronic distances. Thereduced screeningin the first rule isdue to a greater amount of Fermi hole contributions in the state with the highest total spin-angularmomentumS. The reduced screening in the second rule is due to the fact that two valence electronsare more likely to be on opposite sides of the nucleus in the state with the highest totalorbital-angular momentumL. For each of the two rules, the inclusion of correlation does notqualitatively change the HF interpretation, but HF overestimates the energy differenceEbetweentwo levels being compared. The magnitude of the correlation energy is significantly larger for thelowerLstates than for the higherLstates since two valence electrons in the lowerLstates are lesslikely to be on opposite sides of the nucleus. The MCHF evaluation ofEis in excellent agreementwith experiment. The present HF and MCHF calculations demonstrate the above statements thatwere originally given by KatrielTheor. Chem. Acta23, 3091972;26, 1631972. We have, forthe first time, analyzed the correlation-induced changes in the radial density distribution for theexcitedLSterms of the 2pand 3patoms as well as for the groundLSterm. ©2010 AmericanInstitute of Physics.

 

https://sci-hub.se/https://doi.org/10.1063/1.3488099