Ab initio interpretation of Hund's rule for the methylene molecule: Variational optimization of its molecular geometries and energy component analysis

Abstract

ABSTRACT:Hund's spin-multiplicity rule for the ground state of the methylene molecule CH 2 is interpreted by Hartree-Fock (HF) and multi-reference configuration interaction (MRCI) methods. The stabilization of the triplet ground state (X 3 B 1 ) relative to the second singlet excited state (b 1 B 1 ) is ascribed to the greater electron-nucleus attraction energy that is gained at the cost of increasing the electron-electron repulsion energy and with the aid of a reduction in the nucleus-nucleus repulsion energy. The highest spin-multiplicity in the ground state of CH 2 is accompanied by a set of three characteristic features, i.e., elongation of the internuclear distances, reduction in the bond angle, and contraction of the valence electron density distribution around the nuclei involving expansion of the core electron density distribution. The present calculations fulfill the virial theorem to an accuracy of −V/T = 2.000 for both HF and MRCI. Accordingly, the molecular geometries are optimized for each of the two states. The inclusion of correlation by MRCI method reduces the energy splitting between the two states by about 14%. The energy splitting is analyzed by the correlational virial theorem 2T c + V c = 0 to make a clear interpretation of the correlation effect.

Term rules for simple metal clusters

“…Traditionally, Hund’s rules have been interpreted as an energy gain due to the inter-electron repulsion potential energy V ee 35 36 37 , and more recently as an energy gain due to the electronuclear attraction V en 2 4 5 7 8 . In order to analyze whether or not similar energy lowering mechanisms can be invoked for Al 2 and Al 3 , we decompose the total energies given in Table 1 into potential energy components shown in Fig.…”

“…The spin-singlet terms exhibit an opposite trend to Hund’s second rule. Term stabilities have earlier been interpreted by either V ee 35 36 37 or V en 2 4 5 7 8 , which imply that total energy differences are dominated by one potential energy component V i ( i = ee, en , or nn ), i.e., the total energy should follow the trend of this dominant V i . Figure 1 , however, shows that…”

“…Hund’s first rule of maximum spin multiplicity holds for many organic molecules 6 7 8 , but not all 9 . Diatomic molecules on the other hand, tend to have spin singlet ground states with the exception of O 2 and B 2 (see e.g.…”

“…These molecules tend to have ground states that minimize the internuclear bond length, which may be associated with a lowering of the electronuclear attraction energy, but whether or not such discussion generalizes to metallic clusters remains unknown. Moreover, recent attempts to generalize Hund’s rules for molecules 8 20 or clusters 21 22 23 only focus on a spin multiplicity rule, and trends or rules for Ξ (symmetry) terms remain completely uncharted territory.…”

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

“…In the case of CH 2 , it has been concluded by multireference CI ͑MRCI͒ that ͉V en corr ͉ is greater for the ground state ͑ 3 B 1 ͒ than for the second excited state ͑ 1 B 1 ͒, i.e., V en 63 The reason for the above inequality may be considered as follows. In the case of CH 2 , it has been concluded by multireference CI ͑MRCI͒ that ͉V en corr ͉ is greater for the ground state ͑ 3 B 1 ͒ than for the second excited state ͑ 1 B 1 ͒, i.e., V en 63 The reason for the above inequality may be considered as follows.…”