Interpretation of Hund’s multiplicity rule for the carbon atom

Abstract

Hund's multiplicity rule is investigated for the carbon atom using quantum Monte Carlo methods.Our calculations give an accurate account of electronic correlation and obey the virial theorem to high accuracy. This allows us to obtain accurate values for each of the energy terms and therefore to give a convincing explanation of the mechanism by which Hund's rule operates in carbon. We find that the energy gain in the triplet with respect to the singlet state is due to the greater electron-nucleus attraction in the higher spin state, in accordance with Hartree-Fock calculations and studies including correlation. The method used here can easily be extended to heavier atoms.

Virial theorems for trapped cold atoms

“…(14). Alternatively, let us assume that the p n 's are given by the canonical distribution p n ∝ e −En(a)/(kB T ) , where the temperature T varies with a in such a way that the entropy S = −k B n p n ln p n remains constant.…”

“…, r N ), where the domain is simply a set of smooth functions. It states that the kinetic energy T is one half of the virial:for any eigenstate; implying T = n/2 U if U is a homogeneous function of degree n. This theorem is as old as many-particle quantum mechanics [13], and is used e. g. to understand the properties of many-electron atoms [14].In this paper, we present a general virial theorem for a Hamiltonian with an arbitrary domain. In the particular case where the domain does not depend on any length scale, we recover the virial theorem for the unitary gas Eq.…”

“…for any eigenstate; implying T = n/2 U if U is a homogeneous function of degree n. This theorem is as old as many-particle quantum mechanics [13], and is used e. g. to understand the properties of many-electron atoms [14].…”

Magnetism in Simple Metal and 4d Transition Metal Clusters

“…Noting that S, P, D… orbitals can accommodate maximum of 2, 6, 10,… electrons, clusters with 2,8,18,20,34,40,58,… valence electrons will have filled electronic shells, and hence will be more stable than their neighbors. This was in fact demonstrated for the first time in, what has by now become a cult paper in the area of cluster science, by Knight et al [3].…”

Correct Interpretation of Hund’s Rule and Chemical Bonding Based on the Virial Theorem

“…A number of authors have studied Hund's rule for atoms [8][9][10][11][12][13][14][15][16][17][18][19] and light molecules [20][21][22][23][24][25][26][27][28] by Hartree-Fock (HF) and other variational calculations. They have found that the stabilization of the highest multiplicity state relative to the lower multiplicity states is ascribed to a lowering in V en that is gained at the cost of increasing V ee as well as T. Davidson 8,9) has first pointed out that V ee is larger for the triplet than for the singlet by HF calculations for low-lying excited states of the helium atom.…”