Pauli-exchange antisymmetry and steric repulsions

The requirement of overall exchange antisymmetry of the /V-clcct.ron wavefunction H1, 2. N) can be expressed more generally in terms of formal invariance under the TV-electron antisymmetrizer operator A 

As was mentioned previously, simple orbital products (electron configurations) must be converted into antisymmetrized orbital products (Slater determinants) in order to satisfy the Pauli principle. Thus, proper many-electron wavefunctions satisfy constraints of exchange antisymmetry that have no counterpart in pre-quantum theories. 

Natural steric analysis57 allows quantitative evaluation of steric repulsion on the basis of this simple physical picture. Given the converged Fock (or Kohn-Sham) operator F, we can evaluate the average energy of each occupied NBO f2/NI 0) and the associated pre-orthogonal PNBO C/PNIi0j in the usual manner, 

Consider the steric repulsion between two helium atoms at various separations R. In this case, each atom contains only a single doubly occupied ls-likeNBO andEq. (1.47) reduces to a single term 

We can see the effect of steric repulsions on the form of the He ls-like NBO. The plot below compares the form of this NBO at R = 2.5 A (for which the NBO and PNBO are practically identical) with the forms at R = 2.0, 1.5 and 1.0 A, for which the interatomic nodal structure becomes increasingly apparent. 

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