Coulomb cusp condition interelectronic

Whilst CASSCF and related methods give a qualitatively accurate description of static correlation, the effects of dynamic correlation are largely neglected. The inclusion of dynamical correlation is critical for the quantitatively correct simulation of f-element complexes. This can be recovered through the application of full Cl but, as already discussed, this method is intractable for all but very small systems. In fact. Cl expansions converge on the full Cl limit very slowly. The Coulomb cusp condition specifies a relationship between the two-electron wavefunction and its first derivative when the interelectronic separation is equal to zero ... 

Physically, C, which controls the large wavevector decay of ( / i, depends on the behavior of the system at small interelectronic separations. In fact, C is proportional to the system-average of the cusp in the exchange-correlation hole at zero separation. If smooth function of r - r, then g x(r, r) = 0, and C would vanish, as it does at the exchange-only level (i.e., to first order in e2). However, as we saw in section 2.2, the singular nature of the Coulomb interaction between the electrons leads to the electron-coalescence cusp condition, Eq. (31). For the present purposes, we wish to keep track explicitly of powers of the coupling constant, so we rewrite Eq. (31) as... 

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