Static correlation effects

This y value is called an instability value of a chemical bond (or diradical character) [29]. In case of the spin-restricted or spin-adapted (SA) calculations, the y value should be zero. However, if a couple of electrons tend to localize on each atom, in other words the chemical bond becomes unstable with the strong static correlation effect, the y value becomes larger and finally becomes 1.0. So, the y value can be applied for the analyses of di- or polyradical species, and it is often useful to discuss the stability (or instability) of chemical bonds. The idea of effective bond order b), which defined by the difference in occupation numbers of occupied NO (n) and unoccupied NO ( ) as... 

Our expression for [Eq. (105)] is thus far still exact. The first term in (105) is seen to be the contribution from local two-body types of interaction including static correlation effects. This term represents a generalized Boltzmann-Enskog term, which controls the short-time behavior of We note that the first two terms in a power series expansion of (l/z) both come from YG V. The second term in (105) contains recollision and mode-coupling " effects. The T-matrices on the ends have a simple form in the case of hard spheres, and they describe close collisions between two particles. The quantity R describes the motion of these two particles after their collision. 

In Table 11.2, we have listed the correlation en gies per monomer obtained from CISD calculations with and without the Elavidson correction applied. Two series of calculations are listed. In the first series, the geometry (with a bond distance of / , f) is close to the equilitnium structure and represents an electronic structure dominated by dynamical correlation. The second series (with a bond distance of 2Rref) represents a different situation, characterized by large static correlation effects. 

These results for the water molecule are typical of systems with small static correlation effects. For up to ten electrons, the CISD energy with the Davidson correction added is in good agreement... 

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