Domain-averaged Fermi-hole

Pelster, A., Kleinert, H. (1996). Relations between Markov processes via local time and coordinate transformations. Phys. Rev. Lett. 78, 565-569. (arXiv cond-mat/9608120v2) Ponec, R., Cooper, D. L. (2007). Anatomy of bond formation. Bond length dependence of the extent of electron sharing in chemical bonds from the analysis of domain-averaged Fermi holes. FamrfqyDwcMss. 135, 31-42. 

In a recent contribution by Girones et al., MQSSM were calculated from domain-averaged Fermi holes. The correlation between Hammett sigma constants and these MQSSM values for a set of meta- and para-substituted benzene molecules was investigated, and a good linear correlation between both entities was found. The predictive power of the relationship was examined for a test set of molecules, and it was found that the predictive capacity is competitive with the approach described by Sullivan et al., but having the advantage that only one parameter is used instead of five as in the latter study. 

Ponec R, Cooper DL (2007) Anatomy of bond formation. Bond length dependence of the extent of electron sharing in chemical bonds from the analysis of domain-averaged Fermi holes. Faraday Dis 135 31 2... 

Ponec R (2007) Anatomy of bond formation, domain-averaged fermi holes as a tool for the study of the nature of the chemical bonding in Li(2), Li(4), and F(2). J Phys Chem A 111 11294-11301... 

As tools for measuring electron delocalization, we opt for the visual inspection of the occupied orbitals and especially the so-called domain-averaged Fermi-hole (DAFH) analysis and MCI. Both of these require availability of atomic overlap matrices, where the overlap between two molecular orbitals is obtained in atom condensed form. This requires the definition of an atom in the molecule and in this study we chose the Ftirshfeld-I method. Finally, we introduce ring current maps in the ipso-centric approach. 

This is called the domain-averaged Fermi hole (DAFH), although in the general definition above, domain-averaged correlation hole might be more appropriate. It expresses how the presence of electrons in the chosen domain has an impact on the probability of finding an electron at some coordinate r,. As a one electron function. 

The term between square brackets can be diagonalized snch that a set of natnral domain-averaged Fermi hole orbitals can be obtained ... 

In addition to the numerical information provided by the values of various bond indices, the family of tools for the description of molecular structure was complemented some time ago by the new approach based on the analysis of the so-called domain averaged Fermi holes (DAFH). The most straightforward definition of these holes is via the restricted integration of the exchange part of the pair density [cf. eqn (2))... 

The integration over I2 in the QTAIM basin of the atom located at the cell T, Qt yields the spinless domain-averaged Fermi hole... 

The domain-averaged hole density, which is the starting entity for the evaluation of Fermi orbitals as well as the first step in the calculation of delocalization indices (DI), is computed from the exchange-correlation part pxc of the electron-pair density. At the one-determinantal level of... 

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