Short-range Effects Penetration

In the study of weakly bound systems the range of distances around the van der Waals minimum is usually the one of primary interest. Here the performance of the long-range terms in their multipole-expanded forms is somewhat problematic. First, the multipole series may not converge sufficiently fast or not at all and, secondly, penetration effects become non-negligible. 

Penetration effects also occur in the second-order long-range terms and 

---

The dipole moment of a Van der Waals dimer consists in principle of three contributions the dipole moments of the two monomers and the interaction dipole moment. In the usual Van der Waals molecules the interaction dipole is in the order of 0.1 D which for a large part arises from induction. That is, permanent moments on the one monomer induce a dipole moment on the other. Obviously, this effect is absent in the case of a dimer consisting of two noble gases. Here the interaction dipole moment is an order of magnitude smaller and is largely due to the short range effects exchange and penetration . 

As the SIBFA approach relies on the use of distributed multipoles and on approximation derived form localized MOs, it is possible to generalize the philosophy to a direct use of electron density. That way, the Gaussian electrostatic model (GEM) [2, 14-16] relies on ab initio-derived fragment electron densities to compute the components of the total interaction energy. It offers the possibility of a continuous electrostatic model going from distributed multipoles to densities and allows a direct inclusion of short-range quantum effects such as overlap and penetration effects in the molecular mechanics energies. 

Molecular shape complementarity is critical to biomolecular recognition and specificity. Even if the molecules change conformation on binding and water molecules are trapped at the interface, bound complexes show high shape complementarity (31). This shape complementarity is dependent on van der Waals interactions between the binding molecules. Electron-electron repulsion prevents atomic overlap and intermolecular penetration. However, induced dipole effects as atoms approach lead to short-range attractive interactions. 

Again, for the short range, the second order energy contributions, (18), (19), calculated with the exact operator (11) start to deviate from the R power series expansions, (20) and (21), and we can define the penetration effects ... 

Short range penetration, AE eqn. (17), and exchange, AE eqn. (28), effects become visibly important with decreasing R (in first order)... 

For electrons in the multicharged ions or even for the valence electrons in heavy atoms the parameter aZ cannot be considered as small. In case of heavy atoms the reason is that the effective QED potentials of the electron interaction with the nucleus are rather short-range and the interaction occurs when the outer electrons penetrate deeply into the core. Therefore the methods described in Section III are not valid anymore and all-orders in aZ methods axe necessary. 

---