Coulomb interaction contact approximation

Compared to all other types of intermolecular interactions, the Coulomb interaction is a very strong interaction. E.g., for the interaction in vacuum between Na and Cl" at contact (2.76 A), Coulomb s law gives that the interaction energy is approximately 500kJ/mol, i.e., similar to the energy for a covalent bond. 

As compared with the Kohn-Sham functional for electronic systems, the nuclear Skyrme functional is less genuine. The main (Coulomb) interaction in the Kohn-Sham problem is well known and only exchange and corellations should be modeled. Instead, in the nuclear case, even the basic interaction is unknown and should be approximated, e.g. by the simple contact interaction in Skyrme forces. 

Fig. 4.6. Left-hand panels Momentum correlation function (4.20) of the electron momenta parallel to the laser field for nonsequential double ionization computed with the uniform approximation using the contact interaction (4.14b). The field frequency is u> = 0.0551 a.u. and the ponderomotive energy IJP = 1.2 a.u., which corresponds to an intensity of 5.5 x 1014W/cm2. The first two ionization potentials are Soi = 0.79a.u. and I-E02I = 1.51 a.u. corresponding to neon. Panel (a) shows the yield for the case where the transverse momenta pnj (n = 1,2) are completely integrated over, whereas in the remaining panels they are restricted to certain intervals. In panels (6) and (c), p2 is integrated, while 0 < pi /[Up]1/2 < 0.1 and 0.4 < Pi /[Up]1 2 < 0.5, respectively. In panels (d), (e), and (/), both transverse momenta are confined to the intervals 0 < Pn /[Up]1/2 < 0.5, 0.5 < pjn /[Up]1/2 < 1, and 1 < pjn /[Up]1/2 < 1.5, respectively. Right-hand panels, same as left panels, but for the Coulomb interaction (4.14a). From [17]...

In Fig. 4.8 the effect of the initial-state wave functions is explored, for the case where the crucial electron-electron interaction is the two-body Coulomb interaction (4.14a) and for the case where this interaction is the two-body contact interaction (4.14d), which is not restricted to the position of the ion. In both cases, the form factor includes the function (4.23), which favors momenta such that pi + p2 is large. This is clearly visible for the contact interaction (4.14d) and less so for the Coulomb interaction (4.14a) whose form factor also includes the factor (4.19), which favors pi = 0 (or p2 = 0)- We conclude that (i) the effect of the specific bound state of the second electron is marginal and (ii) that a pure two-body interaction, be it of Coulomb type as in (4.14a) or contact type as in (4.14d), yields a rather poor description of the data. A three-body effective interaction, which only acts if the second electron is positioned at the ion, provides superior results, notably the three-body contact interaction (4.14b), cf. the left-hand panel (d). This points to the significance of the interaction of the electrons with the ion, which so far has not been incorporated into the S-matrix theory beyond the very approximate description via effective three-body interactions such as (4.14b) or (4.14c). 

Dunitz and Gavezzotti [50-52] have discussed this important question in depth and concluded that the immediate-contact model is satisfactory and indispensable as the first approximation, but on the whole intermolecular links are not drawn between single atoms . Accordingly, they proposed to replace the old technique of calculating cohesive energy as a sum of pair-wise atom-atom interactions (assuming the atoms spherically-symmetrical and unaffected by their environment) by a more sophisticated approximation, the so-called PIXEL approach. In the latter, the electron density of a separate molecule is calculated by quantum-chemical methods, then intermolecular interactions (coulombic, polarization, dispersion and repulsion components) are calculated between partitions of this electron distributions, much... 

---