Exchange-overlap energies

As mentioned in Sect. 2, the exchange-overlap energy depends on the nature of the spin coupling of the interacting molecules [18, 19]. For closed-shell molecules the resultant total spin is zero, and the first-order contribution to the exchange-overlap component of the interaction can be expressed in closed form if Atp is approximated as a single determinant of Hartree-Fock spin-orbitals of the individual molecules [48-50]. 

Table 2. Exchange-overlap energies and correction A Ef ) for the Ig states of He2 and NE2 at R = lao calculated for Hartree-Fock wfs of separate atoms...

The exchange-repulsion energy is approximately proportional to the overlap of the charge densities of the interacting molecules [71, 72 and 73]... 

To complete the first order terms, the exchange-repulsion energy can be evaluated through an overlap model [14, 59] as ... 

The exchange repulsion energy in EFP2 is derived as an expansion in the intermolecular overlap. When this overlap expansion is expressed in terms of frozen LMOs on each fragment, the expansion can reliably be truncated at the quadratic term [44], This term does require that each EFP carries a basis set, and the smallest recommended basis set is 6-31-1— -G(d,p) [45] for acceptable results. Since the basis set is used only to calculate overlap integrals, the computation is very fast and quite large basis sets are realistic. 

There is no hard boundary between the overlap dependent and independent regions. One can only ask at which point the overlap dependent energies become comparable to the overlap independent. If we take Hj as an example, the separation of the lowest singlet and triplet state depends primarily on overlap (in any model based upon atomic wavefunctions) whereas the absolute energies contain overlap independent terms. Table 2 shows these as a function of interatomic distance 104, IOS with the Coulomb (overlap independent) and exchange (overlap dependent) terms being given by... 

The results of our model are seen to agree well with experiment, and were confirmed by ab initio calculations on the same systems (Magnasco, 2008). It was shown there that the single one-electron bond energy parameter (fi-aS) occurring in Equations (25-28) is just the model representation of the one-electron part of the exchange-overlap component of the interaction due to the exchange-overlap densities [a(r)b(r)— Sa2(r)] on A and [b(r)a(r)-Sb2(r)] on B. 

Exchange Energy Transfer. In this case, the electron cloud of the donor and acceptor molecules should overlap energy transfer can take place over distances of 1-1.5 nm. 

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