The exchange or repulsion term

The exchange terms are related to the introduction of the intermonomer antisymmetrizer Aab in the expression giving the electrostatic contribution. The correction factors introduced in the SAPT methods may be related to a renormalization factor that may be written in the following form when A b is replaced with 1+P for simplicity  

This factor is different from 1, because P contains all the multiple overlap values between MOs of A and B. P may be then expanded into terms containing an increasing number of multiple overlaps (or exchanges of orbitals)  

The exchange energy may be expanded into increasing powers of MO overlap integrals S  

This first term is sufficient for modeling intermolecular potentials. The overlaps depend on the monomer separation roughly as exp(-oR) so flic following terms give small contribution at large-medium distances. At short distances the positive exchange term rapidly increases. Reasons of uniformity wifli the other terms of flic interaction potential sug- 

Jacopo Tomasi, Beaedetta Mennucci, Chiara Cappelli 

This formula derives from the standard RS-PT with the expansion over the excited state truncated at the first term. For isolated atoms i and j, the coefficients C6(i,j) can be drawn from experimental data, while for atomic fragments of molecules only from computations. The exchange (or repulsion) term 

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The destabilization is caused by the exchange of electrons between the occupied orbitals through the orbital overlap. The force is then termed exchange repulsion or overlap repulsion. The exchange repulsion is a major cause of the steric repulsion. There are many occupied orbitals in the sterically crowded space. 

If the basis set is restricted to one pn basis function on each sp2 carbon, if the two-electron integrals ignore all three-center or four-center ones, and if we exclude exchange components, one has the Pariser-Parr-Pople model. If, further, all two-electron integrals are set to zero except for the repulsion between opposite spins on the same site and the one-electron tunneling terms are restricted to nearest neighbors, the result is the Hubbard Hamiltonian... 

Due to the integral approximations used in the MNDO model, closed-shell Pauli exchange repulsions are not represented in the Hamiltonian, but are only included indirectly, e.g., through the effective atom-pair correction terms to the core-core repulsions [12], To account for Pauli repulsions more properly, the NDDO-based OM1 and OM2 methods [23-25] incorporate orthogonalization terms into the one-center or the one- and two-center one-electron matrix elements, respectively. Similar correction terms have also been used at the INDO level [27-31] and probably contribute to the success of methods such as MSINDO [29-31],... 

The exchange contribution in an ab initio perturbation theory is the only repulsive term ) around the energy minimum in most of the stable complexes and consequently we would expect no net repulsion between two closed shell molecules in semiempirical calculations. On the other hand it is known from actual calculations that intermolecular interactions are described more or less correctly by the CNDO/2 procedure. Indeed, strong repulsion is obtained between closed shell molecules. Evidently there must be another approximation which compensates for the neglect of exchange energy. With regard to the simplifications of the CNDO/2 method we find that this is in fact the case. The approximation shown in Eq. (17) is responsible for the repulsive term. 

By that time, the theory of the interactions between electrons and photons had developed to the point where the electrostatic repulsion or attraction between electrically charged particles could be understood in terms of the exchange of photons between diem. In the lowest nontrivial approximation, it gave the Coulomb law for small velocities, The basic interaction was the emission and absorption of virtual photons by charged particles. 

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