Integrals exchange repulsion

In order to obtain nonzero spin densities even on hydrogen atoms in tt radicals, one has to take the one-center exchange repulsion integrals into account in the eigenvalue problem. In other words, a less rough approximation than the complete neglect of differential overlap (CNDO) is required. This implies that in the CNDO/2 approach also, o and n radicals have to be treated separately (98). 

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. 

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],... 

Explicit calculations on the dimer are only required for the exchange-repulsion term, which is obtained as the difference between the SCF energy of the supermolecule and electrostatic and induction terms. To fit the exchange-repulsion term, on the other hand, functions only dependent on overlap integrals of unperturbed SCF wavefunctions of the monomers are used. 

Following previous INDO-based work [21,22], these basic ideas have been implemented at the NDDO level in three steps [48-52]. First, the Pauli exchange repulsions were introduced as valence-shell orthogonahzation corrections only in the one-center part of the core Hamiltonian [48,49]. In the second step, they were also included in the two-center part of the core Hamiltonian [50,51], i.e. in the resonance integrals. In the third step, less important second-order correction terms were omitted [52]. 

Parameters for each effective fragment can be generated in a special GAMESS [20-21] run called "MAKEFP." Summary of the EFP parameters required for each energy term and a relative computational cost of each EFP term is shown in Table 5.1. As follows from Table 5.1, the exchange-repulsion and charge-transfer terms are the most computationally expensive parts of the EFP calculations because evaluations of one-electron integrals are involved. 

Since < Si, it is clear that in its absolute value As < Asi,. Consequently, if both orbitals of the reactants (p and cp are occupied by electron pairs which populate the MO s of the A-B system, then the overall effect of the orbital interaction will be destabilization. The effect of the four-electron destabilization is nothing other than an exchange repulsion of filled electron shells. Its description by means of Eqs. (4.1) and (4.2) is made possible thanks to taking implicit account of the overlap integral ab between the interacting orbitals. 

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