Repulsion integrals, center Coulomb

One-center coulomb repulsion integral at bridgehead nitrogen. s Variable electronegativity SCF method (57TFS397). 

MOyi) Ij. and Zg are the ionization potential of the rth AO in the valence state and the effective core charge of the sth AO,respectively. One center Coulomb repulsion integrals (rrlrr)=Ij.-Ej,(Ei. is the electron affinity of the rth AO in the valence state), the values of which adopted in this paper are collected in Table 1 with the values Ij.. Two center Coulomb repulsion integral are evaluated by the for-... 

The authors revised the PPP method in a few points, especially in the formulation for the two center Coulomb repulsion integrals, in order to calculate the correct values of the triplet state energies (5) The application of the revised method to the calculation of the electronic states of clnnamoyloxy group was found to reproduce well the experimental values of its electronic transitions. The results are also shown in Fig.3. 

B2u, B1u, and. Elu) were separated by electron repulsion both from one another and from the corresponding triplets, and that these energy differences could be interpreted in terms of reasonable values for the Coulomb repulsion integrals between atomic orbitals. They did not find it possible to evaluate all the many-center integrals required, and errors crept into their numerical calculations, but subsequent work11 12-58 68 has left little doubt that the 1800 A band of benzene has an Elu upper state and that the upper states of the 2600 A and 2100 A bands are Biu and Bltt, respectively. There was, therefore, even at that time clear evidence that electron repulsion must be included in any final theory, though aromatic molecules with less symmetry than benzene clearly presented a much more difficult problem. 

The Hiickel and extended Hiickel approximations are one-electron approximations. They are quite useful but they do not take us beyond Hartree-Fock. To do so we need either to use the weak version of the CNDO approximation, as given in Eq. (19) above or to make a further simplification, the strong CNDO approximation, in which we allow only electrons (of opposite spins) which are on the same site to repel. In other words, in the two-center Coulombic repulsion integrals [ijlij], we allow only i = j and... 

Note that the added term, which involves the fit twice, is in that sense less accurate than Sambe and Felton s original term, which involves the fit only once. The point is, however, that if the fitted density is expressed as the exact density minus an error term, then the error in Eq. (5) is the Coulomb repulsion of the error with itself, which is always second order and positive [12]. This approach is readily extended to four-center Coulomb integrals [13],... 

The integrals describing the Coulomb repulsion of electrons in two HOs centered at the same atom appear only in the form of the reduced repulsion integrals for pairs of... 

Pariser and Parr 39,40) proposed an amendment to the n electron theory which was justified on somewhat similar lines. Here, we are concerned only with one aspect of the Pariser-Parr theory, namely the reduction of the Coulomb repulsion energies of electrons. In order to reproduce the spectra of n electron systems, one is forced (among other factors) to reduce the one-center electron repulsion integrals of the carbon atom... 

Numerical differences may originate from alternative approximations to the hardness kernel. The simple expression for the off-diagonal elements of the hardness matrix in EEM (Eq. (18)) stems from the fact that we use a spherical atom approximation and an atomic partitioning of the electron cloud. The two-center electron repulsion integral then reduces to the Coulombic form (4nfio)" e, ep/R p, which equals k/R,p in eV. 

PM3, developed by James J.P. Stewart, is a reparameterization of AMI, which is based on the neglect of diatomic differential overlap (NDDO) approximation. NDDO retains all one-center differential overlap terms when Coulomb and exchange integrals are computed. PM3 differs from AMI only in the values of the parameters. The parameters for PM3 were derived by comparing a much larger number and wider variety of experimental versus computed molecular properties. Typically, non-bonded interactions are less repulsive in PM3 than in AMI. PM3 is primarily used for organic molecules, but is also parameterized for many main group elements. 

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