Atomic orbitals differential overlap between

I lie next level of approximation is the neglect of diatomic differential overlap model (NDDO [Pople et al. 1965]) this theory only neglects differential overlap between atomic orbitals on... 

Such phenomena do not occur in heavier alkaline earth atoms due to a poorer differential overlap between the valence s and p orbitals (smaller Ksp integrals) as explained by... 

Various NDO schemes differ from CNDO in that they do not utilize fully the ZDO approximation. These schemes are discussed in the book by Pople and Beveridge (1970). In the intermediate neglect of differential overlap (INDO) model the differential overlaps between orbitals on the same atom are kept in one-center two-electron integrals, while the neglect of diatomic differential overlap (NDDO) model neglects only diatomic differential overlaps in any two-electron integral. 

Ihc complete neglect of differential overlap (CNDO) approach of Pople, Santry and Segal u as the first method to implement the zero-differential overlap approximation in a practical fashion [Pople et al. 1965]. To overcome the problems of rotational invariance, the two-clectron integrals (/c/c AA), where fi and A are on different atoms A and B, were set equal to. 1 parameter which depends only on the nature of the atoms A and B and the ii ilcniuclear distance, and not on the type of orbital. The parameter can be considered 1.0 be the average electrostatic repulsion between an electron on atom A and an electron on atom B. When both atomic orbitals are on the same atom the parameter is written , A tiiid represents the average electron-electron repulsion between two electrons on an aiom A. 

The Extended Hiickel method neglects all electron-electron interactions. More accurate calculations are possible with HyperChem by using methods that neglect some, but not all, of the electron-electron interactions. These methods are called Neglect of Differential Overlap or NDO methods. In some parts of the calculation they neglect the effects of any overlap density between atomic orbitals. This reduces the number of electron-electron interaction integrals to calculate, which would otherwise be too time-consuming for all but the smallest molecules. 

The NDDO (Neglect of Diatomic Differential Overlap) approximation is the basis for the MNDO, AMI, and PM3 methods. In addition to the integralsused in the INDO methods, they have an additional class of electron repulsion integrals. This class includes the overlap density between two orbitals centered on the same atom interacting with the overlap density between two orbitals also centered on a single (but possibly different) atom. This is a significant step toward calculatin g th e effects of electron -electron in teraction s on different atoms. 

Minimizing the total energy E with respect to the MO coefficients (see Refs. 2 and 3) leads to the matrix equation FC = SCE (where S is the overlap matrix). Solving this matrix is called the self-consistent field (SCF) treatment. This is considered here only on a very approximate level as a guide for qualitative treatments (leaving the more quantitative considerations to the VB method). The SCF-MO derivation in the zero-differential overlap approximations, where overlap between orbitals on different atoms is neglected, leads to the secular equation... 

The second philosophy holds that one should seek agreement with experiment. Therefore the parameters in this case implicitly include some correlation effects. Examples of this approach are MINDO/3 (Bingham et al., 1975) and MNDO (Dewar and Thiel, 1977). [In all of these techniques, C stands for complete, I for intermediate, N for neglect, and DO for differential (diatomic differential in MNDO) overlap differential overlap is the overlap between different orbitals on the same or different atoms.]... 

The Pariser-Parr-Poplc (PPP) method is based on three assumptions (a) Whenever the factor, (n), (n) (where i n is any electron index) appears in the integrand the integi al vanishes zero differential overlap approximation) (b) The resonance integrals between nearest neighbours are treated as empirical parameters those between non-neighbours are neglected (c) The one-centre Coulomb integrals ii, it) are taken to be equal to /, — E where I, and E, are the ionization potential and electron affinity, respectively, of the atomic orbital tpi, when the atom is in the appropriate valence state. 

The second part of Pariser and Parr s theory is concerned with the matrix elements between the terms 1Xo, These depend ultimately upon the matrix elements of unity, of the core Hamiltonian, and of the electron repulsion in the system of atomic orbitals. Pariser and Parr, like Pople, introduced the zero differential overlap approximation which abolishes overlap between different atomic orbitals and includes all electron repulsion integrals except those of the type... 

In addition to the conventional overlap energy term there is a second term that depends on the bond-order Pq and the repulsive integral between an electron in adsorbate orbital 0 and an electron in orbital I on the neighboring atom, is equal to /fjj, Ek).(2.282), and the second term in follows from the first term of (2.283a) when using definition Eq.(2.35c) for the bond-order Pi2 and the zero-differential overlap approximation Eq.(2.284). In section 2 Eq.(2.40b) related to Eq.(2.309) was derived. It was shown to lead to a reduction of the interaction energy of two electrons with different spins in the same orbital (see Eq.(2.42,II)). The result implies that Ucff is not independent of the bond-order. An improved expression for would be ... 

In alternant hydrocarbons, however, the Hiickel bond orders vanish between pairs of atoms in the same set," so that the elements F , like the resonance integrals, vanish unless r and s are in different sets. The upshot of all this, as Pople showed, is that his equations, Eqs. 17, when applied to alternant hydrocarbons yield solutions which have all the pairing properties of the Hiickei molecular orbitals. Pople thus succeeded in showing that the Huckel scheme can be very easily adapted to include electron repulsion, at least under the assumption of zero differential overlap. 

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