Zero-differential-overlap

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. 

Correlation functional due to Wilk, Vosko and Nusair Zero differential overlap... 

Most methods of this type are based on the so-called zero-differential overlap (ZDO) approximation. Their development begins by using an approximation to the atomic-orbital-based two-electron integrals introduced by Mulliken ... 

The central assumption of semi-empirical methods is the Zero Differential Overlap (ZDO) approximation, which neglects all products of basis functions depending on the same electron coordinates when located on different atoms. Denoting an atomic orbital on centre A as /ja (it is customary to denote basis functions with /j, u, A and cr in semi-empirical theory, while we are using Xn, xs for ab initio methods), the ZDO... 

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... 

In the unrestricted Hartree-Fock method, a single-determinant wave function is used with different molecular orbitals for a and jS spins, and the eigenvalue problem is solved with separate F and F matrices. With the zero differential overlap approximation, the F matrix elements (25) become... 

As noted above, many integrals describing electron repulsion are very small in magnitude, especially those such as 4> (1)< jv(1) when p v. The simplest semi-empirical approach, termed the zero-differential overlap (ZDO) approximation, is therefore to assume that these integrals can be ignored. Mathematically expressed, this is equivalent to the following ... 

Zero Defects (ZDs), 21 173 Zero differential overlap (ZDO) technique, 16 737... 

It is assumed that the basic functions have zero differential overlap (ZDO) ... 

Semiempirical methods are widely used, based on zero differential overlap (ZDO) approximations which assume that the products of two different basis functions for the same electron, related to different atoms, are equal to zero [21]. The use of semiempirical methods, like MNDO, ZINDO, etc., reduces the calculations to about integrals. This approach, however, causes certain errors that should be compensated by assigning empirical parameters to the integrals. The limited sets of parameters available, in particular for transition metals, make the semiempirical methods of limited use. Moreover, for TM systems the self-consistent field (SCF) procedures are hardly convergent because atoms with partly filled d shells have many... 

The zero differential overlap approximation can be applied in the localized representation. This was demonstrated by calculating for C H, CioTfio and C14//14, respectively the total energy corrections and the pair correlation energies through second and third order in different approximations. When the strongly local contributions were only... 

Use the zero differential overlap (ZDO) approximation for the two-electron integrals to show that the singly excited configurations and transition dipoles are equal. When they are allowed to interact two states are formed ... 

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