The Neglect of Differential Overlap Approximation

The amount of computation for MP2 is determined by the partial transformation of the two-electron integrals, what can be done in a time proportionally to m (m is the number of basis functions), which is comparable to computations involved in one step of CID (doubly-excited configuration interaction) calculation. To save some computer time and space, the core orbitals are frequently omitted from MP calculations. For more details on perturbation theory please see A. Szabo and N. Ostlund, Modem Quantum Chemistry, Macmillan, New York, 1985. 

HyperChem supports MP2 (second order Mpller-Plesset) correlation energy calculations using any available basis set. In order to save main memory and disk space, the HyperChem MP2 electron correlation calculation normally uses a so called frozen-core approximation, i.e. the inner shell (core) orbitals are omitted. A setting in CHEM.INI allows excitations from the core orbitals to be include if necessary (melted core). Only the single point calculation is available for this option. 

The principal semi-empirical schemes usually involve one of two approaches. The first uses an effective one-electron Hamiltonian, where the Hamiltonian matrix elements are given empirical or semi-empirical values to try to correlate the results of calculations with experiment, but no specified and clear mathematical derivation of the explicit form of this one-electron Hamiltonian is available beyond that given above. The extended Hiickel calculations are of this type. 

The differential overlap approximation says that 1 many 

The second basic approximation is the neglect of diatomic differential overlap 

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Electronic transitions of Z-methylthiothiazole and A-4-thiazoline-2-thione were calculated using Pariser-Parr-Poplc and Complete Neglect of Differential Overlap approximations (61. 72). The major improvements afforded by the CNDO model are the calculation of the n cr transition and the interpretation of the 2.34-nm band as an n transition. 

Most present-day semiempirical methods are based on the idea of the neglect of differential overlap (NDO) of inner electrons developed by Pople and co-workers (see, for example, Pople and Beveridge, 1970 Dewar, 1975). NDO-type approximations generally result in a decrease in computational resource requirements that are 1/100 to 1/1000 of the corresponding ab initio methods. 

The third approach is the complete neglect of differential overlap approximation (CNDO), in which only the one- and two-center, two-electron integrals remain. The direct application of these methods (NDDO, INDO, or CNDO) is not useful because of the approximations, so it is necessary to include parameters in place of all or some of the integrals. These parameters are based on atomic or molecular experimental data. 

Surprisingly for such a conceptually simple method, the EHM has a theoretically-based advantage over otherwise more elaborate semiempirical methods like AMI and PM3, in that it treats orbital overlap properly those other methods use the neglect of differential overlap or NDO approximation (Section 6.2), meaning that they take Stj = f),r as in the simple Hiickel method. This can lead to superior results from the EHM [66]. 

It has been customary to classify methods by the nature of the approximations made. In this sense CNDO, INDO (or MINDO), and NDDO (Neglect of Diatomic Differential Overlap) form a natural progression in which the neglect of differential overlap is applied less and less fully. It is now clearer that there is a deeper division between methods, related to their objectives. On the one hand are approximate methods which set out to mimic the ab initio molecular orbital results. The objective here is simply to find a more economical method. On the other hand, some workers, recognizing the defects of the MO scheme, aim to produce more accurate results by the extensive use of parameters obtained from experimental data. This latter approach appears to be theoretically unsound since the formalism of the single-determinant wavefunction and the Hartree-Fock equations is retained. It can be argued that the use of the single-determinant wavefunction prevents the consistent achievement of predictions better than those obtained by the ab initio scheme where no further... 

The electron densities of the parent l,2,4-triazolo[4,3-c]- and [1,5-c]-pyrimidines (127 and 128) were calculated the total 77-electron density was obtained from HMO calculations and the total electron density by the complete neglect of differential overlap approximation method (CNDO-2). Whereas N6 caused C5 of both systems to be more electrophilic, N2 in the [4,3-c] system 127 decreased the 77-electron density at C5 more than N3 in the [1,5-c] system 128 at the same carbon. The calculations also indicated that the driving force for the 127-to-128 rearrangement should originate from the larger interaction between N1 and N2 in the [4,3-c] system 127 (electron densities, 5.22 and 5.09, respectively) compared to the interaction between N3 and N4 in the [1,5-c] system 128 (electron densities, 5.20 and... 

The semiempirical methods are based on the simplification of the HF LCAO Hamiltonian and require the iterative (self-consistent) density matrix calculations complete and intermediate neglect of differential overlap (CNDO and INDO - approximations), neglect of diatomic differential overlap (NDDO) and others, using the neglect of differential overlap (NDO) approximation. 

A first approximation was to use valence orbitals only, in the assumption that core atomic and molecular orbitals would contribute very little to the properties and the reactivity of organic molecules. This assumption is, in general, a valid one. A further very popular approximation was the neglect of differential overlap (NDO), developed by the Dewar school [12]. The integrals of the type are small ifp q and r s, and one assumes also that the corresponding overlap integrals are small. The NDO conditions were then written as ... 

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. 

Invariant Procedures. Journal of Chemical Physics 43 S129-S135. pie J A and G A Segal 1965. Approximate Self-Consistent Molecular Orbital Theory. II. Calculations with Complete Neglect of Differential Overlap. The Journal of Chemical Physics 43 S136-S149. iple J A and G A Segal 1966. Approximate Self-Consistent Molecular Orbital Theory. III. CNDO Results for AB2 and AB3 systems. Journal of Chemical Physics 44 3289-3296. 

The most elementary all valence electron NDO model is that known as Ippmplete neglect of differential overlap (CNDO). Segal and Pople introduced (his in 1966. Only valence electrons are explicitly treated, the inner shells being tijicen as part of the atomic core. The ZDO approximation is applied to the WO-electron integrals, so that... 

In the Complete Neglect of Differential Overlap (CNDO) approximation only the Coulomb one-centre and two-centre two-electron integrals remain (eq. (3.78)). 

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 simplest theory that is consistent with these requirements employs the complete neglect of differential overlap (CNDO)29. This semi-empirical approach will be discussed in some detail, albeit without extensive mathematical justification, as it illustrates the type of approximations that are made in more advanced theories. In addition to the assumptions outlined above, the remaining Coulomb-type integrals are reduced to a single value -yAB that depends only on the nature of atoms A and B with which < > and t are associated, respectively, and not on the actual type of orbitals that overlap. This is equivalent to stating ... 

Various theoretical methods (self-consistent field molecular orbital (SCF-MO) modified neglect of diatomic overlap (MNDO), complete neglect of differential overlap (CNDO/2), intermediate neglect of differential overlap/screened approximation (INDO/S), and STO-3G ab initio) have been used to calculate the electron distribution, structural parameters, dipole moments, ionization potentials, and data relating to ultraviolet (UV), nuclear magnetic resonance (NMR), nuclear quadrupole resonance (NQR), photoelectron (PE), and microwave spectra of 1,3,4-oxadiazole and its derivatives <1984CHEC(6)427, 1996CHEC-II(4)268>. 

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