NDDO

As indicated above, early attempts to use semiempirical methods had proved unsatisfactory, due to the wrong choice of parameters. A similar situation had existed in the Pople 14 treatment of conjugated molecules using the Huckel o, ir approximation the parameters in this were chosen to fit spectroscopic data and with these the method gave poor estimates of ground state properties. Subsequent work in our laboratories has shown JS) that this approach can lead to estimates of heats of atomization and molecular geometries that are in almost perfect agreement with experiment if the parameters are chosen to reproduce these quantities. 

In MINDO/2, the one-center integrals are, as usual, determined from spectroscopic data, essentially in the same way as in INDO. The two-center repulsion integrals ii, jj) are given by the Ohno-Klopman 1S approximation  

The one-electron core resonance integrals j3. are given by the Mulliken approximation  

M and N and rm the intemuclear separation. Instead, we set CR equal to the following parametric function  

CR is thus the total interelectronic repulsion between atomsM and N when each has enough valence electrons to make it neutral. 

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In order to overcome these weaknesses, Pople and co-workers reverted to a more complete approach that they first proposed in 1965 [14], neglect of diatomic differential overlap (NDDO). In NDDO, all four-center integrals (pv are considered in which p and v are on one center, as are 2 and cr (but not necessarily on the same one as and v). Furthermore, integrals for which the two atomic centers are diEFer-ent are treated in an analogous way to the one-center integrals in INDO, resulting... 

PM3 is a reparam eteri/ation of AM I, wdi ich is based on the n eglect of diatomic differential overlap (NDDO) approximation. XDDO... 

The second summation is over all the orbitals of the system. This equation is used in IlyperChem ah imiio calculations to generate contour plots of electrostatic potential, [fwe choose the approximation whereby we n eglect the effects of the diatomic differen tial overlap (NDDO). then the electrostatic potential can be rewritten... 

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... 

The CNDO, INDO, NDDO, MNDO, and MINDO methods all are defined in terms of an orbital-level Foek matrix with elements... 

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. 

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. 

The mixed models used in MNDO, AMI, and PM3, are identical, because all of these three methods are derived based on NDDO. The core Hamiltonian correction due to the interaction of the charges between the quantum mechanical region and the classical region is... 

A new parametric quantum mechanical model AMI (Austin model 1), based on the NDDO approximations, is described. In it the major weakness of MNDO, in particular the failure to reproduce hydrogen bonds, have been overcome without any increase in eoraputer time. Results for 167 molecules are reported. Parameters are currently available for C, H, O and N. 

Neglect of Diatomic Differentiai Overiap Approximation (NDDO)... 

In the Neglect of Diatomic Differential Overlap (NDDO) approximation there are no further approximations than those mentioned above. Using p and n to denote either an s-or p-type (pj, p or p ) orbital, the NDDO approximation is defined by the following equations. 

The INDO method is intermediate between the NDDO and CNDO methods in tenns of approximations. 

The main difference between CNDO, INDO and NDDO is the treatment of the two-electron integrals. While CNDO and INDO reduce these to just two parameters (7AA 7ab), all the one- and two-center integrals are kept in the NDDO approximation. Within an sp-basis, however, there are only 27 different types of one- and two-center integrals, while the number rises to over 500 for a basis containing s-, p- and d-functions. 

An ab initio HF calculation with a minimum basis set is rarely able to give more than a qualitative picture of the MOs, it is of very limited value for predicting quantitative features. Introduction of the ZDO approximation decreases the quality of the (already poor) wave function, i.e. a direct employment of the above NDDO/INDO/CNDO schemes is not useful. To repair the deficiencies due to the approximations, parameters are introduced in place of some or all of the integrals. 

There are three methods that can be used for transforming the NDDO/INDO/CNDO approximations into working computational models. 

MTNDO/3 has been parameterized for H, B, C, N, O, F, Si, P, S and Cl, although certain combinations of these elements have been omitted. MINDO/3 is rarely used in modern computational chemistry, having been succeeded in accuracy by the NDDO methods below. Since there are parameters in MINDO which depend on two atoms, the number of parameters increases as the square of the number of elements. It is unlikely that MINDO will be parameterized beyond the above-mentioned in the future. 

The MNDO, AMI and PM3 methods are parameterizations of the NDDO model, where the parameterization is in terms of atomic variables, i.e. referring only to the nature of a single atom. MNDO, AMI and PM3 are derived from the same basic approximations (NDDO), and differ only in the way the core-core repulsion is treated, and how the parameters are assigned. Each method considers only the valence s- and p-functions, which are taken as Slater type orbitals with corresponding exponents, (s and... 

There are only five types of one-centre two-electron integral surviving the NDDO approximation within an sp-basis (eq. (3.76)). 

Recently Thiel and Voityuk have constructed a workable NDDO model which also includes d-orbitals for use in connection with MNDO, called MNDO/d. With reference to the above description for MNDO/AM1/PM3, it is clear that there are immediately three new parameters Cd, Ud and (dd (eqs. (3.82) and (3.83)). Of the 12 new one-centre two-electron integrals only one (Gjd) is taken as a freely varied parameter. The other 11 are calculated analytically based on pseudo-orbital exponents, which are assigned so that the analytical formulas regenerate Gss, Gpp and Gdd. 

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