Semiempirical approximations NDDO methods

NDDO [21] goes beyond INDO in that the ZDO approximation (Section 6.2.1, point (3)) is not applied to orbitals on the same atom, i.e. ZDO is used only for atomic orbitals on different atoms. NDDO is the basis of the currently popular semiempirical methods developed by M. J. S. Dewar and by coworkers who took up the torch MNDO, AMI and PM3 (as well as SAMI, PM5, and PM6). NDDO methods are the gold standard in general-purpose semiempirical methods, and the rest of this chapter concentrates on them. 

Because of convention, the symbols for the chemical potential, used in Equation 6.44 and Equation 6.45, and the dipole moment are the same. Further evaluation of Equation 6.48 proceeds through introduction of the LCAO-MO expansion (Equation 6.18) and, dependent on the level of theory, consideration of relevant approximations such as the NDDO formalism (Equation 6.31) in the case of semiempirical MNDO-type methods. Because the calculation of the dipole moment is usually considered a somewhat demanding test of the quality of the wavefunctions employed in the quantum chemical model, this property is included in the comparative statistical analysis of various methods to calculate molecular descriptors as presented in Section V. 

Analogous to the PPP method for planar 7r-systems, semiempirical all-valence methods can be and were extended to include Cl, thus giving rise to a family of procedures based on the CNDO, INDO and NDDO variants of the zero-differential overlap (ZDO) approximation, many of which were applied also to the discussion of Cl effects in radical cations. Due to the parametric incorporation of dynamic correlation effects, such procedures often yield rather accurate predictions of excited-state energies and they continue to be the methods of choice for treating very large chromophores which are not amenable to ab initio calculations. 

Two of these approximations (INDO and NDDO) have received considerable attention in the past 20 years. The most widely used software package that incorporates these approximations is known as MOPAC, which is available from QCPE. " The program was created by J. J. P. Stewart. A related program is AMPAC, which is also available from QCPE. These programs incorporate the MINDO/S and MNDO implementations of the INDO and NDDO methods, respectively. Both programs also include a more recent semiempirical NDDO implementation called AMl, and MOPAC has PM3. ... 

Semiempirical SCF calculations were done using the approximations NDDO (neglect of diatomic differential overlap) [18], MNDO (modified neglect of diatomic overlap) [19], INDO (intermediate neglect of differential overlap) [20], SINDO (symmetrically orthogonalized INDO [21]) [22], and CNDO (complete neglect of differential overlap) [20, 23]. Another type of approximation [24] to the ab initio method was also applied to OF2 [16]. 

The neglect of diatomic differential overlap (NDDO) method [236] is an improvement over the INDO approximation, since the ZDO approximation is applied only for orbital pairs centered at different atoms. Thus, all integrals pv Xa) are retained provided p and v are on the same atomic center and A and a are on the same atomic center, but not necessarily the center hosting p and v. In principle, the NDDO approximation should describe long-range electrostatic interactions more accurately than INDO. Most modern semiempirical models (MNDO, AMI, PM3) are NDDO models. 

Semiempirical methods followed a different path. Instead of trying to solve the integrals, they are replaced by approximations. This resulted in the development of many closely related yet distinct methods, the more popular of which were CNDO, INDO, methods MINDO/3 " and SINDO," the NDDO methods, and ZINDO. All the.se methods use a common approximation, that is, all two-electron three- and four-center integrals are set to zero. Because there are differences... 

In that study [31], we estimated the electronic coupling with the help of HF/6-31G calculations. Any attempt to expand such an investigation into a reasonably quantitative description of the variation of the electronic coupling over time would be much too costly. As noted above, one can overcome that problem by constructing a special semiempirical method (e.g., NDDO-HT) affording sufficiently accurate estimates of electronic matrix elements, or by using an approximate relation between H a and the overlap of related orbitals. 

Numerous other semiempirical methods have been proposed. The MNDO method has been extended to d functions by Theil and coworkers and is referred to as MNDO/d.155>156 For second-row and heavier elements, this method does significantly better than other methods. The semi-ab initio method 1 (SAM1)157>158 is based on the NDDO approximation and calculates some one- and two-center two-electron integrals directly from atomic orbitals. 

J.J.P. Stewart, Optimization of parameters for semiempirical methods V Modification of NDDO approximations and application to 70 elements. J. Mol. Model. 13, 1173-1213 (2007)... 

The popular semiempirical methods, MNDO (Dewar and Thiel, 1977), Austin Model 1 AMI Dewar et al., 1985), Parameterized Model 3 (PM3 Stewart 1989a 1989b), and Parameterized Model 5 (PM5 Stewart, 2002), are all confined to treating only valence electrons explicitly, and employ a minimum basis set (one 5 orbital for hydrogen, and one 5 and three p orbitals for all heavy atoms). Most importantly, they are based on the NDDO approximation (Stewart, 1990a, 1990b Thiel, 1988, 1996 Zemer, 1991) ... 

Most of the semiempirical MO methods currently used are based on SCF theory and differ in the approximations that are made so as to simplify the evaluation of the two-electron repulsion integrals. The approximations are then corrected for by parametrization, wherein parameters are included in the fundamental protocol to make the results match ab initio calculations on known systems. Examples of these semiempirical methods are CNDO (complete neglect of differential overlap), INDO (intermediate neglect of differential overlap), and NDDO (neglect of diatomic differential overlap). An alternative approach is to parameterize the calculations to optimize agreement with measured molecular properties, such as thermochemical, structural, or spectral data. 

In the 1960s, several semiempirical SCF methods were proposed by Pople and co-workers the complete neglect of differential overlap (CNDO) method, the intermediate neglect of differential overlap (INDO) method, and the neglect of differential diatomic overlap (NDDO) approximation " " (Table 1). In 1968, Bene and Jaffe parametrized the CNDO method to study electronic spectra (CNDO/S). Ridley and Zerner developed the INDO method to predict electronic spectra (INDO/S). " In 1977, an alternative semiempirical approach with configuration interaction (Cl), local neglect of differential overlap for spectroscopy (LNDO/S), was proposed. " ... 

Application of the ZDO approximations (CNDO, INDO, and NDDO) to Equation (1) allows derivation of equations for the Fock matrix in different semiempirical methods. 

The CIS approximation is used in a majority of semiempirical SCF methods to calculate energies and oscillator strengths of electronic transitions (CNDO/S, INDO/S, CINDO-E/S, NDDO/MC, NDDO-G). 

AMI A semiempirical method used to calculate molecular geometries and associated properties using the NDDO approximation and variable numbers of Gaussian functions for each element. 

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