NDDO methods molecular properties

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. 

The semiempirical molecular orbital (MO) methods of quantum chemistry [1-12] are widely used in computational studies of large molecules. A number of such methods are available for calculating thermochemical properties of ground state molecules in the gas phase, including MNDO [13], MNDOC [14], MNDO/d [15-18], AMI [19], PM3 [20], SAMI [21,22], OM1 [23], OM2 [24,25] MINDO/3 [26], SINDOl [27,28], and MSINDO [29-31]. MNDO, AMI, and PM3 are widely distributed in a number of software packages, and they are probably the most popular semiempirical methods for thermochemical calculations. We shall therefore concentrate on these methods, but shall also address other NDDO-based approaches with orthogonalization corrections [23-25],... 

Various parameterizations of NDDO have been proposed. Among these are modified neglect of diatomic overlap (MNDO),152 Austin Model 1 (AMI),153 and parametric method number 3 (PM3),154 all of which often perform better than those based on INDO. The parameterizations in these methods are based on atomic and molecular data. All three methods include only valence s and p functions, which are taken as Slater-type orbitals. The difference in the methods is in how the core-core repulsions are treated. These methods involve at least 12 parameters per atom, of which some are obtained from experimental data and others by fitting to experimental data. The AMI, MNDO, and PM3 methods have been focused on ground state properties such as enthalpies of formation and geometries. One of the limitations of these methods is that they can be used only with molecules that have s and p valence electrons, although MNDO has been extended to d electrons, as mentioned below. 

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. 

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. 

One of the basic assumptions of the NDDO semi-empirical methods is the orthogonality of the atomic orbitals. Therefore, if one describes the bond between the quanffim and the classical part by a strictly localized bond orbital (SLBO), i.e. a localized orbital free of localization tails [35] hosting 2 electrons, the molecular orbitals of the quanffim part are orthogonal to the localized one and are able to describe correctly the chemical group of interest. This property has been put forward by Warshel and Levitt in a basic paper [36]. 

A few semiempirical approaches are currently available that may allow treatment of transition metals with efficiency. Two of these fall in the INDO class of HF models. (INDO methods are usually more computationally efficient, though not as accurate, as those based on NDDO theories.) INDO/S developed by Zemer et al. is included in the ZINDO package and has been available for a number of years. It is very successful for the prediction of electronic spectra, for which it was carefully parameterized. However, INDO/S is not usually applied to compute more general properties such as optimized geometries or molecular energies, as it is not deemed to be reliable for these values. SINDOI from Jug et al. has recently been expanded to some transition metal elements and performs as expected within the limited INDO theory used. Again, results are somewhat erratic and the method does not appear to treat open-shell systems with a great deal of success. 

---