MNDO approximation, semiempirical

In the following, experience on semiempirical hypersurface calculations - mostly applying the MNDO approximation(9) - is reported. As will be exemplified, correlation with experimental data on structures, isomer stabilities, ionization patterns or ESR coupling constants ranged between satisfactory and acceptable. Altogether, they have been of great help in tracking some short-lived molecules. 

The solute molecules can, in principle, be treated at any level of QM theory. However, in the majority of QM/MM studies of biologically important systems, C/qM is computed using one of the approximate semiempirical AMI, MNDO, and PM3 methods. The reason for this predominance of semiempirical methods is due solely to the computational cost of conventional ab initio or density functional methods. In fact, semiempirical methods are efficient enough to be used in MD simulations. In the following, we describe the most recent and significant advancements in the development of solvation models based on both semiempirical and ab initio QM/MM methods. 

The MOPAC program (Molecular Orbital PACkag) (26) Is one of the popular quantum mechanical semiempirical methods. The AM1 (Austin Model 1), developed by Michael Dewar (26), is a generalization of the modified neglect of differential diatomic overlap (MNDO) approximation. Often, AM1 is implemented in the MOPAC, and MOPAC(AMt) has been widely used to minimize molecular conformations, to calculate electronic configuration, and to predict such properties as electron distribution and partial charges. 

This second group of neglecting differential overlaps semiempirical methods includes along the interaction quantified by the overlap of two orbitals centered on the same atom also the overlap of two orbitals belonging to different atoms. It is manly based on the Modified Neglect of Diatomic Overlap (MNDO) approximation of the Fock matrix, while introducing further types of integrals in the UHF framework (Dewar and Thiel 1977 Dewar and McKee 1977 Dewar and Rzepa 1978 Davis et al. 1981 Dewar and Starch 1985 Thiel 1988 Clark 1985)... 

Semiempirical calculations were carried out in the MNDO approximation in the AMI parameterization [10]. Ab initio calculations were carried out using a split-valence basis set 6-3IG with ihe d-polarization function for all atoms [11]. The electron correlation was considered by using the Moller-Plesset second order perturbation theory with a frozen skeleton of electrons (frozen core, FC) [13]. 

Ionization potentials of perfiuorinated diamines were calculated as energies of the highest occupied molecular orbitals using the MNDO-PM3 semiempirical molecular orbital approximation (26). Calculations were performed with MOPAC Ver.6 (27) program with a Sony News-830 work station. Bond lengths, bond angles, and edral angles were fully optimized within the MNDO-PM3 framework. 

Semiempirical (CNDO, MNDO, ZINDO, AMI, PM3, PM3(tm) and others) methods based on the Hartree-Fock self-consistent field (HF-SCF) model, which treats valence electrons only and contains approximations to simplify (and shorten the time of) calculations. Semiempirical methods are parameterized to fit experimental results, and the PM3(tm) method treats transition metals. Treats systems of up to 200 atoms. 

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 AMI (8) approximation to molecular orbital theory has been used for these studies. This method overcomes the problems that previous semiempirical methods (notably, MNDO) (9) have in describing hydrogen-bonds. It has been used with success in several hydrogen-bonding studies. (10-12) Ab initio studies of H-bonding systems are very sensitive to basis set and correction for electron-... 

Now we want to discuss IR optical spectra of the C60H36 synthesized at high-pressure. Results of this study were published in Bazhenov et al. (2008). There are a lot of publications devoted to theoretical and experimental study of C60H36. We should pay attention on the existing discrepancies in the results of theoretical calculations of the dipole-active spectra C60H36, compare, for example, papers Bini et al. (1998) and Bulusheva et al. (2001). There were used different theoretical models. Semiempirical method of the MNDO type (Dewar and Thiel 1977) was used in (Bini et al. 1998). Ab initio Hartree-Fock self-consistent field approximation was used in (Bulusheva et al. 2001). 

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. 

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. 

All the normal modes are present in the results of a semiempirical frequency calculation, as is the case for an ab initio or DFT calculation, and animation of these will usually give, approximately, the frequencies of these modes. A very extensive compilation of experimental, MNDO and AMI frequencies has been given by Healy and Holder, who conclude that the AMI error of 10% can be reduced to 6% by an empirical correction, and that entropies and heat capacities are accurately calculated from the frequencies [104], In this regard, Coolidge et al. conclude -surprisingly, in view of our results for the four molecules in Figs. 6.5-6.8 - from a study of 61 molecules that (apart from problems with ring- and heavy atom-stretch for AMI and S-H, P-H and O-H stretch for PM3) both AMI and PM3 should provide results that are close to experimental gas phase spectra [105]. 

The highly specific behavior of transition metal complexes has prompted numerous attempts to access this Holy Grail of the semi-empirical theory - the description of TMCs. From the point of view of the standard HFR-based semiempirical theory, the main obstacle is the number of integrals involving the d- AOs of the metal atoms to be taken into consideration. The attempts to cope with these problems have been documented from the early days of the development of semiempirical quantum chemistry. In the 1970s, Clack and coworkers [78-80] proposed to extend the CNDO and INDO parametrizations by Pople and Beveridge [39] to transition elements. Now this is an extensive sector of semiempirical methods, differing by expedients of parametrizations of the HFR approximation in the valence basis. These are, for example, in methods of ZINDO/1, SAMI, MNDO(d), PM3(tm), PM3 etc. [74,81-86], From the... 

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) ... 

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. 

Ab initio quantum mechanical (QM) calculations represent approximate efforts to solve the Schrodinger equation, which describes the electronic structure of a molecule based on the Born-Oppenheimer approximation (in which the positions of the nuclei are considered fixed). It is typical for most of the calculations to be carried out at the Hartree—Fock self-consistent field (SCF) level. The major assumption behind the Hartree-Fock method is that each electron experiences the average field of all other electrons. Ab initio molecular orbital methods contain few empirical parameters. Introduction of empiricism results in the various semiempirical techniques (MNDO, AMI, PM3, etc.) that are widely used to study the structure and properties of small molecules. 

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