Semi-empirical molecular orbital methods

Semi-empirical methods are the only alternative to molecular mechanics for most molecules of biological interest, especially for the study of hydrogen bonding, since this necessarily involves assemblages of molecules, i.e., hydrogen-bond dimers, trimers, higher polymers and complexes between different molecules. 

In semi-empirical methods, the computational complexity of the ab-initio methods is reduced by making approximations in the computational procedures or by introducing constants derived from experimental data (such as ionization potentials). These methods are more generally applied to the calculation of relative conformational energies rather than to the calculation of quantitative molecular geometries. 

1 This term applies to the classical interaction between charges. It is fundamentally misleading since all interactions involving the electrons and the nuclei are intrinsically electrostatic. 

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Most simple empirical or semi-empirical molecular orbital methods. including all ofthose ii sed in IlyperCh em, neglect inner sh ell orbitals and electrons and use a minimal basis se.i r>f valence Slater orbitals. 

Stewart)) P1990. Semi-empirical Molecular Orbital Methods. In Lipkowitz K B and D B Boyd (Editors). 

In all these examples, the importance of good simulation and modeling cannot be stressed enough. A variety of methods have been used in this field to simulate the data in the cases studies described above. Blander et al. [4], for example, used a semi-empirical molecular orbital method, MNDO, to calculate the geometries of the free haloaluminate ions and used these as a basis for the modeling of the data by the RPSU model [12]. Badyal et al. [6] used reverse Monte Carlo simulations, whereas Bowron et al. [11] simulated the neutron data from [MMIM]C1 with the Empirical Potential Structure Refinement (EPSR) model [13]. 

The absorption bands measured by the flash spectrographic method are often assigned by (a) comparison with known singlet-singlet absorption spectra, (b) comparison of the lifetime of the species responsible for the absorption with the phosphorescence lifetime, (c) comparison with calculated energies and intensities of the various possible absorptions by semi-empirical molecular orbital methods, and (d) comparison with published triplet absorption spectra and decay kinetics of model compounds. 

Geometric Optimization. The structure of the molecule as built by CHEMLAB (or a input from other methods) can be optimized through either a full force field molecular mechanics calculation (MMII) or with the semi-empirical molecular orbital methods MINDO-3 and MNDO. 

Ionization potentials calculated for cyclopentadienide ions (1 -8 ) by a semi-empirical molecular-orbital method (AMI) correlate with the observed electron... 

It is not appropriate in this review to discuss the relative efficiency of minimization routines based on steepest descent procedures, but a few of the more important references are given. If the gradient can be evaluated analytically, and as McIver and Komomicki 25) have pointed out this is the case for many surfaces calculated by semi-empirical molecular orbital methods, then this is the best approach. The methods developed by Davidson 26), Fletcher and oweZZ (27), and AfurfagZz and Sargent 28) assume this to be the case. If the gradient has to be obtained numerically then the method developed by Powell 29) has found wide acceptance for its efficiency. 

Quantum chemical calculations of indolizine and its aza derivatives have been reviewed (77HC(30)117). Attempts to correlate the results with various physical and chemical properties have not always been crowned with success. (A critical discussion of semi-empirical molecular orbital methods is given in Section 3.01.7.) A qualitative discussion using single structures may be appropriate. 

A semi-empirical molecular orbital method for the correlation of charge distributions with 13C shifts in amino acids was described [95]. Plotting of chemical shift parameters versus charge density changes of a-carbon atoms relative to the corresponding atoms in the parent hydrocarbons permits prediction of the chemical shifts of the a-carbons with an accuracy of about 10%. However, the slope (280 ppm per electron) in Fig. 5.12 is... 

As with the solution of other many-body electronic structure problems, determination of the unperturbed eigenvalues is numerically challenging and involves compromises in the following areas (1) approximations to the hamiltonian to simplify the problem (e.g., use of semi-empirical molecular orbital methods) (2) use of incomplete basis sets (3) neglect of highly excited states (4) neglect of screening effects due to other molecules in the condensed phase. 

A series of silyl and disilyl substituted thioketene dimers (2,4-diylidene-1,3-dithietane), including polymers, have been synthesized (33, 34) [117]. HOMO-LUMO calculation by PM3 semi-empirical molecular orbital method predicted an intramolecular CT from the thioketene dimer to the Si-Si bond in disilyl thioketene dimer (33a) and no electronic interaction between the... 

The calculation of log P (octanol) is facilitated by the availability of computer programs that use the group contribution method (27,28). The derivation of log P (octanol) values from relative HPLC retention times (29-31), and from atomic charge densities calculated using semi-empirical molecular orbital methods has also been described (32). 

Inuzuka, K. The calculation of the energy levels of acetaldehyde by a semi-empirical molecular orbital method including the hyperconjugation effect. Bull. Chem. Soc. Japan 36, 1045 (1963). 

The semi-empirical molecular orbital method MINDO/3 has been used to calculate transition state geometries for the following decompositions. 

The treatment of QM/MM electrostatic interactions is not as straightforward when semi-empirical QM methods are used, because semi-empirical molecular orbital methods such as AMI and PM3 include only valence electrons directly. Core electrons are treated together with the nucleus as an atomic core . In semi-empirical QM/MM methods (such as the AM1/CHARMM method developed by Field et al.102), QM/MM electrostatic interactions are calculated by treating the MM atoms exactly as if they where semi-empirical atomic cores. 

Quantum chemical calculations on RE + /3-diketonate complexes are presently restricted to two approaches the effective core potential (ECP) and the SMLC/AMl method. The SMLC/AMl method is a very powerful addition to the semi-empirical molecular orbital method AMI in that it allows the prediction of geometric parameters of rare-earth /3-diketonate complexes of very difficult experimental determination. In this method the RE3+ ion is a sparkle represented by a -i-3e charge in the center of a repulsive spherical potential of the form exp(—ar). Recently, ab initio effective core potential calculations have also succeeded in reproducing the coordination polyhedron geometries of RE + /S-diketonate complexes with high accuracy . 

Semi-empirical molecular orbital methods (AMI, PM3, and PM5) were used to optimize the structures of 5, X = Se and X = Te <2004JMT179>. The calculated C-C distance in the three-membered heterocyclic ring for 5, (X = Se)... 

Quantitative Structure-Cytotoxicity Relationship of Bioactive Heterocycles by the Semi-empirical Molecular Orbital Method with the Concept of Absolute Hardness... 

The third chapter, Quantitative Structure-Cytotoxicity Relationship of Bioactive Heterocycles by the Semi-empirical Molecular Orbital Method with the Concept of Absolute Hardness by Mariko Ishihara, Hiroshi Sakagami, Masami Kawase, and Noboru Motohashi, presents the relationship between the cytotoxicity (defined as 50% cytotoxic concentration) of heterocycles such as phenoxazine, 5-trifluoromethyloxazoles, O-heterocycles such as 3-formylchromone and coumarins, and vitamin K2 derivatives against some tumor cell lines and 15 chemical descriptors. The results suggest the importance of selecting the most appropriate descriptors for each cell type and compound. The review is of interest as it represents the relationship of the molecular structures with the cytotoxic activity of these heterocycles. 

Figure 18 The ball-and-stick model of the Zn" complex of the disubstituted tetramine 11, as calculated through a semi-empirical molecular orbital method. Hydrogen atoms have been omitted for clarity. The Zn" centre (black ball) chose a tetrahedral stereochemistry. Five-coordination (including a solvent molecule) is possible, too. Both stereochemical arrangements put the A/ A -dimethylaniline and anthracene subunits at a distance favourable to the occurrence of a donor-to-fluorophore eT process.

Besides these theories, which are applicable to general systems, some other theories of less general applicability have been proposed. These are outlined separately below. A group of empirical methods which has been omitted from the present review are the semi-empirical molecular orbital methods known by acronyms such as MINDO, INDO and CNDO. The reader is referred to a book by Murrell and Harget259 for a description of these methods and to articles by Chutjian and Segal260 and by MacGregor and Berry261 for examples of their use. 

All valence electron methods In contrast to ab initio methods, the semi-empirical molecular orbital methods only consider the valence electrons for the construction of the atomic orbitals. Well-known semi-empirical methods are EHT, CNDO, MNDO, PCILO, AMI, and PM3. These methods are orders of magnitude faster than ab initio calculations. 

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