Semi-empirical MO method

The relationship between the herbicidal activity of 1,2,5-oxadiazole iV-oxides and some physicochemical properties potentially related to this bioactivity, such as polarity, molecular volume, proton acceptor ability, lipophilicity, and reduction potential, were studied. The semi-empirical MO method AMI was used to calculate theoretical descriptors such as dipolar moment, molecular volume, Mulliken s charge, and the octanol/water partition coefficients (log Po/w) <2005MOL1197>. 

UPS and MO theory are inextricably linked. It is impossible to interpret UPS measurements without at least a qualitative MO treatment, and it is now commonplace to perform quantitative calculations for comparison with the UPS data. The development of UPS techniques since about 1960 helped to popularise MO theory, and semi-empirical MO methods are often calibrated by appeal to UPS data. Thus an approximation which greatly simplifies an MO calculation is held to be justifiable if, over a fair range of molecules, the calculated orbital energies are in good agreement with UPS binding energies. 

The formaldehyde disproportionation has been examined by semi-empirical MO methods (Rzepa and Miller, 1985). With the MNDO procedure, transfer of hydride from hydrate mono-anion to formaldehyde is exothermic by 109 kJ mol-1, and the transition structure [29], corresponding to near symmetrical transfer of hydride, lies 72 kJ mol -1 above the separated reactants. Inclusion of two water molecules, to model solvation effects, stabilizes reactants and transition structures equally. Hydride transfer from the hydrate dianion was found to have a less symmetrical transition structure [30] not unexpected for a more exothermic reaction, but the calculated activation energy, 213 kJ mol-1, is unexpectedly high. Semi-classical primary kinetic isotope effects, kH/kD = 2.864 and 3.941 respectively, have been calculated. Pathways involving electron or atom transfers have also been examined, and these are predicted to be competitive with concerted hydride transfers in reactions of aromatic aldehydes. Experimental evidence for these alternatives is discussed later. 

Semi-empirical MO methods (such as MNDO, AMI, PM3) use the frozen core approximation. All the integrals (except the overlap integrals) related to the valence electrons are calculated approximately. Therefore, the coupling Hamiltonian Hqm/mm should be reformulated to conform to the frozen core approximation in the QM calculation. The additional integrals (eq.(22) and eq.(23)) are also calculated approximately. For details, the reader should consult the papers. [12,19,36]... 

Semi-empirical MO methods address electron correlation implicitly they simply adjust parameters until the calculations give the correct answer compared with experiment. EHT does not address electron correlation at all, so quantitative results from such calculations are almost always wrong unless fortuitous. There are, however, several approaches to explicitly account for electron correlation. One approach is to perform post-ab initio (post-H-F) calculations that in effect mix different electronic configurations involving the ground state and several excited states of the molecule. Such calculations are quite computationally intensive and can be performed only on relatively small molecules. Two commonly-seen acronyms associated with the post H-F approach to electron correlation are MP2 and Cl, which stand for Mpller-Plesset theory at the level of second-order and configuration interaction, respectively. 

Numerous publications have appeared for calculating 13C chemical shifts by ab initio and semi-empirical MO methods (55-58) and correlating the experimental shielding data with the physicochemical parameters and structural properties of the molecules (59, 60). 

Ever since the introduction of the semi-empirical Extent Huckel Theoiy (EHT) by Hoffman [1] in the early 1960s and followed by the Complete Neglect of Differential Overlap (CNDO) method [2], there has been a constant evolution in the field of semi-empirical MO methods. This research has evolved into a situation where at present the computational chemist using the recent Modified Neglect of Differential Overlap (MNDO) [3] version and its more elaborate successors Austin Model (AMI) [4] and Parametrized Model (PM) [5] has a number of impressive tools at his or her disposal to describe the molecular structme and properties of molecules containing several hundreds of atoms. 

PM3, which is the most recent addition in the arsenal of semi-empirical MO methods [5] appears to be an improvement over AMI as far as the accuracy of Af/f is concerned. Nitrobenzene, predicted to be planar, is an example where the caleulated zi//f=14.5 kcal/mol is very near the experimental value of 15.4 kcal/ mol. Much more experience must be gained with PM3 in order to judge its overall accuracy relative to AMI. 

In summary, all semi-empirical MO methods discussed above have their strong and weak points, which unfortunately are not always known prior to the actual calculation. As with all evaluations of theoretical methodologies, making contact and comparing with experimental data is always a wise thing to do. It should be borne in mind that quantum chemical calculations are most often done on the isolated molecule, that is, in absolute vaeuum. More often than not, the results of these calculations are compared to the results obtained from X-ray (crystalline state) or nuclear magnetic resonance (NMR) data (liquid state), from which it follows that discrepancies between theoretieal and experimental results are not necessarily a reflection on the validity and aeeuracy of the former. 

An overview has been presented of the various computational schemes aiming at the calculation of molecular properties such as the minimum energy conformation and free energy differences of molecules. It was seen how scientific rigour goes inversely with the size of the molecular system. Each computational formalism has its own niche where it supposedly performs best. Of the semi-empirical MO methods, the AMI formalism and its possible successors... 

A Hessian computed by semi-empirical MO methods. Some empirical adjustment of the second derivatives is usually necessary, since the semi-empirical methods tend to overestimate some terms and underestimate others. 

The degenerate thermal rearrangement of methylenecyclobutanes has been examined using the MINDO/2 semi-empirical MO method. The retention of configuration of the migrating centre can be attributed to subjacent orbital control (of the kind described by Berson and Salem) and to antarafacial participation of the allyl unit because of Jahn-Teller instabilities in the biradical transition state. The course of the reaction should be very sensitive to substituent effects. 

FE profiles can be expressed as functions of certain reaction coordinates, which are defined by Rc-c -Rn-c nd / n h Menshutkin and ammonia ionization reaction, respectively. We used the QM/MM-MD method to describe both solution systems for the purpose to include the solvent molecular strucmres explicitly. In the original smdies [7-9], the QM parts of the whole solution systems were treated by semi-empirical MO methods, i.e., AMI and PM3 level of theory. 

Through the above applications of QM/MM-FEG method combined with the EVB and the semi-empirical MO method to the chemical species in aqueous solution, it was clearly understood that the structural optimization of some stationary states (SS and TS) on the FES is inevitable to obtain accurate information with respect to a chemical reaction process in solution. However, the conventional QM/MM-FEG method has still three issues unresolved for its wider practical use ... 

Density Functional Theory (DFT), Hartree-Fock (HF), and the Self-consistent Field Divide and Conquer for Semi-empirical MO Methods Localized MO SCF Methods. 

In the 1970s and 1980s the modem, presently used semi-empirical MO methods evolved MINDO/3, INDO/S, and SINDOl on the INDO level, MNDO, AMI, " and PM3i on the NDDO level. 

AMI Combined Quantum Mechanical and Molecular Mechanical Potentials Combined Quantum Mechanics and Molecular Mechanics Approaches to Chemical and Biochemical Reactivity Divide and Conquer for Semi empirical MO Methods Hybrid Methods Hybrid Quan turn Mechanical/Molecular Mechanical (QM/MM) Meth ods Linear Scaling Methods for Electronic Structure Cal culations Mixed Quantum-Classical Methods MNDO MNDO/d Parameterization of Semiempirical MO Meth ods PM3 Quantum Mechanics/Molecular Mechanic (QM/MM) Semiempirical Methods Integrals and Scaling. 

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