Molecular orbital theory MNDO method

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-... 

Semiempirical molecular orbital methods23-25 incorporate parameters derived from experimental data into molecular orbital theory to reduce the time-consuming calculation of two-electron integrals and correlation effects. Examples of semiempirical molecular orbital methods include Dewar s AMI, MNDO, and MINDO/3. Of the three quantum chemical types, the semiempirical molecular orbital methods are the least sophisticated and thus require the least amount of computational resources. However, these methods can be reasonably accurate for molecules with standard bond types. 

As an alternative to ab initio methods, the semi-empirical quantum-chemical methods are fast and applicable for the calculation of molecular descriptors of long series of structurally complex and large molecules. Most of these methods have been developed within the mathematical framework of the molecular orbital theory (SCF MO), but use a number of simplifications and approximations in the computational procedure that reduce dramatically the computer time [6]. The most popular semi-empirical methods are Austin Model 1 (AMI) [7] and Parametric Model 3 (PM3) [8]. The results produced by different semi-empirical methods are generally not comparable, but they often do reproduce similar trends. For example, the electronic net charges calculated by the AMI, MNDO (modified neglect of diatomic overlap), and INDO (intermediate neglect of diatomic overlap) methods were found to be quite different in their absolute values, but were consistent in their trends. Intermediate between the ab initio and semi-empirical methods in terms of the demand in computational resources are algorithms based on density functional theory (DFT) [9]. 

Many approximate molecular orbital theories have been devised. Most of these methods are not in widespread use today in their original form. Nevertheless, the more widely used methods of today are derived from earlier formalisms, which we will therefore consider where appropriate. We will concentrate on the semi-empirical methods developed in the research groups of Pople and Dewar. The former pioneered the CNDO, INDO and NDDO methods, which are now relatively little used in their original form but provided the basis for subsequent work by the Dewar group, whose research resulted in the popular MINDO/3, MNDO and AMI methods. Our aim will be to show how the theory can be applied in a practical way, not only to highlight their successes but also to show where problems were encountered and how these problems were overcome. We will also consider the Hiickel molecular orbital approach and the extended Hiickel method Our discussion of the underlying theoretical background of the approximate molecular orbital methods will be based on the Roothaan-Hall framework we have already developed. This will help us to establish the similarities and the differences with the ab initio approach. 

Semiempirical methods, for example, MNDO. AMI, and PM3. are simplifications of ab initio molecular orbital theory and employ empirically determined parameters in essence, they only differ in the approximations being made. These methods involve adjustable parameters associated with molecular properties that are calibrated against experimental data. The chief advantage of semiempirical calculations over ab initio calculations is that they are several orders of magnitude faster. Thus, calculations for systems of up to c. 200 atoms are currently possible, whereby with ab initio methods, the limit is a moderately sized molecule (about 50 atoms at the time of writing), if rational results are to be obtained. Frequently, semieinpirical methods have proved to be the computational procedures of choice for studying relatively large molecules. 

Semiempirical MO calculations on large systems are discussed in T. Clark and J. J. P. Stewart, MNDO-like Semiempirical Molecular Orbital Theory Chap. 8 of J. R. Reimers (ed.). Computational Methods for Large Systems, Wiley, 2011. SCC-DFTB calculations on... 

HyperChem currently supports one first-principle method ab initio theory), one independent-electron method (extended Hiickel theory), and eight semi-empirical SCFmethods (CNDO, INDO, MINDO/3, MNDO, AMI, PM3, ZINDO/1, and ZINDO/S). This section gives sufficient details on each method to serve as an introduction to approximate molecular orbital calculations. For further details, the original papers on each method should be consulted, as well as other research literature. References appear in the following sections. 

AMI semi-empirical and B3LYP/6-31G(d)/AMl density functional theory (DFT) computational studies were performed with the purpose of determining which variously substituted 1,3,4-oxadiazoles would participate in Diels-Alder reactions as dienes and under what conditions. Also, bond orders for 1,3,4-oxadiazole and its 2,5-diacetyl, 2,5-dimethyl, 2,5-di(trifluoromethyl), and 2,5-di(methoxycarbonyl) derivatives were calculated <1998JMT153>. The AMI method was also used to evaluate the electronic properties of 2,5-bis[5-(4,5,6,7-tetrahydrobenzo[A thien-2-yl)thien-2-yl]-l,3,4-oxadiazole 8. The experimentally determined redox potentials were compared with the calculated highest occupied molecular orbital/lowest unoccupied molecular orbital (HOMO/LUMO) energies. The performance of the available parameters from AMI was verified with other semi-empirical calculations (PM3, MNDO) as well as by ab initio methods <1998CEJ2211>. 

Semi-empirical molecular orbital, MO, theory uses a combination of experimental data and quantum mechanical MO methods to model the valence electronic structure of molecules. In the MNDO (8) method each atom is parameterized using experimental data. This calculation provides molecular orbital descriptions of the valence electrons, as well as effective charges of each atom in the molecule. 

In Fig. 1 we show the correlation between E and experimental heats of formation for the (complete) set of C22H14 benzenoid isomers. For comparison we also present some recent data for the same set of compounds, obtained by a semiempirical MNDO method [21] and by the MMX/PI version of molecular mechanics calculations [22], The only conclusion we wish to draw from Fig. 1 is that HMO theory is capable of reproducing the experimental enthalpies of benzenoid hydrocarbons with an accuracy which is not much worse than that of the much more sophisticated (and highly parametrized) molecular orbital and molecular mechanics approaches. 

The earliest theoretical calculations of cocaine hydrolysis focused on the first step of the hydrolysis of the benzoyl ester [57,58]. hi these computational studies [57,58], MNDO, AMI, PM3, and SM3 semiempirical molecular orbital methods, as well as ab initio procedure at the HF/3-21G level of theory, were employed to optimize geometries of the transition states for the first step of the hydrolysis of cocaine and model esters, including methyl acetate [59,60] for which experimental activation energy in aqueous solu-... 

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