MNDO model development

MNDO, AMI, and PM3 are based on the same semiempirical model [12, 13], and differ only in minor details of the implementation of the core-core repulsions. Their parameterization has focused mainly on heats of formation and geometries, with the use of ionization potentials and dipole moments as additional reference data. Given the larger number of adjustable parameters and the greater effort spent on their development, AMI and PM3 may be regarded as methods which attempt to explore the limits of the MNDO model through careful and extensive parameterization. 

In an overall assessment, the established semiempirical methods perform reasonably for the molecules in the G2 neutral test set. With an almost negligible computational effort, they provide heats of formation with typical errors around 7 kcal/mol. The semiempirical OM1 and OM2 approaches that go beyond the MNDO model and are still under development promise an improved accuracy (see Table 8.1). 

The discussion in Section II.A has shown that many of the currently accepted semiempirical methods for computing potential surfaces are based on the MNDO model. These methods differ mainly in their actual implementation and parametrization. Given the considerable effort that has gone into their development, we believe that further significant overall improvements in general-purpose semiempirical methods require improvements in the underlying theoretical model. In this spirit we describe two recent developments The extension of MNDO to d orbitals and the incorporation of orthogonalization corrections and related one-electron terms into MNDO-type methods. 

Theoretical Linear Solvation Energy Relationship (TLSER) With the LSER descriptors of Kamlet and Taft in mind, Famini and Wilson developed QM-derived parameters to model terms in Eq. [18] and dubbed these the TLSER descriptors. Descriptor calculations are done with the MNDO Hamiltonian in MOPAC and AMP AC. MNDO has greater systematic errors than do AMI and PM3, but the errors tend to cancel out better in MNDO-derived correlation equations. A program called MADCAP was developed to facilitate descriptor calculation from MOPAC output files. 

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. 

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]. 

MNDO, AMI, and PM3 together are all NDDO techniques developed by Dewar and his co-workers, and all use essentially the same model functions. MNDO has been parameterized for 20 elements, AMI for 11, and PM3 for 12. The accuracy of these three methods in reproducing experiment has been examined recently in considerable detail.We review this briefly below and refer in particular to ref. 12. 

This review of semiempirical quantum-chemical methods outlines their development over the past 40 years. After a survey of the established methods such as MNDO, AMI, and PM3, recent methodological advances are described including the development of improved semiempirical models, new general-purpose and special-purpose parametriza-tions, and linear scaling approaches. Selected recent applications are presented covering examples from biochemistry, medicinal chemistry, and nanochemistry as well as direct reaction dynamics and electronically excited states. The concluding remarks address the current and future role of semiempirical methods in computational chemistry. 

Semiempirical quantum mechanics. The computational effort in ab initio calculations increases as the fonrth power of the size of the basis set, and, therefore, its appfication to large molecnles is expensive in terms of time and computer resources. Consequently, semiempirical methods treating only the valence electrons, in which some integrals are ignored or replaced by empirically based parameters, have been developed. The various semiempirical parameterizations now in nse (MNDO, AM 1, PM3, etc.) have greatly increased the molecnlar size that is accessible to quantitative modeling methods and also the accnracy of the resnlts. 

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. 

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