MNDO model

The modified neglect of differential overlap (MNDO) model should probably come next MNDO is like INDO except that MNDO treats the diatomic two-electron integrals more accurately. It retains all two-electron integrals involving monatomic differential overlap, and the paper to read is probably ... 

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. 

MNDO, AMI, and PM3 employ an sp basis without d orbitals [13, 19, 20]. Hence, they cannot be applied to most transition metal compounds, and difficulties are expected for hypervalent compounds of main-group elements where the importance of d orbitals for quantitative accuracy is well documented at the ab initio level [34], To overcome these limitations, the MNDO formalism has been extended to d orbitals. The resulting MNDO/d approach [15-18] retains all the essential features of the MNDO model. 

Due to the integral approximations used in the MNDO model, closed-shell Pauli exchange repulsions are not represented in the Hamiltonian, but are only included indirectly, e.g., through the effective atom-pair correction terms to the core-core repulsions [12], To account for Pauli repulsions more properly, the NDDO-based OM1 and OM2 methods [23-25] incorporate orthogonalization terms into the one-center or the one- and two-center one-electron matrix elements, respectively. Similar correction terms have also been used at the INDO level [27-31] and probably contribute to the success of methods such as MSINDO [29-31],... 

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). 

Semi-empirical models are completely unsatisfactory. The MNDO model performs worst and the PM3 model performs best (paralleling the behavior that was previously noted in other frequency comparisons), but none is successful in properly ordering the frequencies. 

Semi-empirical models do not provide good descriptions of the energy barrier to ring inversion in cyclohexane. The MNDO model underestimates the barrier by a factor of three, and the AMI and PM3 models by almost a factor of two. This behavior is consistent with previous experience in dealing with single-bond rotation barriers. 

Kolb, M. and Thiel, W., Beyond the MNDO model methodical considerations and numerical results, J. Computational Chem., 14, 775-789, 1993. 

The core-core repulsion of the Modified Neglect of Diatomic Overlap (MNDO) model has the form ... 

W. Thiel, The MNDOC method, a correlated version ofthe MNDO model, J. Am. Chem. Soc. 103, 1413-1420(1981). 

The most useful method for background studies is based on the MNDO model [18], which is a valence-electron self-consistent-field (SCF) MO treatment. It takes up a minimal basis of atomic orbitals (AOs) and the NDDO integral estimation. The molecular orbitals, ([), , and the corresponding orbital energies, s , are obtained from the linear combination of the AO base functions, cjaM, and the solution of the secular equations with Suv ... 

In 1983 the first MOPAC program was written and contained both the MlNDO/3 and MNDO models. This program allowed geometry optimization, transition state location by use of a reaction coordinate, gradient minimizations, and vibrational frequency calculations. MNDO has been applied with success to the prediction of polarizabilities, hyperpolarizabilities, ESCA, nuclear quadrupole resonance, and numerous other properties. ... 

The MNDO model is a very successful model, again with some documented limitations. MNDO produces spurious interatomic repulsions, generally... 

Shortcomings in the MNDO model as described in the previous section led to a reexamination of the model, leading to Austin Model 1, AM1. ° In this model a term was added to MNDO to correct for the excessive repulsions at van der Waals distances. Toward this end, each atom was assigned a number of spherical gaussians, which were intended to mimic long range correlation effects. The core-core repulsion term was modified and became... 

The PM3 model is the third parameterization of the original MNDO model, the second being AMI. " These methods are all NDDO methods, but PM3 and AMI utilize Eq. [31] for the core-core repulsion term. The other terms in the Fock matrices are as they appear in MNDO. 

To accomplish this large task of optimizing parameters an automatic procedure was introduced, allowing a parameter search over many elements simultaneously. These now include H, C, N, O, F, Br, Cl, I, Si, P, S, Al, Be, Mg, Zn, Cd, Hg, Ga, In, Tl, Ge, Sn, Pb, As, Sb, Bi, Se, Te, Br, and I. Each atom is characterized through the 13-16 parameters that appear in AMI plus five parameters that define the one-center, two-electron integrals. The PM3 model is no doubt the most precisely parameterized semiempirical model to date, but, as in many multiminima problems, one still cannot be sure to have reached the limit of accuracy suggested by the MNDO model. 

The most popular semiempirical methods for studying ground-state potential surfaces are based on the MNDO model [16]. We shall therefore outline the MNDO formalism for closed-shell molecules as a point of reference for the following discussion. 

The MNDO model is defined by the equations given above. In its original implementation... 

In the MNDO model, the two-center core-core repulsions are composed of an electrostatic term an additional effective term (see Section 21.3.2). The... 

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