MNDO

The modihed neglect of diatomic overlap (MNDO) method has been found to give reasonable qualitative results for many organic systems. It has been incorporated into several popular semiempirical programs as well as the MNDO program. Today, it is still used, but the more accurate AMI and PM3 methods have surpassed it in popularity. 

There are a some known cases where MNDO gives qualitatively or quantitatively incorrect results. Computed electronic excitation energies are underestimated. Activation barriers tend to be too high. The correct conformer is not 

A variation on MNDO is MNDO/d. This is an equivalent formulation including d orbitals. This improves predicted geometry of hypervalent molecules. This method is sometimes used for modeling transition metal systems, but its accuracy is highly dependent on the individual system being studied. There is also a MNDOC method that includes electron correlation. 

Dewar and Thiel (1977) reported a modified neglect of differential overlap (MNDO) method based on the NDDO formalism for the elements C, H, O, and N. With the conventions specified by NDDO for which integrals to keep, which to discard, and how to model one-electron integrals, it is possible to write the NDDO Fock matrix elements individually for 

An off-diagonal Fock matrix element for two basis functions n and v on the same atom A is written as 

To complete the energy evaluation by the MNDO method, the nuclear repulsion energy is added to the SCF energy. The MNDO nuclear repulsion energy is computed as 

Since the report for the initial four elements, AMI parameterizations for B, F, Mg, Al, Si, P, S, Cl, Zn, Ge, Br, Sn, I, and Hg have been reported. Because AMI calculations are so fast (for a quantum mechanical model), and because the model is reasonably robust over a large range of chemical functionality, AMI is included in many molecular modeling packages, and results of AMI calculations continue to be reported in the chemical literature for a wide variety of applications. 

One of the authors on the original AMI paper and a major code developer in that effort, James 

One of the authors on the original AMI paper and a major code developer in that effort, James J. P. Stewart, subsequently left Dewar s labs to work as an independent researcher. Stewart felt that the development of AM 1 had been potentially non-optimal, from a statistical point of view, because (i) the optimization of parameters had been accomplished in a stepwise fashion (thereby potentially accumulating errors), (ii) the search of parameter space had been less exhaustive than might be desired (in part because of limited computational resources at the time), and (iii) human intervention based on the perceived reasonableness of parameters had occurred in many instances. Stewart had a somewhat more mathematical philosophy, and felt that a sophisticated search of parameter space using complex optimization algorithms might be more successful in producing a best possible parameter set within the Dewar-specific NDDO framework. 

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The first quantum mechanical improvement to MNDO was made by Thiel and Voityuk [19] when they introduced the formalism for adding d-orbitals to the basis set in MNDO/d. This formalism has since been used to add d-orbitals to PM3 to give PM3-tm and to PM3 and AMI to give PM3(d) and AMl(d), respectively (aU three are available commercially but have not been published at the time of writing). Voityuk and Rosch have published parameters for molybdenum for AMl(d) [20] and AMI has been extended to use d-orbitals for Si, P, S and Q. in AMI [21]. Although PM3, for instance, was parameterized with special emphasis on hypervalent compounds but with only an s,p-basis set, methods such as MNDO/d or AMI, that use d-orbitals for the elements Si-Cl are generally more reliable. 

A valuable review of th e MOP,AC program an d th e sem i-etn pirical methods MNDO. MINDO/3, AM I. and PM 3, Of particular use are th eoretical discussion s of these sem i-em pirical meth -ods and many tables validating the accuracy of the MOP.AC program and its associated Hamiltonians. 

Using Cl may not necessarily improve the calculation of ground slate cn crgics. Pararn eters for th e MINDO/3, MNDO,. AM I, and PM3 methods already iricltide the effects of Cl. Cl calculation s retjuire m ore corn pii ting time. 

After yon choose the com pn tat ion method and options, you can use Start bog on the file menu to record results, such as total energies, orbital en ergies, dipole m om en Ls, atom ic charges, en Lhalpics of formalion (foritieCNDO, IN DO, MIXDO/3, MNDO, AMI, PM3, ZINDO/1, and ZINDO/S mclh ods), etc. 

Calcu laLiii g th c extra in tegrals takes tim e. MNDO,. AM 1, an d PM3 calculation s typical ly take about on e and on e-h alf tim es as long as IXDO or MIXDO/3 calculations. 

MINDO/3, MNDO, and AM 1 wxrc developed by the Dervar group at the University of i exasat Austin. This group ehose many parameters, such as heats of formation and geometries of sample molecules, to reproduce experimental quantities. The Dewar methods yield results that are closer to experiment than the CN DO and IN DO methods. 

IXDCf is faster than MINDO/3, MNDO, AMI, and PM3 and, unlike C XDO, can deal with spin effects. It is a particularly appealing choice for UHF calculations on open-shell molecules. It is also available for mixed mode calculations (see the previous section ). IXDO shares the speed and storage advantages of C XDO and is also more accurate. Although it is preferred for numerical results, it loses some of the simplicity and inierpretability of C XDO. 

The cIcniciiLs of the MNDO Fock niairix bused on thenef/lecL of diuLmnic din ereii liul overlap approximaiion are described below. When and dy are on dilTeren L cen ters the oIT-diagonal elemen Is of 111 e Hock matrix ai e ... 

Thii MNDO niijthod has 22 iiniqiiLi iwo-ctMUer two-eliicLron irUti-gials Ibr each pair ol heavy (non-hydrogen ) atoms in iheir local atomic frame. They are ... 

In the MNDO rnelluKi Ui e resonance integral, is proportion al Lo the overlap integral, S y ... 

The one-center two-electron integrals in the MNDO method are derived from experimental data on isolated atoms. Most were obtained from Oleari s work L. Oleari, L. DiSipio, and G. DeMich-ells. Mol. Phys., 10, 97( 1977)1, but a few were obtained by IDewar using fits to molecular properties. 

C oniparing ihc corc-core repulsion ol lhe above two ec nations with those in the MNDO method, it can be seen that the only dil -ference is in the last term. The extra terms in the AMI core-core repulsion deline spherical Ciaiissian Tun ctioii s — the a. h, and c are adjustable parameters. AMI has between two and I onr Gaussian full ctiori s per atom, ... 

The core-core repulsion terms are also different in MNDO from those in MlNDO/3, with c)l I and NH bonds again being treated separately ... 

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