MINDO/3 parameterization

The matrix elements of the effective bond Hamiltonians are defined as (with the MINDO/3 parameterization for the Hamiltonian taken for the sake of definiteness) ... 

Numerical experiments concerning the density ESVs transferability. The above analytical results have been supplied by numerical estimates done to get a feeling of the real sense of the first and second order approximations. Numerical results on the ESVs (Tzm), (f2m), and ( +m) obtained by the SLG method eq. (3.1) using the MINDO/3 parameterization and by the approximate formulae of eqs. (3.9), (3.12),... 

The complexity of the parameter-fitting procedure in the MINDO models can only be appreciated by a detailed study of the inherent assumptions. It is perhaps indicative to say the only molecular integral that is calculated exactly from the basis atomic orbitals is the overlap integral, all others being approximated or given empirical values. The repulsion potential of the atomic cores is, for example, one of the critical functions in the theory. There has to the present time been four distinct versions of the MINDO parameterization, and the latest (MINDO/3) (102) is said to remove certain deficiencies in the earlier versions (such as the prediction that HjO was linear and the underestimation of the strain energies in small ring hydrocarbons). 

Sustmann and Binsch132 described a method which started from the same point, but invoked the zero-differential-overlap approximation on the other hand, it was not confined to jr-electrons and the perturbation energy was refined iteratively. Using a MINDO parameterization they then applied the method to Diels-Alder reactions, and were able to account for effects which cannot be explained in terms of simple jr-electron theory, such as the preference for endo addition of cyclopropene to cyclo-pentadiene. 

It should be noted that using an INDO< > rather than a CNDO or MINDO parameterization, one can easily also write the matrix elements for an INDO crystal-orbital theory. This has been done for the sake of brevity we refer the reader to the original paper< > for the details. 

There are three modihed intermediate neglect of differential overlap (MINDO) methods MINDO/1, MINDO/2, and MINDO/3. The MINDO/3 method is by far the most reliable of these. This method has yielded qualitative results for organic molecules. However its use today has been superseded by that of more accurate methods such as Austin model 1 (AMI) and parameterization method 3 (PM3). MINDO/3 is still sometimes used to obtain an initial guess for ah initio calculations. 

Three versions of Modified Intermediate Neglect of Differential Overlap (MINDO) models exist, MINDO/1, MINDO/2 and MINDO/3. The first two attempts at parameterizing INDO gave quite poor results, but MINDO/3, introduced in 1975, produced the first general purpose quantum chemical method which could successfully... 

MTNDO/3 has been parameterized for H, B, C, N, O, F, Si, P, S and Cl, although certain combinations of these elements have been omitted. MINDO/3 is rarely used in modern computational chemistry, having been succeeded in accuracy by the NDDO methods below. Since there are parameters in MINDO which depend on two atoms, the number of parameters increases as the square of the number of elements. It is unlikely that MINDO will be parameterized beyond the above-mentioned in the future. 

This new model f6), called MNDO for Modified Neglect of Diatomic Overlap, was published oy Dewar and Thiel in 1977. With MNDO the average errors (5) for the same survey of C, H, N and O molecules decreased to 6.3 kcal/mol for AHf, 0.014 A for bond lengths and 0.48 eV for ionization potentials. Since MNDO used only atomic parameters, parameterization of MNDO to include additional elements was much easier than with MINDO/3, and, over the next eight years, parameters were optimized for 16 elements in addition to C, H, N and O. 

The first general parameterization to be reported by Dewar and co-workers was a third-generation modified INDO model (MINDO/3 Bingham, Dewar, and Lo, 1975). Some of the specific modifications to the INDO framework included the use of different t exponents in s and p type STOs on the same atom, the definition of pair parameters /Iab between two atoms A and B that were not averages of atomic parameters (actually, four such parameters... 

The theoretical difficulty of making this separation derives from the indistinguish-ability of electrons and the requirement that the total wavefunction be antisymmetric with respect to permutations of the electronic co-ordinates. One approach has been to abandon a full quantum mechanical description in favour of a simplified model hamiltonian which can be conveniently parameterized in terms of experimental quantities. This is the rationale behind Huckel theory, CNDO, and other more sophisticated methods such as MINDO. These techniques have been well documented and reviewed elsewhere (Dewar,1 Pariser, Parr, and Pople,2 Murrell and Hargett,3 etc.) and will not be pursued further here. 

The results of INDO are apparently very similar to those of CNDO when the same set of approximations are used to calculate common integrals. Indeed, the choice of approximations to be used in the (M)INDO method are, as in the other schemes, dictated by the objectives of the method (or the authors preference). The MINDO method is especially parameterized to calculate heats of formation and MINDO/2 85>, which has been specially reparameterized, claims both heats of formation and bond distances. Both of these methods are also suitable for the calculation of open shell systems. An additional approximation, however, was made in order to achieve this, namely that an electron can be treated as half an electron pair (i.e. two halves of one electron). 

The performance of the semiempirical methods for the calculation of thermochemical data depends on the extent to which the physics is included in the model and how well the neglected features can be accounted for by the parameterization. These methods can be assessed by validation against accurate experimental data or high level ab initio predictions. A summary of results for four semiempirical methods (MINDO/3, MNDO, AMI, and PM3) for the neutral enthalpies of formation in the G2/97 test set is given in Table 13. Overall, the newest method, PM3, does the best with an average absolute deviation of 7.02 kcal/mol. It has average absolute deviations of 3.91 and 4.27 kcal/mol for the subgroups of hydrocarbons and substituted hydrocarbons, respectively. 

The electronic energy calculated by the MINDO/3, MNDO, AMI, and PM3 methods is normally converted automatically in the computer program (Table 2) to an enthalpy of formation by subtracting the electronic energy of the isolated atoms and adding the experimental atomic enthalpies of formation. The zero-point energies and temperature corrections (0 to 298 K) are assumed to be included implicitly by the parameterization. For a molecule ABH, the AHf is defined in these methods as... 

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