Molecular orbital theory MINDO

Hiickel and extended Huckel methods are termed semi-empirical because they rely on experimental data for the quantification of parameters. There are other semi-empirical methods, such as CNDO, MINDO, INDO, in which experimental data are still used, but more care is taken in evaluating the Htj. These methods are self-consistent field procedures based on 3 SCF. They are discussed in various works on molecular orbital theory.4... 

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. 

Molecular orbital theory has been applied to the problem of cyclohexane conformations by Dewar and SchoUer.32) Preliminary results using the MINDO/2 method predict a barrier considerably lower than found experimentally. 

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. 

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. 

Several different molecular orbital methods have been used in SAR investigations. These include simple Huckel theory, HT,(38) extended Huckel theory, EHT,(39) CND0,( ) NDD0,(41) MINDO/3,(42) and PCILO,(43)... 

Microwave spectrometer, 219-221 Microwave spectroscopy, 130, 219-231 compilations of results of, 231 dipole-moment measurements in, 225 experimental procedures in, 219-221 frequency measurements in, 220 and molecular structure, 221-225 and rotational barriers, 226-228 and vibrational frequencies, 225-226 Mid infrared, 261 MINDO method, 71,76 and force constants, 245 and ionization potentials, 318-319 Minimal basis set, 65 Minor, 14 Modal matrix, 106 Molecular orbitals for diatomics, 58 and group theory, 418-427 for polyatomics, 66... 

It has recently become clear113 114 that simple Hiickel theory, as well as some more elaborate techniques such as MINDO/2, are unreliable for use in conjunction with frontier orbital theory. For example, Hiickel molecular orbital coefficients suggest97 that acrolein (30) will dimerize to (31), but in fact the product is (32). SCF orbitals... 

Besides these theories, which are applicable to general systems, some other theories of less general applicability have been proposed. These are outlined separately below. A group of empirical methods which has been omitted from the present review are the semi-empirical molecular orbital methods known by acronyms such as MINDO, INDO and CNDO. The reader is referred to a book by Murrell and Harget259 for a description of these methods and to articles by Chutjian and Segal260 and by MacGregor and Berry261 for examples of their use. 

EHT, extended Huckel theory CNDO, complete neglect of differential overlap INDO, intermediate neglect of differential overlap NNDO, neglect of diatomic differential overlap SCF, self-consistent field MINDO, modified INDO ab initio, without the use of independently derived parameters. For an independent assessment of the different molecular orbital methods applied to carbocations, see Ref. 3. 

There is probably no other branch of computational chemistry that arouses such strong emotions as semiempirical molecular orbital (MO) theory. Early controversies between the Dewar and Pople groups about the relative merits of MINDO/3 and HF/STO-3G calculations set the scene for a schism between ab initioists" and semiempiricists that remains in a weakened form today. Perhaps symptomatic of this schism is the controversy that raged when density functional theory (DFT) methods began to make inroads into chemistry as to whether they are ab initio (good) or semiempirical (bad). The facts, also presented by the semiempirical articles in this work, are a little different. 

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). 

The most convenient way of defining MINDO/3 is in relation to the earlier methods. The basic form of the equations was similar to those in INDO, only in MINDO/3 the origin of the parameters was different. For example, rather than use atomic spearal data to define 17, the one-electron integral was made an adjustable parameter. MINDO/3 had several of these parameters, which were adjusted to give the best fit to experimental data for molecules. Here we see a basic difference between Dewar s methods and those that had gone before. Slater s rules were abandoned instead the orbital exponent was made a parameter, as were the multipliers in the resonance integral, By adjusting the parameters to fit molecular data rather than theory, as with Slater s rules, or spectra, as with the values, a vastly improved result was obtained. 

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