Semiempirical limitations

The most severe limitation of ah initio methods is the limited size of the molecule that can be modeled on even the largest computers. Semiempirical calculations can be used for large organic molecules, but are also too computation-intensive for most biomolecular systems. If a molecule is so big that a semiempirical treatment cannot be used elfectively, it is still possible to model its behavior avoiding quantum mechanics totally by using molecular mechanics. 

Semiempiricals n - For small- to medium-size molecules (limited by integrals)... 

Semiempiricals For very large molecules (limited by matrix inversion)... 

There are a few semiempirical methods for modeling transition metals. These tend to have limited applicability. None has yet become extremely far-ranging in the type of system it can model accurately. 

Direct-Liquefaction Kinetics All direct-liquefac tion processes consist of three basic steps (1) coal slurrying in a vehicle solvent, (2) coal dissolution under high pressure and temperature, and (3) transfer of hydrogen to the dissolved coal. However, the specific reac tion pathways and associated kinetics are not known in detail. Overall reaction schemes and semiempirical relationships have been generated by the individual process developers, but apphcations are process specific and limited to the range of the specific data bases. More extensive research into liquefaction kinetics has been conducted on the laboratory scale, and these results are discussed below. 

Before discussing the kinds of kinetic information provided by potential energy surfaces we will briefly consider methods for calculating these surfaces, without going into detail, for theoretical calculations are outside the scope of this treatment. Detailed procedures are given by Eyring et ah There are three approaches to the problem. The most basic one is purely theoretical, in the sense that it uses only fundamental physical quantities, such as electronic charge. The next level is the semiempirical approach, which introduces experimental data into the calculations in a limited way. The third approach, the empirical one, makes extensive use of experimental results. 

The CNDO method has been modified by substitution of semiempirical Coulomb integrals similar to those used in the Pariser-Parr-Pople method, and by the introduction of a new empirical parameter to differentiate resonance integrals between a orbitals and tt orbitals. The CNDO method with this change in parameterization is extended to the calculation of electronic spectra and applied to the isoelectronic compounds benzene, pyridine, pyri-dazine, pyrimidine and pyrazine. The results obtained were refined by a limited Cl calculation, and compared with the best available experimental data. It was found that the agreement was quite satisfactory for both the n TT and n tt singlet transitions. The relative energies of the tt and the lone pair orbitals in pyridine and the diazines are compared and an explanation proposed for the observed orders. Also, the nature of the lone pairs in these compounds is discussed. 

We have a considerable body of knowledge to help us to say something about the third coefficient, the variation of fugacity with composition. Many empirical and semiempirical expressions (e.g., Margules, Van Laar, Scat-chard-Hildebrand) have been investigated toward that end. Most of our experience in this regard is limited to liquid mixture at low pressures, where... 

The semiempirical methods represent a real alternative for this research. Aside from the limitation to the treatment of only special groups of electrons (e.g. n- or valence electrons), the neglect of numerous integrals above all leads to a drastic reduction of computer time in comparison with ab initio calculations. In an attempt to compensate for the inaccuracies by the neglects, parametrization of the methods is used. Meaning that values of special integrals are estimated or calibrated semiempirically with the help of experimental results. The usefulness of a set of parameters can be estimated by the theoretical reproduction of special properties of reference molecules obtained experimentally. Each of the numerous semiempirical methods has its own set of parameters because there is not an universial set to calculate all properties of molecules with exact precision. The parametrization of a method is always conformed to a special problem. This explains the multiplicity of semiempirical methods. 

In most cases the chemist only needs differences of values and/or relative estimations in comparison with a standard. The inaccuracies introduced by semiempirical methods with its relatively drastic approximations can be limited by applying the differences causing the calculated values to possess suitable accuracy. 

Even though molecular mechanics has given satisfactory results (i.e., results that agree with experimental measurements) for many molecules, it is still not totally reliable, since it does fail in certain cases. A further limitation is that it can be used only in cases for which transferable parameters can be obtained from simple molecules. Molecular orbital calculations do not have this limitation, but to some extent semiempirical MO methods do. 

The Stokes-Einstein equation predicts that DfxITa is independent of the solvent however, for real solutions, it has long been known that the product of limiting interdiffusion coefficient for solutes and the solvent viscosity decreases with increasing solute molar volume [401]. Based upon a large number of experimental results, Wilke and Chang [437] proposed a semiempirical equation,... 

Quantum mechanical and selected semiclassical and semiempirical methods for the calculation of electron impact ionization cross sections are described and their successes and limitations noted. Experimental methods for the measurement of absolute and relative ionization cross sections are also described in some detail. Four theoretical methods, one quantum mechanical and three semiclassical, have been used to calculate cross sections for the total ionization of the inert gases and small molecules and the results compared with experimental measurements reported in the literature. Two of the theoretical methods, one quantum mechanical and one semiclassical, have been applied to the calculation of orientation-dependent electron impact ionization cross sections and the results compared with recent experiments. 

Due to the complexity of a full quantum mechanical treatment of electron impact ionization, or even a partial wave approximation, for all but relatively simple systems, a large number of semiempirical and semiclassical formulae have been developed. These often make basic assumptions which can limit their range of validity to fairly small classes of atomic or molecular systems. The more successful approaches apply to broad classes of systems and can be very useful for generating cross sections in the absence of good experimental results. The success of such calculations to reproduce experimentally determined cross sections can also give insight into the validity of the approximations and assumptions on which the methods are based. 

Na3F2 cluster, direct molecular dynamics, semiempirical studies, 415 Near-adiabatic limit, molecular systems,... 

Unless there is some obvious flaw such as those mentioned above, semiempirical methods still give a more reliable answer than qualitative MO arguments which we are about to discuss, and it certainly makes sense to use them if a program and computer time are available, provided that limitations such as the above are recognized. However, what is really needed most is a cheap semiempirical method free of the above disadvantages. 

Because of the inherent limitations of such semiempirical procedures, they can only be relied upon for yielding predictions for a limited set of data, the range of which includes the set of experimental data used for their parametrization. As such data are less abundant for open-shell species, such as radical ions, it is not surprising that there are examples of dramatic failures of semiempirical methods in predicting their electronic spectra, some of which will be discussed later. Ab initio methods are not burdened by these limitations but, as mentioned above, they require additional computations to account for dynamic electron correlation. 

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