Empirical and Semiempirical Methods

The Xa method has been made analytic and variational via single-center, LCGTO, robust, and variational fitting. It is quite promising because, unlike empirical and semiempirical methods, it is applicable to all elements. In fact, it has an independent parameter for each element that can be optimized to give... 

A number of empirical and semiempirical methods have been developed to predict the changes in heat transfer coefficient in pool boiling. Stephan and Korner [128] define an effective temperature driving force for use instead of (Tw -r ) inEq. 15.111 ... 

Up until about 5 years ago, the calculation of absolute electron impact ionization cross sections for molecules relied largely on empirical and semiempirical methods and on simplistic additivity rules because of the complexity of more rigorous calculations for these processes and these targets (Younger and Mark, 1985). In the past 5 years, several new developments have emerged ... 

Until relatively recently, the use of quantum MD for modeling polymers seemed completely unrealistic. This approach, however, is now applicable to polymeric systems that could only be studied by means of empirical and semiempirical methods a decade ago. First-principles MD simulations have been successfully applied to a wide variety of important problems in polymer physics and chemistry and are now beginning to influence biology as well. ° Representative examples include the simulations of polyethylene (PE) (the prediction of Yoimg s modulus for crystalline material, strain energy storage and chain mpture under tensile load, the... 

The design of industrial-scale collectors still rests essentially on empirical or semiempirical methods, although it is increasingly guided by concepts derived from theory. Existing theoretical models frequently embody constants that must be evaluated by experiment and that may actually compensate for deficiencies in the models. 

These approaches may include (1) purely empirical methods that try to simulate conformations by using classical molecular mechanics and adjustable parameters, still employed in very large molecular systems (2) potential energy determination with empirical and semiempirical functions consisting... 

Over the years, several computational methods have been developed. The variational theory can be used either without using experimental data other than the fundamental constants (i.e., ab initio methods) or by using empirical data to reduce the needed amount of numerical work (i.e., semiempirical data methods). There are various levels of sophistication in both ab initio [HF(IGLO), DFT GIAO-MP2, GIAO-CCSD(T)] and semiempirical methods. In the ab initio methods, various kinds of basic sets can be employed, while in the semiempirical methods, different choices of empirical parameters and parametric functions exist. The reader is referred to reviews of the subject.18,77... 

We have seen three broad techniques for calculating the geometries and energies of molecules molecular mechanics (Chapter 3), ab initio methods (Chapter 5), and semiempirical methods (Chapters 4 and 6). Molecular mechanics is based on a balls-and-springs model of molecules. Ab initio methods are based on the subtler model of the quantum mechanical molecule, which we treat mathematically starting with the Schrodinger equation. Semiempirical methods, from simpler ones like the Hiickel and extended Hiickel theories (Chapter 4) to the more complex SCF semiempirical theories (Chapter 6), are also based on the Schrodinger equation, and in fact their empirical aspect comes from the desire to avoid the mathematical... 

Data from a CD detector can be used to successfully confirm the absolute stereochemistries of the eluted enantiomers and the elution order. This important application has been introduced by Salvadori and co-workers [23], More recently it was demonstrated that an on-line detection system can be made which measures the CD spectrum of the eluate by trapping and holding it in the HPLC cell. By comparing the spectrum with data in a CD spectral library, absolute configurations can be confirmed. Where spectra are unavailable, absolute configurations might be obtained by means of either empirical and semiempirical approach or by using nonempirical methods such as the exciton model or the DeVoe approach [22, 23]. 

Both non-empirical <85JMR262> and semiempirical methods <83OMR(2i)50l> have been applied successfully to the interpretation of NMR spectra, particularly to the effects of solvent on chemical shifts. 

Due to its simplicity, its nondestructive nature, and the fact that minimal machining is required to prepare the sample, the use of the Vickers hardness indentations to measure Ki. has become quite popular. In this method, a diamond indenter is applied to the surface of the specimen to be tested. Upon removal, the sizes of the cracks that emanate (sometimes) from the edges of the indent are measured, and the Vickers hardness H in GPa of the material is calculated. A number of empirical and semiempirical relationships have been proposed relating Ki., c, Y, and //, and in general the expressions take the form... 

Diffusion in liquid-filled pores occurs by essentially the same mechanism-as in gaseous systems. However, methods of correlation and prediction are less accurate since the fundamental theory of diffusion in the liquid phase is less well developed than the theory of molecular diffusion in the vapor phase. Correlations based on the Stokes-Einstein and Nemst-Einstein equations must be treated with caution. A wide range of empirical and semiempirical correlations is available but it is generally necessary to select the appropriate correlation with care, taking due account of the nature of the components. Predictive methods are at their best for mixtures of two nonpolar species and at their worst for mixtures of a polar and nonpolar species. 

The most common approaches to predicting spectra are based on empirical modeling, linear additivity, database retrieval, rule sets, and semiempirical methods. The availability of large spectral libraries has proved to be a valuable resource in these studies. Although ab initio theory relating to spectrum prediction is well advanced, the theoretical equations necessary for application to real-world structures are large and complex... 

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