Semiempirical methods computational speed

Semiempirical methods, on the other hand, utilize minimum basis sets to speed up computations, and the loss in rigor is compensated by the use of experimental data to reproduce important chemical properties, such as the heats of formation, molecular geometries, dipole moments, and ionization potentials (Dewar, 1976 Stewart, 1989a). As a result of their computational simplicity and their chemically useful accuracy, semiempirical methods are widely used, especially when large molecules are involved (see, for example, Stewart, 1989b Dewar et al., 1985 Dewar, 1975). 

Compared to other methods (molecular mechanics, semiempirical calculations, density functional calculations - Chapters 3, 6 and 7, respectively) ab initio calculations are slow, and they are relatively demanding of computer resources (memory and disk space, depending on the program and the particular calculation). These disadvantages, which increase with the level of the calculation, have been to a very large extent overcome by the tremendous increase in computer power, accompanied by decreases in price, that have taken place since the invention of electronic computers. In 1959 Coulson doubted the possibility (he also questioned the desirability, but in this regard visualization has been of enormous help) of calculations on molecules with more than 20 electrons, but 30 years later computer speed had increased by a factor of 100,000 [329], and ab initio calculations on molecules with 100 electrons (about 15 heavy atoms) are common. 

A straight forward application of approximation IV to calculate W (r) maps is quite exacting, because the calculation of the potential contribution due to the couple distributions xt li 1S time consuming when directly performed on the Slater functions. This fact clashes with the basic philosophy of semiempirical methods, which is to sacrifice some reliability to speed up the calculations. It has been shown40) that expansion of each Slater-type orbital into three Gaussian functions (3G expansion41)) gives a substantial improvement of the computational times of W (r), without an appreciable reduction in the quality of the results. 

The development of improved algorithms and far faster computers has altered the situation almost out of recognition computers in 2(XX) were about one million times faster than in 1959 (computers were said [4] to be 1(X)(XX) times faster in 1989 than in 1959, the date of Coulson s remarks it seems safe to say that they increased in speed by a factor of 10 in the subsequent decade). A calculation that in 1967 would have taken 200 years can now be run on a cheap computer in less than an hour [6]. Why, then, are SE calculations still used Because they are still about 100-1000 times faster than ab initio (chapter 5) or density functional (chapter 7) methods. The increase in computer speed means that we can now routinely examine by ab initio methods moderately large molecules - up to, say, steroids, with about 30 heavy atoms (nonhydrogen atoms), and by semiempirical methods (and faster with MM, chapter 3) huge molecules, like proteins and nucleic acids. 

This review is organized as follows Section II describes the current status of semiempirical methodology. The currently accepted treatments are characterized briefly with regard to their basic assumptions, computational speed, and accuracy, and their relation to ab initio and density functional methods is discussed in this context. Selected recent applications from fullerene chemistry are included to illustrate the potential and the limitations of the currently available semiempirical approaches. Section III deals with recent and ongoing methodological developments. This includes work on the foundations of semiempirical theory, the improvement of semiempirical methods, the parametrization of such methods, and the progress in computational aspects. Based on these advances, new applications are identified which should soon become more tractable by semiempirical calculations. Section IV offers concluding remarks and an outlook. 

The CLS methodology uses an FE description to model the continuum, classical MD to simulate the evolution of the mesoscopic regime, and a TB molecular dynamics approach to include quantum effects in the overall treatment. The FE description is at the linear elastic level because its use is limited to regions where the atoms are only slightly perturbed from equilibrium. The classical molecular dynamics makes use of semiempirical potentials such as the Stillinger-Weber (SW) potential for Si. Lastly, the tight-binding method was chosen instead of other, more accurate, quantum descriptions because of its computational speed. 

Semiempirical molecular orbital (SEMO) methods have been used widely in computational studies [1,2]. Various reviews [3-6] describe the underlying theory, the different variations of SEMO methods, and their numerical results. Semiempirical approaches normally originate within the same conceptual framework as ab initio methods, but they overlook minor integrals to increase the speed of the calculations. The mistakes arising from them are compensated by empirical parameters that are introduced into the outstanding integrals and standardized against reliable experimental or theoretical reference data. This approach is successful if the semiempirical model keeps the essential physics and chemistry that describe the behavior of the process. 

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