Computer code practicalities

The calculation of atmospheric transport with its many parameters and frequency weighting of the wind rose is practical only with a computer code. Table 8.3-6... 

As a practical point, any computer code has to be transferable between platforms, so there is little point writing code in esoteric but obsolete languages such as French ALGOL. 

Variable viscosity in laminar tube flows is an example of the coupling of mass, energy, and momentum transport in a reactor design problem of practical significance. Elaborate computer codes are being devised that recognize this... 

While TD-DFT continuum calculations for molecules, such as camphor, are not yet quite practicable, efforts to create highly parallel computer codes capable of tackling this scale of problem are expected to be fruitful soon. In the meantime TD-DFT studies for computahonaUy less demanding small molecules [66-68] or highly symmetric molecules, such as SFg [79], have provided indicahons of the general value of the inclusion of electron response effects. 

This chapter summarizes the computational methodologies used for conformational analysis. Specifically, Section 8.1 gives a theoretical outUne of the problem and presents details of various implementations of computer codes to perform conformational analysis. Section 8.2 describes calculations illustrative of the current accuracy in generating the conformation of a ligand when bound to proteins (the bioactive conformer) by comparisons to crystaUographically observed data. Finally, Section 8.3 concludes by presenting some practical... 

In problems in which there are n variables and m equality constraints, we could attempt to eliminate m variables by direct substitution. If all equality constraints can be removed, and there are no inequality constraints, the objective function can then be differentiated with respect to each of the remaining (n — m) variables and the derivatives set equal to zero. Alternatively, a computer code for unconstrained optimization can be employed to obtain x. If the objective function is convex (as in the preceding example) and the constraints form a convex region, then any stationary point is a global minimum. Unfortunately, very few problems in practice assume this simple form or even permit the elimination of all equality constraints. 

The expressions for the transformation matrices presented above cover practically all necessary cases. However, their use is rather complicated. Therefore, for the most often considered configurations and l p, one can start with somewhat simplified formulas for the corresponding matrices of the transformation to jj coupling presented in [94], or use general computer codes for the implementation of such transformations. 

The formulas derived above, despite their cumbersome look, are very practical. Indeed, they present the nonlinear initial susceptibilities of a superparamagnetic particulate medium as analytical expressions of arbitrary accuracy. Another remarkable feature of the formulas of Section III.B.6 is that with respect to the frequency behavior they give the exact structure of the susceptibilities and demonstrate that those dependencies are quite simple. This makes our formulas a handy tool for analytical studies. Yet they are more convenient for numerical work because with their use the difficult and time-consuming procedure of solving the differential equations is replaced by a plain summation of certain power series. For example, if to employ Eqs. (4.194)-(4.200), a computer code that fits simultaneously experimental data on linear and a reasonable set of nonlinear susceptibilities (say, the 3th and the 5th) taking into account the particle polydispersity of any kind (easy-axes directions, activation volume, anisotropy constants) becomes a very fast procedure. 

The detailed study of electron distribution rearrangements in a chemical reaction needs a multiconfiguration ab initio method, because one determinantal wavefunctions are unreliable away from equilibrium geometries. By means of the CASSCF method it is possible to focus attention on the electrons more directly involved in the reaction, allowing the calculation to be done with a relatively limited number of Slater determinants. Moreover, CASSCF uses orthogonal orbitals which are simpler than non-orthogonal orbitals in the development of computer codes. Nowadays CASSCF is, in fact, efficiently included in practically all distributed packages for molecular quantum calculations. 

In practice, one is often faced with choosing a model that is easily interpretable but may not approximate a response very well, such as a low-order polynomial regression, or with choosing a black box model, such as the random-function model in equations (l)-(3). Our approach makes this blackbox model interpretable in two ways (a) the ANOVA decomposition provides a quantitative screening of the low-order effects, and (b) the important effects can be visualized. By comparison, in a low-order polynomial regression model, the relationship between input variables and an output variable is more direct. Unfortunately, as we have seen, the complexities of a computer code may be too subtle for such simple approximating models. 

It is worth noting that practically all non-traditional methods for solving crystal structures have been initially developed for both powder and single crystal diffraction data to manage intrinsic incompleteness or poor quality that cannot be improved experimentally. Despite a variety of structure solution approaches, traditional direct phase determination methods appear to be the most common and successful when powder diffraction data are adequate. Patterson methods also work quite well but they require the presence of a heavy atom and, perhaps, more extensive crystallographic expertise. The non-traditional methods are generally employed when other techniques fail and their use is somewhat restricted by both the complexity and limited availability of computer codes. 

The practical realization of multicomponent MBPT rests on the development of efficient algorithms and the associated computer code. In recent work, we have advocated the use literate programming techniques in the development and publication of computer code for molecular structure calculations. We briefly discuss the application of these methods to the multicomponent many-body perturbation expansion. 

The possibility of incorporating the recipe-like model of CASSCF into computer codes of CQC allowed the extensive and successful application over the years by a large number of research groups, including of course that of Roos, fhereby creafing a huge amount of useful and reliable information on molecular structures and properties. In order to briefly describe here the corresponding concept and practice, I quote from Ref. [3j ... 

The common perception among environmental practitioners, that a modeling program produces a model, is not correct. It is always the modeler, not the computer code, that produces a model. In environmental practice, this misconception, and sometimes misrepresentation, borders on deception of the public, regulators, or clients because most popular modeling codes are distributed by regulatory or federal agencies and therefore carry an air of authority. 

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