Modelling chemistry-based methods

There is a lot of confusion over the meaning of the terms theoretical chemistry, computational chemistry and molecular modelling. Indeed, many practitioners use all three labels to describe aspects of their research, as the occasion demands "Theoretical chemistry is often considered synonymous with quantum mechanics, whereas computational chemistry encompasses not only quantum mechanics but also molecular mechaiucs, minimisation, simulations, conformational analysis and other computer-based methods for understanding and predicting the behaviour of molecular systems. Molecular modellers use all of these methods and so we shall not concern ourselves with semantics but rather shall consider any theoretical or computational tecluiique that provides insight into the behaviour of molecular systems to be an example of molecular modelling. If a distinction has to be... 

Density functional theory-based methods ultimately derive from quantum mechanics research from the 1920 s, especially the Thomas-Fermi-Dirac model, and from Slater s fundamental work in quantum chemistry in the 1950 s. The DFT approach is based upon a strategy of modeling electron correlation via general functionals of the electron density. 

It is a truism that in the past decade density functional theory has made its way from a peripheral position in quantum chemistry to center stage. Of course the often excellent accuracy of the DFT based methods has provided the primary driving force of this development. When one adds to this the computational economy of the calculations, the choice for DFT appears natural and practical. So DFT has conquered the rational minds of the quantum chemists and computational chemists, but has it also won their hearts To many, the success of DFT appeared somewhat miraculous, and maybe even unjust and unjustified. Unjust in view of the easy achievement of accuracy that was so hard to come by in the wave function based methods. And unjustified it appeared to those who doubted the soundness of the theoretical foundations. There has been misunderstanding concerning the status of the one-determinantal approach of Kohn and Sham, which superficially appeared to preclude the incorporation of correlation effects. There has been uneasiness about the molecular orbitals of the Kohn-Sham model, which chemists used qualitatively as they always have used orbitals but which in the physics literature were sometimes denoted as mathematical constructs devoid of physical (let alone chemical) meaning. 

Whether the prediction scheme is a simple chart, a formula, or a complex numerical procedure, there are three basic elements that must be considered meteorology, source emissions, and atmospheric chemical interactions. Despite the diversity of methodologies available for relating emissions to ambient air quality, there are two basic types of models. Those based on a fundamental description of the physics and chemistry occurring in the atmosphere are classified as a priori approaches. Such methods normally incorporate a mathematical treatment of the meteorological and chemical processes and, in addition, utilize information about the distribution of source emissions. Another class of methods involves the use of a posteriori models in which empirical relationships are deduced from laboratory or atmospheric measurements. These models are usually quite simple and typically bear a close relationship to the actual data upon which they are based. The latter feature is a basic weakness. Because the models do not explicitly quantify the causal phenomena, they cannot be reliably extrapolated beyond the bounds of the data from which they were derived. As a result, a posteriori models are not ideally suited to the task of predicting the impacts of substantial changes in emissions. 

In the previous section, it was noted that the MSC method is expected to perform poorly in cases where spectral offset and multiplicative variations are very small relative to those obtained from chemistry-based variations. In response to this, several methods were developed to enable more accurate multiplicative corrections through better modeling of chemistry-based variations in the data [34-35]. One such method is an extension of the MSC method, appropriately called extended multiplicative signal correction (EMSC) [35-37]. 

In order to get more detailed information about, e.g., bond strengths and equilibrium geometries in transition metal systems it is necessary to include electron correlation. This can be done either by traditional ab initio quantum chemistry models, e.g., Cl-methods and coupled cluster methods, or by density functional theory (DFT) based methods. Correlated ab initio methods are often computationally very demanding, especially in cases where multi-reference based treatments are needed. Also, the computational cost of these methods increases dramatically with the size of the system. This implies that they can only be applied to rather small systems. 

The following definition of computational chemistry was published in 1985 (6) quantitative modeling of chemical behavior on a computer by the formalisms of theoretical chemistry. Some quantum theoreticians naturally would like to see computational chemistry as a subset of their field (7). However, today the number of scientists employed as computational chemists well exceeds the number employed as theoreticians (8). A recent textbook author (9) views computational chemistry as encompassing not only quantum mechanics, but also molecular mechanics, [energy] minimization, simulations, conformational analysis, and other computer-based methods for understanding and predicting the behavior of molecular systems. ... 

The term chemometrics was hrst coined in 1971 to describe the growing use of mathematical models, statistical principles, and other logic-based methods in the held of chemistry and, in particular, the held of analytical chemistry. Chemometrics is an interdisciplinary held that involves multivariate statistics, mathematical modeling, computer science, and analytical chemistry. Some major application areas of chemometrics include (1) calibration, validation, and signihcance testing (2) optimization of chemical measurements and experimental procedures and (3) the extraction of the maximum of chemical information from analytical data. 

It would be difficult to find more comprehensive or more detailed studies on the physical chemistry of seawater than those done at the University of Miami (Millero, 2001). Several programs were developed for calculation of activity coefficients and speciation of both major ions and trace elements in seawater. The activity coefficient models have been influenced strongly by the Pitzer method but are best described as hybrid because of the need to use ion-pair formation constants (Millero and Schreiber, 1982). The current model is based on Quick Basic computes activity coefficients for 12 major cations and anions, 7 neutral solutes, and more than 36 minor or trace ions. At 25 °C the ionic strength range is 0-6 m. For major components, the temperature range has been extended to 0-50 °C, and in many cases the temperature dependence is reasonably estimated to 75 °C. Details of the model and the parameters and their sources can be found in Millero and Roy (1997) and Millero and Pierrot (1998). Comparison of some individual-ion activity coefficients and some speciation for seawater computed with the Miami model is shown in Section 5.02.8.6 on model reliability. 

Marsili, N.R., Sobrero, M.S., and Goicoechea, H.C. 2003. Spectrophotometric determination of sorbic and benzoic acids in fruit juices by a net analyte signal-based method with selection of the wavelength range to avoid non-modelled interferences. Analytical and Bioanalytical Chemistry 376 126-133. 

As we saw in Section IIC, in order to begin the GED structure analysis one needs a trial model. In early days this model was based on the chemical intuition of the researcher while nowadays it can be calculated using some of the methods of theoretical chemistry. The role of theory is not limited, however, to calculation of only the geometrical structure as is shown in Fig. 4 it gives also Energy and Force Fields (see mote about theoretical... 

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