Computational chemistry direct functionalization

Many problems in computational chemistry can be formulated as an optimization of a multidimensional function/ Optimization is a general term for finding stationary points of a function, i.e. points where tlie first derivative is zero. In the majority of cases the desired stationary point is a minimum, i.e. all the second derivatives should be positive. In some cases the desired point is a first-order saddle point, i.e. the second derivative is negative in one, and positive in all other, directions. Some examples ... 

The simple-minded approach for minimizing a function is to step one variable at a time until the function has reached a minimum, and then switch to another variable. This requires only the ability to calculate the function value for a given set of variables. However, as tlie variables are not independent, several cycles through tlie whole set are necessary for finding a minimum. This is impractical for more than 5-10 variables, and may not work anyway. Essentially all optimization metliods used in computational chemistry tlius assume that at least the first derivative of the function with respect to all variables, the gradient g, can be calculated analytically (i.e. directly, and not as a numerical differentiation by stepping the variables). Some metliods also assume that tlie second derivative matrix, the Hessian H, can be calculated. 

Ab-initio CAChe features all of the above plus ab-initio and density functional methods. This program requires a workstation (Windows NT minimum or SGI and IBM unix-based machines) and can be used to build and visualize results from ab-initio programs (e.g., Gaussian, see description under Gaussian, Inc.). Also, CAChe directly interfaces to Dgauss , a computational chemistry package that uses density functional theory to predict molecular structures, properties, and energetics. 

For a spectroscopic observation to be understood, a theoretical model must exist on which the interpretation of a spectrum is based. Ideally one would like to be able to record a spectrum and then to compare it with a spectrum computed theoretically. As is shown in the next section, the model based on the harmonic oscillator approximation was developed for interpreting IR spectra. However, in order to use this model, a complete force-constant matrix is needed, involving the calculation of numerous second derivatives of the electronic energy which is a function of nuclear coordinates. This model was used extensively by spectroscopists in interpreting vibrational spectra. However, because of the inability (lack of a viable computational method) to obtain the force constants in an accurate way, the model was not initially used to directly compute IR spectra. This situation was to change because of significant advances in computational chemistry. 

These developments have in turn renewed the interest in understanding the structure and reactivity of radical cations. Modern computational chemistry methods, especially density functional methods, as well as the continued exponential increase in hardware performance provided improved tools for a detailed analysis of these interesting species. At the same time, the unique problems of the computational treatment of radical cations as well as the direct and indirect observation of these short-lived species continue to pose new challenges for the development of new theoretical and experimental methods. 

A more recent development which has now overtaken wavefunction methods as the favorite technique of computational chemistry is density functional theory (DFT). This is based on the total electronic charge density p(r), which is more directly related to observable quantities than is the AT-electron wavefunction i/t(n, T2. .. rxt). The density function can always be determined from the wavefunction using... 

Although it is difficult to directly monitor the heterogeneous chemistry in an operating fuel cell, computational methods can be used to disentangle the individual events and predict the kinetics of these events on well-defined surfaces [88,89]. Among the available computational methods, density functional theory (DFT) has played a dominant role. 

With advancements in computer power and the advantage of reasonable scalability to larger systems, density functional theory has made computational chemistry widely accessible in the chemical sciences, permitting direct comparisons to be made between theory and a wide variety of experiments. Examples of the application of density functional theory for prediction, understanding, and interpretation in surface science and heterogenous catalysis include ... 

Initiated by the chemical dynamics simulations of Bunker [37,38] for the unimolecular decomposition of model triatomic molecules, computational chemistry has had an enormous impact on the development of unimolecular rate theory. Some of the calculations have been exploratory, in that potential energy functions have been used which do not represent a specific molecule or molecules, but instead describe general properties of a broad class of molecules. Such calculations have provided fundamental information concerning the unimolecular dissociation dynamics of molecules. The goal of other chemical dynamics simulations has been to accurately describe the unimolecular decomposition of specific molecules and make direct comparisons with experiment. The microscopic chemical dynamics obtained from these simulations is the detailed information required to formulate an accurate theory of unimolecular reaction rates. The role of computational chemistry in unimolecular kinetics was aptly described by Bunker [37] when he wrote The usual approach to chemical kinetic theory has been to base one s decisions on the relevance of various features of molecular motion upon the outcome of laboratory experiments. There is, however, no reason (other than the arduous calculations involved) why the bridge between experimental and theoretical reality might not equally well start on the opposite side of the gap. In this paper... results are reported of the simulation of the motion of large numbers of triatomic molecules by... 

Since optimization problems in computational chemistry tend to have many variables, essentially all commonly used methods assume that at least the first derivative of the function with respect to all variables, the gradient g, can be calculated analytically (i.e. directly, and not as a numerical differentiation by stepping the variables). Some methods also assume that the second derivative matrix, the Hessian H, can be calculated. 

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