Quantum Mechanical Methods for Structure Elucidation

Robert Carper, Zhizhong Meng, and Andreas Dolle 4.2.1 

The choices of quantum mechanical method typically include the semi-empirical methods AMI, PM3, and MNDO/d [2-4], These three methods (and some of their variations) are those most commonly used in the current literature. Of these semi-empirical methods, only MNDO/d includes the effects of d-orbitals. Some of the problems associated with these semiempirical methods include  

Despite these inconsistencies, the semi-empirical methods produce bond angles, bond lengths and heats of formation that are in reasonable agreement with experimental results. A new version, PM5, will soon be available and is four times more accurate than AMI or PM3. The advantage of PM5 over the other semi-empirical methods is that d-orbitals are being introduced [5]. 

The ab initio methods used by most investigators include Hartree-Fock (HF) and Density Functional Theory (DFT) [6, 7]. An ab initio method typically uses one of many basis sets for the solution of a particular problem. These basis sets are discussed in considerable detail in references [1] and [8]. DFT is based on the proof that the ground state electronic energy is determined completely by the electron density [9]. Thus, there is a direct relationship between electron density and the energy of a system. DFT calculations are extremely popular, as they provide rehable molecular structures and are considerably faster than H F methods where correlation corrections (MP2) are included. Although intermolecular interactions in ion-pairs are dominated by dispersion interactions, DFT (B3LYP) theory lacks this term [10-14]. However, DFT theory is quite successful in representing molecular structure, which is usually a primary concern. 

The investigator s choice of method (semi-empirical or ab initio) hinges on a number of factors, one of which is simple practicahty concerning both time and expense. Semi-empirical methods usually give reasonable molecular structures and thermodynamic values at a fraction of the cost of ab initio calculations. Furthermore, molecular structures calculated by semi-empirical methods are the starting point for more complex ab initio calculations. 

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In this book, the main focus is on the application of quantum-mechanical methods to elucidate the geometric and electronic structures of minerals, so that detailed discussion of the relative merits of the different approaches is not appropriate. Nonetheless, it is important for the reader to appreciate some of the major controversies that have arisen between theoreticians in the field. 

The role of computer modelling in the science of complex solids including microporous materials was surveyed in Faraday Discussion 106 held in 1997. These techniques have now an increasingly predictive role. They can, for example, predict new microporous structures, design templates for their synthesis and model the static and dynamical behaviour of sorbed molecules within their pores,a topic of enduring importance and one of particular interest to Barrer. Computer modelling methods are, of course, most effective when used in a complementary manner with other physical techniques. Ref. 6 nicely illustrates this theme. Here EXAFS and quantum mechanical methods are used in a concerted manner to elucidate the structure of the active site in microporous titanosilicate catalysts. Articles in Faraday Discussions, vol. 106 again illustrate the complementarity of computational and experimental techniques. 

First-principles quantum chemical methods have allowed elucidation of reaction mechanisms for a variety of heterogeneous catalytic reactions. As discussed above, incorporating the nature of the electrochemical double layer into quantum models is limited by the challenges associated with following the structure and dynamics of the electrolyte over the electrode. Further, to capture electro-catalytic reaction mechanisms accurately using DFT methods, the chemical potential of electrons and ionic species that participate in elementary steps must be evaluated. Several DFT modeling approaches have been developed to include the influence of solvent and/or electrochemical potential on surface reactions and to take into account the chemical potential of ionic species. 

The study of the structure and reactivity of organic molecules is one of the most widespread applications of computational methods in other areas of chemistry. The calculation of transition structures and possible intermediates of a reaction has been widely used for the elucidation of reaction mechanisms. The structural information available through these calculations provides valuable assistance for the interpretation of experimental data and allows predictions that in turn inspire new experiments. It is therefore not surprising that with the exponential increase in computer performance and the availability of highly sophisticated software for quantum mechanical calculations, these methods have become a cornerstone of modem organic chemistry. 

As observed in other systems, the obvious difficulty in elucidating reaction mechanisms based on static structural snapshots subsequently initiated structural-dynamic theoretical studies of metalloproteinases. The active site chemistry of zinc-dependent enzymes has been studied using a variety of theoretical approaches. For example, mixed quantum mechaiucal/molecular calculations and classical molecular dynamic simulations have been employed, especially studies using density functional methods on redox-active metal centers (42). 

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