Molecular mechanics calculations general considerations

The quantitative prediction of the stereochemistry of a chemical reaction by strain energies requires knowledge of the reaction mechanism, i.e., the selective intermediates and/or transition states involved, and an accurate force field for the transient species. As discussed above, these are two demanding problems and so far there are no reports of studies in this area that have used molecular mechanics for quantitative predictions at the same level of accuracy as for conformational analyses. The application of empirical force field calculations to the design of asymmetric transformations clearly is a worthy task, and some examples of studies in this area have been discussed above. On the basis of two examples we will now discuss some general aspects highlighting the limitations of the qualitative considerations emerging horn molecular mechanics calculations for the interpretation and support of assumed reaction pathways. 

Because of the approximations involved in this analysis, the thermodynamic results have to be considered with caution. This is not only due to a rather crude analysis of the electrostatic effects but also, and this is a general problem, to the neglect of solvation in the molecular mechanics refinement. However, the structures presented in Fig. 9.6 are valuable because they are based not only on the structure optimization by molecular mechanics but also on spectroscopic data. This example is therefore instructive for two reasons first, it demonstrates that, depending on the study, the often-neglected electrostatic effects may be of considerable importance. Second, not only may experimental observables help to refine solution structures, they can prevent a wrong conclusion. As in this example, the combination of experimental data with molecular mechanics calculations is often the only way to get reliable structural information. 

The application of empirical force field calculations to the design of asymmetric transformations is a worthy task, and some examples of studies in this area have been discussed above. On the basis of two examples we will now discuss some general aspects highlighting the limitations of qualitative considerations emerging from molecular mechanics calculations for the interpretation and support of assumed reaction pathways. 

So far, almost all of the applications of the method have been to the ground states of molecules. Various kinds of excited states are equally susceptible to study. Transition states are likewise open to attack by these methods, although there are of course limitations. Considerable advances here are anticipated in the near future. These areas seem potentially even more useful ones for molecular mechanics calculations than the area of ground states, because ground states can be accurately studied by several experimental methods. The structures of excited states and transition states seem virtually unassailable experimentally, however. They can be attacked by ab initio methods, but the same considerations of general usefulness for routine calculations apply here as discussed at the beginning of this article for ground states. 

Computer simulations of electron transfer proteins often entail a variety of calculation techniques electronic structure calculations, molecular mechanics, and electrostatic calculations. In this section, general considerations for calculations of metalloproteins are outlined in subsequent sections, details for studying specific redox properties are given. Quantum chemistry electronic structure calculations of the redox site are important in the calculation of the energetics of the redox site and in obtaining parameters and are discussed in Sections III.A and III.B. Both molecular mechanics and electrostatic calculations of the protein are important in understanding the outer shell energetics and are discussed in Section III.C, with a focus on molecular mechanics. 

While simple approximate considerations of ET are useful in many cases, it is important to have methods for the rigorous solution of the general quantum mechanical problem. Exact methods without any approximation can be realized at present only for small molecular systems involving a few atoms, and the reason is that the finite basis used in quantum mechanical calculations grows exponentially as the number of degrees of freedom increases. Therefore, certain approximation is always necessary to handle complex systems with many degrees of freedom. One has to balance between the accuracy and the computational cost of the calculation. Considerable progress in this direction has been made over the last few years [116-118, 123-134]. 

Contents Experimental Basis of Quantum Theory. -Vector Spaces and Linear Transformations. - Matrix Theory. -- Postulates of Quantum Mechanics and Initial Considerations. - One-Dimensional Model Problems. - Angular Momentum. - The Hydrogen Atom, Rigid, Rotor, and the H2 Molecule. - The Molecular Hamiltonian. - Approximation Methods for Stationary States. - General Considerations for Many-Electron Systems. - Calculational Techniques for Many-Electron Systems Using Single Configurations. - Beyond Hartree-Fock Theory. 

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