Molecular mechanics energy minimization

Model optimization is a further refinement of the secondary and tertiary structure. At a minimum, a molecular mechanics energy minimization is done. Often, molecular dynamics or simulated annealing are used. These are frequently chosen to search the region of conformational space relatively close to the starting structure. For marginal cases, this step is very important and larger simulations should be run. 

Figure 5. Plots of rings C-H of PbTX-1 resulting from molecular mechanics energy minimization. The two molecules are identical except for ring G. Oxygen atoms are cross-hatched.

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. ... 

Ponder JW, FM Richards (1987) An Efficient Newton-Like Method for Molecular Mechanics Energy Minimization of Large Molecules. J. Comput. Chem. 8 (7) 1016-1024. (See http //dasher.wustl.edu/tinker/)... 

Molecular modeling using either Monte-Carlo simulations or molecular dynamics is used to apply molecular mechanics energy minimizations to very complex systems [348]. In complex flexible molecules such as proteins or nucleic adds, the number of variable parameters, i.e., bond torsion angles, is such that the global search for energy minima becomes impossible The same problem occurs with theoretical calculations of water structure in aqueous solutions or in heavily hydrated crystals. 

A related study on the addition of OH to formamide in water by Weiner et al. should be noted.They obtained potential functions from quantum mechanical calculations and estimated the solvent effect by molecular mechanics energy minimization for the reacting system in a box of TIP3P water. The latter procedure does not provide proper configurational averaging. Nevertheless the computed and AE in water of 22 and 9 kcal/mol are consistent with experimental data on the hydrolyses of amides. As in the present case, the transition state in water is very productlike and is computed to occur at a C-O distance of about 2.0 A. 

TABLE 9.2 Example for energy minimization (geometric optimization). Molecular mechanics energy minimization with Amber is exemplified for geometric optimization of glucagon structure using HyperChem... 

The free demonstration program ChemOffice Net (downloadable from www. camsoft.com/) allows one to build molecules containing a maximum of six nonhydrogen atoms and then to do molecular-mechanics energy minimization on them. The internal coordinates and the Cartesian coordinates of the atoms can easily be obtained before and after the energy minimization. These coordinates can then be used as input to an ab initio program. 

Addition of (16.105) and (16.106) gives the GB/SA expression for AG. The GB/SA expression is readily differentiated analytically, making it easy to use in molecular-mechanics energy minimizations (one finds the geometry that minimizes the sum of the MM steric energy and AG°oiv), and molecular-dynamics and Metropolis Monte Carlo simulations with inclusion of solvent effects. The GB/SA method is available in the MacroModel program (Section 16.6). 

The size, location, and structure of platinum clusters in H-mordenite were modeled by molecular mechanics energy minimization and molecular dynamics simulation techniques [96G1]. It was suggested that the relative stability of monoatomic platinum sites in aluminosilicate mordenites is related to the specific aluminum insertion in T sites of the framework structure. The structural features of the platinum cluster confined to the 12-ring main channel are almost independent of the total Pt content and strongly dependent upon the surrounding zeolite structural field. 

Despite the demands presented by such a calculation, a number of researchers have used ab initio models to treat the electronic and nuclear degrees of freedom for the quantum motif in molecular mechanics, energy minimization studies. Examples of this include the self-consistant reaction field methods developed by Tapia and coworkers [42-44], which represent only the quantum motif explicitly and use continuum models for the environmental effects (classical and boundary regions), and the methods implemented by Kollman and coworkers [45] in their studies of condensed phase (chemical and biochemical) reaction mechanisms. In both of these implementations the expectation value of the quantum motif Hamiltonian, defined in Eqs. (11) and (14) above, is treated at the Hartree Fock level with relatively small basis sets. 

The interpretation and ideas that the chemist gets from viewing a structure will depend on the quality of the computations that led to that representation. This point underscores the importance of understanding the concepts and limitations of the calculations that produced a particular model. For molecular mechanics energy minimizations or for molecular simulations, the quality of the force field and other parameters controlling the calculations underlies the quality of the computed results. In any approach to obtaining three-dimensional molecular structures, the quality of the model should be paramount in the mind of the user. 

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