Computational methods molecular mechanics

Compared to other methods (molecular mechanics, semiempirical calculations, density functional calculations - Chapters 3, 6 and 7, respectively) ab initio calculations are slow, and they are relatively demanding of computer resources (memory and disk space, depending on the program and the particular calculation). These disadvantages, which increase with the level of the calculation, have been to a very large extent overcome by the tremendous increase in computer power, accompanied by decreases in price, that have taken place since the invention of electronic computers. In 1959 Coulson doubted the possibility (he also questioned the desirability, but in this regard visualization has been of enormous help) of calculations on molecules with more than 20 electrons, but 30 years later computer speed had increased by a factor of 100,000 [329], and ab initio calculations on molecules with 100 electrons (about 15 heavy atoms) are common. 

It is not always necessary to detail the electronic behavior of materials an accurate understanding of the atomic interactions is often sufficient to describe the phenomenon of interest with reasonable accuracy. In contrast to ab initio methods, molecular mechanics is used to compute molecular properties, which do not depend on electronic effects. These include geometry, rotational barriers, vibrational spectra, heats of formation, and the relative stability of conformers. As the calculations are fast and efficient, molecular mechanics can be used to examine systems containing thousands of atoms. However, unlike ab initio methods, molecular mechanics relies on experimentally derived parameters so that calculations on new molecular structures may be misleading. 

Before delving into the techniques, a semantic excursion seems necessary. First, computational quantum chemistry as used in this chapter reflects the broader definition, referring to any technique that uses computers to model a chemical system via the Schrodinger equation or some approximation thereof this is a catch-all for every ab initio method, semiempirical scheme, and theoretical model chemistry. (Density functional theory also is included, although it does not stringently satisfy this definition, because it enjoys widespread identification with the ab initio methods.) Molecular mechanics, therefore, is not computational quantum chemistry, but its application to hybrid QM/MM methods will be discussed regardless. 

Given the molecular geometry and a set of force constants for a polyatomic molecule, it is a routine matter to calculate the normal coordinates, a procedure known as normal coordinate analysis. Suites of computer programs are readily available that will calculate vibrational frequencies and the internal coordinate composition of each normal vibration. Most of the early calculation of vibration frequencies were made by Wilson s FG-matrix method, which is briefly summarized below. Today, a number of alternative techniques based on semiempirical methods, molecular mechanics, or density functional theory are also available, in convenient commercial software packages. 

The aim of this chapter is to provide an overview of the theories and methodologies governing MM of crystal structure and surfaces, growth morphology, and the effects of impurities and additives on crystallization. Different computational methods are used in these modelings, including ab initio or molecular orbital calculations, semiempirical methods, molecular mechanics, molecular dynamics, and Monte Carlo (MC) simulation. The reader is recommended to some excellent reference textbooks on the principles of MM and simulation (Hinchliffe 2003 Leach 2001 Myerson 1999). 

The molecular descriptors obtained by computation of molecular mechanics and quantum chemical methods are used to describe the molecular structures of A -(3-Oxo-3,4-dihydro-2//-benzo[l,4]oxazine-6-carbonyl) guanidines. The three-dimensional structures of the molecules are optimized with the software Hyperchem. Prior to the semi-empirical quantum chemical computation, all structures of the compounds are submitted to MM+ computation of molecular mechanics for energy optimization. The structural descriptors are obtained via the computation of semi-empirical method PM3. The computations are carried out at restricted Hartree-Fock level without configuration interaction. 

In view of the complexify of the molecules studied, the method of calculation is simplified in the following way a series of sub-structures with different substituted group R (right part in Fig. 9.7) are used for the computation of molecular mechanics and quantum chemical methods. This kind of simplification is similar to the process of Hansch method considering the effects of various substituted groups. The difference of our method with Hansch method is that we did not treat the contribution of atomic groups separately, but treat the every substructure as a whole... 

Singh, U.C., Kollman, P.A. A combined ab initio quantum mechanical and molecular mechanical method for carrying out simulations on complex molecular systems Applications to the CH3CI 4- Cl exchange reaction and gas phase protonation of polyethers. J. Comput. Chem. 7 (1986) 718-730. 

The classical introduction to molecular mechanics calculations. The authors describe common components of force fields, parameterization methods, and molecular mechanics computational methods. Discusses th e application of molecular mechanics to molecules comm on in organic,and biochemistry. Several chapters deal w ith thermodynamic and chemical reaction calculations. 

An N-atom molecular system may he described by dX Cartesian coordinates. Six independent coordinates (five for linear molecules, three fora single atom) describe translation and rotation of the system as a whole. The remaining coordinates describe the nioleciiUir configuration and the internal structure. Whether you use molecular mechanics, quantum mechanics, or a specific computational method (AMBER, CXDO. etc.), yon can ask for the energy of the system at a specified configuration. This is called a single poin t calculation. ... 

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