Force field parameter

In order to set up a molecular mechanics model it is necessary to find mathematical expressions that are able to define the molecular structures and give the corresponding strain energies, and to find parameter values for these expressions so that the model can reproduce or predict the molecular structures and properties. These two parts of the molecular mechanics package have a direct influence on the optimized structure. The potential energy functions and the force field parameters are interrelated. Therefore, the parameters should not, in general, be transferred from one force field to another. 

The parameterization of a force field can be based on any type of experimental data that is directly related to the results available from molecular mechanics calculations, i. e., structures, nuclear vibrations or strain energies. Most of the force fields available, and this certainly is true for force fields used in coordination chemistry, are, at least partially, based on structural data. The Consistent Force Field (CFF)197,106,1071 is an example of a parameterization scheme where experimentally derived thermodynamic data (e. g., heats of formation) have been used to tune the force field. Such data is not readily available for large organic compounds or for coordination complexes. Also, spectroscopic data have only rarely been used for tuning of inorganic force field parameters113,74,1081. 

In theory, a properly developed force field should be able to reproduce structures, strain energies, and vibrations with similar accuracies since the three properties are interrelated. However, structures are dependent on the nuclear coordinates (position of the energy minima), relative strain energies depend on the steepness of the overall potential (first derivative), and nuclear vibrations are related to the curvature of the potential energy surface (second derivative). Thus, force fields used successfully for structural predictions might not be satisfactory for conformational analyses or prediction of vibrational spectra and vice versa. The only way to overcome this problem is to include the appropriate type of data in the parameterization process1107,1091. 

Most force fields used in coordination chemistry, in respect of the organic part of the molecules, are based on or are at least similar to the MM2[501, MM3 172 751 or AMBER193,94,110,1111 parameterization schemes or mixtures thereof. However, it is important to stress again that transferring parameters from one force field to another without appropriate checks is not valid. This is not only a question of the different potential energy functions that can be used, but is also a consequence of the interrelatedness of the entire set of parameters. Force field parameters imported from any source, whether a well established force field or experimental data should only be used as a starting point for further parameter refinement. 

An important point that needs to be considered during the development of force fields used for coordination compounds is that, upon coordination of an organic 

The implementation of molecular mechanics of coordination compounds in existing modeling packages, particularly those designed for organic molecules, is only possible if there is the possibility of having more than four atoms attached to an atom  

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There are several excellent publications in the literature which compare force fields, their apphcation areas, and their pros and cons [1-5]. Available force field parameters are published in a comprehensive and very extensive form, e.g., within the R views in Computational Chemistry series [6, 7j. 

The modeling of inorganic compounds in general is gaining more and more interest [25-28]. The authors of MOMEC addressed this in a monograph describing how molecular modeling techniques can be applied to metal complexes and how the results can be interpreted [29]. The current force field parameter set is available on the author s web site. 

M. Jalaie, K. B. Lipkowitz, Published force field parameters for molecular mechanics, molecular dynamics, and Monte Carlo simulations, in Reviews in Computational Chemistry, Vol. 14, K.B. Lipkowitz, D. B. Boyd (Eds.), Wiley-VCH, New York, 2000, pp. 441-486. 

Most of the molecules we shall be interested in are polyatomic. In polyatomic molecules, each atom is held in place by one or more chemical bonds. Each chemical bond may be modeled as a harmonic oscillator in a space defined by its potential energy as a function of the degree of stretching or compression of the bond along its axis (Fig. 4-3). The potential energy function V = kx j2 from Eq. (4-8), or W = ki/2) ri — riof in temis of internal coordinates, is a parabola open upward in the V vs. r plane, where r replaces x as the extension of the rth chemical bond. The force constant ki and the equilibrium bond distance riQ, unique to each chemical bond, are typical force field parameters. Because there are many bonds, the potential energy-bond axis space is a many-dimensional space. 

Most existing molecular mechanics studies of inorganic molecules required careful customization of force field parameters. 

Listings of references to all published force field parameters are... 

A comprehensive listing of all published force field parameters is... 

In computational chemistry it can be very useful to have a generic model that you can apply to any situation. Even if less accurate, such a computational tool is very useful for comparing results between molecules and certainly lowers the level of pain in using a model from one that almost always fails. The MM+ force field is meant to apply to general organic chemistry more than the other force fields of HyperChem, which really focus on proteins and nucleic acids. HyperChem includes a default scheme such that when MM+ fails to find a force constant (more generally, force field parameter), HyperChem substitutes a default value. This occurs universally with the periodic table so all conceivable molecules will allow computations. Whether or not the results of such a calculation are realistic can only be determined by close examination of the default parameters and the particular molecular situation. ... 

Table 1 Types and Sources of Target Data Used m the Optimization of Empirical Force Field Parameters...

The parameterization process may be done sequentially or in a combined fashion. In the sequential method a certain class of compound, such as hydrocarbons, is parameterized first. These parameters are held fixed, and a new class of compound, for example alcohols and ethers, is then parameterized. Tins method is in line with the basic assumption of force fields parameters are transferable. The advantage is that only a fairly small number of parameters are fitted at a time. The ErrF is therefore a relatively low-dimensional function, and one can be reasonably certain that a good minimum has been found (although it may not be the global minimum). The disadvantage is that the final set of parameters necessarily provides a poorer fit (as defined from the value of the ErrF) than if all the parameters are fitted simultaneously. 

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