Force fields parameterization

In addition to the functional form of a force field, one needs the corresponding set of force field parameters. In the parlance of force fields, the term atom is defined in a somewhat more narrow way than in quantum mechanics. In quantum mechanical calculations, it is sufficient to specify the element for an atom, and the parameters (basis set) will be usually the same for all atoms of the same element. Force fields require the specification of additional properties for an atom, such as its connectivity, hybridization, and oxidation state. The 

To parameterize a force field, the molecular modeler must usually rely on chemical intuition to establish atom types for the molecular system under study from the beginning. Parameters can then be derived by means of the standard fitting procedure outlined below. With these parameters, properties of the system known experimentally or derived from quantum mechanical calculations can then be calculated and compared. If significant deviations exist between computed and known values, it is necessary either to introduce new atom types or to use different functional forms for the force field. To ensure accurate predictions from a given force field, this fitting process must be repeated until the deviations between computed and observed values are sufficiently small. 

Having settled on the functional description and a suitable number of cross terms, the 

Cross terms may further add some million possible parameters 

To achieve just a rudimentary assignment of the value of one parameter, at least 3-4 independent data should be available. To parameterize MM2 for all molecules described by the 71 atom types would thus require of the order of 10 independent experimental data, not counting cross tenns. This is clearly impossible. Furthermore, the parameters 

The above considerations illustrate the inherent contradiction in designing highly 

The fundamental assumption of force fields is that structural units are transferable between different molecules. A compromise between accuracy and generality must thus be made. In MM2(91) for example the actual number of parameters compared to the theoretical estimated possible (based on the 30 effective atom types above) is shown in Table 2.2.---------------------------------------------------------------------------------- 

Having settled on the functional description and a suitable number of cross terais, the problem of assigning numerical values to the parameters arises. This is by no means trivial. Consider for example MM2(91) with 71 atom types. Not all of these can form stable bonds with each other, hydrogens and halogens can only have one bond etc. For the sake of argument, however, assume that the effective number of atom types capable of forming bonds between each other is 30. 

There are 30 x 30 x 30 x 30/2 = 405 000 possible different tors requiring at least three parameters, /ABCD  

The fundamental assumption of foree fields is that structural units are transferable between different molecules. A compromise between accuraey and generality must thus be made. In MM2(91) for example the actual number of parameters compared to the theoretieal estimated possible (based on the 30 effective atom types above) is shown in Table 2.2. 

Term Estimated number of parameters Actual number of parameters 

These heat of formation parameters may be considered as shifting the zero point of E-pB to a common origin. Since corrections from larger moieties are small, it follows that energy differences between systems having the same groups (for example methyl-cyclohexane and ethyl-cyclopentane) can be calculated directly from differences in steric energy. 

Deriving such heat of formation parameters requires a large body of experimental AHt values, and for many classes of compounds there are not sufficient data available. Only a few force fields, notably MM2 and MM3, also attempt to parameterize heats of formation. Most force fields are only concerned with reproducing geometries and possibly conformational relative energies, for which the steric energy is sufficient. 

Stable bonds with each other, hydrogens and halogens can only have one bond, etc. For the sake of argument, however, assume that the effective number of atom types capable of forming bonds between each other is 30. 

An alternative procedure is to derive the van der Waals parameters from other physical (atomic) properties. The interaction strength between two atoms is related to the polarizabilities a, and Oj, i.e. the ease with which the electron densities can be distorted by an electric field. TTie Slater-Kirkwood equation (2.37) provides an explicit relationship between these quantities, which has been found to give good results for the interaction of rare gas atoms. 

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A molecular modeling and simulation package with various implemented force field parameterizations. Free of charge for academic use. Available for different platforms. 

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. 

The van der Waals scale factors used during force field parameterization are 0.5 for AMBER, 1.0 for BlO-t, and 0.125 for OPLS. Eor 1-4 electrostatic interactions, use 0.5 for AMBER, BlO-t, and OPLS. 

Krieger E, Darden T, Nabuurs SB, Finkelstein A, Vriend G. Making optimal use of empirical energy functions force-field parameterization in crystal space. Proteins 2004 57 678-83. 

As in the case of the MM2 force field, parameterization of MM3 for amines was based mainly on experimental data with occasional references to ab initio calculations, mainly to evaluate relative conformational energies and derive appropriate torsional parameters. As mentioned above, one notable difference between the two force fields is the removal of lp on sp3 nitrogens from MM3. This simplifies the treatment of vibrational spectra and allows for a realistic treatment of nitrogen inversion which could not be handled by MM2. As usual with MM3, parameterization was aimed at reproducing a variety of molecular properties such as structure, steric energy, dipole moments, moments of inertia, heat of formation and vibrational spectra. A complete list of MM3 parameters for amines is provided in Reference 6. 

Comba, P. and Remenyi, R. 2003. Inorganic and Bioinorganic Molecular Mechanics Modeling-the Problem of Force Field Parameterization , Coord. Chem. Rev., 238-239, 9. 

Metal-phosphine bonds can generally be modeled in much the same way as any other metal-heteroatom bond. The fact that phosphines participate in x-backbonding (filled dn (metal) -> empty d or a (phosphorus) interaction) is only of importance for generic force field parameterization schemes, and half-integer bond orders have been used to describe the effect of x-back-donation[ 153). In the usually adopted empirical force field formalism, x-bonding effects, like most of the other structural/elec-tronic effects, are accommodated by the general parameter-fitting procedure (see Parts I and III). 

In this chapter we focus on atomistic predictions of thermophysical and mechanical properties of HMX crystals and liquid important to the development of reliable mesoscale equations of state. The outline of the remainder of the chapter is as follows In section 2 we describe briefly the philosophy and overall approach we have taken to force field development, including the results of quantum chemistry calculations for HMX and smaller model compounds that were used in the force field parameterization. The focus of section 3 is on the properties of liquid HMX, for which experimental data are completely lacking. Structural, thermal, and mechanical properties of the three pure crystal polymorphs of HMX are presented in section 4, where the results are compared to the available experimental data. At the ends of sections 3 and 4 we discuss briefly the importance of the various properties with mesoscale models of high explosives, with an emphasis on conditions relevant to weak shock initiation. We conclude in section 5, and provide our opinions (and justifications, based on our interactions with mesoscale modelers) regarding which HMX properties and phenomena should comprise the next targets for study via atomistic simulation. 

We have adopted a strategy similar to that used in our development of polymer force fields in parameterization of an atomistic potential function for HMX. Specifically, we have undertaken a systematic investigation of conformational and intermolecular binding energies in model nitramine compounds (i.e., those containing the C2N-NO2 moiety ) using high-level QC calculations. In the case of HMX, a QC-based force field is the only realistic option due to insufficient spectroscopic data that would facilitate force field parameterization. 

In the following we describe briefly the procedure for fitting force field parameters, and provide comparisons between force-field and QC predictions. A more detailed discussion of the force field parameterization can be found in Refs. [34] and [35],... 

This treats the bond as a mechanical spring whose force constant is strong for small and weak for large interatomic distances. The disadvantage of using a Morse function in empirical force field calculations is that an exponential in addition to the square function and three parameters are involved, increasing the time requirement for the minimization process and the complexity of the force field parameterization. 

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