Force fields definition

Atom types represen t the chemical environment of an atom. The atom types associated with a given force field could be hard-wired to have specific vahiesand meaning. llyperChem also allows flexible definitions of the atom types and the associated chemical en vironmen Is. Th e ch em ical en viron men t of an atom (a set of rules for defining a type) and the default rules are in a standard ASCII text file, chem.nil. included with llyperChem. You can modify this file and compile it m a binary form that llyperChem... 

V these three functional forms, the improper torsion definition is most widely used as it can then be easily included with the proper torsional terms in the force field. However, the... 

HyperChem uses the improper dihedral angle formed by central atom - neighbor 1 - neighbor 2 - neighbor 3, where the order of neighbors is how they appear in a HIN file. Not all planar atoms customarily have associated improper torsions. The order of atoms is arbitrary but has been consistently chosen by the original authors of the CHARMM force field. The templates contain equivalent CHARMM definitions of improper torsions for amino acids. Improper dihedral angles cannot be defined that do not have a central atom, as is sometimes done in CHARMM calculations. 

At this point, spectroscopists and molecular modellers part company because they have very different aims. Spectroscopists want to describe the vibradons of a molecule to the last possible decimal point, and their problem is how a force field should be determined as accurately as possible from a set of experimental vibrational frequencies and absorption intensities. This problem is well understood, and is discussed in definitive textbooks such as that by Wilson, Decius and Cross (1955). 

The original molecular-mechanics force field was developed by Allinger, and is generally referred to as MM. You should read the definitive text by Burkert and Allinger (1982) for more details. This model was followed by the MM2 model (Allinger, 1977), and I thought that you might like to read the synopsis. 

A few comments on the layout of the book. Definitions or common phrases are marked in italic, these can be found in the index. Underline is used for emphasizing important points. Operators, vectors and matrices are denoted in bold, scalars in normal text. Although I have tried to keep the notation as consistent as possible, different branches in computational chemistry often use different symbols for the same quantity. In order to comply with common usage, I have elected sometimes to switch notation between chapters. The second derivative of the energy, for example, is called the force constant k in force field theory, the corresponding matrix is denoted F when discussing vibrations, and called the Hessian H for optimization purposes. 

Like many other chemical concepts the concept of strain is only semi-quantitative and lacks precise definition. Molecules are considered strained if they contain internal coordinates (interatomic distances (bond lengths, distances between non-bonded atoms), bond angles, torsion angles) which deviate from values regarded as normal and strain-free . For instance, the normal bond angle at the tetra-coordinated carbon atom is close to the tetrahedral value of 109.47°. In the course of force field calculations these normal values are defined more satisfactorily, though in a somewhat different way, as force field parameters. 

In the framework of the force field calculations described here we work with potential constants and Cartesian coordinates. The analytical form of the expression for the potential energy may be anything that seems physically reasonable and may involve as many constants as are deemed feasible. The force constants are now derived quantities with the following definition expressed in Cartesian coordinates (x ) ... 

The results for thrombin show that our previous parametrization of the LIE coefficients holds rather well in this case, provided that a constant term of -2.9 kcal/mol is added. At present it is not clear to us why thrombin would require such a constant term while, e.g., trypsin does not, but this issue is currently under investigation (see also Ref. 47 for a discussion of thrombin versus trypsin). Furthermore, one should note that with our computational procedures and the Gromos87 force field the results for thrombin inhibitors differ from those of Ref. 35 as well as Ref. 43. That is to say, three independent studies involving thrombin inhibitors have arrived at significantly different parametrizations of the LIE equation, that in all cases reproduce the experimental data well. It therefore seems clear that the differences in the computational procedures have a definite effect on the parameters of the binding energy approximation. 

Although we know that the total force field / is conservative, we lack such knowledge concerning the separate pieces fx or A- Therefore some specific path of integration must be chosen to complete the definition (210). Seemingly the most natural path is along the radius on which the point ro lies. As the center of the coordinate system a position of the nucleus is chosen in the case of single-ion system, the center of symmetry for a symmetrical molecule, and some inner point for molecule or cluster with lower symmetry. Then... 

Table 3. The force field of H2O This is defined in the expansion of Pliva, but other definitions are in common usage.

Force field Furan Field definition 75MI31005... 

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