A force field

A physical field is a particular form of matter that links together material particles and transmits an influence from one body to another (with finite velocity). Each type of interaction has its own special corresponding force field. The force field is an area of space in which a force acts on any material particle placed in this space point, depending on coordinates and time. A force field is called a stationary one if the acting forces do not depend on time. A force field at any point of which the acting force has one and the same value (on modulus and direction) is referred to as a uniform one. 

It is possible to characterize a force field by force lines. In this case, the tangent to force lines defines the direction of a force and the line s density is proportional to the force value. 

All the mechanical forces can be divided into two groups conservative forces (acting in potential fields) and nonconservative forces (or dissipative). The forces are referred to as conservative (or potential) ones if their work depends neither on the trajectory form, nor on the path length, and is defined only by the position of the point of the force application in the initial and final positions. The field of conservative forces is called the potential (conservative) one. 

The inverse statement is fair if the work of a force on the closed contour is zero, the forces are conservative and the field is potential. This condition can be written as a contour integral (circulation of a vector along a closed contour)  

The work of the nonconservative (dissipative) forces in the general case depends both on the form of the paths travelled and the lengths of the way. Examples of nonconservative forces can be given by friction and resistance forces. In both cases the mechanical energy transforms into another type of energy. 

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After an initial starting geometry has been generated and optimized (e.g., in a force field), the new conformation is compared with all the previously generated conformations, which are usually stored as a list of unique conformations. If a substantially different geometry is detected it is added to the list otherwise, it is rejected. Then a new initial structure is generated for the next iteration. Finally, a preset stop criterion, e.g., that a given number of loops has been performed or that no new conformations can be found, terminates the procedure. 

D information is available, e.g., in databases without experimental data, the different types of surfaces (sec below) can be calculated only after a 3D structure has been determined by a 3D structure generator, which might be followed by computational refinement, e.g., with a force-field calculation. 

A force field does not consist only of a mathematical eiqjression that describes the energy of a molecule with respect to the atomic coordinates. The second integral part is the parameter set itself. Two different force fields may share the same functional form, but use a completely different parameterization. On the other hand, different functional forms may lead to almost the same results, depending on the parameters. This comparison shows that force fields are empirical there is no "correct form. Because some functional forms give better results than others, most of the implementations within the various available software packages (academic and commercial) are very similar. 

All of the contributions to the energy function presented above assume that pairwise interactions are sufficient to describe the situation within a molecule or molecular system. Whether or not multi-centered interactions are negligible is controversial. On the other hand, failure or success of a force field with its functional form and corresponding parameter set is not a matter of mathematics... 

In stead, these m eth od s solve the poten tial energy surface by using a force field equation (see Molecular Mechanics" on page2] i.The force field equation represen ts electron ic energy implicitly th roil gh param eteri/ation. 

Molecu lar mechari ical force fields use the equation s of classical mech an ics to describe th e poteri tial energy surfaces and physical properties of m olecii Ies. A molecu le is described as a collection of atom slhal in teracl with each other by sim pic an alytical fiiriclions. I h is description is called a force field. One component of a force field is th e eri ergy arisiri g from com pression and stretch in g a bond. 

The potential energy of a molecular system in a force field is the sum of individnal components of the potential, such as bond, angle, and van der Waals potentials (equation H). The energies of the individual bonding components (bonds, angles, and dihedrals) are function s of th e deviation of a molecule from a h ypo-thetical compound that has bonded in teraction s at minimum val-n es. 

Restrain ts add poten lial term s to a force field calcu lalion. ravoriu g ih c value ih at you sped fy in a restrain i. Th e larger th e value of the harm on ic force con stan t. th c m ore tigh tly th e calculation restrain s th c value. 

TlypcrC hcm oilers four molecular mechanics force fields MM+, AMBER, BIO+, and OPES (sec References on page 106). To run a molecular mechanics calciilaLion. yon miisi lirsi choose a force Eeld. The following sections discuss considerations in choosing a force field. 

Eorce fields give the best results for m oleciiles similar to those used to develop its parameters. Choose a force field developed for a range of molecules similar to your molecular system. 

The UyperChem Reference manual and Genius Sianed discuss the sec neiice of steps to perform a molecular mechanics calculation. These steps in elude choosing a force field, force field option s, and possible restrain is. 

In principle, atom types eoiild be assoeiated wilh a partieiilar parameter set rather than the functional form or force field. In HyperChern, however, atoms types are rigorously lied to a force field . M.M-t, AMBER, OPTS, and BIO+. Each of the force fields has a... 

To redefine an atom type associated with a force field, adpist the rules in th e ch cm, ru 1 file to represent the new ehernical environment for a particular type and then compile the new types. It is always desirable to save the origin a I eh cm. nil un dcr an oth cr n am c prior to modifying chem.rul. Having modified chem. nil, you can... 

The AMBER (Assisted Model Building and Energy Refin emeni) is based on a force field developed for protein and nucleic acid computations by members of the Peter Kollman research group at the... 

OPTS (Optim i/.ed Potentials for Liquid Simulations) is based on a force field developed by the research group of Bill Jorgensen now at Yale University and previously at Purdue University. Like AMBER, the OPLS force field is designed for calculations on proteins an d nucleic acids. It in troduces non bonded in leraclion parameters that have been carefully developed from extensive Monte Carlo liquid sim u lation s of small molecules. These n on-bonded interactions have been added to the bonding interactions of AMBER to produce a new force field that is expected to be better than AMBER at describing simulations w here the solvent isexplic-... 

Molccti lar mcchan ics depends on the con cep I of atom types and parameters associated with these atom types. Since the number of atom types is veiy large foi the tin iverse of possible molecules, parameters will probably he missing for a random new molecule tin less a force field has been developed for molecules sim ilar lo the new molecule. Molecu lar m ech an ics predicts how the new molecule will behave based upon the behavior orknown, similar mole-cu les. 

Independent molecules and atoms interact through non-bonded forces, which also play an important role in determining the structure of individual molecular species. The non-bonded interactions do not depend upon a specific bonding relationship between atoms, they are through-space interactions and are usually modelled as a function of some inverse power of the distance. The non-bonded terms in a force field are usually considered in two groups, one comprising electrostatic interactions and the other van der Waals interactions. 

Calculating Thermodynamic Properties Using a Force Field... 

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