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THOR - Classical Force Field

The idea with molecular modeling is a attempt to describe the quantum chemistry bonds in terms of a classical force field in the Newton's equations. In Molecular Mechanics (MM) model the atomic bonds are represented by springs joining the atoms,i.e., the molecule is assumed to be a collection of masses and springs. In this case is necessary find a set of parameters, for this force field, that fit the quantum atomic interactions with sufficient accuracy. Ideally one hopes that such refinements will eventually lead toward a unified computational model that can successfully mimic nature molecular properties.

At moment there are uncountable computational code using a classical force field. Each one of these uses a particular force field to describe different molecular properties and to fit some experimental results. In molecular mechanics the atom is represented by a spherical body with a particular mass equal, in general, to the respective atomic mass. In general the molecular energy (potential function) related with the classical force field can be expressed by the following relationship;

equation5

Where, in summary, the first term of eq. (1tex2html_wrap_inline411 represent the necessary energy to stretch or compress the atomic bond; tex2html_wrap_inline413 is the contribution in the potential that represents the bond-angle bending interaction; tex2html_wrap_inline415tex2html_wrap_inline417 are the torsional contributions that represents the harmonic dihedral bending interaction and the sinusoidal dihedral torsion interactions; tex2html_wrap_inline419 this potential is used to mimics a cytoplasm/membrane environment, with an interface separating two continuous media of different dielectric constants; and the last one tex2html_wrap_inline421 and tex2html_wrap_inline423 contains the nonbounded terms such as Coulombic repulsion, hydrogen bonding and van der Waals interactions. Each of these potential energy functions represents a molecular deformation from an arbitrary reference geometry.

In today's molecular mechanics subject, several force field has been proposed. The most of them is based on equation (1). In particular the program THOR has used the following potential function;

equation18

equation23

equation28

equation34

equation40

equation49

Each terms in the equation set (2-7 ) relates a geometric parameter (such as a bond length, or a bond angle) to potential energy. You could take some 3D molecular conformations and find out how much potential energy is associated with that shape. Molecules tend toward their minimum-energy conformations, except when they are being acted on by thermal excitation or other outside forces.

In general, by itself V has no physical meaning. But the difference in the energy for two molecular conformations is appropriate for comparison to experimental observable physical properties, such as rotations barriers or conformer populations. In the next sections all of this terms will be discussed with more details.

There are a set of reasons which have promoved the success classical molecular mechanics method. The main reason is the computational time. The academic research and the pharmacs industry interests to develop news compounds in biological molecular systems has emphasized the appearing of different computational code based on classical force field. The computational time for the a classical force field methods increase as tex2html_wrap_inline427 , where m is the number of atoms in the molecule. In contrast, the use of the ab-initio quantum methods in this kind of molecular system is computationally impracticable because the computer time just to evaluate the inter-electronic repulsion integral is tex2html_wrap_inline431 , where n is the number of basis orbital. Normally, there are at least several functions per atom. Others reasons to justify the crescent use of MM can be listed, as for example: - MM method (solve Newton's equation) is conceptually easier to understand than the quantum mechanical (Hartree-Fock) methods QM; - in MM is very simple to introduce the time evolution; - in MM is possible to introduce the temperature as an external perturbation.

Unfavorable to the MM methods there are two important questions; the first one is that do not exist defined rules to evaluate the force constants, and the second one is that to choose the best force field is necessary to have, at prior, a good feeling about the molecular system.


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Kleber Mundim

Sat Jul 19 11:13:17 CDT 1997