Force fields of molecular mechanics

Usually the harmonic approximation with some anharmonicity corrections suffice to describe the energy dependence on the interatomic separations of the bonded atoms in the vicinity of the minimum PES. Nevertheless, sometimes, when it attempts either to simultaneously reproduce molecular geometries and the heats formation or simply to cover a wider range of molecular geometries where anharmonicity effects become more pronounced, the bond stretching energy terms are taken in the form  

Further energy contributions defined in terms of bonds are the so-called torsion and improper torsion contributions  

In the first expression, the summation is extended to the quadruples of sequentially bonded atoms ABCD and the energy constants Vn are specific for the quadruples of the types of the atoms involved. The torsion angle is that between the planes ABC and BCD. The n = 1 term describes a rotation which is periodic by 360°, the n = 2 term is periodic by 180°, the n = 3 term is periodic by 120° and so on. The Vn constants determine the contribution of atoms A and D to the barrier of rotation around the 

B-C bond. Depending on the situation, some of these Vn constants may be zero. In the second expression, the summation extends to quadruples of atoms where three of them are linked by the fourth, forming a vertex. In this case the angle 5 is the one between a bond and the plane formed, whereas the distance d is the one between the vertex atom and the plane formed by the other three atoms of the quadruple. Numerical values of the constants (and even their dimensions) Kimp and K imp, of course, differ. 

The presence of these higher cross-terms tend to improve the ability of the force field to predict the properties of unusual systems (such as those which are highly strained) and also to enhance its ability to reproduce vibrational spectra. It must be noticed, however, that any of the cross terms listed above have been proven to be truly of the form in which they are written. No attempts have been reported to derive that or any other form of the coupling between different geometry distortions and to estimate the corresponding constants from some independent point of view. The class III force field will also take into account further features such as electronegativity and hyperconjugation. We shall turn to these problems later. 

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Semiempirical functionals intend to reproduce accurate properties using as many semiempirical parameters as needed. The concept of these functionals may be based on the force fields of molecular mechanics, for example, CHARmm (Brooks et al. 1983) and Amber (Pearlman et al. 1995), which have been established to determine the structures of biomacromolecules such as folded proteins. In most cases, the development of such force fields focuses only on constructing potentials to yield highly accurate molecular structures. Likewise, semiempirical functionals have been developed to provide highly accurate properties. Note, however, that... 

Rappe A K, C J Casewit, K S Colwell, W A Goddard III and W M Skiff 1992. UFF, a Full Periodic Table Force Field for Molecular Mechanics and Molecular Dynamics Simulations. Journal of the American Chemical Society 114 10024-10035. 

UFF (universal force field) a molecular mechanics force field unrestricted (spin unrestricted) calculation in which particles of different spins are described by different spatial functions VTST (variational transition state theory) method for predicting rate constants... 

Weiner, S.J. Kollman, P.A. Case, D.A. Singh, U.C., Ohio, C. Alagona, G. Profeta Jr., S. Weiner, P. Anew force field for molecular mechanical simulation of nucleic acids and proteins 7 Am. Chem. Soc. 106 765-784, 1984. 

A New Force Field for Molecular Mechanics Simulation of Nucleic Acids and Proteins... 

Chemists seeking to use computational chemistry to support experimental efforts now have three generd theoretical tools available to them force field or molecular mechanics models, ab initio molecular orbital (MO) models and semiempirical MO models (1). Each of these tools have strengths and weaknesses which must be evaluated to determine which is most appropriate for a given applications. 

Duan, Y., Wu, C., Chowdhury, S., Lee, M.C., Xiong, G., Zhang, W., Yang, R., Cieplak, P., Luo, R., Lee, T., Caldwell, J., Wang, J., Kollman, P. A point-charge force field for molecular mechanics simulations of proteins based on condensed-phase quantum mechanical calculations. J. Comput. Chem. 2003, 24, 1999-2012. 

Dynamic NMR gives information on the number and symmetries of conformations present in solution and on the energy barriers separating these conformations. This is particularly true for systems with barriers between about 25 and 90 kJ mol-1, a situation which often occurs in the medium ring. The interpretation of the NMR data can be carried out by the examination of molecular models, but this is a relatively crude and sometimes misleading method. Empirical force field (or molecular mechanics) calculations are much superior, even though the parametrization of heteroatoms may be open to question. Quantum mechanical calculations are not very suitable the semiempirical type, e.g. MINDO, do not reproduce conformational properties of even cyclohexane satisfactorily, and the ab initio... 

Weiner SJ, Kollman PA, Case DA, Singh UC, Ghio C, Alagona S, Profeta S, Weiner P. New force field for molecular mechanical calculations simulations of proteins and nucleic acids. J Am Chem Soc 1984 106 765-84. 

Duan Y, Wu C, Chowdhury S et al (2003) A point-charge force field for molecular mechanics simulations of proteins based on condensed-phase quantum mechanical calculations. J Comput Chem 24(16)4999-2012... 

P. Weiner, J. Am. Chem. Soc., 106, 765 (1984). A New Force Field for Molecular Mechanical Simulation of Nucleic Acids and Proteins. 

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