Cross term energy functions, force fields

Terms in the energy expression that describe how one motion of the molecule affects another are called cross terms. A cross term commonly used is a stretch-bend term, which describes how equilibrium bond lengths tend to shift as bond angles are changed. Some force fields have no cross terms and may compensate for this by having sophisticated electrostatic functions. The MM4 force field is at the opposite extreme with nine different types of cross terms. 

A number of more general force fields for the study of small molecules are available that can be extended to biological molecules. These force fields have been designed with the goal of being able to treat a wide variety of molecules, based on the ability to transfer parameters between chemical systems and the use of additional terms (e.g., cross terms) in their potential energy functions. Typically, these force fields have been optimized to... 

These potential energy terms and their attendant empirical parameters define the force field (FF). More complicated FFs which use different and/or more complex functional forms are also possible. For example, the simple harmonic oscillator expression for bond stretching can be replaced by a Morse function, Euorse (3), or additional FF terms may be added such as the stretch-bend cross terms, Estb, (4) used in the Merck molecular force field (MMFF) (7-10) which may be useful for better describing vibrations and conformational energies. 

It has been known for a long time that in order to reproduce vibrational frequencies cross terms are needed in the force field description. These cross terms are not ad hoc functions. The cross terms are natural results of expanding a potential energy surface in a Taylor series. These cross terms involve two dif-... 

COMPASS. COMPASS is an example of a Class II force field parameterized by using an analytic representatiOTi of the ab initio (e.g., HF/6-31G ) potential energy surface. The functional form of the COMPASS force field is the same as CFF93 and includes an out-of-plane potential term (angle X), a U 6-9 potential as well as nonharmonic terms for bond stretching and angle bending, a Fourier cosine series for torsion, and a number of cross-coupled terms for the bonded interactions. The form of the COMPASS force field described in detail by Sun [12] is... 

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