Force field equation

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. 

A6-12 function (also known as a Lennard-Jones function) frequently simulates van der Waals interactions in force fields (equation 11). 

The force field equations for MM+, AMBER, BIO+, and OPLS are similar in the types of terms they contain bond, angle, dihedral, van derWaals, and electrostatic. There are some differences in the forms of the equations that can affect your choice of force field. 

Many force fields use a Lennard-Jones 6-12 potential71 to reproduce nonbonded interactions, see Equation 7. As two atoms approach one another, the steepness or hardness of the energy curve is proportional to r 12. The use of an exponential term instead of the r12 term in force field equations better reproduces experimental data for organic structures, and it is more consistent with quantum chemical calculations. 

The heart of quantum mechanics is the Schrddinger equation the heart of molecular mechanics is the force field equation. A typical molecular mechanics force field is shown below ... 

The molecular mechanics method is extremely parameter dependent. A force field equation that has been empirically parameterized for calculating peptides must be used for peptides it cannot be applied to nucleic acids without being re-parameterized for that particular class of molecules. Thankfully, most small organic molecules, with molecular weights less than 800, share similar properties. Therefore, a force field that has been parameterized for one class of drug molecules can usually be transferred to another class of drug molecules. In medicinal chemistry and quantum pharmacology, a number of force fields currently enjoy widespread use. The MM2/MM3/MMX force fields are currently widely used for small molecules, while AMBER and CHARMM are used for macromolecules such as peptides and nucleic acids. 

The value of S-EWetching in the force field equation (see equation (5.1)) for a structure is given by the sum of appropriate expressions for E for every pair of bonded atoms in the structure. For example, using the Hooke law model, for a molecule consisting of three atoms bonded a-b-c the expression would be ... 

The other energy terms in the force field equation for a structure are treated in a similar manner using expressions appropriate to the mechanical or electrical... 

A way to describe the zeolite framework at a low computational cost is to use quantum mechanic - molecular mechanic methods (QM/MM) (see Figure 6). With QM/MM, only the site of interest (viz. reactants and catalytic active site) are treated at a quantum mechanic level, whereas the zeolite framework is described using force field equations of molecular mechanic." ... 

Additionally, cross terms such as the stretch-bend potential, shown below in [Eq. (10)], may be included in the force field equation to give better agreement between experiment and calculation. 

To theoretical and computational chemists, the world may seem to revolve around the Schrodinger equation, potential energy force field equations, or perhaps some quantitative structure-activity relationship equations for predicting biological activity. These various equations have been the basis of the livelihood of many a computational chemist. Interestingly, author Guillen apparently did not deem these equations to have risen to the level of having... 

Extensive documentation of the accuracy of molecular mechanics calculations has been reported.For the most part, the discrepancies between experimental and calculated molecular geometries are within experimental error. Many of the systematic discrepancies in MM2, for example, have been documented. Some of the apparent errors can be associated with incorrect comparisons of bond lengths that are defined differently in various experimental and computational methods. The bond lengths have different numerical values because they are different physical quantities, rather than being real errors. Other problems have been attributed to a lack of accurate experimental data when the force field equations and parameters were formulated. 

The above internal coordinates and nonbonded interaction terms comprise the force field equations in molecular mechanics to calculate the potential energy of a molecular system. The basic form of empirical force fields has been varied as part of efforts to improve their treatment of various biological systems. Extensive work has been done on the systematic improvement of the both the form and the parameters used (35). However, this consensus form is common to AMBER (36), CHARMM (37), and CVFF (38), three popular classical empirical force fields. 

The functional form of the van der Waals term in the HSEA force field (equation 2)... 

The CFF-PEF force field for carbohydrates proposed by Rasmussen has undergone several developmental refinements leading to numerous parameter sets. The emphasis of the PEF development has been to employ as few parameters and as simple energy expressions as possible. As such, torsion terms were kept to a minimum and no explicit term for the exo-anomeric effect was introduced. The consistent force field (CFF) developed by Lifson and Warshel was chosen as the original framework for the PEF development. The CFF-PEF functional form is similar to that of most macromolecular force fields (equation 9). ... 

Recently the developers of GROMOS extended the united atom version to an all-atom force field (GROMOS96) which uses the 43A1 parameters for solvated simulations. Not only does GROMOS96 include explicit hydrogen atoms, it also introduces mathematical modifications to the force field and so represents more than simply a reparameterization. The modifications to the force field equation have been introduced to save computational steps for example, the use of r in the bond term (equation 19)... 

The individual A values can scale the individual terms of the force field (equation 2), and/or they can scale extra terms added to the force field to generate a different effective pathway. As many extra terms, or mutation bases can be added as are desired, provided that at the endpoints of the simulation... 

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