CHARMM expression

In this case, only two parameters (k and Iq) per atom pair are needed, and the computation of a quadratic function is less expensive. Therefore, this type of expression is used especially by biomolecular force fields (AMBER, CHARMM, GROMOS) dealing with large molecules like proteins, lipids, or DNA. 

MM is a very successful model but it is clear lrom expressions such as (2) that the FF may comprise a very large number of parameters and since the quality of the FF will depend crucially on these parameters, developing a truly universal FF is an enormous (perhaps impossible) challenge (11). Consequently, FFs tend to be applicable to a specific class of molecular system such as small organic molecules (e.g., MMFF (7-10)), or large biomolecules like proteins and DNA (e.g., AMBER (12) or CHARMM (13)) for which the expressions in (2) are suited. 

Transferability, using the same set of parameters to model a series of related molecules, is an important feature of a force field. Concerning the specialized biomolecular force fields, their transferability varies. For example, AMBER is more transferable than CHARMM especially with recent efforts on more automated methods of parameter assignment. 129,193 Essentially the quality of a force field depends on how appropriate is the mathematical form of the energy expression and how accurate are the parameters. 

The most often used force fields are AMBER [11], CHARMM [12], OPLS-AA [13] and GROMOS [14], although some minor differences for the energy expression may exist between these methods. 

In this work, a recently developed semi-empirical method, SCC-DFTB method, is employed to account for the electronic structure of QM part. The details of this method and its implementation to CHARMM have been summarized elsewhere [6, 22-24]. Here we just give a short description. This method is derived by a second order expansion of the DFT total energy functional with respect to the charge density fluctuation around a given reference density. The total energy can be expressed as following [22] ... 

The CHARMm force field [20] is comprised of a series of function terms for both bonded and nonbonded energies and a set of parameters for these terms. The total energy (Ej) of the system is expressed as... 

One should distinguish between a force field, which is defined by the expression for V in (16.94), and a molecular-mechanics program, which is a computer program that uses a force field to perform molecular-mechanics calculations. Sometimes MM programs and force fields have the same name. For example, CHARMM is also the name of a molecular-mechanics program. The CHARMM program has available in it, not only the CHARMM force field, but also MMFF94. 

The multipole expansion of Coulomb s law up to the octupole, which can be found in [48], is more complicated than Eq. 9.3. The advantage is that the complexity in the expression leads to computational efficiency in computer simulations once it is programmed, since only one distance between two interacting water molecules is needed. The downside is that while it becomes more accurate as higher order multipoles are added, it also becomes computationally slower as higher-order multipoles are included since each n-pole involves a (n - 1) rank tensor. A soft-sphere model with a dipole, quadrupole, and octupole (SSDQO], which is exact up to the 1/r term and in addition approximates the 1/r term, has been developed for computational efficiency [48]. However, the recent implementation of a fast multipole method in the molecular dynamics program CHARMM [80] should make this approximation unnecessary specifically, the full multipole expansion up to the... 

Force field parameters for inorganic constituents have been a major hurdle in the quantitative analysis of interfaces in nanocomposites while energy models for surfactants, polymers, and biopolymers have been developed in sufficient reliability to simulate densities, cohesive energies, and interface energies. At the classical atomistic level, several force fields are in use, such as AMBER [50], CHARMM [51], CVFF [52], COMPASS [53], OPLS-AA [54], PCFF [55], and UFF [56]. For example, the energy expressions of CVFF [52], and PCFF [55] (same as COMPASS [53]), are as follows ... 

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