Force parametrization

MMVB is a hybrid force field, which uses MM to treat the unreactive molecular framework, combined with a valence bond (VB) approach to treat the reactive part. The MM part uses the MM2 force field [58], which is well adapted for organic molecules. The VB part uses a parametrized Heisenberg spin Hamiltonian, which can be illustrated by considering a two orbital, two electron description of a sigma bond described by the VB determinants... 

These numbers are not negligible. At present such effects are on the average compensated by other force field terms through empirical parametrization. 

While simulations reach into larger time spans, the inaccuracies of force fields become more apparent on the one hand properties based on free energies, which were never used for parametrization, are computed more accurately and discrepancies show up on the other hand longer simulations, particularly of proteins, show more subtle discrepancies that only appear after nanoseconds. Thus force fields are under constant revision as far as their parameters are concerned, and this process will continue. Unfortunately the form of the potentials is hardly considered and the refinement leads to an increasing number of distinct atom types with a proliferating number of parameters and a severe detoriation of transferability. The increased use of quantum mechanics to derive potentials will not really improve this situation ab initio quantum mechanics is not reliable enough on the level of kT, and on-the-fly use of quantum methods to derive forces, as in the Car-Parrinello method, is not likely to be applicable to very large systems in the foreseeable future. 

P. Ulrich, W. Scott, W.F. van Gunsteren and A. Torda, Protein structure prediction force 6elds parametrization with quasi Newtonian dynamics. Proteins 27 (1997), 367-384. 

Construction of Alignment Charts. Of the ways to constmct alignment charts, the bmte force method, which requires some idea of the geometry for the chart, is the easiest method to use. The mathematical method, which uses parametric equations of scale to determine the placement and scale of each axis, is the most accurate, but the most difficult to apply. 

The only problem with the foregoing approach to molecular interactions is that the accurate solution of Schrddinger s equation is possible only for very small systems, due to the limitations in current algorithms and computer power. Eor systems of biological interest, molecular interactions must be approximated by the use of empirical force fields made up of parametrized tenns, most of which bear no recognizable relation to Coulomb s law. Nonetheless the force fields in use today all include tenns describing electrostatic interactions. This is due at least in part to the following facts. 

Finally, the parametrization of the van der Waals part of the QM-MM interaction must be considered. This applies to all QM-MM implementations irrespective of the quantum method being employed. From Eq. (9) it can be seen that each quantum atom needs to have two Lennard-Jones parameters associated with it in order to have a van der Walls interaction with classical atoms. Generally, there are two approaches to this problem. The first is to derive a set of parameters, e, and G, for each common atom type and then to use this standard set for any study that requires a QM-MM study. This is the most common aproach, and the derived Lennard-Jones parameters for the quantum atoms are simply the parameters found in the MM force field for the analogous atom types. For example, a study that employed a QM-MM method implemented in the program CHARMM [48] would use the appropriate Lennard-Jones parameters of the CHARMM force field [52] for the atoms in the quantum region. 

Molecular mechanics calculations don t explicitly treat the electrons in a molecular system. Instead, they perform computations based upon the interactions among the nuclei. Electronic effects are implicitly included in force fields through parametrization. 

Each force field achieves good results only for a limited class of molecules, related to those for which it was parametrized. No force field can be generally used for all molecular systems of interest. 

Thornton, B. H. and Bogy, D. B., "A Parametric Study of Head-Disk Interface Instability Due to Intermolecular Forces, IEEE Trans. Magn., Vol. 40, No. (1), 2004, pp. 337-343. 

Fig. 23—A schematic force curve plotted as a function of sliding velocity. A viscous friction forms the background of the force curve upon which the frictions from superharmonic and parametric resonance are superposed.

However, due to the availability of numerous techniques, it is important to point out here the differences and equivalence between schemes. To summarize, two EDA families can be applied to force field parametrization. The first EDA type of approach is labelled SAPT (Symmetry Adapted Perturbation Theory). It uses non orthogonal orbitals and recomputes the total interaction upon perturbation theory. As computations can be performed up to the Coupled-Cluster Singles Doubles (CCSD) level, SAPT can be seen as a reference method. However, due to the cost of the use of non-orthogonal molecular orbitals, pure SAPT approaches remain limited... 

Banks JL, Kaminski GA, Zhou RH, Mainz DT, Berne BJ, Friesner RA (1999) Parametrizing a polarizable force field from ab initio data. I. The fluemating point charge model. J Chem Phys 110(2) 741—754... 

A modification of the forcing function approach makes use of linear systems analysis for individual tissue compartments [59], Parametric or nonparamet-ric functions are fitted to observed blood drug concentration-time data and are then combined with tissue drug concentration-time measurements deconvolved... 

Fernandez, B., M. A. Rios, and L. Carballeira. 1991. Molecular Mechanics (MM2) and Conformational Analysis of Compounds with N-C-O Units. Parametrization of the Force Field and Anomeric Effect. J. Comput. Chem. 12, 78-90. 

The choice of the momenta, rather than of the forces, is illustrated by the simple example of a two-dimensional harmonic oscillator described by the parametric equations... 

Daura, X. Mark, A. E. van Gunsteren, W. F., Parametrization of aliphatic CHn united atoms of GROMOS96 force held, J. Comput. Chem. 1998,19, 535-547. 

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