Force field methods cross terms

MMl, MM2, MM3, and MM4 are general-purpose organic force fields. There have been many variants of the original methods, particularly MM2. MMl is seldom used since the newer versions show measurable improvements. The MM3 method is probably one of the most accurate ways of modeling hydrocarbons. At the time of this book s publication, the MM4 method was still too new to allow any broad generalization about the results. However, the initial published results are encouraging. These are some of the most widely used force fields due to the accuracy of representation of organic molecules. MMX and MM+ are variations on MM2. These force fields use five to six valence terms, one of which is an electrostatic term and one to nine cross terms. 

The Merck molecular force field (MMFF) is one of the more recently published force fields in the literature. It is a general-purpose method, particularly popular for organic molecules. MMFF94 was originally intended for molecular dynamics simulations, but has also seen much use for geometry optimization. It uses five valence terms, one of which is an electrostatic term, and one cross tenn. 

COSMIC [181] method uses only harmonic potential with respect to displacements in the diagonal force fields. Neither improper torsion nor cross terms are included. The nonbonding interactions are the sum of van der Waals interactions represented by the Morse potential and the charge-based Coulomb energy. 

Linnett o gives a discussion of the use of valence force fieid with the addition ol selected cross terms. One method of reducing the number of constants to Tdc determined from the frequencies is to carry over from molecule to molecule certain force constants for squared terms and even for cross terms. Linnett mentions in this connection the work of Crawford and Brinkley who studied acetylene, ethane, methylacetylene, dimethylacetylene, hydrogen cyanide, methyl cyanide and the methyl halides in this way, and were able, for all the molecules, to account for 84 frequencies with 31 constants. Linnetttreated some of these compounds using a different force field. He was able to account satisfactorily for 25 frequencies using 11 force constants. From our point of view the trouble with these results is that Linnett obtained a value for the C - C force constant in these acetylene derivatives which was different from that obtained by Crawford and Brinkley. For C - C in methyl cyanide for example, Linnett obtained... 

A few force fields have an accuracy worse than that of semiempirical methods. CVFF was developed from an initially diagonal force field by adding a large number of cross terms, with insufficient reparameterization. It is obvious that this resulted in a force field with low predictivity, and its use cannot be recommended for any application. UFF was intended to cover the entire periodic table and is still the only published force field that can accomplish this task. However, the accuracy for organic molecules was sacrificed in the process the MAE for UFF is ca. 3 kcal/mol. 

Vibrational spectroscopy was a forerunner of molecular mechanics in the sense that spectroscopists used many of the basic methods used in molecular mechanics to calculate spectra, long before it was possible to calculate stiuctures. It was early found that a purely diagonal force field was less accurate than desired, and that cross terms could improve the quality of the spectra calculated. One of these cross terms was a stretch-bend term. It has the form shown in Eq. (4.12) ... 

Over the last decade much effort has been spent on the development of reliable force fields (see Force Fields A General Discussion) for the simulation of lipid bilayer systems. Although this is still an active field of development, we will describe the most common force fields currently in use. The principal differences between these force fields concerns the methods of parameterization and the handling of cut-offs. The potential forms are equivalent or very similar and typically consist of Coulomb and Lennard-Jones terms combined with quadratic bonded terms for bonds, and angles and a cosine series for dihedrals. A new development is the inclusion of cross-terms between these standard terms but this is not common yet. None of the presently used force fields includes atomic polarizability. 

The practical implementation of the reactive force field scheme in materials simulations requires extensive parameterization of the various terms entering the force field description. This parameterization is necessary for any classical MD method, but owing to the comparatively large number of adjustable parameters needed to achieve the added reactive flexibility, this is much more extensive for the reactive force field. There is a minimum of around 30 parameters per element that need to be determined prior to production type simulations, with increasing numbers of cross-terms arising from the many-body interactions in systems with many elements. 

In terms of beam delivery, the DLW method is based on optical microscopy, confocal microscopy [4,6,13] and laser tweezers [14] (for reviews on laser tweezers see [ 15,16]). These techniques allow for a high spatial 3D resolution of a tightly focused laser beam with optical exposure of micrometric-sized volumes via linear and nonlinear absorption. In addition, mechanical and thermal forces can be exerted upon objects as small as 10 nm molecular dipolar alignment can be controlled by polarization of light in volumes of with submicrometric cross-sections. This circumstance widens the field of applications for laser nano- and microfabrication in liquid and solid materials [17-22]. 

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