Empirical force field method

II. Ab Initio, Semi-Empirical and Empirical Force Field Methods... 

Molecula.rMecha.nics. Molecular mechanics (MM), or empirical force field methods (EFF), ate so called because they are a model based on equations from Newtonian mechanics. This model assumes that atoms are hard spheres attached by networks of springs, with discrete force constants. 

It is dangerous to draw too many conclusions from the numerical results of molecular mechanics calculations. In this case, we wanted only to show that the two likely conformations for the E and G-rings of PbTX-1 are roughly equal in energy and that it is plausible that they could both exist in solution at room temperature. It would be very useful to be able to estimate the energy of activation required for the conversions between conformations. Unfortunately, estimation of the energy barrier is beyond the realm of the empirical force field method for all but the simplest cases. 

Emphysema, effect on heart, 5 107 Empirical equations, deficiencies of, 23 192 Empirical force-field methods (EFF),... 

This study uses empirical force-field methods similar to those used by Kotaka and Kakihana (1977), with a focus on octahedral (XT ) molecules and molecule-like complexes. The reader is cautioned that there appear to be typographical errors in the original tabulation. 

The conformational energies of the lower members of POM, 2,4-dioxapentane and 2,4,6-trioxaheptane are estimated by the empirical force field method. The gauche states of the Internal rotation around the skeletal C—0 bonds are successfully predicted to be of lower energies in both molecules. In order to calculate the unperturbed dimension and dipole moment of POM, RIS approximations are made by using the results obtained from the force field calculations on 2,4,6-trioxaheptane. Although these parameters are significantly different from those estimated earlier, they reproduce the observed values fairly well. 

Molecular Mechanics. Molecular mechanics (MM), or empirical force field methods (EFF), are so called because they are a model based on equations from Newtonian mechanics. This model assumes that atoms are hard spheres attached by networks of springs, with discrete force constants. The force constants in the equations are adjusted empirically to repro duce experimental observations. The net result is a model which relates the "mechanical" forces within a structure to its properties. Force fields are made up of sets of equations each of which represents an element of the decomposition of the total energy of a system (not a quantum mechanical eneigy, but a classical mechanical one). The sum of the components is called the force field eneigy, or steric energy, which also routinely includes the electrostatic eneigy components. Typically, the steric energy is expressed as... 

An entirely different approach, based upon classical mechanics, is the molecular mechanics or empirical force field method (82MI5 83AG(E)1 86MI2). It is assumed that the steric energy ( s) of a molecule can be expressed as a sum of energy contributions [Eq. (6)], where each term is obtained from a simple potential function, such as the one given by Hooke s law. 

Analysis of Polysilanes by the Empirical Force Field Method. 

Other important and effective approaches to computational chemistry are those called Empirical Force-Field methods (EFF methods), based on a mechanistic view of the molecule in terms of force constants of bonds, bending, torsion and other special interaction terms. The set of force constants constitutes a field of empirical parameters used for the calculation of molecular geometries and energies. 

Substituent steric descriptor calculated from standard enthalpy of formation obtained by computational chemistry using empirical force field methods. It is defined by the following relationship [Beckaus, 1978 Giese and Beckaus, 1978] ... 

K. Mislow, D. A. Dougherty, and W, D. Hounshell, Bull. Soc. Chem. Belg., 87, 555 (1978). Some Applications of the Empirical Force Field Method to Stereochemistry. 

By the early 1970s, molecular mechanics computer programs such as MMI and MM2 were available, running on the IBM 360. For proteins, ECEPP was developed by Harold A. Scheraga. - Countering the molecular mechanics approach, Michael J. S. Dewar modified John A. Pople s (complete) neglect-of-differential-overlap semiempirical quantum mechanical method (CNDO/2) to calculate quantities such as conformational stability and heats of formation. Such programs (MNDO) were necessarily slower than the empirical force field methods such as MM2 and ECEPP but still had fewer parameters and could account for the effects of polarization in aromatic systems. 

Because of the large computational requirements of modeling macro-molecular systems, empirical force field methods are typically relied on in CADD projects. Given adequate parameterization, such calculations can offer a reasonable balance between accuracy and speed. ... 

The equilibrium conformations of physical complexes of selected PAHTC s with a dinucleotide fragment of B-DNA have been calculated by the all-atom AMBER empirical force field method [112]. The B-DNA has been represented by the dG2.dC2 dinucleotide fragment. No phosphate groups were placed at the ends of the strands, which instead carried terminal 03 and 05 hydroxyl groups. 

Our aim in this chapter will be to establish the basic elements of those quantum mechanical methods that are most widely used in molecular modelling. We shall assume some familiarity with the elementary concepts of quantum mechanics as found in most general physical chemistry textbooks, but little else other than some basic mathematics (see Section 1.10). There are also many excellent introductory texts to quantum mechanics. In Chapter 3 we then build upon this chapter and consider more advanced concepts. Quantum mechanics does, of course, predate the first computers by many years, and it is a tribute to the pioneers in the field that so many of the methods in common use today are based upon their efforts. The early applications were restricted to atomic, diatomic or highly symmetrical systems which could be solved by hand. The development of quantum mechanical techniques that are more generally applicable and that can be implemented on a computer (thereby eliminating the need for much laborious hand calculation) means that quantum mechanics can now be used to perform calculations on molecular systems of real, practical interest. Quantum mechanics explicitly represents the electrons in a calculation, and so it is possible to derive properties that depend upon the electronic distribution and, in particular, to investigate chemical reactions in which bonds are broken and formed. These qualities, which differentiate quantum mechanics from the empirical force field methods described in Qiapter 4, will be emphasised in our discussion of typical applications. 

The explicit expressions used for each of the terms in (16.94) define what is called a molecular-mechanics force field, since the derivatives of the potential-energy function determine the forces on the atoms. A force field contains analytical formulas for the terms in (16.94) and values for all the parameters that occur in these formulas. The MM method is sometimes called the empirical-force-field method. Empirical force fields are used not only for single-molecule molecular-mechanics calculations of energy differences, geometries, and vibrational frequencies, but also for molecular-dynamics simulations of liquids and solutions, where Newton s second law is integrated to follow the motions of atoms with time in systems containing hundreds of molecules. 

Although the modularity has been improved, there are unavoidable interdependencies. Chapters 3,4 and 5 contain the essentials of electronic structure theory, and most would include Chapter 6 describing density functional methods. Chapter 2 contains a description of empirical force field methods, and this is tightly coupled to the simulation methods in Chapter 14, which of course leans on the statistical mechanics in Chapter 13. Chapter 1 on fundamental issues is of a more philosophical nature, and can be skipped. Chapter 16 on mathematical techniques is mainly for those not already familiar with this, and Chapter 17 on statistical meUiods may be skipped as well. 

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