Empirical Force Field or Molecular Mechanics Methods

A method which would seem to have particular relevance to hydrogen-bonded systems in view of the Coulombic nature of the longer-range hydrogen-bond forces is one which evaluates long-range Coulombic interactions within the framework of the LCAO-MO method [314]. Hitherto this method has been applied to infinite polymers, where comparison with experimental structural data is not possible. 

5 Empirical Force Field or Molecular Mechanics Methods 

Some of the more commonly used programs have the advantages for the nonspecialist in the field that they are generally well documented and tested, and the basic principles involve classical rather than quantum mechanics. For 

In the molecular mechanics methods, the energy of the molecule or assemblage of molecules is broken down into a sum of energy terms which are minimized separately, i.e., 

For large distortions from the equilibrium values, an additional anharmonicity term can be included, e.g., [1 +k (r-r0)2] or kj(r-r0)3, but this is rarely necessary. 

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Dynamic NMR gives information on the number and symmetries of conformations present in solution and on the energy barriers separating these conformations. This is particularly true for systems with barriers between about 25 and 90 kJ mol-1, a situation which often occurs in the medium ring. The interpretation of the NMR data can be carried out by the examination of molecular models, but this is a relatively crude and sometimes misleading method. Empirical force field (or molecular mechanics) calculations are much superior, even though the parametrization of heteroatoms may be open to question. Quantum mechanical calculations are not very suitable the semiempirical type, e.g. MINDO, do not reproduce conformational properties of even cyclohexane satisfactorily, and the ab initio... 

Empirical force field or molecular mechanics calculations. These methods are based on classical Newtonian mechanics, but use quantum mechanical concepts to formulate empirical equations. The parameters used are based on experimental data and/or on high level theoretical calculations when experimental data are not available. 

Ab initio methods solve the molecular Schrodinger equation associated with the molecular Hamiltonian based on different quantum-chemical methodologies that are derived directly from theoretical principles without inclusion of any empirical or semiempirical parameters in the equations. Though rigorously defined on first principles (quantum theory), the solutions from ab initio methods are obtained within an error margin that is qualitatively known beforehand thus all the solutions are approximate to some extent. Due to the expensive computational cost, ab initio methods are rarely used directly to study the physicochemical properties of flotation systems in mineral processing, but their application in developing force fields for molecular mechanics (MM) and MD simulation has been extensively documented. (Cacelli et al. 2004 Cho et al. 2002 Kamiya et al. 

A descriptor for the 3D arrangement of atoms in a molceulc can be derived in a similar manner. The Cartesian coordinates of the atoms in a molecule can be calculated by semi-empirical quantum mechanical or molecular mechanics (force field) methods, For larger data sets, fast 3D structure generators are available that combine data- and rule-driven methods to calculate Cartesian coordinates from the connection table of a molecule (e.g., CORINA [10]). 

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. 

The various types of successful approaches can be classified into two groups empirical model calculations based on molecular force fields and quantum mechanical approximations. In the first class of methods experimental data are used to evaluate the parameters which appear in the model. The shape of the potential surfaces in turn is described by expressions which were found to be appropriate by semiclassicala> or quantum mechanical methods. Most calculations of this type are based upon the electrostatic model. Another more general approach, the "consistent force field method, was recently applied to the forces in hydrogen-bonded crystals 48> 49>. 

Schrodinger equation. When the molecule is too large and difficult for quantum mechanical calculations, or the molecule interacts with many other molecules or an external field, we turn to the methods of molecular mechanics with empirical force fields. We compute and obtain numerical values of the partition functions, instead of precise formulas. The computation of thermodynamic properties proceeds by using a number of techniques, of which the most prominent are the molecular dynamics and the Monte Carlo methods. 

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. 

Some of the potential energy functions used to calculate the total strain energy of a molecule are similar to the functions used in the analysis of vibrational spectra. Because the parameters used to derive the strain energies from these functions are fitted quantities that are based on experimental data (e.g., X-ray structures or vibrational spectra), molecular mechanics may be referred to as empirical force field calculations (more often the simplification force field calculations is used). The quality of such calculations is strongly dependent on the reliability of the potential energy functions and the corresponding parameters (the force field). Thus, the selection of experimental data to fit the force field is one of the most important steps in a molecular mechanics study. An empirical force field calculation is in essence a method where the structure and the strain energy of an unknown molecule are interpolated from a series of similar molecules with known structures and properties. 

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