Molecular-mechanics method

Molecular mechanics methods are good for modelling big molecule systems where it is computationally expensive to employ quantum mechanics. These methods employ a molecular force field which is potential energy as a function of all atomic positions. It is used to study the molecular properties without any 

One very common molecular mechanics package is SYBYL. SYBYL is a simple computation that requires very few data to establish parameters. As a result, SYBYL can be used for elements throughout the Periodic Table. The results of SYBYL of are not as accurate compared to high-level computations, and some results are shown in Tables 9-2 and 9-3. 

Another common and more complicated molecular mechanics package is MMFF. MMFF requires much more data to establish the parameters used in the computation. The results are more accurate than SYBYL (as shown in Tables 9-2 and 9-3), but parameters are generally available only for organic molecules and biopolymers. 

Molecular mechanics techniques are valuable computations for establishing good starting points of initial geometry for higher-level quantum mechanical computations. The accuracy of the geometries obtained can be 

Molecular mechanics uses classical mechanics to model molecular systems. The potential energy of all systems in molecular mechanics is calculated using force fields. Molecular mechanics can be used to study small molecules as well as large biological systems or material assemblies with many thousands to millions of atoms. All-atomistic molecular mechanics methods have the following properties  

Molecular mechanics potential energy functions have been used to calculate binding constants, protein folding kinetics, protonation equilibria, active site coordinates, and to design binding sites [4,5]. 

The term AMBER force field generally refers to the functional form used by the family of AMBER force fields. This form includes a number of parameters each member of the family of AMBER force fields provides values for these parameters and has its own name. The functional form of the AMBER force field is (equation 8.1). 

First term (summing over bonds) represents the energy between covalently bonded atoms. This harmonic (ideal spring) force is a good 

Second term (summing over angles) represents the energy due to the geometry of electron orbitals involved in covalent bonding. 

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Singh, U.C., Kollman, P.A. A combined ab initio quantum mechanical and molecular mechanical method for carrying out simulations on complex molecular systems Applications to the CH3CI 4- Cl exchange reaction and gas phase protonation of polyethers. J. Comput. Chem. 7 (1986) 718-730. 

The two ways of learning - deductive and inductive - have already been mentioned. Quite a few properties of chemical compounds can be calculated explicitly. Foremost of these are quantum mechanical methods. However, molecular mechanics methods and even simple empirical methods can often achieve quite high accuracy in the calculation of properties. These deductive methods are discussed in Chapter 7. 

Parameters for elements (basis liinctions in ah miiw methods usually derived from experimental data and empirical parameters in semi-empirical methods nsually obtained from empirical data or ah initu> calcii la lion s) are in depen den t of th e ch em -leal environment, [n contrast, parameters used in molecular mechanics methods often depend on the chem ical en viron-ment. 

Th e ability to perform m oleciilar orbital (MO ) calculation s on m et-als is extremely useliil because molecular mechanics methods are gen erally unable to treat m etals. This is becau se m etals h ave a wide range of valences, oxidation states, spin multiplicities, and have 1111 usual bonding situations (e.g.. d%-p% back bonding). In addition. the 11 on direction al n at are o ( m etallic hon din g is less am en a-ble to a ball and spring interpretation. 

Hach molecular mechanics method has its own functional form MM+. AMBER, OPL.S, and BIO+. The functional form describes the an alytic form of each of th e term s in th e poteri tial. For exam pie, MM+h as both a quadratic and a cubic stretch term in th e poten tial whereas AMBER, OPES, and BIO+ have only c nadratic stretch term s, I h e functional form is referred to here as the force field. For exam pie, th e fun ction al form of a qu adratic stretch with force constant K, and equilibrium distance i q is ... 

All the constants in these equations must be obtained from experimental data or an ah initio calculation. The database of compounds used to parameterize the method is crucial to its success. A molecular mechanics method may be parameterized against a specific class of molecules, such as proteins or nucleotides. Such a force field would only be expected to have any relevance in... 

Molecular mechanics methods are not generally applicable to structures very far from equilibrium, such as transition structures. Calculations that use algebraic expressions to describe the reaction path and transition structure are usually semiclassical algorithms. These calculations use an energy expression fitted to an ah initio potential energy surface for that exact reaction, rather than using the same parameters for every molecule. Semiclassical calculations are discussed further in Chapter 19. 

It is possible to use computational techniques to gain insight into the vibrational motion of molecules. There are a number of computational methods available that have varying degrees of accuracy. These methods can be powerful tools if the user is aware of their strengths and weaknesses. The user is advised to use ah initio or DFT calculations with an appropriate scale factor if at all possible. Anharmonic corrections should be considered only if very-high-accuracy results are necessary. Semiempirical and molecular mechanics methods should be tried cautiously when the molecular system prevents using the other methods mentioned. 

Traditionally, molecular mechanics has not been the method of choice for predicting transition structures. However, since it is the only method viable for many large molecules, some elforts have been made to predict transition structures. Since the bonds are explicitly defined in molecular mechanics methods, it is not possible to simply find a point that is an energy maximum, except for conformational intermediates. 

The technique most often used (i.e., for an atom transfer) is to hrst plot the energy curve due to stretching a bond that is to be broken (without the new bond present) and then plot the energy curve due to stretching a bond that is to be formed (without the old bond present). The transition structure is next dehned as the point at which these two curves cross. Since most molecular mechanics methods were not designed to describe bond breaking and other reaction mechanisms, these methods are most reliable when a class of reactions has been tested against experimental data to determine its applicability and perhaps a suitable correction factor. 

The simplest and most quickly computed models are those based solely on steric hindrance. Unfortunately, these are often too inaccurate to be trusted. Molecular mechanics methods are often the method of choice due to the large amount of computation time necessary. Semiempirical methods are sometimes used when molecular mechanics does not properly represent the molecule. Ah initio methods are only viable for the very smallest molecules. These are discussed in more detail in the applicable chapters and the sources mentioned in the bibliography. 

Csjmhined Quantum and Molecular Mechanics Methods J. Gao, M. Thompson, Eds., American Chemical Society, Washington (1998). 

The use of RECP s is often the method of choice for computations on heavy atoms. There are several reasons for this The core potential replaces a large number of electrons, thus making the calculation run faster. It is the least computation-intensive way to include relativistic effects in ah initio calculations. Furthermore, there are few semiempirical or molecular mechanics methods that are reliable for heavy atoms. Core potentials were discussed further in Chapter 10. 

Molecular mechanics methods have only been used to a limited extent for these classes of compounds. However, molecular mechanics methods do fairly well in describing the geometries and relative energies of compounds with these elements. It is perhaps only for historical and economic reasons that molecular mechanics has not been used more for modeling these elements. Subsequently, there are not as many force fields available. 

Molecular mechanics methods may work well or poorly for compounds containing alkali metals. The crucial factor is often how the force field computes charges for electrostatic interactions. 

Nearly every technical difficulty known is routinely encountered in transition metal calculations. Calculations on open-shell compounds encounter problems due to spin contamination and experience more problems with SCF convergence. For the heavier transition metals, relativistic effects are significant. Many transition metals compounds require correlation even to obtain results that are qualitatively correct. Compounds with low-lying excited states are difficult to converge and require additional work to ensure that the desired states are being computed. Metals also present additional problems in parameterizing semi-empirical and molecular mechanics methods. 

In the past, when molecular mechanics methods were used for transition metals, it was by having a set of parameters for the metal that were parameterized specifically for one class of compounds. There have been a number of full periodic table force fields created, with the most successful being the UFF force field. All the full periodic molecular mechanics methods still give completely unreasonable results for certain classes of compounds. 

One way that molecular mechanics methods have been adapted to transition metal applications is by including one orbital-based term in the force field to describe the metal center. These terms are typically based on semiempirical methods or even some variation of ligand field theory. 

Ah initio calculations of polymer properties are either simulations of oligomers or band-structure calculations. Properties often computed with ah initio methods are conformational energies, polarizability, hyperpolarizability, optical properties, dielectric properties, and charge distributions. Ah initio calculations are also used as a spot check to verify the accuracy of molecular mechanics methods for the polymer of interest. Such calculations are used to parameterize molecular mechanics force fields when existing methods are insulficient, which does not happen too often. 

Molecular mechanics methods have been used particularly for simulating surface-liquid interactions. Molecular mechanics calculations are called effective potential function calculations in the solid-state literature. Monte Carlo methods are useful for determining what orientation the solvent will take near a surface. Molecular dynamics can be used to model surface reactions and adsorption if the force held is parameterized correctly. 

Example Jensen and Gorden calculated the potential energy surface of glycine using ab initio and semi-empirical methods.This study is of special interest to developers of molecular mechanics force fields. They frequently check their molecular mechanics methods by comparing their results with ab initio and semi-empir-ical calculations for small amino acids. 

Before running a molecular dynamics simulation with solvent and a molecular mechanics method, choose the appropriate dielectric constant. You specify the type and value of the dielectric constant in the Force Field Options dialog box. The dielectric constant defines the screening effect of solvent molecules on nonbonded (electrostatic) interactions. 

Previous investigations might influence the choice of a molecular mechanics method. If molecular mechanics calculations of a particular compound or molecule type already exist, choose the same force field so you can make comparisons easily. 

You can use any ab initio SCF calculation and all the semi-empiri-cal methods, except Extended Hiickel, for molecular dynamics simulations. The procedures and considerations are similar for simulations using molecular mechanics methods (see Molecular Dynamics on page 69). 

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