Molecular mechanics approaches, classical

One tool for working toward this objective is molecular mechanics. In this approach, the bonds in a molecule are treated as classical objects, with continuous interaction potentials (sometimes called force fields) that can be developed empirically or calculated by quantum theory. This is a powerful method that allows the application of predictive theory to much larger systems if sufficiently accurate and robust force fields can be developed. Predicting the structures of proteins and polymers is an important objective, but at present this often requires prohibitively large calculations. Molecular mechanics with classical interaction potentials has been the principal tool in the development of molecular models of polymer dynamics. The ability to model isolated polymer molecules (in dilute solution) is well developed, but fundamental molecular mechanics models of dense systems of entangled polymers remains an important goal. 

This section provides the fundamental equations for the quantum mechanical and molecular mechanical approach for determining the energies of molecules interacting with a structured environment. We can illustrate the QM/MM procedure as indicated in Figure 13-1 for a system where one part is described by quantum mechanics (QM) and the other part is described by classical mechanics or molecular mechanics (MM). The electrons and the nuclei of the QM system are treated separately at positions r7 and Rm, respectively. We represent the particles in the MM part by effective charges positioned at the atomic sites, Rs, and induced dipole moments located at (R ). 

This section contains the background for the combination of density functional theory and molecular mechanics. Following the basic philosophy of quantum mechan-ics/molecular mechanics approaches we partition the total system into at least two parts which can be treated simultaneously. The quantum mechanical subsystem is described using DFT and the classical subsystem is given by molecular mechanics. Based on the QM/MM approach we have that the total energy of the system is... 

In the 1970s and 1980s, calculational approaches (in addition to the X-ray studies) were added to the tools for the attack on the structure of water. In the molecular dynamics approach, classical mechanics is used to calculate the successive movements of molecules in the structure. Such an approach is dependent on the correctness of the equation that represents the energies of interaction between the particles. The basic equation for these interactions is the Lennard-Jones 6-12 potential. 

The theoretical background of the molecular mechanics approach has been discussed in detail elsewhere [63]. Briefly, molecular mechanics uses classical mechanics to represent molecules. Therefore, molecules are viewed as collections of spheres connected by mutually independent, flexible springs representing bonds. 

The molecular mechanics approach to conformational analysis has the virtue of describing molecular properties in terms that are physically easily understood. Moreover, the use of carefully chosen potential functions can give highly precise information as to the relative energies of various molecular arrangements. Certainly the quality of the strain-energy calculations performed on hydrocarbons testifies to the capabilities of classical mechanics in simple systems. Concurrent with the improvement in the methodology of molecular mechanical calculations has been the development of approaches to conformational analysis based on molecular orbital... 

AMI AMBER A Program for Simulation of Biological and Organic Molecules CHARMM The Energy Function and Its Parameterization Combined Quantum Mechanics and Molecular Mechanics Approaches to Chemical and Biochemical Reactivity Density Functional Theory (DFT), Hartree-Fock (HF), and the Self-consistent Field Divide and Conquer for Semiempirical MO Methods Electrostatic Catalysis Force Fields A General Discussion Force Fields CFF GROMOS Force Field Hybrid Methods Hybrid Quantum Mechanical/Molecular Mechanical (QM/MM) Methods Mixed Quantum-Classical Methods MNDO MNDO/d Molecular Dynamics Techniques and Applications to Proteins OPLS Force Fields Parameterization of Semiempirical MO Methods PM3 Protein Force Fields Quantum Mechanical/Molecular Mechanical (QM/MM) Coupled Potentials Quantum Mecha-nics/Molecular Mechanics (QM/MM) SINDOI Parameterization and Application. 

The proper representation of solvents in quantum chemical (QC) calculations is of crucial importance for the future success of QC because the vast majority of technical and biological chemistry takes place in fluid systems, while QC has been developed for isolated molecules for 40 years. Because of the extremely large number of molecules necessary for a realistic description of a solvent environment and the exponential increase of the costs of QC calculations with increasing size of the system, a direct extension of QC to such systems appears to be impossible in general, although first steps towards that goal have been made by the Car-Parrinello method (see Combined Quantum Mechanical and Molecular Mechanical Potentials and Combined Quantum Mechanics and Molecular Mechanics Approaches to Chemical and Biochemical Reactivity). Mixed classical quantum methods could... 

Many problems in force field investigations arise from the calculation of Coulomb interactions with fixed charges, thereby neglecting possible mutual polarization. With that obvious drawback in mind, Ulrich Sternberg developed the COSMOS (Computer Simulation of Molecular Structures) force field [30], which extends a classical molecular mechanics force field by serai-empirical charge calculation based on bond polarization theory [31, 32]. This approach has the advantage that the atomic charges depend on the three-dimensional structure of the molecule. Parts of the functional form of COSMOS were taken from the PIMM force field of Lindner et al., which combines self-consistent field theory for r-orbitals ( nr-SCF) with molecular mechanics [33, 34]. 

As we have seen, Anisotropic Polarizable Molecular Mechanics (APMM) procedures such as SIBFA or GEM are more complex than usual classical approaches. 

The inter/intramolecular potentials that have been described may be viewed as classical in nature. An alternative is a hybrid quantum-mechanical/classical approach, in which the solute molecule is treated quantum-mechanically, but interactions involving the solvent are handled classically. Such methods are often labeled QM/MM, the MM reflecting the fact that classical force fields are utilized in molecular mechanics. An effective Hamiltonian Hefl is written for the entire solute/solvent system ... 

Parallel with the phenomenological development, an alternative point of view has developed toward thermodynamics, a statistical-mechanical approach. Its philosophy is more axiomatic and deductive than phenomenological. The kinetic theory of gases naturally led to attempts to derive equations describing the behavior of matter in bulk from the laws of mechanics (first classic, then quanmm) applied to molecular particles. As the number of molecules is so great, a detailed treatment of the mechanical problem presents insurmountable mathematical difficulties, and statistical methods are used to derive average properties of the assembly of molecules and of the system as a whole. 

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