Molecular mechanics potentials, direct

Chakraborty A, Zhao Y, Lin H, Tiuhlm DG (2006) Combined valence bond-molecular mechanics potential-energy surface tmd direct dynamics study of rate constants and kinetic isotope effects for the H + C2H6 reaction. J Chem Phys 124 044315... 

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... 

It is worth to remark that the opposite also happens. There is an evolution in the experimental teehniques too, and in some eases this progress makes possible ( or competitive) the measurement of a quantity formerly available via computations only. One example is the detailed measurement of the electronic density of a molecule, and of the related molecular electrostatic potential. The determination of these two observables has been for many years a task feasible only by quantum-mechanical methods, now the progresses in the elaboration of diffraction technique measurements makes possible a direct determination. 

Molecular mechanics (MM) potentials, direct molecular dynamics ... 

Molecular mechanics force fields rest on four fundamental principles. The first principle is derived from the Bom-Oppenheimer approximation. Electrons have much lower mass than nuclei and move at much greater velocity. The velocity is sufficiently different that the nuclei can be considered stationary on a relative scale. In effect, the electronic and nuclear motions are uncoupled, and they can be treated separately. Unlike quantum mechanics, which is involved in determining the probability of electron distribution, molecular mechanics focuses instead on the location of the nuclei. Based on both theory and experiment, a set of equations are used to account for the electronic-nuclear attraction, nuclear-nuclear repulsion, and covalent bonding. Electrons are not directly taken into account, but they are considered indirectly or implicitly through the use of potential energy equations. This approach creates a mathematical model of molecular structures which is intuitively clear and readily available for fast computations. The set of equations and constants is defined as the force... 

Dramatic examples have also been reported for main-chain supramolecular polymers (SPs Lehn 1993 Ciferri 2005 Fig. 3.1), in which specific and directional molecular recognition events between end groups define the main chain of a linear polymeric assembly. Although main-chain SPs had been created and characterized previously (Broze et al. 1983 Fouquey et al. 1990 Alexander et al. 1993 Bladon and Griffin 1993 St Pourcain and Griffin 1995), it was a groundbreaking paper in 1997 that demonstrated the mechanical potential of supramolecular interactions and catalyzed much of the current interest in the field (Sijbesma et al. 1997). 

The molecular mechanism of local segment rotations can be explained by the occurrence of twin reversals [33, 34] which are induced thermally due to the unusual course of the conformational potential [35]. Those twin reversals are torsion defects causing the helix conformation to change from left-handed to right-handed and vice versa. They are built into the PTFE helix without changing the direction of the molecular long axis (Fig. 23). Additionally, the long... 

Therefore, two parts of any molecular mechanics package that have a direct influence on a particular optimized structure, i. e., on the nuclear coordinates of a specific energy minimum on the calculated potential energy surface, are the mathematical functions and the corresponding parameters. The potential energy functions and the force field parameters are interrelated and, therefore, the parameters may not, in general, be transferred from one force field into another. 

The first derivatives of a potential energy function define the gradient of the potential and the second derivatives describe the curvature of the energy surface (Fig. 3.4). In most molecular mechanics programs the potential functions used are relatively simple and the derivatives are usually determined analytically. The second derivatives of harmonic oscillators correspond to the force constants. Thus, methods using the whole set of second derivatives result in some direct information on vibrational frequencies. 

Two types of information are obtained from any molecular mechanics study, the minimum value of the strain energy and the structure associated with that minimum. Agreement between the energy-minimized and experimental (crystallographic) structures has often been used as the primary check on the validity of the force field and to refine the force field further, but often little predictive use has been made of the structures obtained. As force fields become more reliable, the potential value of structure predictions increases. More importantly, when no unequivocal determination of a structure is available by experimental methods then structure prediction may be the only means of obtaining a three-dimensional model of the molecule. This is often the case, for instance, in metal-macromolecule adducts, and structures obtained by molecular mechanics can be a genuine aid in the visualization of these interactions. In this chapter we consider the ways in which structure prediction by molecular mechanics calcluations has been used, and point to future directions. 

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