Potential functions intramolecular

Potential functions such as MM+ discussed in Chapter 1 are fine for intramolecular interactions. MD was developed long before such sophisticated force fields became available, and in any case the aims of MM and MD simulations tend to be quite different. MM studies tend to be concerned with the identification of equihbrium geometries of individual molecules whilst MD calculations tend to be concerned with the simulation of bulk properties. Inspection of Figure 2.2 suggests that the intramolecular details ought to be less important than the intermolecular ones, and early MD studies concentrated on the intermolecular potential rather than the intramolecular one. 

The rapid rise in computer power over the last ten years has opened up new possibilities for modelling complex chemical systems. One of the most important areas of chemical modelling has involved the use of classical force fields which represent molecules by atomistic potentials. Typically, a molecule is represented by a series of simple potential functions situated on each atom that can describe the non-bonded interaction energy between separate atomic sites. A further set of atom-based potentials can then be used to describe the intramolecular interactions within the molecule. Together, the potential functions comprise a force field for the molecule of interest. 

Jorgensen et al. has developed a series of united atom intermolecular potential functions based on multiple Monte Carlo simulations of small molecules [10-23]. Careful optimisation of these functions has been possible by fitting to the thermodynamic properties of the materials studied. Combining these OPLS functions (Optimised Potentials for Liquid Simulation) with the AMBER intramolecular force field provides a powerful united-atom force field [24] which has been used in bulk simulations of liquid crystals [25-27],... 

Although the equilibrium configuration of a molecule can usually be specified, at ordinary temperatures, all of the atoms undergo oscillatory motions. The forces between the atoms in the molecule are described by a Taylor series of the intramolecular potential function in the internal coordinates. This function can then be written in the form... 

Mahoney, M. W. Jorgensen, W. L., Quantum, intramolecular flexibility, and polarizability effects on the reproduction of the density anomaly of liquid water by simple potential functions, 7. Chem. Phys. 2001,115, 10758-10768... 

The final step in the MM analysis is based on the assumption that, with all force constants and potential functions correctly specified in terms of the electronic configuration of the molecule, the nuclear arrangement that minimizes the steric strain corresponds to the observable gas-phase molecular structure. The objective therefore is to minimize the intramolecular potential energy, or steric energy, as a function of the nuclear coordinates. The most popular procedure is by computerized Newton-Raphson minimization. It works on the basis that the vector V/ with elements dVt/dxn the first partial derivatives with respect to cartesian coordinates, vanishes at a minimum point, i.e. = 0. This condition implies zero net force on each atom... 

Hydrogen bonds. When an N—C—N moiety has hydrogen atoms on either nitrogens, several of its conformations may be stabilized by intramolecular hydrogen bonds. Since MM2 does not have a special potential function for hydrogen bonding, such interactions... 

Further examination of the Williams approach seems called for, both to improve the method for estimating parameters such as the relaxation time, and to clarify the relationship between the intramolecular potential form and non-thermodynamic frictional forces. The method might provide a fairly unified description of non-linear flow porperties if a suitable potential function for large scale molecular friction were found. Aside from the Williams work, there have been no theoretical studies dealing with t] vs. y at low to moderate concentrations. The systematic changes in the master curve /(/ ) with coil overlap c[ij] are thus without explanation at the present time. 

Calculations of the strain energies of the endo and exo forms of the 1-methyl-, 1-fluoro- and 1-chlorosilatranes carried out by the methods of molecular mechanics found these assumptions to be unsound176-180. Even with an additional consideration of the intramolecular electrostatic interactions177-179, employment of the usual force field for tetracoordinate silicon led to potential functions of the endo-exo isomers (equation 44) with a deeper minimum corresponding to the exo form 47, with ouf-orientation of the nitrogen. 

Dihedral angle distribution functions for the various models are shown in figure 5. Models using the Bartell and BHS intramolecular potential functions show a clear bimodal distribution. The former shows a zero intensity near 9 = 0°. The latter shows a small non-zero intensity near 9 = 0°. The Haigh potential shows a distribution which may be described as lying somewhere between bimodal and monomodal. Both the WW and KK models show a monomodal function with a maximum near 9 = 0°, suggesting the most probable conformation is the planar conformation in the room temperature solid phase. The RDFs for these two models show well defined features which seem to be correlated with the monomodal S(9) exhibited by them. 

Recently, detailed molecular pictures of the interfacial structure on the time and distance scales of the ion-crossing event, as well as of ion transfer dynamics, have been provided by Benjamin s molecular dynamics computer simulations [71, 75, 128, 136]. The system studied [71, 75, 136] included 343 water molecules and 108 1,2-dichloroethane molecules, which were separately equilibrated in two liquid slabs, and then brought into contact to form a box about 4 nm long and of cross-section 2.17 nmx2.17 nm. In a previous study [128], the dynamics of ion transfer were studied in a system including 256 polar and 256 nonpolar diatomic molecules. Solvent-solvent and ion-solvent interactions were described with standard potential functions, comprising coulombic and Lennard-Jones 6-12 pairwise potentials for electrostatic and nonbonded interactions, respectively. While in the first study [128] the intramolecular bond vibration of both polar and nonpolar solvent molecules was modeled as a harmonic oscillator, the next studies [71,75,136] used a more advanced model [137] for water and a four-atom model, with a united atom for each of two... 

Of all the vibrational degrees of freedom of H bonded polymers, the Pff and Pfi are the most interesting. Their force constants are indicative of the potential function which determines the length and angular orientation of the H bond. These force constants, if known, could be used to estimate the degree to which a H bond can be distorted to accommodate other geometrical parameters in an intramolecular H bond (e.g., in a protein). Finally, because these vibrations are the lowest in frequency, they provide an important contribution to the entropy of polymer formation. 

In this article, we have presented a series of LD and MD simulations for ice Ih using a variety of water potentials and the results were compared with INS measured DOS. Neutron measurements were shown to provide unique information on the fundamental intramolecular and intermolecular modes, some of which cannot be obtained from the standard IR and Raman techniques. A full knowledge of the intermolecular vibrations as modulated by the molecule s environment in the lattice systems is necessary for a complete analysis of the dynamics of these ice structures. Equipped with the precise knowledge of the structural information obtained by the diffraction measurements [81,82], one can model the system rigorously with suitable force fields or potential functions. The extensive simulation results show that classic pair-wise potentials were unsuccessful in reproducing the measured DOS for ice Ih. 

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