Force-field representations

The fiuid-phase simulation approach with the longest tradition is the simulation of large numbers of the molecules in boxes with artificial periodic boundary conditions. Since quantum chemical calculations typically are unable to treat systems of the required size, the interactions of the molecules have to be represented by classical force fields as a prerequisite for such simulations. Such force fields have analytical expressions for all forces and energies, which depend on the distances, partial charges and types of atoms. Due to the overwhelming importance of the solvent water, an enormous amount of research effort has been spent in the development of good force field representations for water. Many of these water representations have additional interaction sites on the bonds, because the representation by atom-centered charges turned out to be insufficient. Unfortunately it is impossible to spend comparable parameterization work for every other solvent and... 

The chemical shieldings were then recalculated in this same system using the QM/MM method [10], To this end, each molecule was considered individually. The water molecule of interest and its first solvation shell were treated quantum mechanically, whereas the surrounding water molecules were taken into account with an empirical force field representation (MM molecules). The first solvation shell was defined via a distance criterion on the oxygen-oxygen distance. As a threshold, the first minimum of the O-O pair correlation function was taken this occurs at 3.5 A [93]. All... 

In 1996 a force field model was proposed in which geometry-dependent charges are calculated by EEM. This model, called consistent implementation of the electronegativity equalization method (CIEEM), combines a force field representation for the PES (e.g., Eq. [19]) with the EEM equation for the electronic energy (Eq. [7]) in such a way that the atomic terms of Eq. [7] explicitly enter the expression for the potential energy. Thus, within the CIEEM, the expression for the steric energy in the MM force field model will read... 

INS experiments evidence decoupling of the proton bending modes from carbonate entities [Fillaux 1988 Kashida 1994], Simulations of the spectral profile with valence-bond force-field models based on infrared and Raman spectra [Nakamoto 1965], yield spectacular differences between observation and calculations. Discrepancies arise from the force-field representation itself and cannot be eliminated by straightforward adjustment of the force constants. The model protons, bound to oxygen atoms by strong forces, ride displacements at low frequency of carbonate entities, mainly below 200 cm-1. Calculated intensities for these lattice modes are overestimated by at least one order of magnitude. 

One old difficulty of nuclear motion computations for larger systems, namely the representation of PESs, plagues applications of even the most sophisticated procedures. While low-order force fields [68,69] may not provide a good representation of the PES for systems undergoing large-amplitude motions, for many systems of practical interest an anharmonic force field representation of the PES should provide at least the first important stepping stone to understand the complex internal dynamics of the system at low energies. 

The complexes formed, however, are too hydrophilic to leave the aqueous phase, in contrast to what was observed with the other macrocylic complexes. A close examination reveals that this may be related to deficiences in the force field representation of the U02(N03)2 salts, as the structure of U02(N03)2(TBP)2 is far from the D2h one, more hydrophobic, characterized in the solid state ... 

The above representation of external forces combined with the chemical potential force for molecules or ions is quite useful for those external force fields representable by the negative of the gradient of their scalar potentials. We indicate in Table 3.1.1 the value of for 1 gmol of the ith species for a few cases. For magnetic and nonuniform... 

Experimental information alone, apart from extreme cases, is insufficient to uniquely determine even the harmonic force field of polyatomic molecules. Severe difficulties are encountered if vibrational anharmonicity is considered. Since accurate anharmonic force field representations of PESs are of considerable interest in many branches of chemical physics, independent information obtainable from electronic structure calculations on the force fields is of considerable practical importance. 

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