Urey-Bradley potential

An improvement on the valence-force function is the Urey-Bradley potential function, which adds terms to the valence-force function to represent the van der Waals forces between nonbonded atoms. 

The SVFF approach is rougher but physically more significant it neglects all interactions and gives six force constants Fr (CN), Fr (MC) Fa (MCN in-plane), F j (CMC in-plane) F (MCN out-of-plane), F (CMC out-of-plane). In the Ni(CN)4 case, the two potential functions have led to almost similar values. The Urey-Bradley potential function is more sophisticated and has sometimes been used, but it only takes into account the repulsion between neighbouring C or N atoms, which is not the main one. All results from the literature and from our own work are compared in Table 4. 

Because of their small magnitudes, all off-diagonal force constants are ignored. The Urey-Bradley force field (10) takes into account 1-3 nonbonded interactions, Eq. (5). If/,/, and/" are harmonic force constants, then the Urey-Bradley potential is given by... 

In a Urey-Bradley force field, angle bending is achieved using 1,3 non-bonded interaction rather than an explicit angle-bending potential. The stretch-bond term in such a forci field would be modelled by a harmonic function of the distance between the 1,3 atoms ... 

The potential energy expressions used for force field calculations are all descendants of three basic types originating from vibrational spectroscopy (5) the generalized valence force field (GVFF), the central force field, and the Urey-Bradley force field. General formulations for the relative potential energy V in these three force fields are the following ... 

A potentially much more adaptable technique is force-field vibrational modeling. In this method, the effective force constants related to distortions of a molecule (such as bond stretching) are used to estimate unknown vibrahonal frequencies. The great advantage of this approach is that it can be applied to any material, provided a suitable set of force constants is known. For small molecules and complexes, approximate force constants can often be determined using known (if incomplete) vibrational specha. These empirical force-field models, in effect, represent a more sophisticated way of exhapolating known frequencies than the rule-based method. A simple type of empirical molecular force field, the modified Urey-Bradley force field (MUBFF), is introduced below. 

The success of the ligand-ligand repulsion model prompted its adoption as an element of a molecular mechanics program. In the resulting approach the valence angles around the metal ion are modeled solely by nonbonded interactions, using the usual van der Waals potential (for example, Eq. 2.9 kg = 0 in Eq. 2.7 Urey-Bradley approach)136. 6 Again, the fact that the electronic effects responsible for the directionality of bonds are not explicitly modeled here may seem questionable but extensive tests have shown the model to be reliable 371. An explanation for this apparent contra-... 

Intimately connected to the choice of bending parameters is the choice between a general valence force (GVFF) expression (including a stretch-bend interaction) or a UBFF representation. The necessity for the inclusion of either a stretch-bend or a Urey-Bradley term to account for the abnormally long bonds in e.g. norbomane was pointed out by several authors 17,22,31), Several representations have been proposed normal non-bonded interactions 24) the classical UB expression 21) and whittled atoms 7,31,56) (smaller radii in the direction of the geminal atoms), but a further theoretical analysis of the UB potentials seems mandatory. 

Simultaneously, de Vos Burchart and van de Graaf constructed a molecular mechanics force field for modeling silicate structures. The Si-0 bond potential was described by a Morse function, whereas a Urey-Bradley term... 

Many such model force fields have been discussed in the literature. [For general discussions, see Herzberg (1945), Wilson et al. (1955), Woodward (1972), and Califano (1976). For discussions of the Urey-Bradley force field, see the review by Duncan (1975). For discussions of the entirely different consistent force field approach, see Lifson and Warshel (1968), Warshel et al. (1970), and Burkert and Allinger (1982).] We have chosen to use a simplified general valence force field (SGVFF), which has been defined as one which contains the minimum possible number of interaction constants compatible with a good fit of the spectra (Califano, 1976). Such a force field has been demonstrated to be very effective for hydrocarbons (Schachtschneider and Snyder, 1963). For this form the potential energy of Eq. (63) is written explicitly as... 

In the original molecular mechanics work, a steric energy, E, for a molecule was defined as the sum of the potentials for bond stretch, angle bend, Ee, torsional strain, E, nonbonded interactions, Ey f, and other terms, such as Urey-Bradley terms, cross-interaction terms, and electrostatic terms, (8). 

In another approach, Shimanouchi [82] introduced the Urey-Bradley force (UBF) field, which consists of stretching and bending force constants, as well as repulsive force constants between nonbonded atoms. The general form of the potential field is given by... 

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