Urey-Bradley function

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 ... 

A selection of bond stretching force constants, G, taken from the literature is plotted in Fig. 9.2 as a function of the bond valence, S. What is surprising is not that there is some scatter (this is expected from the crudeness of the Urey-Bradley force field) but that an expression such as eqn (9.5) gives such a good fit ... 

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. 

Figure 13. Calculated v(M—S) frequencies for trigonal-prismatic MS6 unit as a function of trigonal-twist distortion. Calculation based on a Urey-Bradley force field for M = Nb with the bidentate bite b = 1.31, K° = 1.57 mdyn A-1 and F = 0.22 mdyn A-1. [Reprinted with permission from K. Tatsumi, I. Matsubara, Y. Sekiguchi, A. Nakamura, and C. Mealli, Inorg. Chem., 28, 773 (1989). Copyright 1989 American Chemical Society.]...

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... 

The functions are similar to those calculated by Hisatsune (5) based on the analysis of Devlin and Hisatsune (6) of the Raman and infrared spectra in terms of Urey - Bradley force constants. Devlin and Hisatsune used observed isotopic shifts in the spectra along with force constants transferred from nitrogen oxides and oxyhalides in order to select the N-N bond distance and the 0-N-N bond angle. 

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. 

DFT, density functional theory NCA, normal coordinate analysis GVF, generalized valence force field UBF, Urey-Bradley force field. 

In early applications of the molecular mechanics method, an evident difficulty was that when the simple expression 2.6a was used, force constants were not transferable even among closely related systems. It was soon realized that the influence of some interaction between atoms not bound together but bound to the same atom (the geminal or 1-3 interactions) or, more generally, also between all other non-bonded atoms, had to be somehow considered. These supplementary non-bonded terms were to represent the change in chemical environment that could not be accounted for when using completely transferable force constants. The Urey-Bradley force field adds these interactions to a valence force field that includes only diagonal terms [4]. For application to molecular mechanics calculations, these non-bonded interactions were simulated by some function of the interatomic distance ... 

Another line of attack upon molecules which resist treatment by simple potential functions was opened by Urey and Bradley who proposed the use of a mixed potential function, that is, a function which is basically of the valence force type, but which includes in addition some (jentral force terms between nonbonded atoms. In physical terms, this sort of potential function seeks to take into account the van der Waals forces between the nonbonded Y atoms. Thus, for a tetrahedral XY4 molecule, the potential function is assumed to have the form ... 

---