Urey-Bradley terms

Witir the correct choice of the parameters k and the ah initio data in Figure 4.50 could be reproduced very well. In this force field a Urey-Bradley term was also included between the silicon atoms in such angles to model the lengthening of the Si—O bond as the angle decreased. 

Improper and Urey-Bradley terms 4C) Condensed phase simulations... 

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... 

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). 

Here / and / are two bonds that are joined to a common atom, and 0 is the angle between those two bonds. For bonds not attached to a common atom, is zero. A Urey-Bradley term may also be used to explicitly account for the repulsion between the two atoms bound to a common atom, as in Eq. [14],... 

If atoms are bound to a common atom, one wonld expect a van der Waals interaction between than. However, if this interaction were included explicitly, since the atoms are quite close together (2-3 A), one wonld have to be carefnl abont the exact shape of this curve to get a correct energy variation with the vibrational motion. A first approximation would be just to find the minimum energy point and add the Urey-Bradley term (the harmonic approximation). And this is a reasonable approximation. But the mathonatics is more simple if one uses a stretch-bend term rather than a Urey-Bradley (UB) term. So this stretch-bend term is important, even in hydrocarbons, and it is easy to see why in the UB model. It is almost as easy to see why in the stretch-bend model. When we need a cross term in the F matrix, it is because the two diagonal elements are not completely independent. That is, they interact. That interaction can be well represented in the present case by just linear terms as in Eq. (4.7). (If the linear terms were to be inadeqnate by themselves, quadratic or higher terms could also be added, but these are not needed here or in most of molecular mechanics.)... 

MOLEC KJELD <-l Torsional and Urey-Bradley terms are included in the computation of total energy. 

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