It's got an extra interaction to calculate, so it's more computationally expensive. If U-B gives a better physical description for certain interactions, as in CHARMM, then that's the functional form of the angles. If not, the force field is parametrized using a "normal" harmonic function, which is cheaper.
Look at the functional form of the force field. A force field that includes U-B terms to describe a 1-3 interaction simply adds a harmonic potential that other force fields don't. In a force field like CHARMM that uses U-B, an angle is described by a harmonic term (like just about all force fields) as well as the U-B term. Other force fields simply don't use U-B and therefore it's one less quantity to compute.
Yes, here are excellent opportunities for overfitting. But why do not use instead of, not as addition?
Indeed, it looks like a historic choice. And I also do not know why and when it was done.
In the CHARMM force field, U-B terms have been used to improve agreement with vibrational spectra when a harmonic term alone would not adequately fit. Indeed the U-B form is not common, but as Jason says, it's certainly not "abandoned." It creates one more layer of complexity in the fitting procedure, though it's not terribly hard to do.
If you look more carefully on what is actually used in the AMOEBA force field (let's take water as an example), you will notice that the Urey-Bradley term is used in addition (not instead!) to the angle bending term. As far as I inderstand, the Urey-Bradley term was (and is) used to mimic the influence of the stretch-stretch and stretch-bend off-diagonal terms on (harmonic) vibrational frequencies. Basically, one can project the cartesian Hessian matrix, calculated ab initio at the optimized geometry, onto any set of internal coordinates (redundant or not) and then fit the intramolecular force field parameters directly. Either Urey-Bradley terms or off-diagonal (stretch-stretch and stretch-bend) terms as the two alternatives can be parametrized. Recently, we have published a paper where such an approach is described in detail:
http://pubs.acs.org/doi/abs/10.1021/jp807487f
just to add to my previous answer. The issue on two alternatives (Urey-Bradley term vs stretch-bend cross-term) is nicely explained in the book of Norman Allinger (p. 66):
Molecular Structure: Understanding Steric and Electronic Effects from Molecular Mechanics:
http://books.google.de/books?id=SzpeidfI8MwC&printsec=frontcover&hl=de#v=onepage&q&f=false
Sorry for resurrecting a long-dead thread - just wanted to add my 2 cents. As pointed out before, the computational cost is not a significant consideration in favor or against UB terms. With that out of the way, the only *advantage* of UB terms is the better reproduction of subtleties in the vibrational spectrum, as explained in Maxim Tafipolski's post. *However*, this advantage is not as big as it seems, as the phenomena a UB term is expected to capture are largely inconsequential for the overall conformational sampling in a typical biomolecular/organic simulation. Conversely, the disadvantages are:
(1) Encumbering the force field parametrization process and making it more underdetermined (as mentioned before).
(2) Poorly transferable! (Because the 1-3 distance can be very different for the same central atom (2) in the same hybridization state.)
For a general force field for organic molecules, disadvantage (2) trumps all other considerations; therefore, we have a standing order not to introduce any new UB terms in the CHARMM General Force Field (CGenFF). It does contain a good number of existing UB terms that were transfered from biomolecular model compounds and would be prohibitively laborious to re-optimize, but I consider them a liability. To be clear, the impact of a poorly transfered UB term is expected to be modest compared to a badly guessed charge or dihedral, but I still would be happier without them.
Of course, in a highly specialized force field for biomacromolecules, disadvantage (2) is much less of an issue, though there's still disadvantage (1), and the fact that the advantage is modest...
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