What does "the natural bond angle" mean in the context of Universal Force Field (UFF) potential energy calculation and how are bond angles calculated?

Question

As the title says, what does "the natural bond angle θ₀" mean in the context of Universal Force Field (UFF) potential energy calculation? The reference appears in section D. Angular Distortions, 1. Angle Bend). The article also talks about "natural bond length" (Section C. Bond Stretch).

I am curious about how molecular dynamics (MD) simulations estimate/calculate bond angles using the Universal Force Field.

At several points in the original UFF paper they mention a "natural angle" but it is not overwhelmingly clear to me what this means. Is it the empirically observed bond angle(s) in particular molecules? How do MD simulations, then, produce bond angles for molecules that there is no published data for?

I understand that the UFF potential energy calculation contains several terms that account for various properties like hybridization, van der Waals interactions, etc. Which of the terms, which are outlined in the first pages, account(s) for steric interactions between molecules and determine the final bond angles?

I am admittedly not very well versed in the types of maths that are involved, but I would appreciate any explanation possible.

Answer 1

The original article on UFF is from 1992, so it is somewhat dated. The selection of "natural bond" values is explained on page 10028:

a. Standard Bond Angles. The natural angles for the group 15, 17, and 18 main group elements are obtained from standard reference structures of the parent hydrides. Thus 0-3 has Bo = 104.5' from HzO, while S3 has Bo = 92.2' from HzS. Exceptions include 0-32, OR, and N-2. The bond angles for 0-32,O-R, and N-2 are fit to (C13Si)z0, methyl vinyl ether, and dimethyl- diazene angles of 146O, 118.3', and 112.3', respectively. Where structural data are unavailable, the natural angles are extrapolated from the element above it in the periodic table. The remaining elements are all assumed to have regular octahedral, tetrahedral, trigonal, or linear structures. The natural angles are collected in Table I.

So yes, the angles are selected from experimental geometries where available, or where not by extrapolation from geometries for compounds in the same group.

References

1. A. K. Rappe et al.. UFF, a Full Periodic Table Force Field for Molecular Mechanics and Molecular Dynamics Simulations. J. Am. Chem. Soc. 1992, 114, 10024-10039.