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The geometries of stiff molecular structures are relatively insensitive to details of the potential energy function

The effect of differences between a model function and physical reality can be described as the effect of a perturbing force field on the model: Consider an N-atom molecular system with configurations specified by a vector of atomic coordinates R = (x0, y0, z0,..., xN−1, yN−1, zN−1), and a potential function ƒ(R), yielding a vector of forces F = −∇ƒ(R), identically zero at the minimum energy configuration R0. A model of this system will be defined by an approximation ƒ′(R) to the true potential ƒ(R), with the model-energy minimized at some configuration R0′. Since the true potential ƒ ≡ &fnof′ + (ƒ − &fnof′), the true potential can be regarded as the sum of the model potential and an additive potential corresponding to the perturbing force field −∇(ƒ − &fnof′).

Viewing errors as perturbing forces makes clear the difference in sensitivity between stiff and floppy molecular systems. In conformationally flexible systems, a modest perturbing force can cause rotation around a bond, resulting in gross changes in geometry. In stiff, stable systems, all motions are opposed by restoring forces, and displacements are inversely proportional to stiffness for a given perturbing force. Stiff systems are less sensitive to the perturbing forces corresponding to model errors.