# 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** = (

**x**_{0},

**y**_{0},

**z**_{0},...,

**x**_{N−1},

**y**_{N−1},

**z**_{N−1}), and a potential function ƒ(

**), yielding a vector of forces**

*R***= −∇ƒ(**

*F***), identically zero at the minimum energy configuration**

*R*

*R*_{0}. A model of this system will be defined by an approximation ƒ′(

**) to the true potential ƒ(**

*R***), with the model-energy minimized at some configuration**

*R*

*R*_{0}′. 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.

#### Stiff *vs.* floppy molecules:

Most large molecules made by conventional synthesis are floppy