Rigid geometry approximation

K. A. Palmer and H. A. Scheraga, J. Comput. Chem., 12, 505 (1991). Standard-Geometry Chains Fitted to X-ray Derived Structures Validation of the Rigid-Geometry Approximation. I. Chain Closure Through a Limited Search of Loop Conformations. 

Figure 3.2. Calibrated set of van der Waals radii for peptide backbone for use with rigid geometry approximation (109). Usual radii shown in parentheses. Carbonyl carbon not modified.

In this simple example, the atoms in an aggregate are all either directly bonded or have a 1-3 relationship (i.e., are related by a bond angle). Because of the rigid geometry approximation, their relative positions are fixed. Atoms contained within the same aggregate do not, therefore, have to be included in the set of those that undergo VDW checks for each con-... 

K. A. Palmer, H. A. Scheraga. Standard-geometry chains fitted to X-ray derived structures Validation of the rigid-geometry approximation. I. Chain closure through a limited search of loop conformations./. Comp. Chem. 1990, 12, 505-526. 

The thermodynamic properties were computed with the molecular geometry and vibrational frequencies given above assuming an ideal gas at 1 atm pressure and using the harmonic-oscillator rigid-rotor approximation. These properties are given for the range 0-2000°K in the Appendix (Table AI). 

The testing of a rigid-sphere approximation must however be logically consistent, and if the anions are big enough they must be in anion-anion contact. The geometry of this is well-known (7) from the halide-radii just obtained from potassium salts, the anions should be in contact in lithium bromide and iodide conversely from their experimental anion-anion distances one would infer for r ... 

The simplest approach to modeling rotational spectroscopy is the so-called rigid-rotor approximation. In this approximation, the geometry of the molecule is assumed to be constant at the equilibrium geometry qeq. In that case, V(qeq) in Eq. (9.37) becomes simply a multiplicative constant, so that we may write the rigid-rotor rotational Schrodinger equation as... 

Less symmetric molecules require a considerably more complicated treatment, but in the end their spectral transitions arc functions of their three moments of inertia (see Section 10.3.5). From a computational standpoint, then, prediction of rotational spectral lines depends only on the moments of inertia, and hence only on the molecular geometry. Thus, any method which provides good geometries will permit an accurate prediction of rotational spectra within the regime where tlie rigid-rotor approximation is valid. 

---