The conformational energy of hindered rotation
in a classical molecular mechanics simulation in the general case is approximated by the equation :
describe a force field with torsion angle
This Demonstration uses a modified version of the potential:
is the energy barrier (kJ/mol) and
are the energy difference gauche(-)/trans and gauche(+)/trans conformers, respectively (kJ/mol).
The effect of excluded volume is neglected in the calculation.
Using the Monte Carlo method, 500 macromolecular chains are generated. For a chain of length
torsion angle values are generated. To simplify the calculation, selection of the torsion angle is performed taking into account the statistical weight based on the cumulative distribution function
, divided into 36 equal intervals with step size 10°. This avoids the calculation of the Boltzmann factor for individual chains:
For each chain, the end-to-end distance
is calculated. The distance is expressed in relative units of carbon-carbon bond length. For visualization, a smoothed function is used to exclude statistical scatter;
values are the result of smoothing and should be ignored.
Based on the distribution, the mean
, root mean square
, end-to-end distance and standard deviation
 M. Bachmann, Thermodynamics and Statistical Mechanics of Macromolecular Systems
, Cambridge, UK: Cambridge University Press, 2014.