Moments of the End-to-End Vector of a Chain Molecule, Its Persistence and Distribution

The persistence vector a is defined as the configurational average of the chain vector r connecting the ends of the molecule and expressed in a reference frame fixed with respect to the first two skeletal bonds. Moments of second and higher orders in the components of r may readily be calculated for real chains in the rotational isomeric state approximation, and from them the corresponding moments of the vector rho = r - a measured from the terminus of a. Development of the density distribution of rho about a is proposed as an alternative to the customary treatment of the density distribution of r about r = 0 on the assumption that this latter distribution should be (approximately) symmetric. Past difficulties in the analysis of cyclization equilibria involving rings of moderate size, such as occur in single strands of polynucleotide chains, conceivably may be overcome by adoption of this alternative.