New Method for Calculation of the Exact End-to-end Distance Distributions for the Freely-rotating Chain

The following contains mathematical formulae and symbols that may become distorted in ASCII text format. We present an efficient method to calculate the exact end-to-end distance distribution for a freely rotating chain. The method is based on the recursive calculation of the probability density function P(rn) for a pair of distances between atoms 1 and n, and 1 and n-1, respectively. The probability density function P(rN) for the end-to-end distance is evaluated from the last pair function P(rN,rN-1) by a single integration. The cost of the method scales linearly with the chain length. The method is especially useful for intermediate length chains for which the gaussian approximation is far from reliable.