  In this paper, the looping kinetics of a long polymer chain in solution has
been investigated by using two state model, where one state represents open
chain polymer molecule and the other represents closed chain polymer molecule.
The dynamics of end-to end distance of both open chain and closed chain polymer
is represented by a Smoluchowski-like equation for a single particle under two
different harmonic potentials. The coupling between these two potentials are
assumed to be a Dirac Delta function in our model. We evaluate two rate
constants, the long term and the average rate constant. We have also
incorporated the effect of all other chemical reactions involving at least one
end of the open chain polymer molecule - on rate of end-to-end loop formation.
The closed chain polymer molecule can be converted to a open chain molecule by
breaking of any bond - the effect of this reaction on the rate of end-to-end
loop formation is also considered in our model.
