symbol: $\lt\!r_{\rm{o}}^{2}\! \gt$; units: $\pu{nm2}$, $\pu{m2}$
https://doi.org/10.1351/goldbook.12199
Mean-square end-to-end distance of a chain having unperturbed dimensions.
Note: \(\lt\!r_{\rm{o}}^{2}\! \gt\) of a hypothetical, sufficiently long, linear chain of identical single skeletal bonds having rotational isomeric states that are independent of each other is given by the equation \[\lt\!r_{\rm{o}}^{2}\!\gt = nl^{2} \frac{(1 + \cos\theta)}{(1 - \cos \theta)} {\cdot} \frac{(1 + \lt\!\cos \phi\!\gt )}{(1 - \lt\!\cos \phi\!\gt)}\] where \(n\) is the number of skeletal bonds of length \(l\) and valence-angle supplement \(\theta\), and \(\lt\!\cos \phi\!\gt\) is the average of the cosine of the dihedral angles \(\phi\) defined over sequences of three contiguous skeletal bonds. This equation is useful for understanding the significance of characteristic ratio, steric factor, and effective bond-length.