March 18, 2008
Rings plus Double Bonds Equivalent (RDBE) (also known as the degree/element of unsaturation or index of hydrogen deficiency) can be determined from a Molecular Formula (MF). The calculation provides insight into the number of rings and/or double bonds and/or triple bonds to expect from an unknown structure.
RDBE = (# of C) + 1 – (# of H)/2 + (# of N(III))/2
For example C5 H9 N1 O1: RDBE = 5 + 1 – 4.5 + 0.5 = 2
Since bivalent atoms such as O and S are not counted in the formula, another way to write it is as follows:
RDBE = (# of Valence IV) + 1 – (# of Valence I)/2 + (# of Valence III)/2
Note: Since this formula will fail for MFs with higher valence states such as N(V), P(V), S(IV) or S(VI), the rest of this blog will focus on the lowest valence state for these elements. For more information on how the formula fails, I recommend reading the following blog by Oliver Fiehn’s group: http://fiehnlab.ucdavis.edu/projects/Seven_Golden_Rules/Ring-Double-Bonds/
An RDBE of 1 indicates that the MF has either 1 ring or 1 double bond present. If NMR data is available and it shows one or two sp2 carbons are present, then one can rule out the ring possibility and therefore only a double bond(s) is present. An odd value for the RDBE with an odd count of sp2 carbons can indicate the presence of an allene (C=C=C) group with 3 sp2’s or a carbonyl group (C=O) with 1 sp2.
Tip: A benzene ring, a carbonyl and a triple bond have an RDBE of 4, 1 and 2, respectively.