degree of unsaturation.” The hydrogen deficiency index is

Hydrogen Deficiency IndexSame as "degree of unsaturation.”The hydrogen deficiency index is the number of molecules of H 2 which would have to be added to themolecule of interest to convert it to a saturated (ie., no pi bonds), acyclic compound. This number isequal to the number of pi bonds plus the number of rings present in the molecule of interest. Someexamples below show how we can deduce HDI from a molecular formula and use this number to generateisomers of that formula. First we calculate a "maximum" number of hydrogens as though the moleculewere saturated and acyclic; then we subtract from this the "actual" number of hydrogens (halogens countas hydrogens, too). Notice that each carbon adds 2 to the HDI since carbon has valence of 4; eachnitrogen (valence = 3) adds 1; oxygen (valence = 2) adds nothing; and halogens (valence = 1) are treatedas though they were hydrogens (valence also 1).1) C 5 H 8 2n + 2 = 2x5 + 2 = 12 maximum; 12 max - 8 actual = 4 H = 2 H 2 ; HDI = 2some possible isomers:C H C C H 2 C H 2 C H 32) C 5 H 8 O 2n + 2 = 2x5 + 2 = 12 maximum; 12 max - 8 actual = 4 H = 2 H 2 ; HDI = 2Notice how we apply same method disregarding O to get the HDI.some possible isomers:OOHOOHOH3) C 6 H 11 Br 2n + 2 = 2x6 + 2 = 14 maximum; 14 max - 12 actual = 2 H = 1 H 2 ; HDI = 1Notice how the halogen (F, Cl, Br, I) is counted as a hydrogen (12 not 11).some possible isomers:BrC H 2 BrBrC H 3BrBr

4) C 4 H 9 N 2n + 2 + 1 = 2x4 + 2 + 1 = 11 maximum; 11 max - 9 actual = 2 H = 1 H 2 ; HDI = 1For each N present the maximum # of hydrogens is increased by 1.some possible isomers:NHNH 2C H 2C HNHCH 3C HC HC H 3 2NCH 2 C H 35) C 6 H 11 ClN 2 O 2 These rules hold simultaneously, of course:2n + 2 + 2 = 2x6 + 2 + 2 = 16 maximum; 16 max - 12 actual = 4 H = 2 H 2 ; HDI = 2some possible isomers:Cl OOOH 2 NNH 2H 2 NONH 2ClCl OClClOCO -NH 2ONHOHNNH+ 32In polycyclic compounds the number of rings is considered to be the minimum number of sigma bondsone must break to arrive at an acyclic structure; below are shown some examples where the dotted line isan imaginary bond cleavage:same as:same as:decalin;2 rings (bicyclic)HDI = 2; C 10 H 18norbornane;bicyclicHDI = 2; C 7 H 12norbornene;bicyclicHDI = 3; C 7 H 10adamantane;tricyclicHDI = 3; C 10 H 16