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The Audier-Stevenson Rule: 2,6-dimethyl-2-heptene Howard Park BACKGROUND The Audier-Stevenson Rule states that in mass spectrometric fragmentation producing a positive ion, the fragment with the higher ionization energy (IE) will preferentially retain the unpaired electron. This would be shown by lower energy cation fragments having higher intensity peaks on a mass spectrum. Through looking at the energies of two particular fragmentations of compound 2,6-dimethyl-2- heptene, we will test the validity of the Audier-Stevenson Rule under conditions where the charged fragment may rearrange. Therefore, if the Audier-Stevenson Rule is correct, it is expected that the fragment with the lower IE will always be more pronounced in a mass spectrum, even when rearrangement takes place. Equation 1A – Reaction producing the m/z 69 cation. vibrational energy difference was 3.9 kJ/mol, both favoring the m/z 57 fragmentation. m/z 69 m/z 57 (t-bu+) m/z 57 (s-bu+) Total E el (a.u.): -353.567001 -353.587552 -353.5410503 Total ZPE (kJ/mol): 628.9 625.0 653.5 Net Relative ∆H 0K (kJ/mol): 0 -57.9 +92.7 Table 1. DFT values of electronic (Eel) and zero point (ZPE) energies for possible reaction pathways Considering the relatively large energy difference between the two fragmentation possibilities, with the rearranged cation m/z 57 being favored (both electronically and vibrationally), the Audier-Stevenson Rule would predict the intensity of the m/z 57 peak to be significantly higher than that of the m/z 69. However, we find that this is not the case experimentally, as shown by the published mass spectrum reproduced below in Figure 1. Although the observed relative intensities in Figure 1 could possibly be the result of subsequent dissociations, this seems unlikely; after taking into account possible dissociations to and from m/z 57 and m/z 69, m/z 69 would still have a higher density. Equation 1B – Reaction producing the m/z 57 tertbutyl cation. the intensity of the m/z 57 peak to be significantly higher than that of the m/z 69. However, we find that this is not the case experimentally, as shown by the published mass spectrum reproduced below in Figure 1. Although the observed relative intensities in Figure 1 could possibly be the result of subsequent dissociations, this seems unlikely; after taking into account possible dissociations to and from m/z 57 and m/z 69, m/z 69 would still have a higher intensity. Equation 1 shows ionic fragmentation of 2,6-dimethyl-2- heptene (mass 126) following electron ionization (EI), 1A being the m/z 69 pathway and 1B being the m/z 57 pathway. Below each structure is its electron energy (Eel) and zero point energy (ZPE) calculated using Density Functional Theory (DFT) by means of the Gaussian09 Program (B3LYP/ cc-pVTZ) . Table 1 lists the sums of the combined energies for both equations. The electronic energy difference between the two fragmentation pathways was 54.0 kJ/mol, and the Figure 1. DFT values of electronic (Eel) and zero point (ZPE) energies for possible reaction pathways Though it seems that the Audier-Stevenson Rule is contradicted by the experimental data, there exists another explanation that involves two different isomers of the m/z 57 cation formed directly from fragmentation. The two conformations of the isobutyl fragment prior to any rearrangement are shown in Figure 2. 2 0 U C R U n d e r g r a d u a t e R e s e a r c h J o u r n a l
The Audier-Stevenson Rule: 2,6-dimethyl-2-heptene Howard Park Unsymmetrical Conformation Symmetrical Conformation Figure 2. The symmetrical and unsymmetrical conformations of an isobutyl cation Considering the concept that a migrating bond must be parallel (or antiparallel) to a vacant p-orbital, an unsymmetrical conformation would rearrange to produce a tert-butyl cation and the symmetrical conformation would produce a sec-butyl cation. Figure 3 shows the energy comparisons of the neutral 2-6-dimethyl-2-heptene conformations that lead to the two isobutyl conformations. The calculations showed that the unsymmetric conformation was more favorable by 12.0 kJ/mol electronically and by 0.3 kJ/mol vibrationally. Friedman’s research has shown experimentally that a cation resulting from an isobutyl structure could rearrange to give a mixture of tert-butyl and sec-butyl cations (shown as the carbocation products in equation 2A and 2B, respectively). An unsymmetrical isobutyl cation, by rearrangement, presumably yields a sec-butyl cation. Our calculations showed that conformer B (unsymmetrical) was more stable than conformer A (symmetrical) by 0.6 kJ/ mol, corresponding to Keq=2.2 (taking into account that B has two enantiomorphs). Equation 2A – The reaction of symmetric (CH3)2CHCH2-N≡N+ and its energy. Unsymmetrical Conformation Symmetrical Conformation Equation 2B – The reaction of unsymmetric (CH3)2CHCH2-N≡N+ and its energy. E el (a.u.): -353.929672 -353.925093 ZPE (kJ/mol): 653.2 653.5 Figure 3. The symmetrical and unsymmetrical conformations of the neutral starting material and their electronic (Eel) and zero point vibrational (ZPE) energies The calculated equilibrium constant at 300K between these two neutral conformers was Keq=0.006, with >99% of the conformations being unsymmetric. Even after ionization the electronic energy of the unsymmetrical cation is favored over the symmetrical cation. The calculated equilibrium explains how an unsymmetric isobutyl cation might rearrange into a sec-butyl cation. Friedman reports that (CH3)2CHCH2-N≡N+ in ethylene glycol solvent yielded over one-third of its hydrocarbon products from an intermediate sec-butyl cation. Therefore the m/z 57 pathway might not produce the tert-butyl cation, but rather the higher energy sec-butyl cation due to the unsymmetrical preference of the isobutyl group in the neutral starting material, as expressed in Figure 3. Considering that tert-butyl cation may not be produced U C R U n d e r g r a d u a t e R e s e a r c h J o u r n a l 2 1
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