Here is a nice example of an interesting synthesis, mechanistic explication using computation (with a bit of an unanswered question), and corroboration of the stereochemistry of the product using computed NMR shifts. Gil and Mischne1 reacted dimedone 1 with dienal 2 under Knoevenagel conditions to give, presumably, 3. But 3 is not recovered, rather the tricycle 4 is observed.

There are four stereoisomers that can be made (4a-d). Computed 13C chemical shifts at OPBE/pcS-1 (this is a basis set suggested for computing chemical shifts2) for these four isomers were then compared with the experimental values. The smallest root mean squared error is found for 4d. Better still, is that these authors utilized the DP4 method of Goodman3 (see this post), which finds that 4d agrees with the experiment with 100% probability!

Lastly, the mechanism for the conversion of 3 to 4 was examined at M06/6-31+G**. The optimized geometries of the starting material, transition state, and product are shown in Figure 1. The free energy barrier is a modest 14.5 kcal mol-1. The TS indicates a conrotatory 4πe- electrocyclization. The formation of the C-O bond lags far behind in the TS. They could not identify a second transition state. It would probably be worth examining whether the product of this 4πe- electrocyclization could be located, perhaps with an IRC starting from the transition state. Does this TS really connect 3 to 4?

3

TS

4

Figure 1. M06/6-31+G** optimized geometries of 3 and 4 and the transition state connecting them.

References

(1) Riveira, M. J.; Gayathri, C.; Navarro-Vazquez, A.; Tsarevsky, N. V.; Gil, R. R.; Mischne, M. P., "Unprecedented stereoselective synthesis of cyclopenta[b]benzofuran derivatives and their characterisation assisted by aligned media NMR and 13C chemical shift ab initio predictions," Org. Biomol. Chem., 2011, 9, 3170-3175, DOI: 10.1039/C1OB05109A

(2) Jensen, F., "Basis Set Convergence of Nuclear Magnetic Shielding Constants Calculated by Density Functional Methods," J. Chem. Theory Comput., 2008, 4, 719-727, DOI: 10.1021/ct800013z

(3) Smith, S. G.; Goodman, J. M., "Assigning Stereochemistry to Single Diastereoisomers by GIAO NMR Calculation: The DP4 Probability," J. Am. Chem. Soc., 2010, 132, 12946-12959, DOI: 10.1021/ja105035r

InChIs

1: InChI=1/C8H12O2/c1-8(2)4-6(9)3-7(10)5-8/h3-5H2,1-2H3
InChIKey=BADXJIPKFRBFOT-UHFFFAOYAX

2: InChI=1/C12H12O/c1-11(10-13)6-5-9-12-7-3-2-4-8-12/h2-10H,1H3/b9-5+,11-6+
InChIKey=VFBDYWDOVMUDEB-MPEOSAONBY

3: InChI=1/C20H22O2/c1-15(8-7-11-16-9-5-4-6-10-16)12-17-18(21)13-20(2,3)14-19(17)22/h4-12H,13-14H2,1-3H3/b11-7+,15-8+
InChIKey=IBEGRISKTNRVOU-YQQAFNMCBC

4d: InChI=1/C20H22O2/c1-19(2)11-15(21)17-16(12-19)22-20(3)10-9-14(18(17)20)13-7-5-4-6-8-13/h4-10,14,18H,11-12H2,1-3H3/t14-,18+,20+/m1/s1
InChIKey=VEGSTZFBNRXEAX-WNYOCNMUBZ