¹³C-¹H Coupling Constants:
Determining Hybridization in Strained Alkanes

Carbon-13 NMR spectra are often collected in a decoupled mode so that the number of peaks corresponds to the number of unique carbon atoms. The coupling, of course, contains valuable information that need not be thrown away. Qualitatively, the multiplicity of each peak provides the number of attached protons (the "N+1 Rule"). Quantitatively, the coupling constant, ¹J_CH, is related to the s-character of the C-H bond. Coupling is thought to arise from Fermi contact at the nucleus. Higher s-character increases this contact and, therefore, increases the size of the coupling constant.

Most carbon sigma bonds have predictable hybridization. For instance, the C-H bonds in 4-ethynyltoluene are sp³, sp², and sp hybridized, as indicated. Not all hybridizations are equally predictable and the purpose of this laboratory is to determine the hybridization of carbon in strained rings. For instance, cyclobutane cannot have maximum orbital overlap in it's C-C bonds if the hybridization remains sp³. There are two possible bonding schemes for the bonding of cyclobutane (see table below). Either or both of these bonding schemes may help cyclobutane make C-C bonds with C-C-C angles much less than 109.5°.

Bonding Scheme 1: In the first bonding scheme, one would argue that the C-C sigma bonds in strained cycloalkane rings should not be completely sp³ hybridized like other alkanes. Maximum electron density can lie directly between the carbon atoms by using unhybridized p orbitals to make sigma bonds at 90° angles within the ring framework. If two p orbitals were used to make the C-C bonds, the remaining C-H bonds would be made from the remaining orbitals, one s and one p orbital, so they each would need to be sp hybridized.

Bonding Scheme 2: On the other hand, the sigma bond framework of strained cycloalkanes need not be made up of bonds whose electron density lies directly between the nuclei (in fact this is impossible for cyclopropane because the internuclear angles are less than 90 degrees). The second bonding scheme suggests that "banana bonds" allow strained rings to form without any change in hybridization. The disadvantage to banana bonding is the energetic cost in moving the electron density off center (a typical C-C sigma bond with electron density between the nuclei has a Bond Dissociation Enthalpy around 100 kcal/mol while C-C π bonds, with overlap above and below the internuclear plane, is less than 70 kcal/mol).

Two Bonding Schemes for Strained Ring Bonding
Scheme 1	Scheme 2
pure p orbitals for C-C bonds	"banana bonds" made from sp3 hybrids
provide a 90° bond angle C-H bonds must be sp hybridized (180° angle).	all C-C and C-H bonds are made from sp3 hybrids sp3 hybrids point 109.5° apart and the C-C bonds do not have highest density between the nuclei.
C-C bonds made from pure p orbitals (0%s) x 2 = 0% s C-H bonds made from sp hybrids (50%s) x 2 = 100% s	C-C bonds made from sp3 hybrids (25%s) x 2 = 50% s C-H bonds made from sp3 hybrids (25%s) x 2 = 50% s

Either one or both of these bonding schemes may explain the bonding in cyclobutane but the acute angle in cyclopropane requires use of the banana-bond model to some extent. The bonding in cyclobutane and cyclopropane will probably lie in between the two extremes of "banana bonding only" (all bonds sp³) and "pure p" C-C bonding (C-H bonds sp hybridized). Thus the C-C bonds should contain between 25% s character (sp³ hybrids) and 0% s character (pure p orbitals). The C-H bonds would contain between 50% s character (sp hybrids) and 25% s character (sp³ hybrids).

The hybridization need not be a nice round number. Let's work through an example of how one would calculate the hybridization of the C-H bonds if we know the %s character. Let's suppose the %s character in the cyclobutane C-H bonds is 30%. Since all four bonds on any one carbon atom must use up all four atomic orbitals, it is an easy matter to calculate the %s character of the C-C bonds [(100%-(30% x 2))/2 = 20% s-character in the C-C bonds] or the hybridization of the C-H bonds [sp^x, where x = (%p)/(%s) = (100%-%s)/(%s)] of sp^2.3 in this example.

In this experiment we will use the values of ¹J_CH in cyclopropanecarboxylic acid and cyclobutanecarboxylic acid to determine the %s character in these strained ring systems. First, however, we must correlate the %s character versus ¹J_CH using a model system with known C-H hybridization of sp³, sp², and sp (4-ethynyltoluene). Using a plot of %s character versus ¹J_CH for these three types of C-H bonds should allow assignment of the %s character in a compound with unknown hybridization.

Procedure:

Spectra will need to be collected for three different chemicals: 4-ethynyltolueone, cyclobutanecarboxylic acid, and cyclopropane carboxylic acid. We will divide up the work so that each person in the class collects spectra for only one chemical. We will prepare a sample in CDCl₃ for the class and share these samples. You will need to collect a decoupled spectrum using 32-64 scans for each chemical to help assign the peaks positions. The coupled spectra (or, if you don't nevermind no double negatives these would be called the "undecoupled spectra") take longer but since these spectra contain all our data it is essential to have multiple spectra for the standard, 4-ethynyltoluene. The class will collect:

• three or four independent coupled (undecoupled) spectra of 4-ethynyltoluene so that we can have an accurate calibration curve.
• three independent spectra of cyclopropanecarboxylic acid.
• three independent spectra of cyclobutanecarboxylic acid.

The coupled C-13 NMR spectra should be collected with 160 to 640 scans. Enter 640 into the number of scans and continue until the noise is low enough to accurately measure the coupling constant. Once each spectrum is collected all of the data work-up can be done on the computers in the Physical Science computer lab or down in the NMR room itself.

When analyzing data, use the 1:1:1 triplet of CDCl₃ as a reference by setting the central peak to 77.2 ppm. Print out the decoupled spectrum in ppm scale and record the frequency for each peak in Hz. (You may write it on the print-out.) Using the chemical shifts from the decoupled spectrum and the splitting from the coupled spectrum you will be able to assign each peak. Each split peak will be centered around the frequency of the decoupled singlet. Note that each peak will be split by the attached hydrogens with a coupling constant may be further split by longer range coupling (coupling constants less than 100 Hz). Be consistent when comparing the coupling constants for each peak to measure from the analogous peak. Print a blow up of the peaks for which coupling is determined, label the axis in Hz. Include these print outs with your write-up.

[Note: The two doublets from sp2 hybridized CH's in 4-ethynyl toluene overlap a bit. The right-most peak of one doublet overlaps the left-most peak of the other doublet. Make sure that the peaks used to measure the coupling constant are equidistant from the position of the original (decoupled) peak.]

Write-up

Use the class data for the peaks in 4-ethynyltoluene to plot %s character versus ¹J_CH. (If you plot %s on the y-axis, you can use the line of best fit to calculate an unknown %s from a coupling constant directly, otherwise you may need to use some algebra.) Determine the %s character and hybridization in the C-H bonds of the two cylcoalkanes, and therefore, the %s character in each C-C bond within the ring (don't bother calculating the sp^x hybridization of the C-C bonds).

Attach the decoupled spectrum you collected and blow ups of the coupled peaks that you analyzed.

Questions to Consider in your Discussion:

• Evaluate the range of error in terms of %s character from each of the following sources of error:
  the difference between the line of best fit (calibration curve) and the presumed %s-character, the scatter in individual data points measured by different individuals, differences from different carbon atoms within the same molecule. Use these error values when answering the following questions.
• Is the "calibration curve" linear? Is the intercept nearly 0? Should it be?
• Is the hybridization significantly different when you compare different carbons within the same ring?
• Is the hybridization of cyclopropane significantly different than cyclobutane? Why?
• To what extent is the hybridization changed to create better bonding in these strained rings? (I.E., How much does the first bonding scheme contribute?)
• Does a majority of the error come from the measurement of a coupling constant, from the chemical systems used as standards, or something else? Is the error large enough to jeopardize your conclusions?
• Quantum mechanics calculations predict an H-C-H bond angle of 118° in cyclopropane [for those of you who have had P-Chem the level of theory was quite respectable, B3LYP/6-311G(d,p)]. How well does this agree with your experimental data?