Information-Rich 13C Satellites

Seemingly simple NMR spectra often contain much more information than one might think.  For example, the ¹H NMR spectrum of 1,4-dioxane is primarily a singlet from which one obtains only an isotropic ¹H chemical shift value.  There is however much more information available in the spectrum which is often not recognized or used.  The ¹H NMR spectrum of a naturally occurring sample of 1,4-dioxane is the weighted sum of the ¹H spectra of all possible isotopomers.  It is the dominant tetra-¹²C isotopomer that gives rise to the singlet but since ¹³C (spin I = 1/2) is 1.1% naturally abundant, one expects to observe also the mono-¹³C isotopomer.  The di-, tri- and tetra-¹³C isotopomers are very rare and can be neglected.  The symmetry in the mono-¹³C isotopomer is lost compared to the tetra-¹²C isotopomer and one obtains a complex second-order spectrum, part of which can be represented by an AA'BB'X spin system.  The spectrum of the AA'BB'X spin system depends on many more parameters than just the isotropic ¹H chemical shift.   This is illustrated in the figure below.

The bottom panel of the figure is the measured 300 MHz ¹H NMR spectrum of 1,4-dioxane with an exaggerated vertical scale to accentuate the ¹³C satellites resulting from the protons color coded in pink in the mono-¹³C isotopomer.  The large central region of the spectrum is the result of all the protons color coded in yellow from both the tetra-¹²C and mono-¹³C isotopomers.   A simulation of this second-order spectrum was calculated from the parameters below and is shown in the top panel of the figure. 

Any isotope shifts in the ¹H frequencies due to ¹³C vs ¹²C bonding were neglected in the simulation.  The fit of the simulation to the ¹³C satellites is particularly sensitive to ¹J_C-Ha,  ¹J_C-Hb,  ³J_Ha-Hc,  ³J_Ha-Hd, ³J_Hb-Hc and ³J_Hb-Hd and much less sensitive to  ²J_C-Hc,  ²J_C-Hd,  ²J_Ha-Hb and  ²J_Hc-Hd.  A fit of the simulation to the experimental spectrum produces estimates for all of the coupling constants in the AA'BB'X spin system - much more information than a single ¹H isotropic chemical shift!

Multiplets for Spin I = 1/2 Nuclides Coupled to Quadrupolar Nuclides

When a spin I = 1/2 nuclide is coupled to a qudrupolar nuclide of spin S, one will observe one of three things: (1) a sharp singlet; (2) a sharp multiplet consisting of (2NS + 1) lines, where N is the number of equivalent quadrupolar nuclides or; (3) a broadened signal intermediate between a sharp singlet and a sharp multiplet.  An example of a sharp singlet is the proton decoupled ¹³C spectrum of CHCl₃.  In this case, the lifetimes for each of the (2S + 1) Zeeman states of the quadrupolar ³⁵Cl and ³⁷Cl nuclides are much shorter than the reciprocal of the J coupling interaction with the ¹³C.  As a result, the  ¹³C "sees" an average state for the ³⁵Cl and ³⁷Cl nuclides and appears as a sharp singlet (neglecting any isotope effects).  This phenomenon is quite common and is sometimes referred to as "self-decoupling".  An example of the a sharp multiplet is the ¹³C spectrum of CDCl₃. In this case, the lifetimes of each of the three Zeeman states of the deuterium are much longer than the reciprocal of the J coupling interaction with the ¹³C.  As a result, the ¹³C "sees" each of the three Zeeman states of the deuterium and appears as a 1:1:1 triplet.  Examples of broadened signals, intermediate between sharp singlets and sharp multiplets are often observed in the signals of ¹³C bound to ¹⁴N ( I = 1 ).  In these cases, the lifetimes of the three Zeeman states of the ¹⁴N are of the same order as the reciprocal of the J coupling interaction with the ¹³C.  It is very interesting to note that the lifetimes for each of the quadrupolar Zeeman states are not necessarily the same.  As a result, for cases where the lifetimes are comparable to the reciprocal of the J coupling interaction, one can observe differential broadening in the lines of the multiplet.  This can be seen for the  ¹³C signals for tetraalkyl ammonium salts  or the ¹H signal for dilute HDO where, in each case, the outer two lines of the observed triplets are broadened more than the central line such that the intensity (height) of the lines does not appear to be 1:1:1.  A more dramatic example is shown in the figure below for the ¹³C spectrum of K₃[Co(CN)₆].

 For this compound, the lifetimes of the ¹⁴N Zeeman states are sufficiently short such that the ¹⁴N is self-decoupled from the ¹³C.  The lifetimes of the ⁵⁹Co ( I = 7/2, 100% naturally abundant) Zeeman states, on the other hand, are comparable (although somewhat longer than) the reciprocal of the J coupling interaction with the ¹³C.  As a result, an eight line multiplet is observed with equal integrals for each of the component lines.  In this case, the lifetimes of the eight ⁵⁹Co Zeeman states are not equal and one can see that lines 2 and 7 of the multplet are the most broadened.  Lines  3 and 6 are the second most broadened followed by lines 4 and 5.  Lines 1 and 8 are the least broadened and therefore the highest in intensity.  The calculation of the relevant lineshapes has been presented in the early (and no so early) literature.^1-4

1. J.A. Pople, Mol. Phys. 1, 168 (1958).
2. J. Bacon, R.J. Gillespie and J.W. Quail. Can. J. Chem. 41, 3063 (1963).
3. M. Suzuki and R. Kubo, Mol. Phys. 7, 201 (1964).
4. N.C. Pyper, Mol. Phys. 19, 161 (1970).
5. P. Kofod, J. Magn. Res. A. 119, 212 (1996).

Measurement of Long Range C H Coupling Constants

The stereochemistry of compounds is assigned very often with proton - proton NOE's by applying the 2D NOESY technique or the 1D selective gradient NOESY technique.  These methods fail, however when the distance between protons is too large to measure an NOE.  When faced with this situation, it may be possible to measure long range proton - carbon coupling constants which are able to provide the necessary information.  Three-bond carbon - proton couplings follow a Karplus relationship where the magnitude of the coupling constant is related to the dihedral angle between the carbon and the proton.  In some cases, these dihedral angles may be used to assign the stereochemistry.  Coupling constants are largest for dihedral angles of 0° and 180° and smallest for dihedral angles of 90°. The simplest way to measure the long range coupling constants is to collect a ¹³C NMR spectrum without ¹H decoupling.  These spectra can be very complicated as can be seen from the figure below showing the C2 and C3 aromatic carbons of toluene.

Extracting specific long range carbon - proton coupling constants is quite tedious.  One way to simplify matters and obtain specific carbon - proton coupling constants is to apply the selective 2D heteronuclear J-resolved technique first introduced by Bax and Freeman in 1982 (JACS 104, 1099).  This method employs a ¹³C spin echo with a selective ¹H 180° pulse applied simultaneously with the ¹³C nonselective 180° pulse. A version of this sequence is shown in the figure below with a shaped adiabatic ¹³C 180° pulse.

In this sequence one obtains a 2D spectrum with ¹³C in the F2 domain and the long range couplings to the selectively inverted proton in the F1 domain.  An example is shown in the figure below for toluene where the methyl protons were selectively inverted with a 20 msec Gaussian pulse.

All of the carbons coupled to the methyl protons are split into quartets in the F1 domain and the long range coupling constants which were very difficult to obtain from the coupled ¹³C spectrum can simply be read directly from the 2D spectrum.    

E.COSY and the Relative Signs of Coupling Constants

Spin-spin coupling constants can have values greater than or less than zero. The absolute sign of the coupling constants cannot be discerned from the simple examination of a ¹H NMR spectrum. The E.COSY¹ (Exclusive COrrelation SpectroscopY) technique is one method which can be used to determine the relative signs of coupling constants. E.COSY is a phase sensitive COSY variant which produces off-diagonal signals showing only the active coupling (i.e. the coupling directly responsible for the cross-peak) as 2x2 antiphase square tetrads displaced in both the F2 and F1 domains by an amount equal to the passive coupling constants (i.e. the couplings not directly responsible for the cross peak). The slope of a line drawn through the cross-peaks is used to determine the relative signs of the passive coupling constants. The sign of the slope depends on whether the signs of the passive couplings are the same or whether they differ. The figure below shows the gradient E.COSY spectrum² (using the Bruker pulse program,"ecosygpph" ) for the ABX three-spin system in phenylalanine.The cross-peaks highlighted in yellow in the top panel of the figure are expanded in the bottom panel. Black contours are positive and red contours are negative. The panel on the bottom left shows the cross-peaks for AX and BX. In the case of the AX cross-peak, the line drawn through the cross peak has a positive slope indicating that the passive couplings J_AB and J_BX are of opposite sign. The line drawn through the BX cross peak also has a positive slope indicating that the passive couplings J_AB and J_AX are of opposite sign. From this we can deduce that J_AX and J_BX are of the same sign. The panel on the bottom right shows the cross-peak for AB. In this case, the line drawn through the cross peak has a negative slope confirming that the passive couplings J_AX and J_BX are of the same sign. In conclusion, the geminal and vicinal coupling constants are of opposite sign.

1. C. Griesinger, O.W. Sorensen & R.R. Ernst, J. Magn. Reson. 75, ; 474 - 492 (1987).

2. The ecosygpph pulse program produces spectra similar to those described in reference 1 as "complimentary" E.COSY spectra. The slope of the lines through the cross peaks in "complementary" E.COSY spectra are of opposite sign to those obtained from the E.COSY spectra described in reference 1.

Dilute "D2O" in Benzene-d6

The ¹H NMR spectrum of a mixture of H₂O and D₂O is a single line at about 4.8 ppm. The H₂O and HDO resonances are unresolved in the spectrum due to fast chemical exchange between the isotopomers and possibly line broadening due to radiation damping. When traces of D₂O are added to benzene-d₆, which already contains traces of H₂O, the situation is different. The resonance is shifted by more than 4 ppm to lower frequency compared to the bulk and since the water is now dilute and in small quantities, chemical exchange is slow on the NMR time scale and radiation damping is no longer a problem. The figure below shows the 500 MHz ¹H NMR spectrum of dilute D₂O in benzene-d₆. The isotope shift between H₂O and HDO and the HD coupling constant can easily be measured from the spectrum.

Second Order 1H NMR Spectra of Isopropyl Groups

One of the first things a chemistry student learns about NMR is how to interpret the coupling patterns in first order NMR spectra. With the high magnetic fields available for NMR today, this really goes a long way in interpreting spectra. Chemistry students also learn that when the chemical shift difference between two spins is comparable to their coupling constant that second order NMR spectra are observed and furthermore, that these second order spectra are "very complicated". Many do not bother to understand the line shapes. Sadly, many students carry around laptops with software packages capable of simulating these spectra and do not even know it. Several years ago, a student came to me with a proton NMR spectrum of an isopropylsilyl compound and asked why he could not see the typical septet - doublet isopropyl pattern in the spectrum. He was very concerned that he did not have the right compound. I told him he had a second order spectrum and that it was just as "beautiful" as any first order spectrum.

The first figure below shows simulations (carried out in TOPSPIN) for an isopropyl group as a function of the C-H chemical shift. One can see the typical septet -doublet pattern when the chemical shift difference between the methyl and CH protons is much greater than the coupling constant. When the shift difference is comparable to the coupling constant, complicated second order spectra are obtained. When the shift difference is zero one obtains a singlet.

The left panel of the second figure shows the isopropyl region of the experimental NMR spectrum of (triisopropylsilyl)acetylene. The complicated second order spectrum is simulated in the right hand panel.

Thank you to Mattieu Leclere for providing the sample used in the figure above.

Spin-Spin Coupling Between Equivalent Nuclei

When many chemists are asked what is the ²J_H-H coupling for compounds like methane, acetone, methylene chloride, dimethyl ether or DMSO, they will often return a look of confusion. "There is no coupling," they will say, "the proton spectrum is a singlet". Indeed the proton spectrum is a singlet for these compounds but ²J_H-H is not equal to zero. The only reason that the coupling is not observed in the spectrum is because the chemical shifts of each proton are identical. The coupling can easily be measured by observing the spectrum of a partially deuterated isotopomer. The ²J_H-H coupling constant is equal to ²J_H-D multiplied by the ratio of the gyromagnetic ratios of ¹H to ²H. This is illustrated in the figure below for methylene chloride.In fact, ²J_H-H is -7.192 Hz not +7.192 Hz however, this cannot be determined simply by observing the spectrum. Both spectra were measured for dilute solutions with CDCl₃ as solvent. The residual protons of CDCl₃ were used as the chemical shift reference (7.26 ppm). The chemical shift difference between CH₂Cl₂ and CHDCl₂ is due to an isotope effect.