Nuclear Magnetic Double Resonance Using Weak Perturbing RF Fields
G. Fredric Reynolds Mlchlgan Technolog~calUnlverslty Houghton. 49931
Electron-coupled spin-spin interactions can be either positive or negative, with the difference in sign being related to.the way the nuclear spins are coupled via their bonding electrons. The positive J value denotes an antiparallel arrangement of nuclear spins as the spin state of lowest energy, while a negative J value denotes a parallel arrangement of the nuclear spins as the state of lowest energy. The reference for the spin convention is the one-bond WYH coupling constant with J > 0 ( I ) . In the case of protons bonded to spa carbon atoms, the signs of the coupling constants vary in a regular way, with two-bond (geminal) coupling being negative and three-bond (vicinal) coupling being positive. In the case of protons bonded to sp2 carbon atoms, the vicinal coupling is again positive, but the geminal coupling can either he positive or negative as shown in Table 1. Of the methods available for determining the relative signs of the geminal and vicinal coupling constants in three-spin systems, spin tickling with weak perturbing R F fields is orobablv the easiest method to use. T o date, only a limited numheiof papers describing spin tickling experiments have appeared in the literature, the example usually cited in nmr texts being 2,3-dibromopropionic acid (3).The purpose of this paper is to give another example of spin tickling, as well as to discuss the most direct approach for verifying the relative signs of coupling constants in three-spin cyclopropyl systems. The compound employed for this example is l-methyltrans-1,2-cyclopropanedicarboxylicacid, which can be prepared as described in the literature (4). Since this compound exists in two optically active forms which are mirror images of each other ((I) and (11) below), it is important to note that both optical isomers give identical nmr spectra in the deuterioacetone solvent employed in this experiment. Themagnetic environments of the various atoms are equivalent in both cases as long as the solvent employed is not optically active. HOOC
Table 1. Approximate Values for Geminal and Vicinal Coupling Constants 121
rotation)
H-4-C-Hlfree
H
I
+6
to
48
to +10 (cis)
+S
+4 to +6 (trans)
is referred to as a regressive relationship, while the latter case is referred to as a progressive relationship. Rule (3) is illustrated for the example of two coupled spins in Figure 1. Thus, the four lines observed for the allowed transitions shown in Figure 1correspond to two regressive pairs, A,, B I and Az, B2 and two progressive pairs, A I, B2 and As, B1.Tickling one line of a regressive pair causes the other line of the pair to split into a well-resolved doublet, and tickling one line of a progressive pair causes the other line to broaden or show a less well-resolved doublet. When the spin tickling experiment is extended to the three-spin system, identification of the regressive and progressive transitions allows the ordering of theenergy levels, and this allows the relativesigns ofthe coupling constants to be determined.
Method For simplicity in the analysis, we will assume the approximation of a loosely coupled three-spin system, giving three sets of quartets for the three protons. The relative frequencies of the 12 lines of the first-order spectrum are given by the equations
CH,
VCOOH
COOH
([I) Theory The spin tickling experiment, first described by Freeman and Anderson (3), is essentially a double resonance nrnr experiment in which the perturbing H2decoupling field that is set at the frequency of a particular line to be irradiated has a magnitude in cps only on the order of the width of the irradiated line. Under these conditions, the following three rules apply 1) Any nmr transition that has an energy level in common with a
given nondegenerate transition which is being irradiated by the Hz decoupling field will be split into a doublet,or st least broadened. 2) The magnitude of the splitting depends both on the strength of H2and the square root of the intensity of the line irradiated. 3) The degree of splittingdepends on the arrangement of the common energy level. When an energy level is common to another transition, then the other two energy levels involved may either have the same magnetic quantum number (M), giving a well-resolved doublet, or the quantum numbers of the other two energy levels may differ by two units, yielding a broad doublet. The formercase 390 1 Journal of Chemical Education
I\ b
01
1
' 1-1
-
t
t
Po(lltion Sf
PoslTio"
irradistian
irrdlatisn
Of
Figure 1. Left: allowed transnions far a twc-spin system. Right: (a) n m l Irequency sweep spectrum and (b). (c)spin t~cklingspectra expected for an AB system.
Table 2. NMR Transitions for Weakly Coupled ABC System with JBC >JAC > J A B
Table 3. Experimental Results Transition irradiated CI C1 C4
. A -
Care 2.
JAB=J A C , JBC = Care 3.
B -
+
+
-
- +
C
A +
Case 4 . A J8c=B + JAB.JAC=+ C
- +
+
+
+
-
+
Results A,, B,regrel$ive with C , and A., B , regvesrlve with C, A A:,, B, BI r?g,rerrive ~rogressive with withC and As. 8 , regressive with C, and A , . B, progressive with C,
-
- - + - - + -
+ +
- - + + + - + - + - +
+ -
-
Case I all J's positive
Case 3.
JAC z - ; JAB,Jet=+
Case 4. J a c = - ; J A ~JAC , =+
Figure 2. Energy level diagrams for an ABC system depicting the 12 allowed first-ardertransitions. Spin states +'A or -% are denoted by w - signs.
+
where the value of the proton nuclear spin, m, is either +'k or -K. From theseequations, the arderingof the peaks in thespectrum can be seen to depend on both the sign and magnitude of the coupling constants, J,as well as on the val& of the n&lear spin, m. ~ u p p o s ; that we have ascertained, as in the case of our example, that JBC > Jac > JAB.Using the above equations, we can now construct a table of the order of the transitions from the highest frequency transition, A l , t o the lowest frequency transition, C4,assuming initially that all J values are positive, as shown in Case 1 of Table 2. Thus, for the lowest frequency absorption of Case 1, Cn,the spin of nucleus C is changing by one unit while hoth mA and mu = -'h, and so forth. In Cases 2,3and 4, as one J value a t a time takes an a negative sign, four pairs of lines related by this coupling constant are caused t o switch oositions. The 12 first-order transitions in which onlv one of the coupled sprni ix changing at a time ran be dep~ctpdas the 12 edges 181 s rube as shown in Figure 2. The purpwe uf runitructing Casrs 1 thruughdofFigure2 for the transitionsofTable2 is tvallux the rcgressively and progressively related transitions t o be easily identified. Although a three-spin sptem with different values for the coupling constants which can be independently positive or negative yields 2:' = 8 combinations.. onlv,the four eases shown are unioue. as the soin rirklmg expmment only diatrnpishes the relative s g n relationship. For example, mnkmg d l J values negative aimply inverts the energy diagram shown for Case 1 in w h ~ all h J values nre psitrve, and leaws the spectrum unchanged.
Figure 3. Frequency sweep 'H nmr spectrum of 1-mthyl-trans-1,2cyclopropanedicarboxylic acid; (a) single resonance spacmrm. ( b t ( d ) decoupling frequency centered on line giving beat panern. me spectra were recwded at 100 MHz on a Varisn HA-100 spectrometer; the more intense methyl resonance has been amlned in (b)-Id). shown in Figure 3. These experiments yield the information shown in Table 3 regarding regressive and progressive lines. Only one such tickling experiment is necessary to choose the correct energy diagram, the other two experiments serving as checks. The onlv enerev diagram which fits the exneriments is Case 2 in result is in agreement with several other 'Hnmr studies of cyclopropanes (5-7) which also found the geminal coupling constant to be of opposite sign tu tht, vicinnl n,uplmg constanla. The actual magnitude, o i thr three coupling constants for I methvl-rrons-1 .?-cvrlo~ru~nn~dlcnrhoxvlic acid were obtained by computer simulation o f t h i 60 MHz spectrum. The results are JAH = J,, = -4.1; J a c = J,ia= 8.5; and J e c = Jtrans = 6.5. The rangeof values for geminal coupling in cyclopropanes does not appear in the usual reference tables of coupling constants given in nmr texts. From this example and two other eyclopropyl spectra also matched a t the same time by computer simulation, as well as from the data in the references mentioned above (5-7).the range of geminal coupling in cyclopropanes is typically -4 to -8 Hz. Acknowledgment The author wishes to thank Dr. Ronald E. Erickson for his generous gift of 1-methyl-trans-1,2-cyclopropanedicarboxylic acid.
Results
Appendlx
The results for the spin tickling of three different lines in the spectrum of l-methyl-trans-1,2-cyclopropanedicarboxylic acid are
In addition to the example of l-methyl-trans-1.2-cyclopropanedicarboxylic acid given here and the frequently cited example Volume 54. Number 6,June 1977 1 391
(3),other compounds in which the relof coupling constants have deduced spin in three-spin systems are styrene sulfide and atwnimine (8),and 13-naphthyridine (9). Any of thesecompoundswould he satisfadory for a spin tickling experimentin which studentacould their results with the literature. of 2,s-dihromopropionic acid
Literature Cited Ill Emsley, J. W., Fecney. J., and Suteliffc, L. H., "Hibh Resolution Nuclear Magnetic Resonance Spectrmopy." Vol. 2, Pergamon Preas, New Yark, 1966.p. 682.
392 1 Journal of Chemical Education
121 varian ~ssoeisfe~'compi~ation of mupiing can st an^ distributed at ~ i c h~. e e huniv. . NMR Workshop, July, 1969andreL ( I ) . Vol 1 and 2. (31 Freeman. R..and Anderson, W. A . J. Chsm Phyr.. 37,2053ll962l. 141 st.ul~ko.~.,and~eyden-~onne, J., MI. SO
