Addison Ault
Cornell College Mt. Vernon, Iowa 52314
Classification of Spin Systems in NMR Spectroscopy
O n e of the most interesting aspects of nmr spectroscopy is the interpretation of spin-spin splitting patterns in terms of the structural and configurational relationships among the magnetic nuclei of the molecules of the sample. Such an interpretation may be considered to consist of two steps. The first is to account for the spin-spin splitting patterns in terms of the number of nuclei involved and their chemical shift differences and coupling constants, or, in other words, to determine the types of spin systems responsible for the observed spin-spin splitting patterns. The second is to account for the spin systems in terms of structural and configurational relationships between the nuclei. For example, an nmr spectrum is observed to consist only of a 1:3: 3: 1quartet of relative intensity two and a 1:2: 1 triplet of relative intensity three. The spacings between members of each multiplet correspond to a coupling constant of seven Ha and the chemical shift difference between the multiplets is about two ppm. These resonances can be accounted for by an A3X2spin system with a chemical shift difference, ASnx, equal to 2 ppm and a coupling constant, JAx,equal to 7 Hz (Step 1). The protons of an isolated ethyl group, such as in ethyl chloride, ethyl bromide, or ethyl iodide, could be expected to give such an A& system (Step 2). This would complete the analysis of the spin-spin splitting pattern of the spectrum, and a choice between the three possibilities could be made upon the basis of the chemical shifts of the two multiplets relative to a standard. I n carrying out the first step of such an analysis, it is very helpful to know the types of spin-spin splitting patterns which can be expected from various spin systems with different chemical shift differences and coupling constants. I n carrying out the second step, it is necessary to know what features of molecular structure can give the different spin systems under various conditions. It is convenient, therefore, to classify spin systems both as to the expected appearance of their resonances and as to the types of molecular structures which would be expected to give them. Unfortunately, in most introductory discussions of nmr spectroscopy, two important distinctions which must be made in order to classify spin systems in these two ways are not made clearly or are not made a t all. The first distinction which must be made is that between nuclei which are chemical-shift-equivalent and those which are not. Chemical-shift equivalent nuclei References of this type me to "High Resolution NMR Spectra Catalog," Vmim Associates, Volumes 1 and 2 (1962 and 1963), and the number indicates the serial number of the spectrum.
812
/
Journol of Chemicol Education
are a set of spin-coupled nuclei which all have exactly the same chemical shift. Whether or not nuclei are chemical-shift-equivalent may be determined by application of the following criteria. I n rigid molecules or in a particular fixed conformation, all nuclei (of the same element and isotope) which can be interchanged by a symmetry operation will necessarily be chemicalshift-equivalent. Examples of this are the protons of benzene or cyclopropane, and the axial or equatorial protons of cyclohexane in a rigid chair conformation. Nuclei which cannot be interchanged by a symmetry operation can be chemical-shift-equivalent only by chance (all four protons of methyl acetylene in dilute chloroform solution, for example; Varian 16', or by a time-averaging process. The most common type of time-averaging process is that of conformational interconversion. If (1) in any one conformation which can be attained by the molecule in the course of conformational isomerism, nuclei can be interchanged by a symmetry operation, these nuclei will be chemical-shift-equivalent under conditions of rapid conformational isomerization. It is in this first way that the methyl protons of nitromethane, the methyl protons of most ethyl groups, the protons of cyclohexane, the four protons of 1,2-dichloroethane, and the two protons of each individual methylene group in 1chloro-2-bromoethane can be seen to be chemical-shiftequivalent under conditions of rapid conformational isomerization. If (2) rotation about a single bond will allow nuclei to experience identical environments, these nuclei will be chemical-shift-equivalent under conditions of rapid conformational isomerization. It is in this second way that the methyl protons of a molecule such as 1-bromo-1-chloro-1-iodoethane can be seen to be chemical-shift-equivalent under conditions of rapid conformational isomerization. A second very common type of time-averaging process is that of chemical exchange as exemplified by the exchange of OH and RTH protons among both the sample and solvent molecules. A third type of time-averaging process is that of structural isomerization, for example that of bullvalene at higher temperatures. If all the nuclei in an isolated spin-coupled set are chemical-shifbequivalent, their resonance will appear as a singlet whether the coupling constants between members of the set are all equal (nitromethane) or not (benzene, cyclohexane, 1,2-dichloroethane). Conversely, the appearance of a singlet in the nmr spectrum implies the presence of a set of spin-coupled nuclei, aU of which are chemical-shift-equivalent, and gives no information concerning the coupling constants between members of the set. Such a set of chemical-shift-equivalent nuclei is usually represented by the symbolism A, or X, where
the subscript indicates thenumber of nuclei in the set. Some questions of chemical-shift-equivalence are rather subtle. For example, in a molecule such as I WCHrCXYZ I
the methylene protons are not necessarily chemicalshift-equivalent since they can neither he interchanged by any symmetry operation in any conformation nor can they attain identical environments upon rotation about the carbon-carbon hond. The two protons in I form an AX system and would be expected to show mutual splitting unless by chance the chemical shift difference between them approaches zero; in this case, they would he an A2system. If W = H, as in l-bromo1-chloro-1-iodoethane, the three protons can be chemical-shift-equivalent since they can attain identical environments upon rotation about the carbon-carbon bond. The chiral center which results in the difference in chemical shifts of the protons of the methylene group of I need not he based on carbon, as in the example, hut may be based on other atoms such as sulfur (in sulfonium ylids, sulfoxides, or sulfonium salts) or nitrogen (in quaternary ammonium salts). I n a molecule such as I1
each methylene group still comprises an AX system (the two systems are identical) since the protons within each methylene group cannot be interchanged by any symmetry operation in any conformation. I n both I and 11, if the hydrogen atoms were methyl groups, the methyl resonances would appear a t two different chemical shifts. In a system such as HC(Me)2-CXYZ or HC(Me)2-CXY-CH(Me)2two methyl doublets should be observed. I n a molecule such as I11
the two methylene protons arenot chemical-shift-equivalent in the meso configuration, but are chemical-shiftequivalent in the cl and l configurations; in the meso configuration, the two protons cannot he interchanged by a symmetry operation in any conformation, hut in the d or l configuration, they may be interchanged by a symmetry operation (C2)in at least one conformation. Since the magnitude of the effect of a chiral center depends upon the substituents involved and upon the distance. from the center, the expected difference in chemical shift may be too small to be observed experimentally. In addition, the difference in chemical shift which may be observed depends upon the relative populations of different conformational isomers; it is therefore both temperature dependent and solvent dependent. The second distinction which must be made is that between sets of magnetically equivalent nuclei and sets of magnetically non-equivalent nuclei. If the coupling constant, J , between any nucleus in one set of chemicalshift-equivalent nuclei and any member of a second set of chemical-shift-equivalent nuclei is exactly the same as all the others, the two sets of nuclei are said to be sets of magnetically equivalent nuclei. Or, in other words, if in the spin system A,X,, J Ais~exactly the same for all possibilities, the A nuclei and the X nuclei are each
said to be sets of magnetically equivalent nuclci. Examples of spin systems made up of two sets of magnetically equivalent nuclei include 1,l-dichloro-2,2dihromoethane (an AX system), 1,1,2-trichloroethane and 1,1,2,3,3-pentachloropropane(hoth AzX systems), 1,l-dichloroethane (an A3X system), isopropyl chloride (an A& system), 1,1,3,3-tetrachloropropane (an AsX2 system), the isolated ethyl group (an A1X2 system) and l,l,l-trifluoro-2-butyne(an A3X3system). Such A,X, systems result in a resonance whose appearance depends only upon the chemical shift difference between the two sets of nuclei, A&x, and the coupling constant between the nuclei in the two sets, JAx. If the ratio A8Ax/Jnxis large, the resonance will have a "first order" appearance wherein the resonance of the A nuclei will appear as an (m 1)-tuplet and the resonance of the X nuclei will appear as an (n 1)-tuplet with the peaks within each mnltiplet separated by JAXand the intensities of the peaks in each multiplet following the coefficients of the binomial expansion to the m and nth power, respectively. The spectra of A.X, systems can give information concerning the values of A 6 ~ xand Jnx,hut no information concerning coupling constants between A nuclei or between X nuclei. If the condition described for magnetic equivalence is not met, the groups of chemical-shift-equivalent nuclei are said to he magnetically non-equivalent. That is, if more than one Jnx relate nuclei in the two sets of chemical-shift-equivalent nuclei, the two groups are said to he magnetically non-equivalent. Very common examples of a type of spin system made up of two sets of magnetically non-equivalent nuclei are the 1-X,4-Y-disubstituted benzenes such as l-chloro-4hromobenzene. This type of spin system is represented by the symbolism AA'XX' by which it is implied that JAX = JArx, # JA'X = JAX,. The appearance of the resonance of an AA'XX' system depends upon hoth JAU and Jxx, as well as upon JAX and JA,x, and A ~ A x . Also, even when Ahnx is large relative to both JAXand JApx,the resonance will no1 necessarily have a first order appearance. Other examples of AA'XX' systems include 1,2-di-X-substituted benzenes, 1,l-difluoroethylene, 1,2-difluoroethylene,1,3-difluoroallene,furan, thiophene, and 1-X,2-Y-substituted ethanes such as 1bromo-2-chloroethane. The latter are AA'XX' systems despite "free" rotation about the carbon-carbon hond. True AIXz systems are quite rare (examples include difluoromethane, 1,l-difluoroallene, and 1,1,3,3tetrachl~ropro~ane)and most systems which are described as A2Xzsystems should really he classified as AA'XX' systems. One reason for the confusion between AA'XX' systems and AzXzsystems is that under certaineonditions, an AA'XX' system can give a resonance with the first order appearance of a true A2Xz system. The first condition, but not the only one, is that A h be large relative to JAxand JArx. The second is that the ratio (JAx- JA,x)2/21JnA, - Jxx,l be less than the resolving power of the instrument (typically 0.5 Hz) (1). This condition is not equivalent to JAX?X J ~ f but x is less strict and more common. Thus if JAA,and Jxx* are sufficiently different, the resonance of an AA'XX' system may appear as a pair of approximately 1:2: 1 triplets even though JAx and J m are not the same. The apparent coupling constant, J , in such a case is the
+
+
Volume 47, Number 12, December 7 970
/
813
average of JAx and JUX. Thus the appearance of the nmr spectrum of furan as a pair of 1 : 1 triplets (Varian 50) can be accounted for by observing that on the basis of average coupling constants determined for substituted furans, J A A ,- Jxx, = 2.0 even though JAX - JAL =~ 1.0, giving a value for the ratio of 0.25 (1). I n contrast, the nmr spectrum of thiophene (Varian 52) is complex. For this reason, if the resonance of a spin system which might be expected to be anAA1XX' ~ystemappears as "apair of 1 :2: 1 triplets," it does not necessavily mean that JAX s JASX and that the spin system is approximately an A2X2 system. Similarly, the appearance in an nmr spectrum of "apair of 1:2: 1 triplets" does not necessarily imply the presence of an A& spin system in the molecules of the sample with the molecular symmetry and equality of inberset coupling constantsof the A& system. The simplest system involving magnetically nonequivalent sets of nuclei, the AA'X system, is quite rare since the molecular symmetry which ensures equality of chemical shift for the A and A' nuclei will necessarily ensure equality of Jnx and J A ~Thus . AA'X systems must arise by accidental equality of chemical shift for the A and A' nuclei. Some of the possible spin systems made up of two sets of spin coupled, chemical-shift-equivalent nuclei are summarized in Appendix I. If in an AA'XX' system, JXX* approximately or exactly equals zero, the second condition under which the resonance of an AA'XX' system will appear as a pair of 1:2: 1 triplets reduces to (JAX - Jn.x)'/21 JuJ 5 the resolving power of the instrument. I n other is sufficiently large, words, given that Jxx, g 0, if JAA, the resonance of an AA'XX' system will appear a a pair of 1 :2: 1triplets. The special case of an AA'XX' systemin which J x x r E 0 is conveniently represented by the notation XAA'X', and is the first of a series of spin systems of the general type X.AAIX,' in which JXX,is assumed to be small or zero. One limiting case of the general X.AAIX,' system (and, by symmetry, JUX)is small is that in which JAX, or zero, and JAA, is large. If JMis sufficientlylarge that (JAx)2/21JAa.I5 the resolving power of the instrument, theX resonances will appear as a 1:2: 1triplet and the A resonance as a first order mnltiplet of 2n 1 peaks (8). An example of this type of system, in which n = 6, is tetramethyldiphosphine IV.
A second example, in which n = 3, is the spin system of 2,5-dimethylquinoneV1 for which the methyl resonances appear as a 1: 1 doublet and the olefinic resonances as a 1:3:3:1 quartet (4).
An intermediate case of the general X,AAIX.' system is that in which JAX, (and, by symmetry, J A ~ xequal ) approximately zero and J h A ,is neither so large that (JAx)2/21J4 5 the resolving power of the instrument so that the resonance of the system will appear as that of an A2XZnsystem, or so small that the resonance will appear as that of two identical AX, systems. One example, for which n = 2, is that of trans-1,4-dichloro-2butene VII (Varian 404) in which the resonance of the methylene protons appears as a "filled in" doublet (the "filling in" has not quite proceded to the point of converting the doublet to a triplet) and the resonance of the olefinic protons is complex. H
\
,CH,-CI
CI-CHP/c=c\ W
A second example, for which n = 3, is that of 2,6dimethylquinone VIII for which the resonance of the methyl groups appears as a doublet which has been "filled in" somewhat and the olefinic resonance has become complex (4).
+
The methyl resonance of this substance appears as an approximately 1:2: 1 triplet, and the phosphorus resonance presumably as a thirteen line first order multiplet (5). A n ~ t h e r l i m i t i n ~ c a sofe the general X,AAIX,' system is that in which Jnx,(and, by symmetry, Jnrx) is small or zero, and 2jJAA,Iis somewhat smaller than (JAx)~.I n this case, the resonances will appear as those of two identical AX, systems. One example of this case, in which n = 2, is the formal of cis-1,4-dihydroxy-2-buteneV (Varian437) in which the resonance of the olefinicprotons appears as a 1 :2: 1triplet and the resonance of the allylic methylene protons appears as a 1 :1 doublet. 814
/
Jourml of Chemical Education
These possibilities for the X,AAIX,' spin system are summarized in the last part of Appendix I. First order suectra are often considered to be characteristic of spin systems made up of sets of magnetically equivalent nuclei in which the chemical shift difference islarge relative to the corresponding coupling constant However, as indicated above, first order spectra may be observed under certain conditions for spin systems made up of sets of magnetically non-equivalent nuclei, and such first order spectra have sometimes been called deceptively simple spectra (I). They are simple in the sense that the number of lines observedis muchless than one expects in general from spin systems made up of sets of magnetically non-equivalent nuclei, and deceptive in the sense that one might wrongly conclude that the
spin system is made up of sets of magnetically equivalent nuclei rather than sets of magnetically nonequivalent nuclei. Under the conditions indicated above, it is possible to observe a first order spectrum for a spin system made up of two sets of magnetically non-equivalent nuclei even if JAzx = JAX, = 0 if the difference I J u , - Jxx.1 is large enough. Since the apparent J of the first order spectrum is the average of JAxand JASX, in cases when JAjx E 0, the apparent J will be '/% JAX. If in such a case the spectrum is (wrongly) interpreted in terms of the first order analysis appropriate to a spin system made up of two sets of magnetically equivis not zero alent nuclei, it will appear that JAX but equal to JAx.Such a large apparent coupling constant in place of a nearly or exactly zero coupling constant is sometimes called a virtual coupling constant (6). It should be appreciated that the concept of a virtual coupling constant becomes necessary because of an attempt to apply a first order analysis when a first order analysis is not appropriate. Examples of such situations are relatively common in X.AA1A,' systems (JxK,E 0) in which JAA,is large relative to JAX (and JApx,) since in these systems JArx (and JAX,)can be small or aero. The case of hexamethyldiphosphine IV is probably an example of this, and the cases of trans1,4dichloro-2-butene VII and 2,6-dimetbylquinone VIII appear to he borderline cases. The spin systems considered so far have been made up of a maximum of only two groups of spin coupled chemical-shift-equivalent nuclei. Cases in which both groups are magnetically equivalent and in which both groups are magnetically non-equivalent were discussed. The concepts of magnetic equivalence and magnetic non-equivalence can be generalized, however, to spin systems made up of more than two groups of spin coupled chemical-shift-equivalent nuclei. If a set of spin coupled nuclei consists of three or more groups of chemical-shift-equivalent nuclei, any one group is a group of magnetically equivalent nuclei if, for each other chemical-shift-equivalent group considered in turn, the coupling constants between each nucleus in the one group and each nucleus in the other are all the same. Some of these coupling constants may be zero. The simplest case involving three groups of chemicalshift-equivalent nuclei is that in which there is only one nucleus in each group. Since in this case there is only a single coupling constant possible between members of any two groups, the three groups are necessarily magnetically equivalent. By analogy with cases involving two groups of magnetically equivalent nuclei, one would expect a first order spectrum when all differences in chemical shift are large relative to the corresponding coupling constant. When this is so, the spin system is usually called an AMX system. I n general, for the AMX case, if all three coupling constants are different, the resonance of each nucleus will appear as a doublet of doublets. Examples of such spin systems include the olefinic protons of p-chlorostyrene (Varian 498) (6) and the ring protons of methyl furoate (Varian 125). If all the coupling constants happen to be the same, the spectrum will appear as three 1 :2: 1 triplets, as in 1hromo-3-chloro-5-iodobenzene (7), and if one coupling constant is zero, two of the resonances will appear as
doublets, as with the aromatic protons of 2,4dinitroanisole (Varian 143). The AMX case may be considered to be the first member of a series of spin systems which may be represented in general by the notation A,R'I,X,. If, as implied by this notation, all chemical shift differences are large relative to the corresponding coupling constants, the appearance of the resonance of each of the three sets of magnetically equivalent nuclei can be considered to be the result of splitting first by members of one other set and then by members of the last set. That is, the A resonance, for example, can be considered to be a first order p 1membered multiplet with spacings corresponding to J*M,each line of which is further split into a first order m 1 membered multiplet with For example, in the spacings corresponding to JAX. spectrum of 2-hutenoic acid ylactone I X (Varian 51)
+
+
an AMXz system, the resonance of both the A proton and the M proton appear as pairs of triplets, and the resonance of t h e X protons appears as a pair of doublets. Similarly, in the spectrum of crotonic acid X (Varian 61)
an AMXa system, the resonances of both the A proton and the M proton appear as pairs of quartets, and the resonance of t h e X protons appears as a pair of doublets. Finally, in the spectrum of a-angelicalactone X I (8)
an M I X Bsystem, the resonance of the A proton appears as a triplet of quartets, the resonance of the A4 protons as a pair of 1 :3 :3: 1quartets which, since JAX = JMX overlap to give a 1:4:6:4: 1 quintet, and the resonance of the X protons as a pair of triprets. I n this last example, a pair of overlapping quartets appears as a 1:4:6:4:1 quintet because of the equality of the two coupling constants. This illustrates one of several possible ways in which lines of overlapping multiplets may coincide. As another example, in the spectrum of a-methylstyrene XI1 (9) HA \ ~ + / @
H ~ l
\c(H~)~
xn
the resonance of t,he X protons appears as a pair of doublets, the resonance of the M proton appears as a 1:4: 6 :4: 1 quintet because, as in the previous example, Volume 47, Number 12, December 1970
/
81 5
JAM= J M Xbut , the resonance of the A protons appears as a symmetrical, but non-binomial, 1 : 3 :4:4: 3 : 1 sextet because J*M = W A X . I n the AMX3 system which can result when an ethyl group is connected to an asymmetric center, the A and M resonances may each appear as a pair of quartets (or, from a different but equivalent point of view, as an "AB quartet" each line of which is split into a 1 :3 : 3 : 1 quartet), but the X resonance will always appear as a 1 : 2 : 1 triplet because JAx J M Xthrough the same averaging process which makes the three X protons chemical-shifbequivalent. A nice example of this case, which is of the type WCH,-CXY-CH2W in which W is methyl, is that of 2-diethylsulfurauylidine-1,3-indanedione XI11 (10).
-
observe an X resonance made up of six lines symmetrically placed about a midpoint. If JAX = Jsx, the X resonance will appear as a 1:2 : 1 triplet. This type of analysis may be extended in a general way. Thus for an ABX, system, the A and B resonances may be considered to be an "AB quartet" with the A lines each split into a first order m 1membered multiplet with spacings corresponding to JAXand the two B lines each split into a first order m 1 membered multiplet with spacings corresponding to J B X . The X resonance will appear as described for the ABX system. An example of this in which m = 3 is, as indicated above, the spectrum of compound XIII. If in an ABX system the differencein chemical shift between the A and B nuclei is small compared to JAB, and if the difference between JAXand Jsx is small compared to .JAB,the resonance of an ABX system can have the first order appearance of an A X system. More exactly, the condition is that the ratio ( ( A ~ A B I 'lzl(J~x Jsx)l)'/2Jm be equal to or less than the resolving power of the instrument (1). The apparent J under these conditions is the average of JAXand Jsx. Presumably, this condition can he extended in general and one would expect the resonance of an ABX, system to have the first order appearance of an AzX, system if Ahs and IJAx - Jsxl are small and/or JAB is large. The X resonance of an ABX system will always appear as a 1 :2 : 1 triplet when JAx = J B X but , it may appear as a triplet when JAX Z Jsx under the conditions just described. Thus, observing the resonance of X as a triplet does not necessarily mean that JAX= J B X . I n fact, one coupling constant, say J B X ,may be equal to zero if JABis large enough and ASAB is small. The apparent Jsx (which will be equal to the average of JAx and J B X or , '12JAX) which may be deduced by the inappropriate application of a first order analysis must then be called a virtual coupling. An example of this is the spectrum of 2,5-dichloronitrohenzeneXVI
+
+
+
If a spin system is made up of more than three groups of chemical-shift-equivalent nuclei, all of which are magnetically equivalent, and the chemical shift differences are large relative to the corresponding coupling constants, a first order spectrum will be observed which may be analyzed in a manner analogous to that described for spin systems made up of two or three groups of magnetically equivalent nuclei. Examples of spin systems of this type made up of four groups of magnetically equival.ent nuclei include those of crotonaldehyde XIV (Varian 60) and p-angelicalactone XV (11).
Although a first order analysis is generally not possible for A,M,X, systems when the chemical shift differences are not large relative to the corresponding coupling constants, an approximate first order analysis may be applied to certain intermediate cases. For example, in the AMX case, if one chemical shift difference, say ASnnr,is not large relative to the corresponding coupling constant, J*M,giving what is usually called an ABX system, the A and B resonances may be interpreted as an "AB quartet" with the two A lines each split into a doublet with a spacing corresponding to J A X and , ivith the two B lines each split into a doublet with a spacing corresponding to J B X . These doublet spacings are equal to JAxand Jsx only when J A X = Jsx; otherwise, when JAx # JBX,the doublet spacings are only approximately equal to JAXand J B X and , the approximation increases in error as IJAx - Jsxl increases or as AS*B decreases. The four A lines and the four B lines may overlap, andsome may coincide. T h e X resonance of an ABX system often consists of a doublet of doublets with spacings corresponding to JAx and J B X ,as a first order analysis would predict, but one can sometimes 816
/
Journal of Chemical Education
in which the resonance of A and B appears as a 1 : 1 doublet and the resonance of X as a 1 : 2 : 1 triplet with an apparent J of 1.6 Hz (4). A first order analysis of the spectrum would lead to the conclusion that JAX= Jax = 1.6 He, whereas JAXwould be expected to he approximately zero, and J B Xto be approximately 3 He. I n a molecular fragment such as XVII
XVII
the resonance of the methyl group would ordinarily be expected to appear as a 1 : 1 doublet with a splitting corresponding to Jsx since JAXwould be expected to be zero. However, as in the ABX system just described,
when A ~ A Bis very small or zero and if JAB is large enough, the methyl resonance can appear as a 1 : 2 : 1 triplet and the A and B resonance as a 1:3: 3: 1quartet. That is, the resonance of t,he ABXb system would appear as that of an A2X8system. Again, the apparent JAx (which, if JAX = 0, will equal '/JBx) which would be deduced by the inappropriate application of a first order analysis would be called a virtual coupling. Since JAB is approximately equal to Jsxin systems of this type, even when Aans = 0 an in between case is observed in which the methyl doublet has only a partially "filled in" appearance (the "filling in" has not reached the point of making the doublet appear as a triplet) and the A and B resonance is complex. An example is the spectrum of 2,3-dibromopropionic acid XVIII (Varian 403). Br Br
I I
HOOC-C-C-CH,
I
I
fi fi XWI
Further examples of related cases are discussed in reference ( I d ) . Some of the possible spin systems made up of three sets of spin coupled, chemical-shift-equivalent nuclei are summarized in Appendix 11. I n analogy with spin systems made up of two groups of magnetically non-equivalent nuclei, spin systems composed of three or more groups of nuclei a t least two of which are magnetically non-equivalent (it would be impossible for only one group to be magnetically nonequivalent) would be expected in general to give complex spectra even when all chemical shift differences are large relative to the corresponding coupling constants. While the spectra of certain systems support this expectation, for example the spectra of some 1-X,4-fluombenzenes, the spectra of certain very common spin systems give simple spectra. For example, l-bromopropane, which might be expected to be an AA'MM'X, system (by imagining it to be derived from l-bromo2-chloroethane by replacement of chlorine by methyl) gives a spectrum which can be interpreted as that of an A2M2X3system in which JAM E JMX S 4 7 Hz and JAx = 0. The vicinal coupling constants of a molecular fragment of the type Y-CH,-CH2-X can have the same value if (1) each of the two gauche conformations and the one trans conformation are equally populated and (2) J,,.a. are all equal in all conformations and Jc.., are all equal in all conformations. This, then, is one way that the requirement that ( J A X - JA,X)2/21JAA,Jxx,] 5 0.5 Hz can be met so that the spectrum of a 1,2-disubstituted ethane can appear as that of an A& system (when JAX = J*,x, the system is by definition an A,X2 system), and may also explain why the spectra of isolated n-propyl groups appear as those of A&X, systems rather than of AA'ILIIVI'X3 systems. The fact that 1-chloro-3-bromopropane (Varian 29) gives the first order spectrum expected of an A2M2XZsystem in which JAM = JMX and Jnx= 0, while 3-trimethylsilylpropane-1-sodium sulfonate (Varian 481) gives a complex spectrum may be interpreted similarly. Literature Cited (1) A B R A ~ A R.~ J., , Awn BERNSTEIN, H . J., Con. J . Chem., 39,216 (1961). (2) H ~ n m sR. . K.. Con. J . Chcm.. 42,2275 (1964).
, G., Con. J . Chem., 42,2282 (1964). (3) Hnssrs, R. K.. A N D H ~ r r n n R. (4) BECKER. E. D.. J. CXEM.EDDC., 42,591 (1965). (5) M u s n ~ RJ. , I.. AND CORET, E . J., Telrahedron, 18,791 (1962). (6) AULT,A,. "Problems in Organic Structure Determination.'' McGr&xuHill. N e v York. 1961, p. 32.
(7) AUGT.A,. unoublished observation. ~~r&'(si, P. 29. (9) Reference ( 6 ) . P. 39. (lo) Coor, A. F., m n Mormrr, J. G., . I Amer. . Chem. Soo., 90,740 (1968). (n)Reference (6).P. 30. (12) ANET,F. A. L.. Can. J . Cham., 39.2262 (1961).
isj
Appendix I: Spin Systems Made U p of T w o Sets of Spin Coupled Nuclei Magnetically Equivalent Sets of Nuclei The AX, AzX, AsX,. . ., A& AaX2,. . ., A S m Cases. The appeerance of the spectrum will depend upon the values of JAX and A ~ A only, X and will be independent of values of JAA and Jxx When n = m, the spectrum will be symmetrical ahout the midpoint. These system will give spectra which will have a first order appearance when the ratio Adlx/J~xis large.
Mogneticafly Nan-equivalent Sets of Nuclei The AA'X Case. The appearance of the spectrum will depend JA.X, JAAP, and A6~x;in general, it will npon the values of he complex. The resonance of the AA'X system will have a. first order appearance (the resonance of A and A' appearing ss s. 1: 1 doublet and the resonance of X as a. l:2: 1 triplet) when (1) A ~ A Xis large, and (2) when the ratio ['/&TAX - J A , ~ ) I ~ ~ / ~ \ J A A , ~ is less than the resolving power of the instrument (typ~cally0.5 He) (I). Under these conditions, the apparent J is the average and JA~x. of JAX The AA'XX' Case. The appearance of the spectrum will deJA,x, JAAZ, Jxx,, and Ahx. In pend upon the values of JAX, general, it will he complex, and it will always be symmetrical about the mid~oint. The resonance of an AA'XX' svstem will have a first orher appearance (it will appear a s a pail of 1:2:1 triplets) when (1) A6~xis large, and (2) when the ratio (JAXJA.x)~/ZIJAA. - Jxx.l is less than the resolving power of the instrument (I). Under these conditions, the apparent J is the and JA~x. average of JAX The X.AA'X.' Case (Jxx, Z 0). 1. Wben (1) A6~xis large, and (2) when the ratio (JAX J A . X ) ~ / ~ ~ Jis A less A , I than the resolving power of the instrument (A and A' are strongly coupled), the A resonance will appear as a first order 2n 1 membered multi~let,and the X resonance as s 1 : triplet 8 In other word;, u h e r these conditions, the resonance of the XAA'X.' system will appear as that of en A&, system. The apparent J will be equal to the average of JAX and JA,?, When J A ~ (and, X by symmetry, JLX,)E+ 0, the retio of cond~tlon(2) reduces to (J~x)~/21J~n,l. 2. When (1) A6~xis large, and (2) when the ratio (JAXJAex)2/21J.uZlis somewhat greater than one (A and A' are weakly 1 memcoupled), the A resonance will appear as a first order n bered multiplet, and the X resonance as a 1: 1doublet; the resonance of the XAA'X,' system will appear as that of two identi~ by symcal, independent, AX, system (8). When J A , (and, metry, JAX,)Z 0, the ratio of condition (2) reduces to ( J A x ) ~ /
+
+
~IJAA.~.
Appendix 11: Spin Systems Made U p of Three Sets of Spin Coupled Nuclei Magnetically Equivalent Sets of Nuclei The AMX, AMXZ,..., AM& AM2Xa,..., A ~ M S X ~AT , Max3,.. ., A,MpX, Cases. The appearance of the spectra of spin systems of these types depend upon the vadues of three JAX, and JYX, and two chemical shift coupling constants, JAM, differences (the third chemical shift difference is determined by the other two). When all chemical shift differences are large relative to the corresponding coupling constants, the resonance of each group of magnetically equivalent nuclei will appear as a regular multiplet of multiplets. When one coupling constant is an integral multiple of another, some lines may coincide. The ABX, ABXa ABXa,. . ., ABX, Cases. The A and B resonances may he interpreted as hn "AB quartet" in which each 1 membered multiplet of the A lines has been split into an m with spacings wrresponding to JAX,and each of the B lines has
+
Volume 47, Number 12, December 1970
/
817
+
been split into an m 1membered multiplet with spacings corresponding to J B X . Thii approximation increases in error a s I J A ~- Jsx( increases or as A ~ A Bdecreases. The X resonance will be a 1:2: 1 triplet if J A X = J s x , but usually it appears as a doublet of doublets with spacings corresponding to J A X and Jsx. With certain values for the coupling constants and chemical shift differences, six lines, symmetrically placed about a midpoint, may be observed. The ABX system will have the &st order appearance of an
818
/
Journnl of Chemical Education
+
A X system if the ratio ( 1 ~ 6 ~ ~'lnl(J*x 1 - J B X )JP/2J*s ~ is equal to or less than the resolving power of the mstrument (1). Under these conditions, the apparent J equals the average of JAXand J s x . The AA'X case of Appendix I may be seen to be the ABX case when A h approaches zero. Presumably, the ABX, system will have the first order rtp pearance of an A2Xmsystem when A h and IJAX - Jsxl are small and/or JABis large. The ABC,. ., LB,C, Cases. The spectra, of these systems will be complex.
.
