Weak coupling between magnetically inequivalent spins: The deceptively simple, complicated spectrum of a 13C-labeled trimethylated amine

Magnetic inequivalence of nuclear spins is well known to cause additional splittings that complicate spectral analysis. Here, we present an extraordinary case of magnetic inequivalence, manifested in the 13-spin system of a C,N-labeled trimethylated amine. All methyl group protons are chemically equivalent due to the molecular symmetry, but not all are magnetically equivalent as they have different JCH and JCH couplings. In general, spectra of such a large spin system can be expected to be extremely complicated by the presence of hundreds if not thousands of extra lines, caused by the strong coupling between inequivalent nuclei. Surprisingly, the H spectrum presented consists of very few lines, in a pattern of the utmost simplicity. Using sub-spectral analysis we show that this is due to weak coupling between the magnetically inequivalent nuclei, as a consequence of the particular combination of coupling constants. We find that the JHH geminal methyl coupling constant is 0.43 Hz and JCC is 0 Hz. In addition, we demonstrate that homo-decoupling can be used to transform the spin system to a set of fully equivalent spins, resulting in disappearance of JHH-splittings. We believe this curious case is a highly instructive example of magnetic inequivalence. The spectra may be considered deceptively simple, as fewer lines are observed than one would anticipate. At the same time, the spectra are deceptively complicated, as they can very well be approximated by intuitive reasoning. 2017 The Authors. Published by Elsevier Inc. This is an openaccess article under the CCBY license (http:// creativecommons.org/licenses/by/4.0/).


Introduction
Scalar coupling between nuclear spins is one of the defining features of solution NMR. It is used as a rich source of information on molecular structure [1], and encountered in the everyday practice of spectroscopists through the fine structure of resonance lines. The exact shape of the multiplet pattern that is generated by scalar coupling depends critically on the ratio of the frequency separation between the two nuclei, Dm, and their coupling constant, J. In the weak coupling regime (Dm ) J) simple rules can predict the observed multiplet patterns. Spins that are strongly coupled (Dm [ J) give rise to more complicated multiplets: the intensity of individual components depends strongly on Dm/J, and in larger spin systems additional, so-called combination lines may be observed. At the extreme end of strong coupling is the coupling between spins with identical chemical shifts (Dm = 0). In this case, the spins are either magnetically equivalent, when they have identical coupling constants to all other (non-equivalent) spins in the molecule, or magnetically inequivalent, when this is not the case [2]. The coupling between magnetically equivalent spins is inconsequential, as it cannot be observed. On the contrary, the coupling between magnetically inequivalent spins is observable and responsible for additional line splitting, a fact well established since the pioneering work of McConnell, McLean and Reilly [3]. The theory of magnetically inequivalent spin systems and analysis of their spectra has been thoroughly described in the 50s and 60s of last century [4][5][6][7][8][9][10]. These and other analyses show that, in particular for large spin systems, the strong coupling between magnetically inequivalent nuclei can generate so many additional splittings and additional lines that the extraction of accurate spin frequencies and scalar coupling constants is severely challenged [11][12][13].
Here, we revisit the analysis of magnetically inequivalent spin systems to describe an exceptional scenario where this spectral complexity is lost and a simple, essentially weakly coupled spectrum is obtained. We demonstrate this effect experimentally in a 13-spin system, a 13 C, 15 N-labeled trimethylated amine, in which the three methyl groups are magnetically inequivalent. We show that the combination of large and small coupling constants in this spin system results in a system that can very well be treated as weakly coupled magnetically inequivalent spin pairs. We further demonstrate that the effects from magnetically inequivalence can be completely removed in this case by 13 C-spin state selective proton homo-decoupling. The curious spectrum of this compound and the controlled transformation to magnetic equivalence highlight the richness of scalar coupling phenomena in NMR.

NMR spectroscopy
NMR spectra of compound 1 ($20 mM) in 100% D 2 O were obtained at 298 K on a Bruker Avance III HD spectrometer operating at 600 MHz 1 H Larmor frequency and equipped with a cryoprobe. All 1D 1 H spectra were acquired in a single scan and zero-filled two times before Fourier transformation. Highest resolution spectra were obtained with 8 s. acquisition time and Lorentz-to-Gauss apodization with negative exponential broadening À1 Hz and the center of the Gaussian placed at 30% of the FID. Other spectra, including 15 N/ 13 C decoupled spectra, were recorded with 5 s acquisition time and apodized with À0.8 Hz negative exponential broadening and the center of the Gaussian shifted to 40% of the length of the FID. In order to obtain a highresolution 15 N/ 13 C-decoupled 1D, a low power on-resonance WALTZ16-decoupling field was used: 260 Hz cB 2 at 49.9 ppm for 15 N, and 640 Hz cB 2 at 53.0 ppm for 13 C. The 15 N and 13 C chemical shifts were obtained from 2D H(C)N and 2D HMQC spectra. The homo-decoupled spectrum was recorded using the zghd.2 pulse program with continuous wave irradiation ($70 Hz cB 2 ) centered on the upfield 1 J CH doublet component and 5 s acquisition time.

Simulations
There are several powerful programs that can simulate solution-state NMR spectra, e.g. [14][15][16]. We preferred to write our own simulation script as part of our learning process and to be able to tailor the simulations to our needs and requirements. Spectra of various AX-type spin systems were simulated using an in-house written GNU Octave [17] script that implements the composite particle approach (CPA) [18,19], as outlined by Diehl and coworkers [10]. Briefly, magnetically equivalent spins are grouped into a single composite particle, with total spin F max equal to the sum of the grouped spins, e.g. F max = 3/2 for three equivalent methyl protons. This particle can exist in independent spin states with a maximum spin F equal to F max , F max À 1, . . .; e.g. for a system of one methyl group the allowed spin states are quartet (F = 3/2, Q) and doublet (F = 1/2, D), such that a trimethyl group can exist in any of 8 states such as QQQ, QQD, QDQ, etc. To solve the A-spin ( 1 H) spectrum, the Hamiltonian is factorized according to the total spin of the system m T, the spin state of each particle, and the total spin m T,X of the X-nuclei ( 13 C). This procedure breaks down the 4096 Â 4096 matrix for the 12-spin case into much smaller matrices of at most 36 Â 36. The transition frequencies and intensities are then calculated using standard approaches. Each subspectrum is multiplied with a statistical weight to account for the degeneracy of the involved spin states. Lines corresponding to transitions with extremely low probability (intensity lower than 1Á10 À4 , whereas the largest peak has intensity 36) are omitted to ensure efficient drawing of the spectrum. For all remaining transitions an FID is simulated, these are subsequently added, an exponential decay to match the experimental lineshape is added, and the final FID is processed according to the experimental settings to yield the final spectrum.
In the weak-coupling approximation, the experimental spectrum was simulated by calculating FIDs according to the experimental settings for the outer, center and inner lines individually. For all three signals a weak 2 J NH coupling was added. The effect of inequivalence was simulated by adding a weak 4 J HH coupling to either 0, 3, or 6 equivalent protons for the outer, center and inner line, respectively. An exponential decay was added to match the experimental lineshape. Processing was identical to the experimental situation. All simulation scripts are available upon request.

Theory
In this section, we will, after a brief introduction, use the subspectral analysis approach to derive the boundary conditions that result in weakly coupled spectra of magnetically inequivalent spins. 15

Sub-spectral analysis
The sub-spectral analysis framework was developed by Diehl, Bernstein and co-workers to ease the accurate determination of J-coupling values and chemical shifts in magnetically inequivalent systems [8,10]. The basic principle of this approach is to decompose the spectrum into much simpler sub-spectra, each with well-defined (apparent) chemical shifts and coupling constants. This decomposition reflects the factorization of the Hamiltonian, or equivalently the energy level diagram, into independent parts. Considering the A-spin spectrum of AX-type spin systems, the energy level diagram can be factorized based on the total magnetic quantum number m T,X for the X-spins: transitions of spin A are only allowed between wave functions that have Dm T,X = 0 (the so-called X-approximation), in addition to the usual Dm = ±1 selection rule. Further factorization can be obtained by using wave functions that are constructed using the molecular symmetry, since selection rules only allow transitions between states of the same symmetry class [4]. Thus, the sub-spectra in the A-spectrum correspond each to a sub-energy level diagram formed by wave functions of one particular m T,X value and one particular symmetry class.

Conditions for weakly coupled sub-spectra
To explain how weakly coupled sub-spectra can arise, we turn to the textbook case of a 4-spin system with two pairs of magnetically inequivalent spins [3,5,20,21]. This spin system is labeled AA 0 XX 0 in the extended notation of Pople [22,23], or [AX] 2 in the notation of Haigh [24]. The spin system is schematically illustrated in Fig. 1A together with definition of the coupling constants. The spectrum of the inequivalent A/A 0 spins consists of eight lines, decomposed into two a 2 and two ab sub-spectra (sub-spectra are denoted in lowercase italics) (Fig. 1B). The two a 2 sub-spectra originate from sub-energy level diagrams that have the same functional shape as that for two equivalent spins, hence the a 2designation. These corresponds to m T,X + 1, i.e. X-spins in the aastate, and to m T,X À 1, i.e. X-spins in the bb-state. In both subspaces, the A/A 0 -spins are described by fully equivalent, virtual a-spins with frequency m a ¼ m A AE jJ AX þ J AX 0 j. Their equivalence may be intuitively understood by imagining a molecule with the X/X 0 -spins both in the a or both in the b-spin state: the A/A 0 -spins are indistinguishable due to the twofold symmetry of the molecule. This is not true for mixed a/b-states; hence the A/A 0 -spins in the m T, X = 0 space are magnetically inequivalent and subject to J AA /J XXcoupling. In this subspace, the A/A 0 -spins form a strongly coupled ab-type spin system, with frequency difference Dm ab ¼ jJ AX À J AX 0 j and J-coupling J ab ¼ jJ AA 0 j AE jJ XX 0 j between the virtual a and bspins. Since this space is formed by both symmetrical and antisymmetrical wave functions there are two ab-sub-spectra. An explicit presentation of the wave functions and energy diagram of the AA 0 XX 0 -system, based primarily on the analysis by Flynn et al. [20], is presented in Fig. S2.
We will now set two boundary conditions that will result in a dramatic simplification of the spectrum. First, either J XX or J AA is near zero. In this case the two ab-sub-spectra in Fig. 1B have the same effective splitting and collapse into a single ab-subspectrum, as shown in Fig. 1C. Second, the frequency separation between the virtual a and b-spins Dm ab is much larger than their effective coupling constant J ab , i.e. when J XX $ 0: Because the a,b-spins are now no longer strongly coupled, we redefine them as weakly coupled a,x-spins. The m T,X = 0 subspectrum is a symmetric doublet, split by J AA , and is best labeled as an ax-sub-spectrum (Fig. 1D). Thus, under the above two conditions the spectrum of 8 lines and 5 different intensity levels of Fig. 1A is reduced to 6 lines with only 2 different intensities, the m T,X : sum of two a 2 and two overlapping ax-sub-spectra in Fig. 1D. This dramatic simplification may arise if J AX is very large compared to the other coupling constants.

Extension to [AX] 3 and [A 3 X] 3 spin systems
The simplified pattern of Fig. 1D in the [AX] 2 spin system can be extended to more complicated AX-type spin systems in a predictable manner. As an intermediate step towards the [A 3 X] 3 system, it is useful to consider the A-spin spectrum in the 6-spin system [AX] 3 , first described by Jones et al. [9]. In general, this spectrum consists of 56 transitions that can be grouped in six sub-spectra of three virtual spins: two a 3 -patterns for m T,X = ± 3 / 2 , i.e. where the X-spins are in the aaa/bbb-spin state, two ab 2and two abc-patterns for m T,X = ± 1 / 2 . In the special case where J XX = 0, it can be shown that the abc-pattern is reduced to another ab 2 -pattern [9], a situation depicted in Fig. 2A. The frequency difference between the virtual a and b spin is |J AX À J AX 0 |, with apparent coupling constant J AA (when J XX = 0). Here, we label the m T, X = ± 1 / 2 sub-spectra on one side of A-multiplet as ab 2 and as a 2 b on the other side, reflecting the different orientations of the ab 2pattern. This complicated multiplet is again dramatically simplified when |J AX À J AX 0 | ) |J AA |, as shown in Fig. 2B. Under these conditions, the a and b spins are effectively weakly coupled and the sub-spectra reduce to a 2 x and ax 2 -patterns. The logical progression from a 3 to a 2 x and ax 2 can also be appreciated considering the X spin states: from aaa (m T,X = + 3 / 2 , a 3 ) to states of the aab (m T,X = + 1 / 2 , a 2 x) to abb-type (m T,X = À 1 / 2 , ax 2 ).). We note that while the [AX] 2 system is symmetrical with respect to J AA and J XX , this is not true for [AX] 3 systems. The A-spin spectra for J AA = 0 and J XX ( |J AX À J AX 0 | in [A n X] 3 spin systems feature very distinct multiplets of five lines in addition to the singlet a n sub-spectrum [25]. In addition, it can be noted that weakly coupled sub-spectra arise in the [AX] 2 system as long as |J AX À J AX 0 | ) |J AA | + |J XX | (see also Fig. S2). This is not sufficient in [A n X] 3 spin systems, where J XX must be negligible.
We now turn to the [A 3 X] 3 system. In general, without simplifying assumptions about the values of the coupling constants, there are 9312 allowed A-transitions in this spin system out of which many hundreds can result in distinct lines [26]. Even with negligible J XX , the spectrum is characterized by the presence of many lines, with wildly varying intensities (Fig. 2C). Under the simplifying conditions J XX $ 0 and |J AX À J AX 0 | ) |J AA | the spectrum can now again be decomposed in simple sub-spectra. As there are three possible m T,X -states for each side of the main J AX doublet (e.g. À 3 / 2 , À½, +½ for the downfield triplet), there are again three sub-spectra. Recognizing that there are nine A-spins, the outer line is of the a 9 -type. Since the spins within one A 3 group are magnetically equivalent, the center line becomes an a 6 x 3 quartet, and the inner line is part of an a 3 x 6 sub-spectrum, resulting in a septet (1:6:15:20:15:6:1) (Fig. 2D).
Similar reasoning can be used to show that [A 2 X] 2 systems would have a 4 and a 2 x 2 sub-spectra, and that spectra of [A 2 X] 3 systems reduce to a 6 , a 4 x 2 , and a 2 x 4 sub-spectra. In short, we show here that in case of large |J AX À J AX 0 | with respect to J AA 0 and negligible J XX , the a and b species in sub-spectral analysis are in fact weakly coupled and the sub-spectra are simple multiplet patterns as in the case of weakly coupled spins.

Results
The focus of our study is a 13 C, 15 N-labeled trimethyl amine, abbreviated as compound 1 (Fig. 3). While all methyl protons are chemically equivalent due to the molecular symmetry, the introduction of 13 C-isotopes breaks their magnetic equivalence. This 13-spin system is thus best described as an A 3 A 0 3 A 00 3 MXX 0 X 00 , or more compactly as a [A 3 X] 3 M system, where A 3 represents the three 1 H spins in a methyl group, M is the 15 N spin, X is the 13 C carbon spin and the quotes are used to indicate magnetically inequivalent spins. As a result of the inequivalence, the proton 1D NMR spectrum of compound 1 can be expected to show splittings due to the four-bound coupling between the geminal methyl groups ( 4 J HH ) and the two-bond carbon-carbon coupling ( 2 J CC ).
As set out in the Theory section above, the appearance of AA 0 . . .XX 0 . . .-type spin systems depends strongly on the relative magnitudes of the coupling constants J AX , J AX 0 , J AA , J XX . In general, when all couplings are of comparable strength, the resulting spectrum will feature many lines with varying intensities, reflecting the strong coupling between magnetic inequivalent spin pairs. Moreover, the spectral complexity will increase rapidly with increasing size of the spin system, resulting in hundreds to thousands of distinct lines for an [A 3 X] 3 spin system [26]. On the other hand, when some coupling constants dominate and others are negligible, the spectrum is greatly simplified. In particular, in case J XX $ 0 and | J AX À J AX 0 | ) |J AA |, the magnetic inequivalent nuclei become weakly coupled and the spectrum will reduce to a simple pattern of axtype sub-spectra (see Theory section). In our case |J AX À J AX 0 | corresponds to | 1 J CH À 3 J CH |, while J AA and J XX correspond 4 J HH and 2 J CC respectively. Thus, we may expect this simplifying condition to hold true for compound 1, resulting in a spectrum similar to that in Fig. 2D.

Assignment of splittings in the 1 H spectrum
The proton 1D NMR spectrum of compound 1 is characterized by two highly asymmetric multiplet patterns separated by the large 1 J CH (Fig. 4A). Ignoring the asymmetry, these patterns have the appearance of triplets, as expected considering the methyl protons are coupled to two 13 C spins by 3 J CH . Peak integration of the three triplet components shows the expected 1:2:1 ratio. As we will show below, the asymmetry is caused by unresolved 4 J HH splittings.
The outer triplet component appears as a sharp doublet with 0.75 Hz splitting (Fig. 4B). This splitting is removed upon 15 N decoupling (Fig. 4C,D), proving that it is due to the 2 J HN coupling interaction. This splitting is masked on the central and inner line of the triplet by their much broader appearance (Fig. 4B), but clearly present as can be inferred from the peak sharpening upon 15 N-decoupling (Fig. 4D).
The center and inner lines in the spectra of Fig. 4 show subtle signs of additional splittings. In an attempt to resolve these splittings, a high resolution spectrum was recorded with 8 s acquisition time and processed using different degrees of resolution enhancing Lorentz-to-Gauss transformations (Fig. 5). Without any window-function the spectrum shows a near perfect triplet, although the 2 J HN -splitting is only visible on the outer line (Fig. 5A). Processing with moderate or strong resolution enhancement uncovers small splittings on the center and inner lines only (Fig. 5B,C). This fine structure is different for the center and inner component, as is clear from their different shapes. This is consistently visible on both sides of the 1 J CH doublet. The apparent coupling constant is on the order of 0.4 Hz, in line with J-coupling values expected for 4 J HH or 2 J CC , and much smaller than | 1 J CH À 3 J CH | (141.3 Hz). The increase in additional splittings going from the outer to center to the inner lines, i.e. there is a 13 C spin state dependent pattern of splittings, obeys the pattern shown in Fig. 2D fully.

Estimation of 4 J HH and 2 J CC
We next applied the theory described above and decomposed the experimental spectrum into ax-type sub-spectra to extract an estimate for the 4 J HH between the geminal methyl groups, thus assuming 2 J CC is zero. Since compound 1 is an [A 3 X] 3 M spin system, each line of the a 9 , a 6 x 3 and a 3 x 6 sub-spectra in Fig. 2D will now be split into a doublet due to 2 J HN . The downfield component of the main 1 J CH doublet was thus fitted as a sum of a doublet, a quartet of doublets and a septet of doublets. The resulting stick-plot and a simulated spectrum with the experimental lineshapes is shown in Fig. 6A,B. The best fit is obtained using 0.43 Hz for | 4 J HH |, and agrees very well with the experimental spectrum. An exact calculation of the 1 H spectrum of the [A 3 X] 3 M system using the composite particle approach is shown in Fig. 6C, underscoring the validity of the weak coupling approximation. The numerical approach also allows evaluating the impact of non-zero values for 2 J CC (Fig. 6C). Significant deviations from the experimental lineshape are already visible with very small non-zero values (0.4 Hz), most notably around the center of the inner multiplet. Furthermore, strong inequivalence effects are absent from the 13 C 1D spectrum (Fig. S3). Together, the exact simulations of both the 1 H and 13 C spectra strongly support a near-zero value for 2 J CC , at least | 2 J CC | < 0.4 Hz.
Notably, comparison of the experimental and numerically simulated spectrum highlights that the observed linewidths of the outer, center and inner line are unequal (Fig. 6A,C). There is a small, but significant, increase in linewidth going from the outer to the center and inner line. This effect has been accounted for in the fit

Transformation to magnetic equivalence
The close agreement between the experimental spectrum and a fit based on a decomposition into ax-type sub-spectra suggests that the different methyl groups are in fact weakly coupled to each other due to 4 J HH . Phrased differently, the downfield center line and the upfield inner line form a weakly coupled ax spin system as do the downfield inner and upfield center line (cf. Fig. 2D). This effect can also be seen in the 2D DQF-COSY spectrum, which shows crosspeaks between the center and inner line (Fig. S4). Since spins a and x are weakly coupled and since there is a large frequency separation between them (cf. Fig. 2D), one may hypothesize the possibility to decouple their interaction. Indeed, a homodecoupling experiment where the upfield component of the main 1 J CH doublet, corresponding to the x spin species, are irradiated during acquisition results in the removal of all 4 J HH splittings (Fig. 7A,B). The multiplets are collapsed to the expected triplet for a set of three fully equivalent methyl groups. Composite particle based calculation of this spin state-selective homo-decoupling experiment confirms the controlled transformation to a magnetically equivalent spin system (Fig. 7C). It is also of interest to note that the linewidths for each of the triplet components are very similar upon homo-decoupling.

Discussion
Magnetic inequivalent nuclei are regularly encountered in organic or inorganic compounds, where their presence can be used to infer molecular symmetry. Their NMR signals feature more lines and more intensities levels compared to a first-order coupling pattern, due to the strong coupling between magnetically inequivalent spin pairs. In this paper, we have presented an exceptional case of how magnetic inequivalence can affect the appearance of spectra, resulting in a sum of first-order coupling patterns. Compound 1, an isotope-labeled trimethyl amine, presents an [A 3 X] 3 M spin system where the coupling constants produce an extreme simplification of a spectrum that in typical cases would consist of hundreds to thousands of lines. We showed that this simplification depends on two conditions: (i) J XX is near-zero; and (ii) |J AX À J AX 0 | ) |J AA |. We derived that under these conditions the spectrum can be decomposed into sub-spectra formed by fully equivalent spins (a 9 -sub-spectra), and subspectra formed by weakly coupled a and x spins with coupling constant J AA (a 6 x 3 /a 3 x 6 -sub-spectra).
We presented a stepwise analysis of [AX] 2 , [AX] 3 and [A 3 X] 3 spin systems, to understand and illustrate the salient features of the experimental spectrum, rather than a complete analytical description of the [A 3 X] 3 M system. As noted by Diehl et al., the composite particle approach offers the most convenient route to solving the Hamiltonian [10]. In particular, this approach does not rely on molecular symmetry to factorize the Hamiltonian but rather factorizes based on spin states of the (composite) particles. In this description, the 1 H spectrum is described as a sum of 16 non-identical sub-spectra, where each sub-spectrum corresponds to one m T,X state and one particular combination of quartet and doublet spin states for the three methyl groups (see Fig. S5). Notably, all sub-spectra with the same m T,X value overlap and add up to the observed a 9 , a 6 x 3 or a 3 x 6 patterns.
The overall spectrum can be reproduced using just 48 lines, thus classifying as a 'deceptively simple' spectrum where many transitions are (nearly) degenerate and/or have low transition probabilities [27]. This spectral simplicity made it possible to fit the experimental spectrum and extract a value of 0.43 Hz for the 4 J HH between geminal methyl group in compound 1. This is well in line with previous reports on geminal methyl coupling constants [28], in particular with a value of 0.41 Hz for the primary amine tertbutyl-amine [29]. Notably, direct measurement of 4 J HH from the 13 C satellite peaks in an unlabeled compound failed since the presence of the quadrupolar 14 N nucleus induces 1 H line broadening through scalar relaxation of the second kind (data not shown). A near-zero value for the 2 J CC matches the observation that these couplings are generally small in saturated aliphatic groups, and that they can be both positive and negative [30]. Notably, a reverse assignment of J HH and J CC is not possible since the A-spin spectrum of a [A 3 X] 3 systems has different multiplet structures when J AA = 0 [25].
When fitting the experimental lineshape with the weak coupling approximation, we found small but significant linewidth differences between the outer, center and inner line. This differential line broadening effect is removed in the homo-decoupled experiment, where the x-spins are decoupled from the a-spins. The observed broadening is thus most likely due to relaxation interference between the different 1 H-1 H dipolar interactions. A full analysis of this effect is beyond the scope of this paper.
The peculiar spectral manifestation of magnetic inequivalence in compound 1 may also be found in other compounds as long as the two limiting conditions are met. We thus expect that isotope labeled compounds with carbon/nitrogen-atoms separated by another hetero-nucleus such as C-O-C or C-S-C, or N-C-N type structures, as for instance 13 C-labeled dimethyl-ether, will show similar spectra with ax-type sub-spectra. The presence of the hetero-nucleus is required to make sure J XX is negligible.
To the best of our knowledge this report is the first explicit analysis and experimental demonstration of a completely first-order spectrum for a magnetically inequivalent spin system. Other limiting cases resulting in spectral simplification have been described before, particularly in the work of Harris et al. [25,[31][32][33]. In the case of [PF 2 ] 2 -containing complexes, they showed that some subspectra may become first-order when one of the J PF constants is very large [33]. Since in that case both J PP and J FF were non-zero, additional second-order sub-spectra remain. Another report on phosporous-fluorine complexes shows, without analysis, the 19 F spectrum of Ni[PF 3 ] 4 which is reminiscent of the spectrum of compound 1 [34]. Even though not all splittings can be resolved, it is clear that the spectrum deviates from the expected a 9 x 3 quartet, suggesting that 2 J PP is not negligible. The case described here stands out from such previous reports, as it presents an extreme simplification afforded by a 'perfect storm' of coupling constants.
Lastly, our work demonstrates a remarkable consequence of the weak coupling between the magnetically inequivalent nuclei: they can effectively be decoupled by spin state selective homodecoupling. This transforms the spin system into a fully equivalent system, removing all 4 J HH splittings from the multiplet. In our opinion, the spectrum of the 13 C-labeled trimethyl amine presented here is an extremely instructive illustration of the effects of magnetic inequivalence. Depending on your viewpoint the spectrum may be considered deceptively simple or deceptively complicated.