13C-detected 1H–2H separated local field NMR spectroscopy

Chemical Physics Letters 382 (2003) 410–417 www.elsevier.com/locate/cplett

13

C-detected 1H–2H separated local field NMR spectroscopy S.V. Dvinskikh a b

a,*,1

€m a, H. Zimmermann b, A. Maliniak , D. Sandstro

a

Division of Physical Chemistry, Arrhenius Laboratory, Stockholm University, SE-10691 Stockholm, Sweden Department of Biophysics, Max-Planck-Institut f€ur Medizinische Forschung, D-69120 Heidelberg, Germany Received 8 September 2003; in final form 17 October 2003

Abstract We present a new NMR method for measuring 1 H–2 H dipolar couplings in macroscopically oriented media. To overcome the lack of dipolar resolution in 1D 1 H and 2 H spectra of deuterated molecules, we use a 2D heteronuclear correlation experiment where 1 H chemical shifts and 1 H–2 H dipolar interactions in the first dimension are correlated with 13 C chemical shifts and 2 H–13 C dipolar interactions in the second dimension. The technique is demonstrated on a columnar liquid-crystalline phase. Ó 2003 Elsevier B.V. All rights reserved.

1. Introduction The measurement of dipolar couplings by NMR spectroscopy is a powerful tool for probing molecular structure and dynamics in anisotropic systems [1]. In macroscopically oriented samples such as single crystals, liquid crystals, and biomolecules in lipid bilayers, site-resolved dipolar interactions can be obtained under stationary (non-spinning) conditions [2–8]. A high degree of chemical-site resolution, which allows for an accurate determination of the dipolar couplings, can be achieved if one of the spin species belongs to a rare nucleus with a large chemical shift (CS) dis-

*

Corresponding author. Fax: +46-8-15-21-87. E-mail address: [email protected] (S.V. Dvinskikh). 1 On leave from: Institute of Physics, St. Petersburg State University, 198904 St. Petersburg, Russia.

persion range. Important examples presented in the past include short-range 1 H–15 N and 1 H–13 C couplings [7,8]. In order to determine the molecular structure of complex molecules, it is often necessary to increase the number of conformational constraints by measuring longer-range dipolar interactions [7,9]. In the following, measurements of heteronuclear couplings between 1 H, 2 H, and 13 C nuclei in partially deuterated molecules will be considered. Resolved 2 H–13 C dipolar couplings in mono-deuterated compounds have been observed in one-dimensional (1D) [3,10–13] and two-dimensional (2D) 13 C NMR spectra [14]. The separated local field (SLF) NMR technique provides means for measuring 1 H–13 C dipolar interactions with high chemical resolution [2]. This method can also be adapted for estimating 2 H–13 C couplings (see below). In contrast, heteronuclear spin–spin interactions between abundant protons and rare deuterons

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S.V. Dvinskikh et al. / Chemical Physics Letters 382 (2003) 410–417

in partially deuterated samples are rarely explored. These weak and often ill-resolved couplings have only been occasionally observed in 1D 2 H [10,15– 18] and 1 H [19] spectra of liquid crystals. Moreover, the limited CS range for these nuclei precludes the separation of the various 1 H–2 H dipolar interactions on the basis of their chemical shifts. In this Letter, a method that significantly enhances the resolution of 1 H–2 H dipolar couplings is presented. The technique is based on a 2D heteronuclear 1 H–13 C correlation experiment, where 1 H chemical shifts and 1 H–2 H dipolar interactions in the first dimension are correlated with 13 C chemical shifts and 2 H–13 C dipolar interactions in the second dimension. The method is demonstrated on a columnar liquid-crystalline phase formed by 1,2,3,5,6,7-hexaoctyloxy-rufigallol (RufH8O).

2. Implementation The employed pulse sequence (see Fig. 1a) uses correlations between 1 H and 13 C resonances anal(a)

1H -2H SLF

sequence

90oy

I (1 H)

BLEW-48

CPx/y

t 180o 1 S (13C)

CPx

L (2H)

CW

TPPM

t2

CW

(b) 2H -13C SLF sequence 90o

I (1 H)

CP

CW

TPPM

180o

S (13C)

90 o 90o

t2

CP 180o

L (2H)

Fig. 1. Pulse sequences for: (a) 2 H–13 C SLF spectroscopy.

ogously to the 2D heteronuclear chemical shift correlation (HETCOR) technique [20]. The important difference is that dipolar evolution due to 1 H–2 H and 2 H–13 C couplings is allowed. The initial 1 H 90° pulse prepares transverse 1 H magnetization, which evolves under the 1 H CS and 1 H–2 H dipolar interactions during the variable evolution period t1 . Homonuclear 1 H–1 H couplings during t1 are suppressed by the homonuclear decoupling sequence BLEW-48 [21], which also scales the 1 H–2 H heteronuclear couplings and 1 H CSs. The 13 C 180° pulse at t1 =2 refocuses the 1 H–13 C couplings. The proton magnetization is then transferred to 13 C via cross-polarization (CP) and is finally observed during the detection period t2 under the 13 C CS interactions, 2 H–13 C dipolar couplings, and 1 H heteronuclear decoupling. We used 1 H heteronuclear TPPM decoupling [22] since it is more efficient in liquid crystals than continuous-wave (CW) irradiation [23]. Phase sensitive detection in the first dimension is achieved by phase cycling of the 1 H CP pulse [24]. Because the 1 H–2 H heteronuclear dipolar couplings correspond to local magnetic fields, this technique can be referred to as 13 C-detected 1 H–2 H SLF NMR spectroscopy. For signal assignment and spectral simplification purposes, 2 H heteronuclear CW decoupling may be applied in the first and/or second dimension, thus suppressing 1 H–2 H and/or 2 H–13 C couplings, respectively. Dashed lines in Fig. 1a indicate this optional 2 H radio-frequency (RF) irradiation. The pulse sequence shown in Fig. 1b results in 2D separation of the 2 H–13 C dipolar splittings on the basis of the 13 C chemical shifts, and is used for the assignment of overlapping 2 H–13 C multiplets. During the t1 period, CP-enhanced 13 C magnetization evolves under the influence of 2 H–13 C dipolar interactions. A pair of 180° pulses is applied simultaneously at t1 =2 to refocus 13 C CSs while retaining the 2 H–13 C couplings. The signal is, after a z-filter, finally detected under 1 H and 2 H heteronuclear decoupling.

t1 CW

13

411

C-detected 1 H–2 H and (b)

3. Theoretical background Before presenting the experimental results, we briefly discuss the theory of the 13 C-detected

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1

H–2 H SLF experiment shown in Fig. 1a without the optional 2 H irradiation. Proton, deuterium, and carbon-13 spins will be denoted by I, L, and S, respectively. We start by considering an ensemble of isolated 1 H–2 H–13 C three-spin systems. The spin interactions effective during the evolution and detection are mentioned in Section 2. Using product operator calculations and the special properties of matrix representations of spin-1 operators [24,25], one obtains the following expressions for the density operator at the end of the detection period:

þ sin½ðxI
2dIL Þt1  expð
i2dLS t2 Þ:

ð2bÞ

The S spin CS term during t2 can be accounted for by adding a multiplicative factor of exp½ixS t2  to Eq. (2). Combining the two expressions in Eq. (2) and including the S spin CS, one obtains the following relationship for the NMR signal: sðt1 ; t2 Þ ¼ sðt1 ; t2 ÞCPðIÞx þ isðt1 ; t2 ÞCPðIÞy þ exp½iðxI þ 2dIL Þt1   exp½iðxS þ 2dLS Þt2  þ exp½iðxI
2dIL Þt1   exp½iðxS
2dLS Þt2 :

¼ Sx ð1L
L2z Þ cosðxI t1 Þ þ Sx L2z cosðxI t1 Þ cosð2dIL t1 Þ cosð2dLS t2 Þ

ð3Þ ð1aÞ

rðt1 ; t2 ÞCPðIÞy ¼ Sx ð1L
L2z Þ sinðxI t1 Þ þ Sx L2z sinðxI t1 Þ cosð2dIL t1 Þ cosð2dLS t2 Þ þ Sy L2z cosðxI t1 Þ sinð2dIL t1 Þ sinð2dLS t2 Þ;

/ sinðxI t1 Þ þ sin½ðxI þ 2dIL Þt1  expði2dLS t2 Þ

/ expðixI t1 Þ  expðixS t2 Þ

rðt1 ; t2 ÞCPðIÞx


Sy L2z sinðxI t1 Þ sinð2dIL t1 Þ sinð2dLS t2 Þ;

sðt1 ; t2 ÞCPðIÞy

ð1bÞ

where only observable single-quantum coherences have been kept. Here, dLS is the heteronuclear dipolar interaction between S and L spins, and xI and dIL are the scaled I chemical shift and heteronuclear dipolar interactions between I and L spins, respectively. In Eq. (1), the S spin CS has not been taken into account. The subscripts CPðIÞx and CPðIÞy refer to the phase of the I spin-lock pulse (see Fig. 1a), and it has been assumed that the I–S CP step achieves full polarization transfer of the spin-locked magnetization component. Note that the 2 H quadrupolar coupling does not enter the expressions above since the quadrupolar Hamiltonian commutes with all other spin interactions and with the density operator at all times. Employing the relationship between the density operator and the time-domain signal, sðtÞ / Tr frðtÞðSx þ iSy Þg, Eq. (1) yields the following observable signals: sðt1 ; t2 ÞCPðIÞx / cosðxI t1 Þ þ cos½ðxI þ 2dIL Þt1  expði2dLS t2 Þ þ cos½ðxI
2dIL Þt1  expð
i2dLS t2 Þ; ð2aÞ

After a double Fourier transformation of Eq. (3), a 2D spectrum is obtained containing three peaks of equal intensity with frequency coordinates ðxI
2dIL ; xS
2dLS Þ,ðxI ; xS Þ, andðxI þ 2dIL ;xS þ 2dLS Þ. In a 2D plot, this corresponds to a tilted triplet centered on the I-S heteronuclear CS correlation peak. The tilt is positive if the signs of the two dipolar couplings are the same, and negative if opposite. The projections on the x1 and x2 axes correspond to, respectively, I–L and L–S dipolar spectra. For many deuterated compounds, it is necessary to take into account spin clusters containing more than one deuteron. We will here consider a 1 H–2 H2 – 13 C four-spin system relevant for, e.g., a methylene group with a nearby proton. In practice, the two 2 H spins in a CD2 group are often equivalent in terms of heteronuclear dipolar couplings to the 1 H and 13 C spins. This results in a situation in which the homonuclear 2 H–2 H interaction commutes with all other relevant Hamiltonians and density operators [26]. In this case, the spin dynamics is again governed by the heteronuclear interactions. Straightforward but tedious calculations [27,28] show that the 2D spectrum consists of a tilted quintet with an intensity distribution of 1:2:3:2:1, and with frequency coordinates ðxI
4dIL ; xS
4dLS Þ, ðxI
2dIL ; xS
2dLS Þ, ðxI ; xS Þ, ðxI þ 2dIL ; xS þ 2dLS Þ, and ðxI þ 4dIL ; xS þ 4dLS Þ. The situation becomes more involved when the two 2 H spins are nonequivalent in terms of heteronuclear dipolar couplings to the 1 H and 13 C spins. Nine peaks (triplets of

S.V. Dvinskikh et al. / Chemical Physics Letters 382 (2003) 410–417

a triplet) is expected if the 2 H–2 H homonuclear interaction is neglected. Numerical simulations using realistic interaction parameters show that the influence from the 2 H–2 H interaction and 2 H quadrupolar couplings on the 2D spectrum is minor. 4. Experimental Two different isotopomers of RufH8O were synthesized according to previously described procedures [29]: RufH8O singly labeled with 2 H (RufH8O–(2 H2 )a ), and doubly labeled with 13 C and 2 H (RufH8O–(13 C2 H2 )a ) at the a position of the aliphatic chains. RufH8O forms hexagonal columnar phases in the temperature range 19–95 °C [30,31]. In the mesophase, the molecules undergo fast reorientation about the columnar axes. The experiments discussed below were carried out on stationary samples which were oriented in the magnetic field of the NMR spectrometer by slowly cooling from the isotropic phase. All NMR experiments were performed at a magnetic field of 9.4 T on a Chemagnetics Infinity400 spectrometer equipped with 6 mm doubleresonance and 4 mm triple-resonance magic-angle spinning probes. Typical 1 H RF field strength was 70 and 50 kHz for homonuclear and heteronuclear decoupling, respectively. Deuterium heteronuclear decoupling was performed using a 15 kHz RF field, and the decoupler frequency was set to the center of the 2 H spectrum. Proton–carbon CP with nutation frequencies of 50 kHz, and contact times of 1–3 ms was used. Radio-frequency heating effects in liquid-crystalline samples have been discussed elsewhere and is of minor importance in columnar phases [32]. The multiple-pulse scaling factor was calibrated by observing the scaling of the 1 H frequency offset under BLEW-48 irradiation. The experimental value, 0.42  0.01, is in good agreement with the theoretical counterpart 0.424 [21]. Numerical simulations were performed using the SIMPSON programming package [33]. 5. Results and discussion The measurement of 1 H–2 H dipolar couplings by the new NMR method discussed above is based

413

on the presence of resolved 2 H–13 C dipolar splittings in the 13 C spectrum. This situation occurs frequently for liquid-crystalline systems containing directly bonded 2 H–13 C spin pairs [3,10–13]. Fig. 2a shows the conventional proton-decoupled 13 C spectrum of RufH8O–(2 H2 )a in the columnar phase at 85 °C. The spectrum exhibits several multiplets in the spectral region of the a methylenes. These multiplets were assigned previously by a variety of NMR techniques [30]. The most prominent quintet shows splittings of 1.05 kHz, and stems from the one-bond 2 H–13 C dipolar interactions between the a3 carbon and the two equivalent a3 deuterons. The observed differential line broadening is presumably due to cross-correlation effects [34] and/or a small distribution of the director orientations [35]. The partially resolved multiplets with smaller splittings result from the a1 and a2 methylene groups (the index of the as refers to the chain labeling shown in Fig. 2a). In Fig. 2b, we show parts of a 2D spectrum of RufH8O–(2 H2 )a obtained with the pulse sequence in Fig. 1a without 2 H decoupling. The resonances with 1 H CSs of 3 and 7–8 ppm in the first dimension are signals originating from the aliphatic protons and the aromatic proton H4 , respectively. The spectrum resembles the conventional HETCOR spectrum except that some of the peaks are split, shifted and broadened in x1 and x2 due to 1 H–2 H and 2 H–13 C dipolar interactions, respectively. The effect from the heteronuclear couplings is most pronounced for the 1 H4 –13 Ca3 correlation. Dipolar splittings in both dimensions due to the 1 H4 –2 Ha3 (in x1 ) and 2 Ha3 –13 Ca3 (in x2 ) interactions result in a tilted 2D multiplet (see the dashed line in Fig. 2b). Note that the 1 H4 –2 Ha3 dipolar coupling is not resolved in the x1 projection. When correlated with the well-resolved 2 Ha3 –13 Ca3 splitting in x2 , however, the 1 H4 –2 Ha3 interaction is clearly visible. From the splitting Dm ¼ j2dHD j=2p along the x1 axis, the magnitude of the 1 H4 –2 Ha3 dipolar coupling in frequency units is readily estimated to 150  20 Hz. The negative slope of the 2D multiplet suggests that the 1 H4 –2 Ha3 and 2 Ha3 –13 Ca3 interactions have opposite signs (see Section 3). Note also that in contrast to conventional SLF spectroscopy, where the dipolar couplings are extracted from 1D slices along the dipolar dimension, the

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S.V. Dvinskikh et al. / Chemical Physics Letters 382 (2003) 410–417 R

(a)

H

R1

O

O

O

9 9a 1

R

10 4a 4

O

O

R2

2 3

Ri= -CD2-C7H15

O O

O

H

i=1,2,3

R

R3 C1+C4a

C9

220

C3 C2

200

180

α1,2

α3

80

60

C9a C4

160

140

120

100

40

20

ppm

1

H frequency ω1 (ppm)

(b) 2 4 6

8dHD

8 10 220

200

180

160

90

80

70

60

50

40

30

25

20

15

13

C frequency ω2 (ppm)

Fig. 2. NMR spectra of RufH8O–(2 H2 )a in the columnar phase at 85 °C. (a) 1 H–decoupled 1D CP spectrum (see molecular structure in inset). The assignment of C1 and C2 is uncertain. (b) 2D 1 H–2 H SLF spectrum obtained by the pulse sequence in Fig. 1a without 2 H irradiation. The x1 -axis is corrected by the multiple-pulse scaling factor of the BLEW-48 sequence. The x1 projection is shown to the right.

13

C-detected 1 H–2 H SLF experiment requires determination of the peak positions in a 2D plane. The experimentally obtained 1 H4 –2 Ha3 interaction in RufH8O–(2 H2 )a3 can directly be used to extract structural information. The value of 150 Hz, estimated from Fig. 2b, is only consistent with a situation in which the R3 chain is located in the core plane, pointing towards the aromatic proton H4 [30]. This fully agrees with results from our previous studies of this molecule by other NMR techniques [30,31]. The correlations between the aliphatic protons and a3 carbon also result in a slightly tilted 2D multiplet. Most likely, this tilt originates from the 1 Hb3 –2 Ha3 dipolar coupling. Similar features, but with opposite slopes, are observed for the corre-

lations between the chain protons and the a1 and a2 carbons. Two-dimensional 13 C-detected 1 H–2 H SLF spectra, recorded with and without 2 H decoupling in the first, second or both dimensions are compared in Fig. 3. Doubly labeled RufH8O (RufH8O–(13 C2 H2 )a ) was used in these experiments. The manipulation of the 2D maps, as shown in Fig. 3, is helpful for assignment and spectral simplification purposes when overlap of the 2D multiplets occurs. In Fig. 3a, a fully 2 H–coupled spectrum at 85 °C is shown (this spectrum is analogous to the one in Fig. 2b). In the presence of 2 H decoupling, the multiplets collapse in one (see Figs. 3b, c) or two dimensions (see Fig. 3d). With the couplings to 2 H removed in both dimensions,

S.V. Dvinskikh et al. / Chemical Physics Letters 382 (2003) 410–417

415

60 80

α2

-3

-2

-1

0

1

2

3

13

α1

C chemical shift (ppm)

α3

100

the conventional 1 H–13 C HETCOR spectrum is obtained (Fig. 3d). The prominent quintet structure observed in Figs. 2 and 3 is a consequence of the equivalence of the two 2 Ha3 –13 Ca3 dipolar couplings at high temperatures. In general, however, nine peaks (triplets of a triplet) are expected for this kind of spin system. Such a nine-peak multiplet is indeed observed in the 13 C spectrum of RufH8O at lower temperatures within the columnar phase. In this case, the a3 methylene group is essentially rigid and adopts a conformation in which the two C–2 H vectors have different orientations with respect to the core rotation axis [30,31]. This results in non-equivalent 2 Ha3 –13 Ca3 couplings, and the 13 C spectrum consists of triplets of a triplet (see Fig. 4). Due to the severe spectral overlap in the 2 H-coupled 13 C spectrum at low temperatures (not shown), it proved necessary to separate the individual 2 H–13 C dipolar multiplets by using the 2D SLF pulse sequence displayed in Fig. 1b. The magnitudes of the two 2 Ha3 –13 Ca3 couplings are estimated to 515  30

40

Fig. 3. 2D 1 H–2 H SLF spectra of RufH8O–(13 C2 H2 )a in the columnar phase at 85 °C obtained by the pulse sequence in Fig. 1a. Only the a methylene regions are shown. The spectra were collected with the 2 H decoupler turned: (a) off, (b) on during t1 , (c) on during t2 , and (d) on during both t1 and t2 .

ω1/2π (kHz)

Fig. 4. Dipolar cross-sections through a 2D 2 H–13 C SLF spectrum of RufH8O–(13 C2 H2 )a in the columnar phase at 40 °C. The spectrum was obtained by the pulse sequence in Fig. 1b. The x2 projection is shown to the right.

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S.V. Dvinskikh et al. / Chemical Physics Letters 382 (2003) 410–417

(a) 0

1

H frequency (ppm)

2 4

1.0

6

0.5 0.0

8

-0.5

10 -3

100

-2

-1

80

0

1

60

2

-1.0 3 kHz

40

20

13

C frequency (ppm)

(b)

1.0 0.5 0.0 -0.5

1

H frequency (kHz)

-1.0 1.0 0.5 0.0 -0.5 -1.0 1.0

and 770  30 Hz at 40 °C. Geometry considerations indicate that both dipolar interactions are positive. These values are consistent with results obtained at the same temperature in a protonated sample of RufH8O [31,32]. Corresponding nine-peak multiplets are observed in the 2D spectrum obtained by the 13 Cdetected 1 H–2 H SLF experiment at 40 °C (see Fig. 5a). The signals within the marked region stem from a correlation between 1 H4 –2 Ha3 couplings in x1 and 2 Ha3 –13 Ca3 couplings in x2 . In conformity with the non-equivalence of the 2 Ha3 – 13 Ca3 interactions, the experimental peak pattern shows that the two 1 H4 –2 Ha3 dipolar couplings are different. From the signal positions in the x1 dimension, the magnitudes of the 1 H4 –2 Ha3 couplings were estimated to 140  30 and 210  30 Hz. The sign of both these interaction parameters is negative as suggested from the negative slopes of the multiplets, and from the fact that the 2 Ha3 – 13 Ca3 couplings are positive. It is instructive to compare the experimental 2D spectrum in Fig. 5a with calculated counterparts. The simulated spectra in Fig. 5b show three different cases: dHDi ¼ dHDj (top), dHDi < dHDj (middle), and dHDi > dHDj (bottom). The indexes i and j have been chosen so that dDiC < dDjC holds for the two a3 deuterons. Clearly, only the middle map with dHDi < dHDj is consistent with the experimental spectrum. Note that the linear appearance of the bottom multiplet is purely accidental.

0.5

6. Conclusions

0.0 -0.5 -1.0 -3

-2

-1 13

0

1

2

3

C frequency (kHz)

Fig. 5. (a) Experimental 2D 1 H–2 H SLF spectrum of RufH8O– (13 C2 H2 )a in the columnar phase at 40 °C obtained by the pulse sequence in Fig. 1a. Only the aliphatic region is shown. (b) Numerical simulations using 2 H–13 C couplings of dDiC =2p ¼ 515 and dDjC =2p ¼ 770 Hz. The 1 H–2 H dipolar interactions were set to: dHDi =2p ¼ dHDj =2p ¼
175 Hz (top), dHDi =2p ¼
210 and dHDj =2p ¼
140 Hz (middle), and dHDi =2p ¼
140 and dHDj =2p ¼
210 Hz (bottom). In the simulations, 2 H quadrupolar couplings of qi ¼ 37 kHz and qj ¼ 25 kHz, and a 2 H–2 H dipolar coupling of dDiDj =2p ¼
200 Hz were used.

We have reported an NMR technique for measurements of long-range 1 H–2 H dipolar couplings in macroscopically oriented media. These spin– spin interactions provide useful constraints for the molecular structure and dynamics in anisotropic materials such as liquid crystals and biomembranes. The novel approach is based on a 2D heteronuclear 1 H–13 C correlation experiment, where 1 H chemical shifts and 1 H–2 H dipolar interactions in the first dimension are correlated with 13 C chemical shifts and 2 H–13 C dipolar interactions in the second dimension. The basic version of the pulse sequence requires only 1 H/13 C double-reso-

S.V. Dvinskikh et al. / Chemical Physics Letters 382 (2003) 410–417

nance hardware. A third channel for 2 H RF irradiation may be useful for assignment and spectral simplification purposes. If severe overlap of the various 2D multiplets occurs, the method can be extended to three dimensions by including a pure 13 C chemical shift evolution period. The results from such experiments will be reported elsewhere.

[10] [11] [12] [13] [14]

Acknowledgements

[18] [19]

This work was supported by the Swedish Research Council, the Carl Trygger Foundation, the Magn. Bergvall Foundation, and the Deutscher Akademischer Austauschdienst together with the Swedish Institute under project No. 313-S-PPP-7/ 98.

[15] [16] [17]

[20] [21] [22] [23] [24]

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