Journal of Magnetic Resonance 242 (2014) 143–154

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‘‘Perfect echo’’ INEPT: More efficient heteronuclear polarization transfer by refocusing homonuclear J-coupling interaction Bikash Baishya ⇑, C.L. Khetrapal Center of Biomedical Research (Formerly Centre of Biomedical Magnetic Resonance), SGPGIMS Campus, Raebareli Road, Lucknow 226014, India

a r t i c l e

i n f o

Article history: Received 21 November 2013 Revised 10 February 2014 Available online 3 March 2014 Keywords: Perfect echo INEPT Long range heteronuclear polarization transfer Broadband homonuclear decoupling J-refocusing

a b s t r a c t A ‘‘perfect echo’’ based INEPT experiment that demonstrates more efficient heteronuclear polarization transfer over conventional INEPT has been developed. This scheme refocuses the effect of homonuclear 1 H–1H J-evolution and simultaneously allows heteronuclear 13C–1H J-evolution to continue during INEPT. This improves one bond heteronuclear polarization transfer efficiency at longer INEPT transfer delays and also enhances the sensitivity of long range INEPT. The refocusing of homonuclear 1H–1H J-coupling could be achieved by doubling the INEPT transfer period leading to a doubling of T2 losses. Therefore, the sensitivity gain is observed when loss of magnetization due to homonuclear 1H–1H J-modulation is more severe than that of T2 decay. However, in general, INEPT transfer period is rather short compared to the longer T2 observed in small molecules. The long range PE-INEPT transfer to carbonyl carbon in betabutyrolactone, showed much faster build up of C-13 signal than conventional long range INEPT as the long range heteronuclear J-coupling is comparable in magnitude to homonuclear 1H-1H J-coupling in this case. For one bond heteronuclear polarization transfer at shorter delay, PE-INEPT and conventional INEPT displays equal transfer efficiency. Efficient polarization transfer is observed for small molecules dissolved in isotropic as well as weakly aligned media. Further, simulation results obtained using the full propagator and product operator analysis agree well with the experimental observations. Ó 2014 Elsevier Inc. All rights reserved.

1. Introduction In a conventional INEPT [1] experiment, heteronuclear polarization transfer takes place via a heteronuclear spin echo sequence. This spin echo refocuses 1H chemical shift evolution and creates an antiphase SQ coherence HXCZ via evolution through the unrefocused heteronuclear scalar couplings. Ideally this happens when a pure heteronuclear J-coupling interaction evolves during the spin echo. However, evolution of the spin system under the undesired homonuclear 1H–1H J-coupling interaction can reduce the amount of targeted heteronuclear antiphase state (HXCZ). As a result, polarization transfer becomes less efficient. This can be viewed as 1H–1H J-dephasing of antiphase magnetization during INEPT transfer. Owing to very small magnitude of 1H–1H J-coupling interaction compared to the one bond 1H–13C J-coupling, this destructive interference is in general very small for short INEPT transfer delays. However, for long range INEPT experiment this interference becomes significant. Typical range of 1JCH is 110–250 Hz while that of 1JNH is 70–100 Hz. There are broadband INEPT schemes [2] and related ⇑ Corresponding author. Fax: +91 522 2668215. E-mail address: [email protected] (B. Baishya). http://dx.doi.org/10.1016/j.jmr.2014.02.017 1090-7807/Ó 2014 Elsevier Inc. All rights reserved.

developments [3–6] that improve the performance of INEPT experiments for such a range of heteronuclear coupling constants. The 1 H–1H J-couplings are of the order of 0–20 Hz. In a molecule there may be many such homonuclear J-couplings. When too many 1 H–1H J-coupling evolutions compete with 1H–13C J-coupling evolution during INEPT, a part of the targeted antiphase state is lost via creation of multiple quantum coherence. Further, there are several one dimensional and two dimensional NMR pulse techniques such as HMBC [7] and HSQMBC [8] that utilize long range heteronuclear J-couplings for the sensitivity enhancement of insensitive nuclei such as C-13 or N-15. Such long range polarization transfer is essential when insensitive nuclei occur in nonprotonated sites. In such a situation, during long INEPT transfer delays competition arises between long range heteronuclear J-couplings (of the order of 1–15 Hz) and homonuclear 1H–1H J-couplings which are of comparable magnitude. As a result, loss of magnetization occurs during INEPT transfer [8]. Also for molecules dissolved in weakly aligned media homonuclear Residual Dipolar Couplings (RDC) are significant, leading to less efficient INEPT transfer. In an attempt to suppress homonuclear J-coupling interaction, while simultaneously allowing heteronuclear J-evolution to continue, CPMG-HSQMBC [9] experiment was developed followed by other variants [10–12]. The CPMG pulse train [13–15] is

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simultaneously applied on both protons and heteronuclei during long INEPT transfer period for locking homonuclear couplings and keeping heteronuclear coupling evolution intact. Such a procedure still suffers from pulse imperfections associated with a large number of pulses, off-resonance effect of heteronuclei such as C-13 having large chemical shift dispersion, and from heating effect [12]. Homonuclear decoupling during long INEPT transfer period can also be carried out via insertion of a BIRD [16,8] block but such a procedure refocuses only vicinal couplings between protons directly attached to C-13 and protons attached to neighboring C-12. It does not refocus the homonuclear 1H–1H J-coupling among neighboring C-12 attached protons. Further, BIRD scheme fails to refocus geminal 1H–1H J-couplings [17]. Yet another alternative would be to apply selective refocusing pulses [18,19] on protons during INEPT, but such a procedure allows study of one resonance at a time and requires the existence of well separated 1H resonances. Many innovative methods of suppressing homonuclear J-couplings and the modifications of these methods have appeared in literature [20–52]. The perfect echo based homonuclear scalar decoupling sequence has been recently employed for perfecting WATERGATE [51], measuring transverse relaxation rates without significant sample heating [28], suppressing JHH during diffusion measurement [29], and enhancing spectral resolution and sensitivity in heteronuclear correlation NMR spectroscopy [55]. In another application, we have demonstrated perfect echo based broadband homonuclear decoupling that enhances the sensitivity and resolution of 2D HMQC spectra [53]. The perfect echo sequence is a double spin echo scheme with insertion of a J-refocusing 90° pulse at the center of the two refocusing pulses [26–28]. This scheme performs homonuclear refocusing even for relativelyi longer inter pulse delays h 1 compared to CPMG s  JHH vs s  D1X and can be applied to any general spin systems of N weakly coupled spin-½ nuclei and ideal in situations where too many pulses are not desirable. Recently, the perfect echo scheme has been demonstrated to refocus homonuclear scalar couplings in any arbitrary networks of weakly coupled spins, as long as s  J 1 where s is the interpulse HH delay, an easy condition to be fulfilled for smaller 1H–1H J-couplings [28]. In the present work, the perfect echo scheme is combined with INEPT transfer scheme. This method refocuses the effect of homonuclear scalar couplings during INEPT transfer period and thereby improves the sensitivity of long range INEPT experiment. In spin systems, where loss of magnetization due to homonuclear J-modulation is more severe than that of T2 decay, the perfect echo INEPT demonstrates more efficient short range polarization transfer over conventional INEPT for longer INEPT delays. For shorter delays equal efficiency of polarization transfer is observed. Experimental results are presented for molecules dissolved in isotropic as well as weakly aligned media. Simulation using the full propagator and product operator analysis supporting the sensitivity enhancement is also provided.

2. Description of the ‘perfect echo’ INEPT pulse sequence The perfect echo INEPT (abbreviated PE-INEPT) pulse sequence is displayed in Fig. 1(c). For clarity, a conventional perfect echo and a conventional INEPTRD sequence is also shown in Fig. 1(a) and (b) respectively. For current discussion we focus on the sequence in Fig. 1(c). As evident from Fig. 1(c) in addition to the second refocusing pulse on 1H between time points ‘d’ and ‘e’, simultaneous refocusing pulse on X nuclei (C-13) is also applied to convert the 2nd spin echo into a heteronuclear spin echo. Considering the 1st spin echo between time point ‘b’ and ‘c’, the first 180° pulse on protons in the perfect echo block refocuses 1H chemical shifts and n 13 J( C–1H) (where n = 1, 2. . ., n bonds) evolutions at the center of

the block (time point ‘c’ shown in Fig. 1c) while nJ(1H–1H) evolutions continue. Subsequently a 90° pulse is applied between time point ‘c’ and ‘d’, which exchanges antiphase magnetizations of coupled proton spins [26,27]. Consequently, homonuclear 1H–1H J-couplings refocus perfectly at the end of the second echo at time point ‘e’ for a two spin system and also for multispin systems pro1 vided that s  JHH . Since 1H–1H J-couplings are rather small (in general 5–15 Hz so that their periods are 200–66 ms) this means the 1 condition s  JHH is easier to fullfil for scalar coupled 1H spin systems. However, from time point ‘d’ to ‘e’ heteronuclear J-coupling evolutions continue creating heteronuclear single quantum antiphase coherence (HXCZ) at time point ‘e’ which is subsequently converted into C-13 single quantum antiphase coherence (HZCX) at time point ‘h’. This antiphase state HZCX subsequently refocuses to C-13 inphase single quantum coherence CY at time point ‘i’ for detection during acquisition with 1H decoupling. In overall, the first half of the sequence ‘prefocuses’ the J-modulation, so that it refocuses (at least partially) in the second half. The value of 2s can be tuned to 1/2[(1JCH)] or 1/2[(nJCH)] (n > 1) depending on whether short range or long range INEPT transfer is desired. For large molecules, such as proteins, the value of 2s is kept shorter because of T2 losses. The requirement of symmetric homonuclear J-coupling evolution demands that the length of the INEPT part be same as the 1st spin echo period from time point ‘b’ to ‘c’. The killer gradient G1 between time points ‘f’ and ‘g’ ensures suppression of unwanted coherence transfer pathways that might result from pulse imperfections. The product operator formalism and Matlab simulation using the full propagator is discussed in the following sections. 3. Product operator analysis (i) Conventional INEPT In this section we discuss the homonuclear J-coupling driven loss of magnetization during a conventional INEPTRD experiment displayed in Fig. 1(b). Later we will show that in a PE-INEPT experiment homonuclear J-modulation can be refocused during the heteronuclear spin echo for a two proton spin system coupled to a C13. The refocusing works well even for multispin systems provided 1 the condition s  JHH is satisfied and detailed elsewhere [28]. A

spin system of the form HA–12C–13C–HK is considered. The product operator calculation is discussed below where the 1H–1H J-coupling (3JHA-HK) is denoted as JH and 1H–13C J-coupling as 1JCH for one bond J-coupling (J13C-HK) and 2JCH for two bond J-coupling (J13C-HA) respectively. During a conventional INEPT experiment shown in Fig. 1(b), the typical heteronuclear polarization transfer delay 2s is chosen such that 1/2s  (DX), where, DX is the offset difference between coupled spin pairs. Also the condition, DX  pJH remains valid. Therefore, from time point ‘b’ to ‘c’ of Fig. 1(b), the spin system can be assumed to evolve under the weak homonuclear 1H–1H J-coupling interaction [47] as well as heteronuclear 1H–13C J-coupling interaction. Since this two weak coupling terms commute, we can consider the evolution of homonuclear 1H–1H J-coupling first from time point ‘b’ to ‘c’ and then consider the evolution of heteronuclear 1H–13C J-coupling interaction. Considering only homonuclear J-coupling evolution between time point ‘b’ to ‘c’ the operators present at time point ‘c’ are:

½I1Y cosðpJ H 2sÞ þ 2I1X I2Z sinðpJ H 2sÞ  I2Y cosðpJ H 2sÞ þ2I2X I1Z sinðpJ H 2sÞ 1

13

ð1Þ

Here I1 operator corresponds to HK bound to C and I2 corresponds to 1HA bound to 12C. The C-13 operator is denoted as S. Considering heteronuclear J-coupling evolution as well, the operators present at time point ‘c’ are:

B. Baishya, C.L. Khetrapal / Journal of Magnetic Resonance 242 (2014) 143–154

(a)

145

(b)

(c)

(d)

(e)

(f)

(g)

Fig. 1. (a) A conventional perfect echo sequence. Thin bars in all cases represent 90° pulse while wide bars represent 180° pulse. The phases are U1 = 0, U2 = 1 and UR = 1. (b) A conventional INEPTRD pulse sequence, s = 1/4(1J(13C–H), and the phases are U1 = 0, U2 = 1, U3 = 0, 2 and UR = 0, 2. The dotted box from time point ‘f’ to ‘g’ acts as the refocusing block for converting anti-phase HZCY magnetization to in-phase CX coherence which can be detected with 1H decoupling. (c) Perfect echo INEPTRD pulse sequence. The dotted box on left from time point ‘a’ to ‘e’ is a conventional perfect echo sequence. It is converted into an INEPT by applying simultaneous refocusing pulses on 1H and X nuclei between time point ‘d’ and ‘e’. This allows heteronuclear scalar couplings to evolve between time point ‘d’ and ‘e’ whereas homonuclear couplings refocuses during this period. The proton 90° pulse between time point ‘e’ and ‘f’ creates HZCZ coherence for a 13C–1H pair. The z gradient during d suppresses unwanted transverse magnetization order HZCY. The C-13 90° pulse between time point ‘g’ and ‘h’ creates C-13 transverse magnetization. The dotted box from time point ‘h’ to ‘i’ acts as the refocusing block for converting anti-phase HZCY magnetization to in-phase CX which can be detected with 1H decoupling. For performing INEPT experiment without refocusing HZCX coherence, this block is removed and then FID is acquired just after time point ‘h’ without 1H decoupling. The phases of the pulses are U1 = 0, U2 = 1, U3 = 0, 2 and UR = 0, 2. (d) A conventional INEPTRD pulse sequence of the same length as the PE-INEPTRD pulse sequence. In order to compare the PE-INEPTRD and INEPTRD sequence under same condition, i.e. equal extent of T2 decay and homonuclear scalar coupling evolution, two extra s delays are added to INEPTRD in fig (d) with a 1H refocusing pulse to refocus the heteronuclear scalar couplings from ‘b’ to ‘c’. The phases of the pulses are same as in (c). (e) Structure and numbering of carbons in menthol. (f) Structure and numbering of carbons in beta-butyrolactone. (g) Structure and numbering of carbons in propylene oxide.

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 cosðpJ H 2sÞ½I1Y cosðp1 J CH 2sÞ  2I1X SZ sinðp1 J CH 2sÞ þ I2Y cosðp2 J CH 2sÞ  2I2X SZ sinðp2 J CH 2sÞ  þ sinðpJ H 2sÞ 2I1X I2Z cosðp1 J CH 2sÞ þ 4I1Y I2Z SZ sinðp1 J CH 2sÞ  þ2I2X I1Z cosðp2 J CH 2sÞ þ 4I2Y I1Z SZ sinðp2 JCH 2sÞ

ð2Þ

Now, we can consider two cases. In the 1st case, the delay 2s is tuned to one bond transfer delay (short range INEPT transfer) and in the 2nd case it is tuned to two bond transfer delay (long range INEPT transfer). Case (a) one bond transfer or INEPT with short transfer delay [2s = 1/2(1JCH)]: We assume 1J(13C–HK) of 125 Hz, 2J(13C–HA) of 7 Hz and 1H–1H J-coupling JH of 10 Hz. Considering one bond transfer [1HK to 13C] and plugging above J-coupling values, the following terms survive at time point ‘f’ after the 90°y pulse on 1H’s (at ‘c’) and 90°x on C-13 (at ‘e’), ignoring the gradient dephasing of the multiple quantum terms-

ð3Þ

The term ð0:12Þ  4I1Y I2X SY originates from 4I1Y I2Z SZ sinðpJH 2sÞ sinðp1 JCH 2sÞ and represents the magnetization loss determined by the magnitude of 2s and JH and in general very small for short transfer delays tuned to 1/2[1JCH], i.e. 4 ms here. The desired short range transfer term 2I1Z SY is also scaled by ð0:99Þ  2I1Z SY , i.e. cosðpJH 2sÞ sinðp1 JCH 2sÞ and again only longer 2s and large JH can reduce this antiphase content. Even for longer 2s delays, the value of sinðp1 JCH 2sÞ can be significant, when, it satisfies 2s = n/2[1JCH] (where n = 1, 3, 5,. . ., n) and thereby significant one bond transfer can take place. However, for such longer 2s delays cos(pJH2s) term in 2I1Z SY cosðpJH 2sÞ sinðp1 JCH 2sÞ being very small can lead to reduced antiphase content. Alternatively, longer 2s delays lead to significant build up of the multiple quantum precursor state 4I1Y I2Z SZ sinðpJ H 2sÞ sinðp1 J CH 2sÞ in Eq. (2) through the term sin(pJH2s). This represents the magnetization loss via homonuclear J-modulation and thereby the inefficiency of short range transfers for longer delays. Case (b) two bond transfer or INEPT with long transfer delay (2s = 1/2[2JCH] and 2s = n/2[1JCH] where n = 5, 7 or 9): Considering two bond transfer [1HA to 13C] and the same J-coupling values, the following terms survive at time point ‘f’ after the 90° pulse on 1H’s (at ‘c’) and on C-13 (at ‘e’),

¼ ð0:62Þ  2I1Z SY þ ð0:62Þ  2I2Z SY  0:78  4I1Y I2X SY  ð0:78Þ  4I2Y I1X SY 

(ii) Perfect echo INEPT The PE-INEPTRD sequence is displayed in Fig. 1(c). All previous terminology is kept same. The operators present at time point ‘b’ and ‘c’ are:

I1Y  I2Y and

½I1Y cosðpJ H 2sÞ þ 2I1X I2Z sinðpJ H 2sÞ  I2Y cosðpJ H 2sÞ þ2I2X I1Z sinðpJ H 2sÞ

¼ ð0:99Þ  2I1Z SY  ð0:98Þ  I2Y þ ð0:08Þ  2I2Z SY  ð0:12Þ  4I1Y I2X SY  ð0:12Þ  2I2Z I1X  ð0:09Þ  4I2Y I1X SY

hinders the efficiency of short range as well as long range polarization transfer at longer 2s value. In fact, if the effect of homonuclear J-modulation can be recused, the build up of multiple quantum precursor terms in Eq. (2) can be avoided, leading to more efficient long range as well as short range transfer for longer 2s delays. Such a possibility is predicted by the calculation of the PE-INEPT sequence in the next section.

ð4Þ

The multiple quantum terms ð0:78Þ  4I2Y I1X SY and ð0:78Þ  4I1Y I2X SY originate from 4I2Y I1Z SZ sinðpJH 2sÞ sinðp2 J CH 2sÞ and 4I1Y I2Z SZ sinðp1 J CH 2sÞ sinðpJ H 2sÞ in Eq. (2) and represent the magnetization loss determined by the increasing magnitude of sin(pJH2s) with longer 2s (71.4 ms in this case) and JH. Also more importantly JH in this case being comparable to 2JCH and 2s delay being tuned to 1/2[2JCH], the loss of magnetization through the build up of these multiple quantum terms are significant (indicated by the amplitude 0.78). Alternatively, it can be pointed out that, the desired long range transfer term 2I2Z SY is also significantly scaled (0.62)  2I2Z SY and again if we look at the precursor term 2I2X SZ cosðpJH 2sÞ sinðp2 JCH 2sÞ we find that the magnitude of cos(pJH2s) decreases with longer 2s and large JH. In overall, the loss of polarization transfer is attributed to the build up of the multiple quantum precursor terms 4I1YI2ZSY and 4I2YI1ZSZ The homonuclear J-modulation term sin(pJH2s) in Eq. (2) is responsible for the magnetization loss as the multiple quantum precursor terms in Eq. (2) is multiplied by this sine modulation and becomes significant as 2s value increases. This

ð5Þ

The heteronuclear 1H–13C J-coupling interaction is not allowed to evolve during this time period. The operators at time point ‘d’ just after the J-refocusing 90°y pulse can be written as:

½I1Y cosðpJ H 2sÞ  2I1Z I2X sinðpJ H 2sÞ  I2Y cosðpJ H 2sÞ 2I2Z I1X sinðpJ H 2sÞ

ð6Þ

The exchange of antiphase states by J-refocusing 90°x pulse is evident. Again invoking the same argument as in case (i) we consider refocusing of homonuclear J-coupling first and then the evolution under heteronuclear J-coupling. Therefore, during the next 2s period tuned to 1/2[2JCH] or n/2[1JCH] from time point ‘d’ to ‘e’ the in-phase operator can be restored as detailed in [27] and the operator at time point ‘e’ is:

I1Y  I2Y

ð7Þ

However, the additional C-13 refocusing pulse between time point ‘d’ and ‘e’ leads to evolution under 1H–13C J-coupling interaction for 2s (=1/2[2JCH] or n/2[1JCH]). As a result heteronuclear antiphase state at time point ‘e’ for any arbitrary value of 2s can be written as:

a2I1X SZ þ b2I2X SZ

ð8Þ

where ‘a’ and ‘b’ are scaling factor depending on 2JCH and 1JCH. The homonuclear J-coupling during the heteronuclear transfer period is refocused whereas in a conventional INEPT it evolves. The operators present between time point ‘f’ and ‘g’ are:

2I1Z SZ þ 2I2Z SZ

ð9Þ

And those present at time point ‘h’ are:

2I1Z SY  2I2Z SY

ð10Þ

These terms are free from homonuclear J-modulations as in Eq. (2) and also the signal losses via multiple quantum terms are absent. The same result is obtained by considering the heteronuclear J-coupling evolution 1st and then homonuclear J-coupling evolution for the duration ‘d’ to ‘e’. 4. Simulation using the full propagator (i) Short range INEPTRD Simulation of the creation of CX SQ coherence as a function of the INEPT transfer delay 2s was performed in conventional INEPTRD sequence (Fig. 1(b)) and also in PE-INEPTRD pulse sequence

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(a)

147

1



0.5 0

−0.5 −1

−0.992 −0.994 9.9

2

4

6

8

10

τ in ms

10

10.1

14

12

16

18

(b) 0.4 0.2



0 −0.2 −0.4

−0.98

−0.6

−1 34

36

38

−0.8 −1

2

5

10

15

20 21.5 25

τ in ms

30

35

40

Fig. 2. (a) Simulation of the modulation of the CX SQ coherence as a function of the delay s in INEPTRD pulse sequence of Fig. 1(b) and (c) for a spin system of the form HA–12C–13C–HK. The s delays are incremented in steps of 100 ls and D is kept equal to 1/4(1J(13C–HK) so that only one bond polarization transfer contribute to the observed C-13 signal. The thin red curve is obtained for conventional INEPTRD in the absence of homonuclear J-couplings and considering evolution under 1J(13C–HK) of 125 Hz and 2 13 J( C–HA) of 8 Hz. As expected the magnitude of CX signal is highest for s values of 2, 6, 10, 14 and 18 ms. The thick black curve displayed is again for conventional INEPTRD sequence obtained when homonuclear 3JHA-HK of 10 Hz is introduced in addition to the 1J(13C–HK) and 2J(13C–HA). The maximum achievable magnetization (1) for s = 2 ms is evident for the thin red curve and thick black curve. However, for s = 6 ms, the maxima of the thick black curve is slightly lower than that of thin red curve implying that for longer INEPT transfer delays the evolution of homonuclear J-coupling is significant leading to loss of magnetization. With longer s delays (10, 14 and 18 ms) the departure of the thick black curve from the thin red curve is even more significant. The dashed blue curve is obtained for the PE-INEPTRD sequence of Fig. 1(c) displaying more efficient polarization transfer achieved even for longer s delays, in the same spin system considering all the couplings including homonuclear J-coupling. From 2 to 18 ms the thin red and dashed blue curves are overlapped showing identical build up of CX SQ coherence. This implies that the effect of homonuclear scalar coupling has been completely refocused by PE-INEPTRD enhancing the sensitivity of the polarization transfer at longer s delays for short range transfer. (b) The same simulation as in 2(a) performed to investigate long range INEPT transfer. The spin system of the form (12C)HK–12C(HA)–13C-is considered so that there is no 1JCH contribution. The long range coupling, 2J(13C–HA) is 7 Hz and 3J(13C–HK) is assumed 0 Hz. Under these assumptions, only two bond polarization transfer can contribute to the observed signal. The 1H–1H J-coupling, 3JHA-HK is 7 Hz. The refocusing delay D is kept equal to s for all increments of s. The thin red curve is obtained for conventional INEPTRD in the absence of homonuclear scalar couplings (i.e. 3JHA-HK = 0 Hz) and considering evolution only under long range heteronuclear J-coupling, 2J(13C–HA) of 7 Hz. The amplitude of CX SQ coherence starts with a value close to zero for s = 2 ms and then slowly build up from 2 to 35 ms. Maximum antiphase state at s = 35 ms is clearly observed. The thick black curve is obtained when homonuclear Jcoupling of 7 Hz (3JHA-HK) is introduced in addition to the heteronuclear J-coupling, in the same conventional INEPTRD sequence. Unlike the thin red curve, the build up of magnetization in this case does not reach a high value due to loss of magnetization through homonuclear J-dephasing. The highest 0.38 is achieved at s = 21.5 ms. However, for the same value of s, the thin red curve reaches a much higher value of 0.65. During the s interval from 0 to 35 ms, comparison of the thin red and thick black curve reveals that, when homonuclear J-coupling is absent, the CX SQ coherence created via long range transfer attains a value of 1 at 35 ms (red curve) three times higher in magnitude than the highest value of 0.38 (for the black curve). The dashed blue curve is obtained for the PE-INEPTRD pulse sequence in the same spin system considering all the couplings. From 2 to 35 ms, the thin red and dashed blue curves are overlapped showing identical build up of CX SQ coherence. This implies that the effect of homonuclear Jcouplings has been completely refocused enhancing the sensitivity of the long range polarization transfer even for relatively shorter s value. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

(Fig. 1(c)) using the full propagator and the full Hamiltonian. The result of the simulation is shown in Fig. 2(a). A spin system of the form HA–12C–13C–HK is considered, where the two protons 1 HA and 1HK are assumed to be weakly coupled. The single bond (1HK to 13C) transfer efficiency [i.e. the amplitude of SQ coherence] was evaluated without considering relaxation during the sequence. Fig. 2(a) displays the modulation of CX SQ coherence as a function of the delay s incremented in steps of 100 ls from 2 to 18 ms. The refocusing delay D is kept equal to 1/4[1J(13C–HK)] for all values of s so that only one bond antiphase coherence, HKZCY, refocus to in phase coherence, CX, while two bond HAZCY coherence does not refocus in such small duration of time, and, therefore, does not contribute to the observed inphase CX signal. This way we ensured evaluation of short range transfer efficiency via 1JCH for longer s delay. The thin red curve displays the modulation of CX SQ coherence in the absence of homonuclear J-couplings and considering evolution under short range heteronuclear J-couplings 1J(13C–HK) of 125 Hz and long range heteronuclear J-couplings, 2J(13C–HA) of

8 Hz from time point ‘b’ to ‘c’ and ‘f’ to ‘g’ of the conventional INEPTRD sequence shown in Fig. 1(b). Evolution during the pulses is ignored. As expected the magnitude of CX signal is highest for s values of 2, 6, 10, 14 and 18 ms (the delay where antiphase state becomes maximum at time point ‘f’ of the sequence). Therefore, in the absence of relaxation the maximum heteronuclear polarization transfer can be achieved for a range of s values. The thick black curve is obtained when homonuclear J-coupling of 10 Hz (3JHA-HK) is introduced in addition to the 1J(13C–HK) and 2 13 J( C–HA) in the same conventional INEPTRD sequence from time point ‘b’ to ‘c’. The maximum achievable magnetization for s = 2 ms is evident for the thin red curve and thick black curve, both curves starting at 1. Since the evolution under 3JHA-HK is very small compared to 1J(13C–HK) for s values of 2 ms, the loss of magnetization through evolution of the homonuclear scalar couplings is negligible for such short interval. However, for s = 6 ms, whereas the maxima of the thin red curve is +1, the maxima of the thick black curve is slightly less than +1. This indicates that for longer INEPT transfer delays even in the absence of relaxation, the

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maximum achievable heteronuclear polarization transfer becomes less. This is attributed to the build up of the multiple quantum precursor terms in Eq. (2) under evolution of the 1H–1H J-coupling interaction. With longer s delays this loss becomes severe. From the plot, the deviations of the thick black curve from the thin red curve is found to be correlated to s values, 10, 14 and 18 ms confirming the prediction of Eq. (2) where sin(pJH2s) becomes significant with longer s delays. Thus, 1H–1H J-dephasing of the antiphase state (HXCZ) is clearly observed in simulation. Based on the above simulation it can be predicted that efficiency of polarization transfer can be retained even for longer s delays such as 6, 10, 14 and 18 ms, provided homonuclear scalar couplings can be suppressed and transverse relaxation time is not very short. This possibility is clearly observed in the simulated dashed blue curve obtained using the PE-INEPTRD sequence of Fig. 1(c), considering the same spin system and all the J-couplings-1J(13C–HK), 2J(13C–HA) and 3JHA-HK. From 2 to 18 ms, the thin red and dashed blue curves are overlapped showing identical build up of CX SQ coherence. This implies that the effect of homonuclear scalar coupling has been completely refocused by PE-INEPTRD enhancing the sensitivity of short range polarization transfer (1HK to 13C) even at longer s delays. (ii) Long range INEPTRD Simulation was also carried out to explore the effect of perfect echo on long range INEPT transfer via long range heteronuclear J-coupling, 2JCH. A spin system of the form (12C)HK–12C(HA)–13Cis considered, where the two protons are assumed to be weakly coupled and here C-13 is a nonprotonated site so that short range heteronuclear J-coupling is absent. The long range coupling, 2 13 J( C–HA) is 7 Hz and 3J(13C–HK) is 0 Hz. The 1H–1H J-coupling, 3 JHA-HK is also 7 Hz. Fig. 2(b) displays the modulation of CX SQ coherence as a function of the delay s incremented in steps of 100 ls from 2 ms to 42 ms and refocusing delay D is kept equal to delay s for all increments of s. In this simulation, only 2JCH mediated transfer leads to observed magnetization. The thin red curve displays the modulation of CX SQ coherence in the absence of homonuclear J-couplings (i.e. 3JHA-HK = 0 Hz) and considering evolution only under long range heteronuclear J-couplings, 2J(13C–HA) of 7 Hz from time point ‘b’ to ‘c’ and ‘f’ to ‘g’ of the sequence in Fig. 1(b). The amplitude of CX SQ coherence starts with a value close to zero when s value is 2 ms and then slowly builds up from 2 to 35 ms. As predicted the antiphase state for a 7 Hz coupling, attains its maximum value at s = 35 ms. The thick black curve illustrates the same conventional INEPTRD sequence obtained when homonuclear J-coupling of 7 Hz (3JHA-HK) is introduced in addition to the heteronuclear J-coupling, 2 13 J( C–HA) from time point ‘b’ to ‘c’. Unlike the thin red curve, the build up of magnetization in this case does not reach a high value due to loss of magnetization through homonuclear J-dephasing. The highest magnitude is rather small, 0.38 achieved at s = 21.5 ms shown with an arrow in 2(b). However, for the same value of s, the thin red curve reaches a much higher value of 0.65. Comparison of the thin red and thick black curve reveals that, when homonuclear J-coupling is absent, the CX SQ coherence created via long range heteronuclear polarization transfer attains a value of 1 (thin red curve at 35 ms), approximately three times higher in magnitude than 0.38 (for the thick black curve) during the long INEPT transfer delay from 0 to 35 ms. Provided effect of homonuclear scalar couplings could be refocused, then a more efficient long range polarization transfer could be achieved. This possibility is shown in dashed blue curve obtained for the PE-INEPTRD pulse sequence in Fig 1(c) for the same spin system and considering all the couplings. From 2 to 35 ms the thin red and dashed blue curves are overlapped showing

identical build up of CX SQ coherence. This implies that the effect of homonuclear J-couplings has been completely refocused by PEINEPTRD enhancing the sensitivity of the long range polarization transfer. 5. Experimentals For experimental demonstration of the sensitivity enhancement afforded by the PE-INEPTRD (Fig. 1(c)) over conventional INEPTRD (Fig. 1(b)), these experiments were performed on- (i) menthol in CdCl3, (ii) beta-butyrolactone in CdCl3 and (iii) propylene oxide in PBLG (poly c-bezyl L-glutamate) and CdCl3 as weakly orienting media. INEPTRD experiment with same T2 decay time (Fig. 1(d)) as in PE-INEPTRD was also performed for comparison. All experiments were performed on a Bruker avance 800 MHz NMR spectrometer equipped with a cryoprobe at 298 K. The chemical structures of the molecules are shown in Fig. 1(e-g). Details of experimental and processing parameters are given in the figure captions. For oriented sample of propylene oxide in PBLG and CdCl3, 42.5 mg of the sample, 78 mg of PBLG with DP782 procured from Sigma and 580 mg of CdCl3 were taken. The sample was taken in a 5 mm NMR tube and then centrifuged back and forth for several hours till the visually homogeneous phase was observed [54]. For INEPT experiments on beta-butyrolactone, the experimental parameters are: SW of 197 ppm, number of scans 16 and dummy scans 4, acquisition time of 600 ms, the time domain data was zero filled to 128 k points. For INEPT experiments on menthol the experimental parameters are: SW of 70 ppm, number of scans 32 and dummy scans 4, acquisition time of 1 s with WALTZ-16 decoupling during acquisition, the time domain data was zero filled to 128 k points. For INEPT experiments on propylene oxide the experimental parameters are: SW of 197 ppm, number of scans 48 and dummy scans 8, acquisition time of 1 s the time domain data was zero filled to 128 k points. 6. Results and discussion While interpreting the experimental results we emphasize on two points- (1) improvement of the efficiency of short range polarization transfer at longer s delays and (2) efficiency of long range polarization transfer. Since at longer s delays, the short range transfer efficiency of the PE-INEPTRD sequence is higher than INEPTRD as predicted from simulation (note the blue dotted line in Fig. 2a has higher positive and negative amplitude than thick black line), therefore, initially we focus our attention on experimental demonstration of this aspect. Particularly, we focus on situation where loss of magnetization due to homonuclear 1H–1H J-modulation is more severe than that of T2 decay, The carbon marked ‘7’ in menthol is such an example as this carbon is attached to a 1H which is scalar coupled to too many neighboring protons. Fig. 3(a) illustrates the experimental C-13 signal of carbon ‘7’ of menthol. In this experiment, the refocusing delay D is kept equal to 1/4(1J(13C–HK) for all values of s so that only short range transfer of polarization via 1 JCH contributes to the observed C-13 signal. As shown for each s value, the left peaks in blue color correspond to PE-INEPTRD, the middle peaks in red color corresponds to INEPTRD, and right peaks in green color from modified INEPTRD sequence (for same T2 decay time as PE-INEPTRD). Comparisons of the signals are shown for s delays of 2, 6, 10, 14 and 18 ms and signal to noise ratios are reported on bottom of the peaks. The 1st line of numbers below the peaks representing SNR are obtained by taking the highest SNR out of the three peaks for each s value as 1 and expressing the other two w.r.to 1. The 2nd line of numbers in italic bold represents SNR obtained by taking the highest SNR out of all the

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(a)

(b)

Fig. 3. (a): The experimental C-13 signal of carbon ‘7’ of menthol. For each s value, the left peaks in blue color correspond to PE-INEPTRD, the middle peaks in red color corresponds to INEPTRD, and right peaks in green color from modified INEPTRD sequence (for same T2 decay time as PE-INEPTRD). Comparisons of the signals are shown for s delays of 2, 6, 10, 14 and 18 ms and signal to noise ratios are reported on top of the peaks. The refocusing delay D is fixed to 2 ms for all values of s so that only short range transfer of polarization via 1JCH contributes to the observed C-13 signal. The 1st line of numbers below the peaks representing SNR are obtained by taking the highest SNR out of the three peaks for each s value as 1 and expressing the other two w.r.to 1. The 2nd line of numbers in italic bold representing SNR are obtained by taking the highest SNR out of all the s values as 1 and expressing all other peaks with respect to that. As evident the J-dephasing mediated signal loss is prominent at s values of 10, 14, and 18 ms for conventional INEPTRD (middle red peaks) and modified INEPTRD (right green peaks) while, this loss is prevented in PE-INEPTRD (left side blue peaks) as it displays stronger signal strength compared to the other two sequences. For longer values of s delays (14 and 18 ms) the SNR gain in PE-INEPTRD blue peaks is noteworthy over the conventional INEPTRD red peaks despite the fact that T2 loss is two times longer than that of conventional INEPTRD. This will be true when J-dephasing is more prominent than T2 decay. In agreement with simulation, the perfect echo method of homonuclear decoupling suppresses the signal loss in PE-INEPTRD sequence. (b) The experimental C13 signal of carbonyl carbon of beta-butyrolactone. Left peaks in blue color correspond to PE-INEPT and right peaks in red color correspond to conventional INEPT. The refocusing 2D delay and 1H decoupling during acquisition is not considered while performing the sequences of Fig. 1(b) and (c). As a result, the antiphase pattern of peaks is obtained. Comparisons of the signals are shown for s values of 2, 6, 10, 14, 18, 22 and 35 ms and signal to noise ratios are reported on top of the peaks. For longer s values, contribution from long range polarization transfer and 1H–1H J-dephasing becomes significant. The two lines of numbers below the peaks are SNR calculated as mentioned in (a). Noteworthy enhancement is observed for carbonyl carbon (long range transfer) at 10, 14 and 18 ms in PE-INEPT over conventional INEPT. Slight enhancement at 6 ms and equal transfer efficiency is observed at 2 ms. Particularly at s values of 14 ms and 18 ms (red color peaks on right) very less polarization transfer from CH2 protons to CO carbon is observed in conventional INEPT as a result of the competition between comparable long range heteronuclear J-couplings and homonuclear J-couplings. However, for the same values of s (left side blue color peaks at 14 and 18 ms) significant enhancement is observed in PE-INEPT due to the suppression of homonuclear J-couplings. This enhancement occurs even at the cost of longer T2 loss of magnetization during PE-INEPT compared to INEPT. Note the T2 loss occurs over 4s in PE-INEPT whereas for 2s in conventional INEPT. The entire left side row of blue color peaks displays a smooth increase in C-13 signal, free from homonuclear 1H–1H J-modulation allowing heteronuclear transfer to build up smoothly, while, the peaks in red color is highly oscillatory due to the simultaneous presence of both homo and heteronuclear J-couplings. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

s values as 1 and expressing all other peaks with respect to that. As evident the J-dephasing mediated signal loss is prominent at s values of 10, 14, and 18 ms for conventional INEPTRD (middle peaks in red color) and modified INEPTRD (right peaks in green color) while such loss is prevented for the same s value in PE-INEPTRD (all the left peaks in blue color) as it displays higher SNR compared to the other two sequences. For longer s delays of 14 and 18 ms the SNR gain in PE-INEPTRD peaks is noteworthy over the conventional INEPTRD despite the fact that T2 loss in PE-INEPTRD is two times longer than that of conventional INEPTRD. The 1H attached to carbon ‘7’ is scalar coupled to too many protons, the two methyl group protons at positions ‘8’and ‘9’ and also the methine proton at ‘2’. In case, the sensitivity gain by PE-INEPTRD over suppressing 1H–1H J-modulation is equal to the loss caused by its two times longer T2 decay, then the PEINEPTRD and INEPTRD peaks will have identical SNR. However, if the signal gain achieved by suppressing 1 H–1H J-modulation exceeds the loss caused by two times longer

T2 decay, then the PEINEPTRD peaks will have higher SNR than INEPTRD and this is clearly visible at s values of 10, 14, and 18 ms for the left peaks in blue color. Therefore, signal loss due to 1H–1H J-dephasing at longer s delays can be recovered by the PE-INEPTRD sequence. This demonstrates the improvement of short range INEPT at longer INEPT transfer delays. Since the short range transfer efficiency could be sustained for longer s delays as just demonstrated, it also gives rise to the possibility that long range polarization transfer in the same system can build up significantly over such longer s values. Since the long range heteronuclear couplings are small, it is necessary to wait for longer time for such polarization transfer to build up. For example, the antiphase state for a 2JCH value of 7 Hz is maximum at 71.4 ms (1/2 * (2JCH)). And since the competition from the comparable 1H–1H J-modulation is more severe in this case, the PE-INEPTRD should provide an efficient method for long range transfer. This possibility already displayed in simulation

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Fig. 4. The C-13 signal for one component of the multiplets of ‘CH2’ carbon (a), ‘CH’ carbon (b) and ‘CH3’ carbon (c) of beta-butyrolactone, right peaks in red color corresponds to INEPT and left peaks in blue color corresponds to PE-INEPT. For these experiments the refocusing 2D delay and 1H decoupling during acquisition is not applied in Fig. 1(b) and (c). Comparisons of the signals are shown for 2, 6, 10, 14, 18 and 22.22 ms and signal to noise ratios are reported on top of the peaks. For these groups the detected C-13 signal is the resultant of short range as well as long range transfer for the longer s values. In the figures, only one component of the multiplets is shown. In all cases (a), (b) and (c), the highest value of SNR observed in the series of peaks from 2 to 22.22 ms is normalized to 1 and SNR of the rest of the peaks are expressed by dividing with that highest SNR. CH2 carbon (a): For s values of 6, 10 and 14 ms higher SNR is observed in PE-INEPT over INEPT. Equal SNR is observed for 18 ms. For 22.22 ms, the conventional INEPT has higher SNR, implying that for very long s interval, T2 decay take its toll since homonuclear J-refocusing by perfect echo becomes less efficient. CH carbon (b): For s values of 10, 14, 18 and 22.22 ms good SNR enhancement is observed in PE-INEPT over INEPT. For s values of 2 ms almost equal transfer efficiency is observed and for 6 ms lower sensitivity for PE-INEPT is observed. CH3 carbon (c): For all s values comparable SNR is observed in both PE-INEPT as well as INEPT. Thus, PE-INEPT at these s values just compensate for the magnetization loss occurred by two times longer T2 decay. For s values of 22.22 ms PE-INEPT has very low SNR. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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70

60

50

40

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50

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30

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70

30

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Fig. 5. The C-13 signals of carbons ‘1’ to ‘10’ of menthol are shown for s values of 2 and 6 ms in figures (a), and (b) respectively. For each C-13 site, the left side blue color peaks are obtained from PE-INEPTRD sequence (Fig. 1(c)), middle peaks in red color from conventional INEPTRD sequence (Fig. 1(b)) and right peaks in green color from modified INEPTRD sequence. The numbers by the side of the peaks in (b) represents SNR obtained by taking the SNR of the PE-INEPTRD peak (left blue color in each) as 1 and expressing the other two w.r.to that. Note, the T2 loss of magnetization and time of evolution of homonuclear scalar couplings for PE-PEINEPTRD sequence is twice that of conventional INEPTRD sequence, despite that the SNR gain in PE-INEPTRD spectrum is observed for peaks marked 6, 4, 5 7, 9 and 10 in Fig. (b) for s value of 6 ms. Comparisons of the left and right side peaks in blue and green color [for PE-INEPTRD and modified INEPTRD] in (a) and (b) reveals that significant amount of magnetization can be lost in the later case when length of the sequences are kept same. Particularly in (b) for sites C-1 to C-7 for longer s value of 6 ms, all the right side green color peaks have very low SNR. The T2 decay being same for both, the severe loss of signal is attributed to undesired 1H–1H J-coupling evolution. Exception to these rule are C-10 and C-9 sites where sequence 1(d) has higher SNR and could not be accounted for. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

[Fig. 2(b)] will be now experimentally demonstrated. We focus on long range transfer efficiency to a non-protonated C-13 site, the carbonyl carbon in beta-butyrolactone [marked ‘1’ in Fig. 1(f)] from the neighboring diastereotopic protons on carbon ‘3’ and other protons in the vicinity. The extracted heteronuclear J-couplings from carbonyl carbon to CH2 protons attached to carbon ‘3’ is found to be (2JCH) 6.9 Hz which is in fact smaller than the geminal homonuclear 1H–1H J-coupling (2JHH) of 16.4 Hz among the diastereotopic 1H’s in CH2 group (measured from 1D 1H spectra). To make 1H–1H J-modulation worse, diastereotopic protons are also coupled to the methine 1H at carbon ‘2’ by 3JHH of 5.8 Hz. Therefore, polarization transfer from these CH2 protons to the carbonyl carbon via small 2JCH of 6.9 Hz has to compete with too many 1H–1H J-modulation (predicted by Eq. (2)). The sin(pJH2s) term in Eq. (2) will be very significant when JHH is larger than 2JCH and there will be too many such terms in this case. Fig. 3(b) displays the experimental C-13 signal of carbonyl carbon of beta-butyrolactone. Left peaks in blue color correspond

to PE-INEPT and right peaks in red color correspond to conventional INEPT. The refocusing 2D delay and 1H decoupling during acquisition is not considered while performing the sequences of Fig. 1(b) and (c). As a result, the antiphase pattern of peaks in Fig. 3(b) is obtained. Comparisons of the signals are shown for s values of 2, 6, 10, 14, 18, 22 and 35 ms and signal to noise ratios are reported on top of the peaks. For longer s values, contribution from long range polarization transfer and 1H–1H J-dephasing becomes significant. All spectra from 2 to 35 ms are plotted on the same noise level. The two lines of numbers below the peaks are SNR calculated as mentioned for Fig. 3(a). Noteworthy, enhancement of the carbonyl carbon signal is observed at s values of 10, 14 and 18 ms in PE-INEPT over conventional INEPT. Slight enhancement is observed at 6 ms and equal enhancement at 2 ms. Particularly at s values of 10, 14 and 18 ms (right peaks in red color) very less polarization transfer occurs in conventional INEPT as a result of the competition between comparable long range heteronuclear J-coupling and homonuclear J-couplings.

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49.0

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20

19

18

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Fig. 6. The C-13 signals of ‘CH2’ and ‘CH’ carbons (top panel) and ‘CH3’ carbon (bottom panel) of propylene oxide in weakly aligned medium of PBLG and CdCl3. ‘CH2’ and ‘CH’ carbon resonances appear at nearly same frequencies. The left side peaks in red color corresponds to INEPT while right side blue color peaks corresponds to PE-INEPT. The s value is 9 ms for these experiments, and therefore, the presence of too many residual homonuclear dipolar couplings can reduce the polarization transfer in conventional INEPTRD. Therefore, all the left side red color peaks displays lower SNR compared to the right side blue color peaks. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

However, for the same values of s (left peaks in blue color at 10, 14 and 18 ms) significant enhancement is observed in PE-INEPT. The SNR enhancement in PE-INEPT over conventional INEPT is larger by a factor of almost 3 and 4 at s values of 14 and 18 ms. This enhancement occurs even at the cost of longer T2 loss of magnetization during PE-INEPT compared to INEPT. Note the T2 loss of magnetization occurs over 4s in PE-INEPT whereas for 2s in conventional INEPT. The 4s values are 56 ms and 72 ms (corresponding to panels marked with s values 14 and 18 ms), whereas the corresponding 2s values in conventional INEPT are 28 ms and 36 ms. The entire row of blue color peaks displays a smooth increase in C-13 signal, free from homonuclear 1H–1H J-modulation allowing heteronuclear polarization transfer to build up smoothly which is in agreement with the simulation of long range PE-INEPTRD (blue curve in Fig. 2(b)) and the product operator calculations. The row of all red color peaks is highly oscillatory due to the simultaneous presence of both homo and heteronuclear J-couplings again following the prediction of simulation of Fig. 2(b). Comparison of the left side blue color peaks and right side red color peaks reveals that PE-INEPTRD has more advantage over the conventional INEPTRD in carrying out more efficient long range heteronuclear polarization transfer. However, longer T2 decay will be a critical factor for this performance. Nevertheless, the 1H and C-13 in such transfer being separated by many bonds distance, the dominating 1H–13C dipolar relaxation is very insignificant. The C-13 signal of carbons ‘3’ ‘2’ and ‘4’ of beta-butyrolactone corresponding to CH2, CH and CH3 groups are shown in Fig. 4(a)– (c) respectively. These peaks are obtained from the same PE-INEPT

experiment in Fig. 3(b). For these groups the detected C-13 signal is the resultant of short range as well as long range transfer for the longer s values. In the figures, only one component of the multiplet is shown. Comparisons of the signals are shown for s values of 2, 6, 10, 14, 18, 22.22 ms and signal to noise ratios are reported on top of the peaks. For each s value, the peak on the right side (in red color) corresponds to INEPT and the peak on left side (in blue color) corresponds to PE-INEPT plotted on the same noise level. In all cases 4(a)–(c), the highest SNR observed in the series from 2 to 22.22 ms is normalized to 1 and SNR of the rest of the peaks are expressed by dividing with that highest SNR. For CH2 carbons in Fig. 4(a), PE-INEPT spectrum displays higher SNR at s values of 6, 10 and 14 ms than conventional INEPT spectrum. Both sequences display equal SNR for 18 ms. For 22.22 ms, the conventional INEPT has higher SNR, implying that for very long s interval either T2 decay take its toll or homonuclear refocusing by perfect echo scheme fails to work. For CH carbon in Fig. 4(b), good enhancement is observed at s values of 10, 14, 18 and 22.22 ms in PE-INEPT over INEPT. For s value of 2 ms almost equal transfer efficiency is observed for both sequences and for 6 ms PE-INEPT has lower SNR. For CH3 carbon, in Fig. 4(c), SNR for both sequences at all s values are nearly equal. Thus, PE-INEPT in this case just compensate for the magnetization loss occurred by T2 decay. In overall, only CH proton, which has five 3JHH coupled neighbor displays enhancement at 10, 14, 18 and 22.22 ms suggesting that transfer efficiency is improved when 1H–1H J-dephasing is more prominent than T2 loss. Same interpretation can be extended to CH2 and CH3 where CH2 having two significant coupling (2JHH and 3JHH), displays

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better SNR (for 6, 10 and 14 ms) than CH3 having only one significant 3JHH coupling compared to their conventional INEPT signal. At s value of 35 ms in 4(b) and (c) the conventional INEPT is slightly better than PE-INEPT as the as the refocusing condition sJHH  1 is difficult to fulfil (for the larger JHH couplings) and also the twice longer relaxation losses associated with it. The C-13 resonances of carbons ‘1’ to ‘10’ of menthol were also investigated for s values of 2, 6, 10, 14 and 18 ms. Fig. 5(a) and (b) displays the spectrum for s values of 2 and 6 ms while spectrum for 10, 14 and 18 ms is added as supporting information. For each C-13 site, the left side blue color peaks are obtained from PEINEPTRD sequence (Fig. 1(c)), middle peaks in red color from conventional INEPTRD sequence (Fig. 1(b)) and right peaks in green color from modified INEPTRD sequence [Fig. 1(d)) taken for same T2 decay time as PE-INEPTRD]. The numbers by the side of the peaks in 5(b) represents SNR obtained by taking the SNR of the PE-INEPTRD peak (left blue color in each) as 1 and expressing the other two w.r.to that. For shorter transfer delay of s (=2 ms), almost equal SNR of the PE-INEPTRD and INEPTRD peaks are observed in Fig. 5(a). Despite longer T2 decay of magnetization, the PE-INEPTRD sequence displays higher SNR which is clearly observed for the left side blue color peaks in Fig. 5(b) for the C-13 resonances marked 6, 4, 5, 7, 9 and 10. However, the same peaks in conventional INEPTRD spectrum, i.e. middle peaks in red color for the same resonances in panel (b) displays lower SNR. Next, we compare the left side blue color peaks (PEINEPTRD) vs right side green color peaks (modified INEPTRD with same T2 decay) in panels (a) and (b) for all peaks. Inspection of these peaks reveals that significant amount of magnetization can be lost in the later case when lengths of the sequences are kept same. This is clearly seen for the sites C-1 to C-7 in 5(b) when s value is 6 ms. Now, the T2 decay being same for both sequences, the severe loss of signal is attributed to undesired 1H–1H J-coupling evolution in the modified INEPT which is just the conventional INEPT with equal time for 1H–1H Jevolution as in PE-INEPT. Exception to these rule are C-10 and C-9 sites where sequence 1(d) has higher SNR and could not be accounted for. In the supporting information, in Fig. S1a and b, we have demonstrated that for s = 10 and 14 ms, there is still gain in SNR for many of the blue color peaks in PE-INEPTRD compared to the red color peaks in INEPTRD. However, at 18 ms, in Fig. S1c (in supporting information), only one peak in PE-INEPTRD has better SNR than conventional INEPTRD. For other peaks in S1c, PE-INEPTRD has either slightly lower or equal SNR to that of conventional INEPTRD. This demonstrates that 1H–1H J-refocusing becomes less efficient at higher s values and T2 loss becomes more prominent. This shows the drawback of PE-INEPTRD. Finally, we show the experiments performed on propylene oxide dissolved in weakly aligned media of PBLG/CdCl3. Fig. 6 displays the C-13 signals of ‘CH2’ and ‘CH’ carbons (a), and ‘CH3’ carbon (b), of propylene oxide. The left side peaks in red color corresponds to INEPT while slightly displaced right side blue color peaks corresponds to PE-INEPT. The s value is 9 ms for these experiments, and therefore, the presence of too many residual homonuclear dipolar couplings can reduce the polarization transfer in conventional INEPT. As a result, all the left side red color peaks display lower SNR compared to the right side blue color peaks. The entire blue color peaks in both (a) and (b) are obtained from PE-INEPT and displays higher SNR. 7. Conclusion We have demonstrated a perfect echo based INEPT experiment where undesired homonuclear 1H–1H J-coupling evolution can be refocused while simultaneously allowing the heteronuclear J-coupling evolution to continue during INEPT transfer. This leads to improvement of short range polarization transfer efficiency at

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longer INEPT transfer delays and also enhances the sensitivity of long range INEPT experiment. This improvement is observed provided loss of magnetization due to homonuclear 1H–1H J-modulation is more severe than that of T2 decay. This is found to be true in PE-INEPT experiments carried out on menthol and beta-butyrolactone for numerous C-13 resonances. The long range heteronuclear couplings (2JCH) being comparable in magnitude to homonuclear 1 H–1H J-couplings between the geminal protons in CH2 group of beta-butyrolactone, the sensitivity enhancement of adjacent carbonyl carbon in PE-INEPT could be observed by suppressing JHH. We have also shown that utilizing very long INEPT transfer delay would not be very useful for PE-INEPT as the decoupling condition sJHH  1 is difficult to fulfil (for the larger JHH couplings) and also the twice longer relaxation losses associated with it and is shown for 22 and 35 ms in Fig. 4a–c and for 18 ms in Fig. S1c. Thus, relaxation loss becomes more severe and efficiency of J-refocusing declines in those cases. However, transfer efficiency seems to be improved in many C-13 resonances for many s values (in Figs. 3a, b, 4a, b, 5a, b, 6 and S1a, b) when too many homonuclear couplings are present to interfere with the transfer. In certain cases, the PE-INEPT just compensate for the magnetization loss occurred by T2 decay. Efficient polarization transfer has been demonstrated for molecules dissolved in isotropic as well as weakly aligned media. We have presented experimental results and also the product operator analysis and simulation results using the full propagator. The scheme is simple and easy to implement and unlike CPMG INEPT which applies a large number of refocusing pulses, this scheme contains only two additional pulses than that of conventional INEPT during the whole INEPT transfer period. We predict such experiments will be useful in C-13 enriched small molecules where hyperpolarization from C-13 to remote insensitive spins is desired. C-13 to 1H back polarization transfer in small proteins enriched in C-13 is another area where such PE-INEPT scheme might be useful. All such possibilities will be explored in near future. Acknowledgment Bikash Baishya acknowledges Council of Scientific and Industrial Research (CSIR), India for research fellowship provided through sanction No. IA-27416. Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.jmr.2014.02.017. References [1] G.A. Morris, R. Freeman, Enhancement of nuclear magnetic resonance signals by polarization transfer, J. Am. Chem. Soc. 101 (1979) 760–762. [2] Stephen Wimperis, Geoffrey Bodenhausen, Heteronuclear coherence transfer over a range of coupling constants. a broadband-INEPT experiment, J. Magn. Reson. 69 (1986) 264–282. [3] T.J. Henderson, Sensitivity-enhanced quantitative 13C NMR spectroscopy via cancellation of 1JCH dependence in dept polarization transfers, J. Am. Chem. Soc. 126 (2004) 3682–3683. [4] B. Jiang, N. Xiao, H. Liu, Z. Zhou, X.-A. Mao, M. Liu, Optimized quantitative dept and quantitative POMMIE experiments for 13C NMR, Anal. Chem. 80 (2008) 8293–8298. [5] A. Mäkelä, I. Kilpeläinen, S. Heikkinen, Quantitative 13C NMR spectroscopy using refocused constant-time INEPT, Q-INEPT-CT, J. Magn. Reson. 204 (2010) 124–130. [6] V.S. Manu, Anil Kumar, Fast and accurate quantification using genetic algorithm optimized 1H–13C refocused constant-time INEPT, J. Magn. Reson. 234 (2013) 106–111. [7] A. Bax, M.F. Summers, 1H and 13C assignments from sensitivity-enhanced detection of heteronuclear multiple-bond connectivity by 2D multiple quantum NMR, J. Am. Chem. Soc. 108 (1986) 2093–2094. [8] R.T. Williamson, B.L. Marquez, W.H. Gerwick, K.E. Kover, One and twodimensional gradient-selected HSQMBC NMR experiments for the efficient

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