The DEPTQ⁺ Experiment: Leveling the DEPT Signal Intensities and Clean Spectral Editing for Determining CH_n Multiplicities

Abstract

We propose a new ¹³C DEPTQ⁺ NMR experiment, based on the improved DEPTQ experiment, which is designed to unequivocally identify all carbon multiplicities (Cq, CH, CH₂, and CH₃) in two experiments. Compared to this improved DEPTQ experiment, the DEPTQ⁺ is shorter and the different evolution delays are designed as spin echoes, which can be tuned to different ¹J_CH values; this is especially valuable when a large range of ¹J_CH coupling constants is to be expected. These modifications allow (i) a mutual leveling of the DEPT signal intensities, (ii) a reduction in J cross-talk in the Cq/CH spectrum, and (iii) more consistent and cleaner CH₂/CH₃ edited spectra. The new DEPTQ⁺ is expected to be attractive for fast ¹³C analysis of small-to medium sized molecules, especially in high-throughput laboratories. With concentrated samples and/or by exploiting the high sensitivity of cryogenically cooled ¹³C NMR probeheads, the efficacy of such investigations may be improved, as it is possible to unequivocally identify all carbon multiplicities, with only one scan, for each of the two independent DEPTQ⁺ experiments and without loss of quality.

1. Introduction

Two-dimensional heteronuclear NMR techniques for ¹³C assignment have long been considered extremely powerful since they are much more sensitive than, e.g., one-dimensional (1D) ¹³C spectral editing experiments [1], and the corresponding spectra contain a lot of information. Nevertheless, “old” 1D experiments such as SEFT [2], APT [3] and PENDANT [4,5], refocused variants of INEPT [6], DEPT [7,8], DEPTQ [9,10,11] and SEMUT [12], continue to be very useful for routine applications [13]. A likely reason for the popularity of these 1D experiments is the rather low resolution achieved in the indirect dimension (¹³C) with 2D heteronuclear experiments, such as HSQC [14], HMBC [15,16,17] or LR-HSQMBC [18], under standard experimental conditions, thus potentially preventing the unambiguous differentiation between closely spaced ¹³C resonances. In principle, this problem can easily be alleviated [19,20] but the required experiments/methods can only be routinely applied to a certain extent, as they require in-depth knowledge of theoretical and experimental NMR spectroscopy.

One-dimensional ¹³C experiments such as APT [2], PENDANT [4,5], and DEPTQ [9,10,11], provide information about both quaternary and protonated carbons in the spectra, with the signals of Cq and CH₂ carbons being 180° out-of-phase with respect to the signals of CH and CH₃ carbons. Among those experiments, the DEPTQ encompasses all the known advantages of the basic DEPT experiment but includes the signals of quaternary carbons. The DEPT pulse sequences, thanks to their marked insensitivity to experimental parameters compared to other experimental schemes, have proven to be the experiments of choice for obtaining the chemical shift and multiplicity information for all types of protonated carbons [8]. Additionally, a version of DEPTQ with the length of the initial ¹H pulse adjusted accordingly allows simplified spectral editing: with this first and the final proton pulse adjusted to 45° and 90°, respectively, for a DEPTQ90 (DEPTQ90₄₅) and adjusted to 90° and 135°, respectively, for a DEPTQ135 (DEPTQ135₉₀), the intensities of CH signals are equal in both experiments, since they are reduced to 70% of their maximum value with the DEPTQ90₄₅ experiment. Thus, subtracting the DEPTQ90₄₅ and the DEPTQ135₉₀ from each other yields a CH₂/CH₃ edited spectrum with the signals of the two carbon types in opposite phase [11]. The DEPTQ90 spectrum shows exclusively, and with opposite phase, the signals of Cq and CH.

Therefore, although no Cq-. CH-, CH₂- and CH₃-only spectra result, the pairwise editing with opposite signs for the signals of different multiplicities allows unambiguous spectral editing with only two experiments, and conceivably, with only one scan each, e.g., for highly concentrated samples [11].

Experimentally, we found that with the DEPTQ experiment, the editing filter quality in the Cq/CH and CH₂/CH₃ subspectra is not satisfactory, with a breakthrough of many artifacts originating from other CH_n multiplicities [13]. We also observed that for molecules possessing large ranges of ¹J_CH coupling constants, DEPTQ135 spectra and edited subspectra are obtained, with missing or very weak signals, especially CH₃ or alkyne CH groups (Figure 1). For instance, in the DEPTQ135₉₀ spectrum of 4-methyl-N,N-di(prop-2-yn-1-yl)aniline, the resonance of the methyl group C8 at 20.6 ppm is almost invisible (Figure 1). While the DEPTQ90₄₅ spectrum appears satisfactory, the edited CH₂/CH₃ subspectrum is misleading, as the resonance of the methyl group C8 at 20.6 ppm is absent. We thought it useful to develop a modified DEPTQ scheme for obtaining consistent DEPTQ and edited subspectra for all classes of molecules. This could potentially be very attractive for rapid ¹³C analysis of newly synthesized or isolated compounds, especially for high-throughput NMR analysis.

In this article, we present a new pulse sequence, DEPTQ⁺, possessing all these attributes, and compare it with the modified DEPTQ experiment, designed to unequivocally identify all carbon multiplicities (Cq, CH, CH₂, and CH₃) in two experiments. We show both theoretically and experimentally that the DEPTQ⁺ pulse sequence always provides unambiguous DEPTQ spectra with a leveling of all carbon intensities. This generally results in processed spectra with a clean separation of the Cq and CH signals in one spectrum and the CH₂ and CH₃ signals in the other, with both spectra showing the signals of the two carbon species in opposite phases. It must be emphasized, however, that these properties only come into play and are relevant for molecules possessing a large range of ¹J_CH coupling constants.

2. Results and Discussion

2.1. Theory

2.1.1. Original DEPTQ Pulse Sequence

Despite their known tolerance to the experimental parameters, edited DEPTQ spectra may show undesirable residual CH_n signals from “wrong” carbon types, a phenomenon termed dubbed J cross-talk [21]. These signals arise, among other things, with non-ideally adjusted delays and occur for both the coherences resulting from initial ¹H- and from ¹³C-polarization. These signals are particularly troublesome in the pairwise edited CH_n spectra, as they can lead to misinterpretation, particularly if the editing is performed in an automatic or semi-automatic way and with samples containing several, differently concentrated components [22,23,24,25,26,27]. Therefore, this study predominantly focuses on suppressing remaining CH_n signals in the different subspectra as efficiently as possible.

The general condition δ ≠ 1/(2 * ¹J_CH) is assumed in the following first product operator treatments of the original DEPTQ pulse sequence (Figure 2). For simplicity, ¹H- and ¹³C-shift evolutions during the delays δ and the gradients G₁–G₃ used in practice are not considered (the overall result is identical, except that only one of the ¹³C magnetization terms at coherence level −1, C⁻, is detected if the PFGs are considered). We use here the bracket notations proposed by Mateescu and Valeriu [28].

Quaternary Carbons

The first ¹³C pulse φ is set arbitrarily (Ernst angle)

$$\begin{array}{cc}\hfill \left[z\right]\stackrel{\varnothing °yC}{\to }cos\varnothing \left[z\right]& +sin\varnothing \left[x\right]\stackrel{\delta }{\to }cos\varnothing \left[z\right]+sin\varnothing \left[x\right]\stackrel{\mathsf{\Omega }°xH}{\to }\stackrel{180°xC}{\to }\stackrel{\delta }{\to }-cos\varnothing \left[z\right]\hfill \\ & +sin\varnothing \left[x\right]\stackrel{180°xH}{\to }\stackrel{90°xC}{\to }cos\varnothing \left[y\right]+sin\varnothing \left[x\right]\stackrel{\delta }{\to }cos\varnothing \left[y\right]\hfill \\ & +sin\varnothing \left[x\right]\stackrel{180°xC}{\to }\stackrel{\theta °yH}{\to }-cos\varnothing \left[y\right]+sin\varnothing \left[x\right]\stackrel{\delta }{\to }\stackrel{90°-xC}{\to }cos\varnothing \left[z\right]\hfill \\ & +sin\varnothing \left[x\right]\hfill \end{array}$$

(1)

Of course, the outcome for quaternary carbons is identical in both experiments, DEPTQ135₉₀, Ω = 90° and DEPTQ90₄₅, Ω = 45°, irrespective of the length of the proton pulse θ.

DEPTQ135, Ω = 90°, θ = 135°

Subsequently, the following abbreviations will be used:

c = cos πJδ and s = sin πJδ  c2 = cos 2πJ_CHδ and s2 = sin 2πJ_CHδ

For the observable signals originating from the polarization transfer from ¹H to ¹³C (DEPT135), we obtain [7,8,29]:

1. CH groups

$$\begin{array}{l}\left[1z\right]\stackrel{\varnothing °yC}{\to }\stackrel{\delta }{\to }\left[1z\right]\stackrel{90°xH}{\to }\stackrel{180°xC}{\to }-\left[1y\right]\stackrel{\delta }{\to }s\left[zx\right]\stackrel{\left(180°\right)xH}{\to }\stackrel{\left(90°\right)xC}{\to }-s\left[yx\right]\stackrel{\delta }{\to }\\ -s\left[yx\right]\stackrel{\left(180°\right)xC}{\to }s\left[yx\right]\stackrel{135°yH}{\to }0.7s\left[yx\right]\\ +0.7s\left[yz\right]\stackrel{\delta }{\to }\stackrel{90°-xC}{\to }\stackrel{1_{H-decoupling}}{\to }0.7s^2\left[x1\right]\end{array}$$

(2)

2. CH₂ groups

$$\left[1z1\right]+\left[11z\right]\stackrel{\varnothing °yC}{\to }\stackrel{\delta }{\to }\dots \stackrel{\delta }{\to }\stackrel{90°-xC}{\to }0.35s{2}^2\left[x11\right]-s^4\left[x11\right]$$

(3)

3. CH₃ groups

$$\begin{array}{l}\left[1z11\right]+\left[11z1\right]+\left[111z\right]\stackrel{\varnothing °yC}{\to }\stackrel{\delta }{\to }\dots \stackrel{\delta }{\to }\stackrel{90°-xC}{\to }0.53s{2}^2{c}^2\left[x111\right]\\ -0.75s{2}^2{s}^2\left[x111\right]+1.06s^6\left[x111\right]\end{array}$$

(4)

The final carbon signal intensities, represented by I, for the three groups CH, CH₂ and CH₃ for Ω = 90° and θ = 135°, as a function of the evolution delay δ and the actual coupling constant J_CH, are thus (the operators [x1], [x11], and [x111] have been replaced by the Cartesian operator C_x for simplicity):

I_CH = C_x [0.71 sin²(πJ_CHδ)]
I_CH2 = C_x [0.35 sin²(2πJ_CHδ) − 1.00 sin⁴(πJ_CHδ)]
I_CH3 = C_x [0.53 sin²(2πJ_CHδ) cos²(πJ_CHδ) − 0.75 sin²(2πJ_CHδ) sin²(πJ_CHδ) + 1.06
sin⁶(πJ_CHδ)]

(5)

which reduces with δ = 1/(2 * ¹J_CH) (matched delay) to:

I_CH = +0.71 C_x
I_CH2 = −1.00 C_x
I_CH3 = +1.06 C_x

(6)

Equation (5) provides the analytical expressions to calculate the carbon signal intensities for the three groups CH, CH₂ and CH₃ as a function of the evolution delay δ and the actual coupling constant J_CH. Obviously, very weak resonances result in cases of large mismatches between actual ¹J_CH coupling constants and the average ¹J_CH⁰ coupling constant set (=1/(2 * δ)) in the DEPTQ experiment. In detail, large mismatches exist (i) for acetylenic CH (¹J_CH ~ 250 Hz) or hetero aromatic rings (¹J_CH ~ 170–210 Hz) when ¹J_CH⁰ is set to the classical value of 145 Hz, and (ii) for typical methyl groups (¹J_CH ~ 110–135 Hz) when ¹J_CH⁰ is set to an average value 185 Hz, to account for the whole range of ¹J_CH coupling constants (100–250 Hz) when acetylenic CH or hetero aromatic rings are present (Figures S1 and S2).

DEPTQ90, Ω = 45°, θ = 90°

1. CH groups

$$\begin{array}{l}\left[1z\right]\stackrel{\varnothing °yC}{\to }\stackrel{\delta }{\to }\stackrel{180°xC}{\to }\left[1z\right]\stackrel{45°xH}{\to }-0.7\left[1y\right]\stackrel{\delta }{\to }0.7s\left[zx\right]\stackrel{\left(180°\right)xH}{\to }\stackrel{\left(90°\right)xC}{\to }-0.7s\left[yx\right]\stackrel{\delta }{\to }\\ -0.7s\left[yx\right]\stackrel{\left(180°\right)xC}{\to }0.7s\left[yx\right]\stackrel{90°yH}{\to }-0.7s\left[yz\right]\stackrel{\delta }{\to }\stackrel{90°xC}{\to }0.7s^2\left[x1\right]\end{array}$$

(7)

2. CH₂ groups

$$\left[1z1\right]+\left[11z\right]\stackrel{\varnothing °yC}{\to }\stackrel{\delta }{\to }\dots \stackrel{\delta }{\to }\stackrel{90°-xC}{\to }0.35s{2}^2\left[x11\right]$$

(8)

3. CH₃ groups

$$\left[1z11\right]+\left[11z1\right]+\left[111z\right]\stackrel{\varnothing °yC}{\to }\stackrel{\delta }{\to }\dots \stackrel{\delta }{\to }\stackrel{90°-xC}{\to }2.11s^2{c}^4\left[x111\right]$$

(9)

The final carbon signal intensities, represented by I, for the three groups CH, CH₂, and CH₃ for Ω = 45° and θ = 90°, as a function of the evolution delay δ and the actual coupling J_CH, are thus:

I_CH = C_x [0.71 sin²(πJ_CHδ)]
I_CH2 = C_x [0.35 sin²(2πJ_CHδ)]
I_CH3 = C_x [2.11 sin²(πJ_CHδ) cos⁴(πJ_CHδ)]

(10)

which reduces with δ = 1/(2 * ¹J_CH) (matched delay) to:

I_CH = +0.71 C_x
I_CH2 = 0
I_CH3 = 0

(11)

DEPTQ135₉₀ − DEPTQ90₄₅, edited CH₂/CH₃ subspectrum

The subtraction of the two data, DEPTQ135₉₀ − DEPTQ90₄₅, leads to:

I_CH = C_x [0.71 sin²(πJ_CHδ)] − C_x [0.71 sin²(πJ_CHδ)] = 0
I_CH2 = C_x [0.35 sin²(2πJ_CHδ) − 1.00 sin⁴(πJ_CHδ)] − C_x [0.35 sin²(2πJ_CHδ)] = −C_x
sin⁴(πJ_CHδ)
I_CH3 = C_x [0.53 sin²(2πJ_CHδ) cos²(πJ_CHδ) − 0.75 sin²(2πJ_CHδ) sin²(πJ_CHδ) + 1.06
sin⁶(πJ_CHδ)] − C_x [2.11 sin²(πJ_CHδ) cos⁴(πJ_CHδ)]

(12)

which reduces with δ = 1/(2 * ¹J_CH) (matched delay) to:

I_CH2 = −1.00 C_x
I_CH3 = +1.06 C_x

(13)

For the typical J-coupling constant ranges (for which δ is usually set to an average value of 145 Hz), the artefacts originating from CH₂ groups in the DEPTQ90₄₅ spectrum are expected to be weak: due to its sin²-dependence, the intensity of the cross-talk term 0.35 sin²(2πJ_CHδ) in Equation (10) is generally small, which is also shown in Figure S3. However, CH₂ artifacts can also be very intense and actually troublesome when the full J-coupling constant range is taken into account (100–250 Hz), for which δ is usually set to a larger average value around 180 Hz (Figure S4) [19,30]. Likewise, for a CH₃ group, the intensity of the cross-talk term 2.11 sin²(πJ_CHδ) cos⁴(πJ_CHδ) in Equation (10) and, thus, CH₃ artifacts, will be very weak for the usual J-coupling constant ranges, as shown in Figure S3, but can also be very intense and troublesome when the full J-coupling constant range is considered (Figure S4) [19,30].

The DEPTQ experiment has two potential drawbacks: (i) the problem of missing or very weak resonances in the DEPTQ135₉₀ when large ¹J_CH coupling constant ranges are considered, and (ii) the existence of artefacts, possibly strong, originating from CH₂- and CH₃ groups in the DEPTQ90₄₅ spectrum. We propose the modification of the DEPTQ experience to remedy these two weaknesses.

2.1.2. The DEPTQ⁺ Pulse Sequence

The proposed DEPTQ⁺ pulse sequence is depicted in Figure 2 together with the original DEPTQ pulse sequence [10]. Compared to the latter, the evolution periods of length δ = 1/(2 * ¹J_CH) are replaced by three spin echoes of different length [21,30]. Interestingly, these spin-echoes make it possible to omit the first evolution period in the standard DEPTQ pulse sequence that must precede the DEPT pulse sequence for proper refocusing of the Cq-magnetization generated with the first ¹³C excitation pulse. Therefore, as in the PENDANT sequence [4,5], both the ¹H and ¹³C excitation pulses are synchronized. The total length of DEPTQ⁺ is, thus, shorter than that of DEPTQ and identical to a standard DEPT experiment, which will reduce the relaxation losses.

The advantages of the DEPTQ⁺ compared to the DEPTQ experiment, which result from the individual tuning of the three spin echo periods to different ¹J_CH coupling constants are: (i) a mutual leveling of the DEPT signal intensities, similar to that achieved with the ACCORD-DEPT experiment, which systematically samples a range of ¹J_CH coupling constants [31]. The accordion principle is, however, more complicated to implement than tuning the three spin echo periods, as shown subsequently. (ii) A reduction in J cross-talk in the CH/Cq spectrum (DEPTQ90), although this J cross-talk reduction is only noticeable and disturbing for molecules with a large range of ¹J_CH coupling constants, as shown theoretically (Figures S3 and S4), and subsequently in the experimental part.

Note that the intensities of quaternary carbon resonances are, of course, not affected by these three echo periods used with DEPTQ⁺ and are the same as with DEPTQ. However, compared to the DEPTQ experiment, note that while the first ¹³C pulse φ is ≠90°, the additional 180° pulses during the three spin echo periods invert the sign of the residual z-magnetization that is not detected. Thus, the phase of the additional 90° ¹³C pulse prior to data acquisition must be applied along the +x axis to re-establish the residual ¹³C-z magnetization left with the initial ¹³C pulse.

Quaternary Carbons

The first ¹³C pulse ϕ is set arbitrarily (Ernst angle):

$$\begin{array}{cc}\hfill \left[z\right]\stackrel{\varnothing °yC}{\to }\stackrel{{\delta }_1}{\to }\stackrel{180°xC}{\to }& -cos\varnothing \left[z\right]+sin\varnothing \left[x\right]\stackrel{90°xC}{\to }cos\varnothing \left[y\right]\hfill \\ & +sin\varnothing \left[x\right]\stackrel{{\delta }_2}{\to }\stackrel{180°xC}{\to }\stackrel{{\delta }_3}{\to }\stackrel{180°xC}{\to }cos\varnothing \left[y\right]+sin\varnothing \left[x\right]\stackrel{90°xC}{\to }cos\varnothing \left[z\right]\hfill \\ & +sin\varnothing \left[x\right]\end{array}$$

(14)

The product operator evaluation for the CH_n coherences originating from initial ¹H-polarization is applied in the DEPTQ⁺ pulse sequence, using the following abbreviations:

c = cos (πJ_CHδ₁), s = sin (πJ_CHδ₁)

c’ = cos (πJ_CHδ₂), s’ = sin (πJ_CHδ₂)

c’’ = cos (πJ_CHδ₃), s’’ = sin (πJ_CHδ₃)

s2’’ = sin (2πJ_CHδ₃)

DEPTQ⁺135₉₀, Ω = 90°, θ = 135°

The final carbon signal intensities, represented by I, for the three groups CH, CH₂, and CH₃ for Ω = 90°, θ = 135°, as a function of the evolution delay δ, and the actual coupling constant J_CH, are:

1. CH groups

$$\left[1z\right]\stackrel{90°xH}{\to }\stackrel{\varnothing °yC}{\to }\stackrel{{\delta }_1}{\to }\stackrel{180°xC}{\to }\stackrel{180°xH}{\to }-\left[zx\right]\dots \stackrel{90°xC}{\to }-0.71s{s}^{″}\left[x1\right]$$

(15)

2. CH₂ groups

$$\begin{array}{l}\left[1z1\right]+\left[11z\right]\stackrel{90°xH}{\to }\stackrel{90°x{H}^{\prime }}{\to }\stackrel{\varnothing °yC}{\to }\stackrel{{\delta }_1}{\to }\stackrel{180°xC}{\to }\stackrel{180°xH}{\to }\stackrel{180°x{H}^{\prime }}{\to }\dots \stackrel{90°xC}{\to }0.71s{c}^{\prime }s{2}^{″}\left[x11\right]\\ -s{s}^{\prime }{s}^{″2}\left[x11\right]\end{array}$$

(16)

3. CH₃ groups

$$\begin{array}{l}\left[1z11\right]+\left[11z1\right]\\ +\left[111z\right]\stackrel{90°xH}{\to }\stackrel{90°x{H}^{\prime }}{\to }\stackrel{90°x{H}^{″}}{\to }\stackrel{\varnothing °yC}{\to }\stackrel{{\delta }_1}{\to }\stackrel{180°xC}{\to }\stackrel{180°xH}{\to }\stackrel{180°x{H}^{\prime }}{\to }\stackrel{180°x{H}^{″}}{\to }\dots \stackrel{90°xC}{\to }\\ -2.11s{c}^{\prime 2}{s}^{″}{c}^{″2}\left[x111\right]+3s{c}^{\prime }{s}^{\prime }{s}^{″2}{c}^{″}\left[x111\right]-1.06s{s}^{\prime 2}{s}^{″3}\left[x111\right]\end{array}$$

(17)

The final carbon signal intensities, represented by I, for the three groups CH, CH₂, and CH₃ for Ω = 90° and θ = 135°, as a function of the evolution delay δ and the actual coupling constant J_CH, are thus:

I_CH = C_x [−0.71 sin(πJ_CHδ₁) sin(πJ_CHδ₃)]
I_CH2 = C_x [0.71 sin(πJ_CHδ₁) cos(πJ_CHδ₂) sin(2πJ_CHδ₃) − 1.00 sin(πJ_CHδ₁) sin(πJ_CHδ₂)
sin²(πJ_CHδ₃)]
I_CH3 = C_x [−2.11 sin(πJ_CHδ₁) cos²(πJ_CHδ₂) sin(πJ_CHδ₃) cos²(πJ_CHδ₃) + 3 sin(πJ_CHδ₁)
cos(πJ_CHδ₂) sin(πJ_CHδ₂) cos(πJ_CHδ₃) sin²(πJ_CHδ₃) − 1.06 sin(πJ_CHδ₁) sin²(πJ_CHδ₂)
sin³(πJ_CHδ₃)]

(18)

DEPTQ⁺90₄₅, Ω = 45°, θ = 90°

1. CH groups

$$\begin{array}{l}\left[1z\right]\stackrel{45°xH}{\to }\stackrel{\varnothing °yC}{\to }\stackrel{{\delta }_1}{\to }\stackrel{180°xC}{\to }\stackrel{180°xH}{\to }-0.71s\left[zx\right]\stackrel{\left(90°\right)xC}{\to }0.7s\left[yx\right]\stackrel{\left(180°\right)xH}{\to }\stackrel{180°xC}{\to }\stackrel{{\delta }_2}{\to }\\ -0.71s\left[yx\right]\stackrel{90°yH}{\to }0.71s\left[yz\right]\stackrel{\left(180°\right)xC}{\to }\stackrel{\left(180°\right)xH}{\to }\stackrel{\delta }{\to }\stackrel{90°xC}{\to }\\ -0.71s{s}^{″}\left[x1\right]\end{array}$$

(19)

2. CH₂ groups

$$\left[1z1\right]+\left[11z\right]\stackrel{45°xH}{\to }\stackrel{\varnothing °yC}{\to }\stackrel{{\delta }_1}{\to }\stackrel{180°xC}{\to }\stackrel{180°xH}{\to }\stackrel{180°x{H}^{\prime }}{\to }\dots \stackrel{\delta }{\to }\stackrel{90°xC}{\to }-0.71s{c}^{\prime }s{2}^{″}[x11]$$

(20)

3. CH₃ groups

$$\begin{array}{l}\left[1z11\right]+\left[11z1\right]+\left[111z\right]\stackrel{45°xH}{\to }\stackrel{\varnothing °yC}{\to }\stackrel{{\delta }_1}{\to }\stackrel{180°xC}{\to }\stackrel{180°xH}{\to }\stackrel{180°x{H}^{\prime }}{\to }\dots \stackrel{\delta }{\to }\stackrel{90°xC}{\to }\\ -2.11s{c}^{\prime 2}{s}^{″}{c}^{″2}\left[x111\right]\end{array}$$

(21)

The final carbon signal intensities, represented by I, for the three groups CH, CH₂, and CH₃ for Ω = 45° and θ = 90°, as a function of the three evolution delays δ₁, δ₂ and δ₃ and the actual coupling J_CH, are therefore:

I_CH = −C_x [0.71 sin (πJ_CHδ₁) sin (πJ_CHδ₃)]
I_CH2 = −C_x [0.71 sin (πJ_CHδ₁) cos (πJ_CHδ₂) sin (2πJ_CHδ₃)]
I_CH3 = −C_x [2.11 sin (πJ_CHδ₁) cos²(πJ_CHδ₂) sin (πJ_CHδ₃) cos²(πJ_CHδ₃)]

(22)

For the DEPTQ and DEPTQ⁺ experiments, the approximate carbon signal intensities, represented by I (for ¹J_CH ≈ ¹J_CH⁰), for the three groups CH, CH₂, and CH₃ for Ω = 90° and θ = 135°, as a function of the coupling constant ¹J_CH and δ, δ₁, δ₂, and δ₃, are summarized in

Table 1. Final carbon signal intensities, represented by I, for the three groups CH, CH₂, and CH₃ for Ω = 90°, θ = 135°, as a function of the coupling constant J_CH and the delays δ, δ₁, δ₂, and δ₃.

	DEPTQ	DEPTQ+
CH groups	$0.71C_x$sin2(πJCHδ)	$-0.71C_x$sin(πJCHδ1) sin(πJCHδ3)
CH2 groups	$-C_x$sin4(πJCHδ)	$-C_x$sin(πJCHδ1) sin(πJCHδ2) sin2(πJCHδ3)
CH3 groups	$1.06C_x$sin6(πJCHδ)	$-1.06C_x$sin(πJCHδ1) sin2(πJCHδ2) sin3(πJCHδ3)

:

According to the above relations for Ω = 90° and θ = 135° and compared to the DEPTQ experiment, the signs of the signal intensities for CH and CH₃ groups are inverted using the DEPTQ⁺ experiment, while the sign of the signal intensities for CH₂ groups is identical. Consequently, the usual angle θ for achieving the DEPT editing, CH/CH₃ positive, CH₂ negative, is obtained for θ = 45° and not for θ = 135°, as would be valid for DEPTQ (

Table 2. DEPTQ and DEPTQ⁺: maximal amplitude of CH, CH₂, and CH₃ groups for the three usual angles θ and for Ω = 90°.

Experiment	Angle θ	Amplitude of CH	Amplitude of CH2	Amplitude of CH3
DEPTQ+	45°	−0.71	1	−1.06
DEPTQ		0.71	1	1.06
DEPTQ+	90°	−1	0	0
DEPTQ		1	0	0
DEPTQ+	135°	−0.71	−1	−1.06
DEPTQ		0.71	−1	1.06

).

To separate the signals of CH, C_q and CH₂, CH₃ groups in different sub-spectra and to obtain different signs for the signals of CH₂ and CH₃ groups the first adjustable proton pulse Ω and the editing pulse θ must therefore be set for the DEPTQ⁺ experiment to 45° and 90° (DEPTQ⁺90₄₅) and to 90° and 45°, respectively (DEPTQ⁺45₉₀). Subtracting the DEPTQ⁺90₄₅ spectrum, showing exclusively the Cq and CH signals with opposite phases, from the DEPTQ⁺45₉₀ spectrum results in a CH₂/CH₃ edited spectrum with the signals of the two carbon types with opposite phases.

Interestingly, equations 15–22 show that the intensities of the signals of the three carbon types depend differently and for CH solely on two (δ₁ and δ₃) of the individual delays δ₁, δ₂, and δ₃, which is the basis for efficiently leveling the signal intensities for all multiplicities with the DEPTQ⁺ pulse sequence, even for large ¹J_CH coupling constant ranges. Indeed, and with the specific ranges of ¹J_CH-coupling constants for the three carbon types, i.e., CH: [120 < ¹J_CH < 250 Hz], CH₂: [115 < ¹J_CH < 175 Hz], CH₃: [100 < ¹J_CH < 135 Hz], the three delays δ₁, δ₂, and δ₃ can be individually and optimally adjusted. For instance, δ₂ which does not affect CH-intensities can be adjusted for small ¹J_CH coupling constants, typically 120 Hz, to maximize the signals of CH₂ and CH₃ groups. On the other hand, δ₁ can be adjusted for large ¹J_CH coupling constants, typically 220–230 Hz, to maximize the signals of acetylenic CH groups. Finally, δ₃ can be adjusted for an average ¹J_CH coupling constant, typically 185 Hz, to account for all carbon types present. This enables real leveling of the signal intensities with the DEPTQ⁺ experiment, as demonstrated theoretically (Figures S3–S5), and, in the following section, practically.

2.2. Experimental Results

2.2.1. Cholesteryl Acetate

We first used a sample of 100 mmol cholesteryl acetate (Figure 3, 30 mg dissolved in 0.7 mL CDCl₃) for testing the performance of the DEPTQ⁺ experiment.

In Figure 4 and Figure 5, the DEPTQ135₉₀, DEPTQ90₄₅, the difference between DEPTQ135₉₀ and DEPTQ90₄₅ (Figure 4), the DEPTQ⁺45₉₀, DEPTQ⁺90₄₅, and the difference between DEPTQ⁺45₉₀ and DEPTQ⁺90₄₅ (Figure 5) of cholesteryl acetate are shown. Cholesteryl acetate (Figure 3) is a molecule exhibiting a narrow range of coupling constants ¹J_CH (122 Hz for ¹J_C26H26 to 155 Hz for ¹J_C6H6). Accordingly, both the DEPTQ90₄₅ providing a Cq/CH edited spectrum and the DEPTQ90₄₅ providing a CH₂/CH₃ edited spectrum (difference between DEPTQ135₉₀ and DEPTQ90₄₅) are of high quality, with few and weak CH₂/CH₃ artefacts in the DEPTQ90₄₅ and some residual CH peaks in the difference spectrum, respectively (Figure 4).

The same, nearly identical results have been obtained using the proposed DEPTQ⁺ pulse sequence. Thus, the DEPTQ⁺ behaves similarly to the DEPTQ experiment if the narrow, usual range of coupling constants ¹J_CH is present: the mutual signal intensity leveling and the J cross-talk reduction only provide very minor improvements.

However, the superiority of the DEPTQ⁺ experiment becomes clear when there is a larger range of coupling constants ¹J_CH. First, with the sole aim of demonstrating the potential and performance of the DEPTQ⁺ experiment, we used the same molecule of cholesteryl acetate but adjusted the three delays in the experiments as if all ¹J_CH coupling constants (alkanes, aromatics, alkynes) were present. The spectra are shown in Figures S8 and S9.

In this case, it is clear that the DEPTQ⁺ behaves much better than the DEPTQ experiment; even the standard DEPTQ135 spectrum is confusing, since the resonances of the methyl groups between 10 and 30 ppm are barely visible (Figure S8), as predicted theoretically (Figure S2). This is due to the very large mismatch between the actual ¹J_CH coupling constants in methyl groups (~125 Hz) and the average ¹J_CH⁰ coupling constant set in the DEPTQ experiment, ¹J_CH⁰ = 185 Hz, intentionally set to cover the whole range of ¹J_CH coupling constants (100–250 Hz). The DEPTQ90₄₅ is also confusing, with many residual CH₂/CH₃ signals present, which makes the identification of CH groups difficult, as they are as intense (strong J cross talk) and have the same sign as the CH signals (Figure S8). Finally, the “CH₂/CH₃” edited spectrum (difference between DEPTQ135₉₀ and DEPTQ90₄₅) is extremely confusing, as only the resonances of CH₂ groups are present, while the resonances of CH₃ groups are either barely visible or even completely absent (Figure S8).

In contrast, the spectra obtained using the DEPTQ⁺ pulse sequence are much better and sufficient for reliable identification of CH_n groups: In the DEPTQ⁺45₉₀ spectrum, the resonances of the methyl groups between 10 and 30 ppm are clearly visible and intense (Figure S9), as predicted theoretically (Figure S7). This is because the three delays δ₁, δ₂, and δ₃ in the DEPTQ⁺ experiment are matched to three different ¹J_CH⁰ coupling constants (230, 125, 165 Hz, respectively), which results in a mutual leveling of the DEPT signal intensities. In the DEPTQ⁺90₄₅, there are only very few and weak CH₂/CH₃ artefacts (weak J cross talk), which enables easy identification of CH groups (Figure S9). Finally, the “CH₂/CH₃” edited spectrum also allows a reliable identification of the clearly visible resonances of CH₂ groups and of CH₃ (Figure S9).

2.2.2. 4-Methyl-N,N-di(prop-2-yn-1-yl)aniline

In order to test the effective performance, we finally tried the DEPTQ⁺ experiment on the demanding sample of ~30 mg of 4-methyl-N,N-di(prop-2-yn-1-yl)aniline dissolved in 0.7 mL CDCl₃ (Figure 1). 4-methyl-N,N-di(prop-2-yn-1-yl)aniline contains alkane, aromatic and alkyne groups with the full range of ¹J_CH coupling constants (125 Hz for ¹J_C8H8 to 248 Hz for ¹J_C1H1). Note also the very particular case of C2 at 79.4 ppm, which, with its large long-range coupling (²J_C2H1 ~ 50 Hz), behaves like a pseudo- or only partially quaternary carbon.

In Figure 6 and Figure 7, the DEPTQ135₉₀, DEPTQ90₄₅, the difference between DEPTQ135₉₀ and DEPTQ90₄₅ (Figure 6), and the DEPTQ⁺45₉₀, DEPTQ⁺90₄₅, and the difference between DEPTQ⁺45₉₀ and DEPTQ⁺90₄₅ (Figure 7) of 4-methyl-N,N-di(prop-2-yn-1-yl)aniline are shown.

With 4-methyl-N,N-di(prop-2-yn-1-yl)aniline, it is clear that the DEPTQ⁺ performs much better than the DEPTQ experiment: the standard DEPTQ135 spectrum is useable, but the resonance of the methyl group C8 at 20.6 ppm is very weak (Figure 6). As already mentioned, this is due to the very large mismatch between the actual ¹J_CH coupling constants in methyl groups (~125 Hz) and the large average ¹J_CH⁰ coupling constant set in the DEPTQ experiment, ¹J_CH⁰ = 185 Hz (Figure S2). Artefacts (J cross talk) belonging to the CH₂ C3 at 40.9 ppm and to the CH₃ C8 at 20.6 ppm are visible in the DEPTQ90₄₅, even if their intensities are rather small (Figure 6). Such artefacts can be problematic with unknown molecular structures or if the attribution is performed in an automatic or semi-automatic way using dedicated attribution software. Particularly confusing is the “CH₂/CH₃” edited spectrum obtained with DEPTQ (difference between DEPTQ135₉₀ and DEPTQ90₄₅), with a strong signal of the CH₂ groups C3 at 40.9 ppm and a weak residual signal of the CH group C1, while the resonance of the CH₃ group C8 at 20.6 ppm is almost invisible (Figure 6). In addition, the residual signal of C1 at 72.8 ppm could be misleading or misinterpreted by attribution/analysis software.

In contrast, the spectra obtained using the DEPTQ⁺ pulse sequence are less confusing and sufficient for reliable carbon type identification: in the DEPTQ⁺45₉₀, the resonance of the methyl group C8 around 20 ppm is clearly visible and intense (Figure 7). This must be attributed to the individual tuning of the three delays to different ¹J_CH⁰ coupling constants (125, 175, 230 Hz), which results in a mutual leveling of the DEPT signal intensities. The DEPTQ⁺90₄₅ shows—besides the negative quaternary carbon signals—the three strong CH signals with only one weak CH₂ artifact (weak J cross talk) present (Figure 7). Finally, the CH₂/CH₃ edited spectrum is almost perfect, with the strong resonances of the CH₂- and CH₃ groups C3 and C8 in anti-phase and only very weak residual signals left (Figure 7).

2.3. Practical Aspects

Our theoretical and practical investigations show that the proposed new DEPTQ⁺45₉₀ and DEPTQ⁺90₄₅ experiments work well. However, the experimental results suggest that the quality of spectral editing also depends on the relaxation delay. While for medium sized molecules such as cholesteryl acetate, the length of the relaxation delay affects only the intensity of the slow relaxing carbons but not the editing quality (Figure S10), it becomes critical also for the editing procedure for small molecules and/or groups exhibiting long T₁ relaxation times.

This manifests itself with 4-methyl-N,N-di(prop-2-yn-1-yl)aniline, for which the intensities of the CH signals in the DEPTQ⁺90₄₅ spectra can be drastically different to that obtained in the DEPTQ⁺45₉₀ if overly short relaxation delays are used. The numerous and intense “CH-artefacts” showing up in the edited CH₂/CH₃ spectrum may be potentially attributed to CH₃ groups. The influence of relaxation and the need for choosing the relaxation delay(s) long enough with DETPQ⁺ to achieve a sufficient editing quality are corroborated by simulated spectra, which are in good agreement with the corresponding experimental spectra shown in Figures S11 and S12.

Finally, we wish to concentrate on the overall sensitivities of DEPTQ⁺, and to compare it with DEPTQ and the usually performed “tandem alternatives” such as ¹³C one-pulse/DEPT. In previous reports [9,10,11], Bigler et al. have compared spectra acquired DEPTQ and the ¹³C one-pulse spectra with an equal number of scans within the same total measuring time, and found that the DEPTQ spectrum decreases signal intensities of quaternary carbons by 15% and 10% when compared to the ¹³C one-pulse. The corresponding experiments (DEPTQ vs. ¹³C one-pulse + DEPT) based on equal total measuring times showed average S/N ratios of about 70% and 85% for the CH_n signals in the DEPT spectrum, compared to the corresponding values of the DEPTQ experiment [10]. While the signal intensities of quaternary carbons are identical in DEPTQ and DEPTQ⁺ spectra, the comparison of the average S/N ratio for the CH_n signals between DEPTQ and DEPTQ⁺ is not so straightforward. While for standard DEPTQ experiments, as shown in this manuscript, the signals at the extremes of the ¹J_CH coupling range suffer in intensity or cannot be detected, DEPTQ⁺ experiments (similar to ACCORD-DEPT experiments [31]) provide spectra with notably improved S/N ratios for these specific signals. However, owing to the mutual signal intensity leveling, DEPTQ⁺ always provides either better or worse signal intensity compared to standard optimization. The S/N ratio for some signals will correspondingly decrease compared to a standard optimized DEPTQ experiment.

3. Materials and Methods

3.1. Synthesis and Characterization of 4-Methyl-N,N-di(prop-2-yn-1-yl)aniline

The chemicals were purchased from Aldrich, Alfa Aesar, Acros Organics, and TCI Chemicals and used without further purification, In a flame-dried round bottom flask equipped with a magnetic stirrer, p-toluidine (0.5 g, 4.6 mmol) and anhydrous K₂CO₃ (0.77 g, 5.52 mmol) were mixed in dry dimethylformamide (10 mL). Propargyl bromide (0.65 g, 5.52 mmol) was then added dropwise during a period of 15 min and the resulting mixture was stirred under nitrogen atmosphere for 5 h. After completion of the reaction (monitored by TLC), the mixture was poured into water (10 mL) and extracted with ethyl acetate (2 × 15 mL). The combined organic layers were washed with water (4 × 10 mL) and brine (10 mL), dried over sodium sulfate, filtered, and concentrated under reduced pressure [32,33]. The reaction crude was purified by column chromatography (Silica, 230–400 mesh) using mixtures of hexane/ethyl acetate (30:1). The desired product was obtained as a highly dense yellow oil (110 mg, 13%) along with the product of mono substitution 4-methyl-N-(prop-2-yn-1-yl)aniline (500 mg, 75%).

4-methyl-N,N-di(prop-2-yn-1-yl)aniline:¹H NMR (300 MHz, CDCl₃) δ 7.12 (d, J = 8.6 Hz, 2H), 6.92 (d, J = 8.6 Hz, 2H), 4.11 (d, J = 2.4 Hz, 4H), 2.30 (s, 3H), 2.26 (t, J = 2.4 Hz, 2H). ¹³C NMR (75 MHz, CDCl₃) δ 145.8 (C4), 129.8 (C5), 129.7 (C7), 116.7 (C6), 79.4 (C2), 72.8 (C1), 40.9 (C3), 20.6 (C8). The spectra are referenced with respect to the residual CHCl₃ resonance (7.264 ppm) and to the ¹³C resonance of CDCl₃ (77.16 ppm).

3.2. NMR Measurements

All DEPTQ and DEPTQ⁺ experiments were recorded on a Bruker AvanceII 500 MHz NMR spectrometer equipped with a 5 mm BBI Inverse probehead. The samples used were: (i) the standard test sample provided with Bruker NMR spectrometers, 30 mg of cholesteryl acetate dissolved in 0.7 mL CDCl₃, and (ii) ~30 mg of 4-methyl-N,N-di(prop-2-yn-1-yl)aniline dissolved in 0.7 mL CDCl₃. ¹H and ¹³C 90° pulse lengths were 8.4 μs and 13.2 μs, respectively. The composite chirp pulse for refocusing has a duration of 2 ms, is defined by 4000 points and by 20% smoothing and 60 kHz sweep width (Crp60comp.4 in the Bruker wave form library). The experimental details of the measurements are as follows. Cholesteryl acetate: if not otherwise mentioned, all spectra were acquired with 128 k real data points with a relaxation delay of 4 s, a NOE building period of 3 s, 64 scans for a total experimental time of approximately 7 min. ¹³C spectral widths were 200 ppm, leading to an acquisition time of 2.60 s. Data were processed with 128 k data points using exponential multiplication with a line broadening of 1 Hz. 4-methyl-N,N-di(prop-2-yn-1-yl)aniline: the spectra were acquired with 128 k data points with a relaxation delay of 10 s, a NOE building period of 5 s, 16 scans for a total experimental time of approximately 3 min. ¹³C spectral widths were 200 ppm, leading to an acquisition time of 2.60 s. Data were processed with 128 k data points using exponential multiplication with a line broadening of 1 Hz.

3.3. Numerical Simulations

The numerical simulations shown in Figures S1–S7 have been performed with Microsoft Excel^®, Office 365 for Windows. Relaxation effects during both pulse sequences were not considered.

3.4. NMR Simulations

The simulations shown in Figures S10 and S11 have been performed with the BRUKER NMRSIM program for MAC (version 5.5.3. 2012). The simulated DEPTQ and DEPTQ⁺ spectra are obtained for 4-methyl-N,N-di(prop-2-yn-1-yl)aniline. The parameters used for the simulations were: ¹J_C1H1 = 260 Hz, ¹J_C3H3 = 145 Hz, ¹J_C5H5 = ¹J_C6H6 = 165 Hz, ¹J_C8H8 = 125 Hz, ²J_C2H1 = 50 Hz. The relaxation times have been set to T₁ = 1 s for all CH_n groups, and T₁ = 5 s for the quaternary carbons, T₂ = 0.5 s, and full relaxation during both the pulse sequence and final data acquisition were considered. The chemical shifts set in the simulations were the experimental chemical shifts.

4. Conclusions

Compared to the DEPTQ experiment, the proposed new DEPTQ⁺ experiment is shorter and the different evolution delays are designed as spin echoes, which can be matched to different ¹J_CH values. We have shown, both theoretically and experimentally, that for molecules with a standard range of ¹J_CH coupling constants (i.e., 110,180 Hz), the differences between DEPTQ and DEPTQ⁺ are minimal. The differences become appreciable for molecules possessing a large range of ¹J_CH coupling constants. The DEPTQ⁺ experiment makes it possible to obtain DEPTQ spectra with (i) a mutual leveling of the DEPT signal intensities, (ii) a reduction in J cross-talk in the Cq/CH spectrum, and (iii) more reliable CH₂/CH₃ edited spectra.

The influence of relaxation and the need to choose a relaxation delay that is sufficiently long, with DETPQ⁺, to obtain reliable data and clean edited spectra represents the only limitation of this study, but this is valid for molecules with long T₁ relaxation times. This is, however, also the case with the original DEPTQ experiment.

In conclusion, the new DEPTQ⁺ experiment is expected to be attractive for fast ¹³C analysis of small-to medium sized molecules, especially those with a large range of ¹J_CH coupling constant, and especially in high-throughput laboratories. With concentrated samples and/or by exploiting the high sensitivity of cryogenically cooled ¹³C NMR probeheads, the efficacy of such investigations may be improved, as it is possible to unequivocally identify all carbon multiplicities with only one scan for each of the two independent DEPTQ⁺ experiments.