^{1}and N. Suryaprakash

^{2,a)}

### Abstract

In the present work we demonstrate a novel method for spectral simplification and determination of the relative signs of the scalar couplings using a spin selective multiple quantum NMR experiment. A spin selective excitation of double quantum coherence of A and M spins in a weakly coupled three spin system of the type AMX, results in a doublet in the double quantum dimension whose separation corresponds to the sum of couplings of the active spins to the passive spin X. One component of the doublet has the passive spin X in state while the other component has the passive spin X in state. The spin selective conversion of double quantum coherence to single quantum coherence does not disturb the spin states of the passive spin thereby providing the spin state selection. There will be two domains of single quantum transitions in single quantum dimension at the chemical shift positions of A and M spins. The domain of A spin is a doublet because of and states of M spin only, while that of domain is another doublet in a different cross section of the spectra. The scalar coupling can be extracted from any of the and domain transitions while the relative displacements of the two doublets between the two domains at the two chemical shifts provides the magnitude and sign of the scalar coupling relative to the coupling . Similar result is obtained for zero quantum studies on AMX spin system. The proposed technique is discussed theoretically using product operator approach. The new spin state selective double quantum -resolved sequence has also been developed. The methodology is confirmed experimentally on a homonuclear weakly coupled three spin system and applied to two different heteronuclear five spin systems.

One of the authors (N.S.) gratefully acknowledges the financial support by the Department of Science and Technology, New Delhi, for Grant No. SR/SI/PC-13/2004. Another author (B.B.) thanks the Council of Scientific and Industrial Research (CSIR), India, for research fellowship.

I. INTRODUCTION

II. EXPERIMENTAL

A. Multiple quantum (MQ) and spin state selection

B. Three spin system of the type AMX: 2,3-dibromopropionic acid. Spin selected double quantum experiment

C. Spin selected zero quantum experiment

D. Spin system of the type AFKPX: The spectrum of 2-fluoropyridine

E. New spin state selected DQ-J resolved sequence

F. Spin system of the type AFKPX: The spectrum of 1-chloro-2-fluorobenzene

III. A COMMENT ON THE DIPOLAR COUPLED SYSTEMS

IV. CONCLUSIONS

### Key Topics

- Protons
- 34.0
- Chemical shifts
- 24.0
- Nuclear magnetic resonance
- 13.0
- Coherence
- 11.0
- Acids
- 8.0

## Figures

(A) The pulse sequence used for the spin selective DQ-SQ correlation experiments. The delay was optimized for the excitation of proton homonuclear DQ in 2,3-dibromopropionic acid. The phases of all the pulses and the receiver were set to zero as we are dealing with even order quantum and gradient selection, . The gradient ratio was set to for homonuclear quantum of proton. (B) The pulse sequence used for the multiple quantum 2D experiments with nonselective excitation of homonuclear 4Q in 2-fluoropyridine and 1-chloro-2-fluorobenzene. The delay was optimized for the selection of proton homonuclear 4Q for both the molecules. The gradient ratio was set to 1:4. In heteronuclear spin systems this mimics spin selective pulse sequence used for the homonuclear spin system. The phase cycling is . (C) Pulse sequence identical to A, but the 180° pulse in the middle of period is nonselective for protons applied for the spin state selective DQ-J resolved experiment in 2-fluoropyridine. The phase cycling is . Other details are discussed in the text.

(A) The pulse sequence used for the spin selective DQ-SQ correlation experiments. The delay was optimized for the excitation of proton homonuclear DQ in 2,3-dibromopropionic acid. The phases of all the pulses and the receiver were set to zero as we are dealing with even order quantum and gradient selection, . The gradient ratio was set to for homonuclear quantum of proton. (B) The pulse sequence used for the multiple quantum 2D experiments with nonselective excitation of homonuclear 4Q in 2-fluoropyridine and 1-chloro-2-fluorobenzene. The delay was optimized for the selection of proton homonuclear 4Q for both the molecules. The gradient ratio was set to 1:4. In heteronuclear spin systems this mimics spin selective pulse sequence used for the homonuclear spin system. The phase cycling is . (C) Pulse sequence identical to A, but the 180° pulse in the middle of period is nonselective for protons applied for the spin state selective DQ-J resolved experiment in 2-fluoropyridine. The phase cycling is . Other details are discussed in the text.

(a) one dimensional proton spectra of 2,3-dibromopropionic acid in the solvent , (b) one dimensional proton spectra of 2-fluoropyridine, and (c) one dimensional proton spectrum of 1-chloro-2-fluorobenzene in the solvent acetone-. Expansions of the selected parts of the spectrum are indicated by the arrows.

(a) one dimensional proton spectra of 2,3-dibromopropionic acid in the solvent , (b) one dimensional proton spectra of 2-fluoropyridine, and (c) one dimensional proton spectrum of 1-chloro-2-fluorobenzene in the solvent acetone-. Expansions of the selected parts of the spectrum are indicated by the arrows.

two dimensional spectrum correlating DQ coherence to its SQ coherence in 2,3-dibromopropionic acid, an AMX spin system along with the molecular structure. The corresponding and projections are also given. The DQ dimension pertains to the nonselective excitation of all the three double quanta. Sum of the chemical shifts given at the right side identifies the different double quanta. The AX DQ-SQ spectrum has the doublet in the DQ dimension but is unresolved due to very small difference between and which are of opposite signs. A, M and X corresponds to chemical shifts of the protons indicated in the structure. The other experimental details are given in the text.

two dimensional spectrum correlating DQ coherence to its SQ coherence in 2,3-dibromopropionic acid, an AMX spin system along with the molecular structure. The corresponding and projections are also given. The DQ dimension pertains to the nonselective excitation of all the three double quanta. Sum of the chemical shifts given at the right side identifies the different double quanta. The AX DQ-SQ spectrum has the doublet in the DQ dimension but is unresolved due to very small difference between and which are of opposite signs. A, M and X corresponds to chemical shifts of the protons indicated in the structure. The other experimental details are given in the text.

(A) two dimensional spectrum correlating AM selective DQ coherence to its SQ coherence in AMX spin system in 2,3-dibromopropionic acid along with the corresponding projections. The doublet separation in the dimension corresponds to . and correspond to spin states of X in the DQ dimension. A and M refers to the chemical shift positions of A and M spins, respectively. The cross section along the SQ dimension for any spin state of X in the DQ dimension provides the active coupling which is marked for the cross section corresponding to spin state . The displacement of the doublets between the two SQ cross sections provides passive couplings and which are also marked. Tilt angle smaller than 90 for both A and M indicates that the relative signs of and are the same. Other experimental details are given in the text. (B) (i) spectrum of, 2,3-dibromopropionic acid plotted for the spins A and M, (ii) the corresponding projection along SQ dimension of Fig. 4(A), (iii) the cross section taken along SQ dimension at the spin state of X spin in the DQ dimension, and (iv) the cross section taken along SQ dimension at the spin state of X spin in the DQ dimension and in the DQ dimension. The other experimental details are given in the text.

(A) two dimensional spectrum correlating AM selective DQ coherence to its SQ coherence in AMX spin system in 2,3-dibromopropionic acid along with the corresponding projections. The doublet separation in the dimension corresponds to . and correspond to spin states of X in the DQ dimension. A and M refers to the chemical shift positions of A and M spins, respectively. The cross section along the SQ dimension for any spin state of X in the DQ dimension provides the active coupling which is marked for the cross section corresponding to spin state . The displacement of the doublets between the two SQ cross sections provides passive couplings and which are also marked. Tilt angle smaller than 90 for both A and M indicates that the relative signs of and are the same. Other experimental details are given in the text. (B) (i) spectrum of, 2,3-dibromopropionic acid plotted for the spins A and M, (ii) the corresponding projection along SQ dimension of Fig. 4(A), (iii) the cross section taken along SQ dimension at the spin state of X spin in the DQ dimension, and (iv) the cross section taken along SQ dimension at the spin state of X spin in the DQ dimension and in the DQ dimension. The other experimental details are given in the text.

(A) two dimensional spectrum correlating MX spin selective DQ coherence to its SQ coherence in AMX spin system in 2,3-dibromopropionic acid along with the corresponding projections. The doublet separation in the dimension corresponds to . and corresponds to two spin states of A in the DQ dimension. M and X refers to the chemical shift positions of M and X, respectively. The cross section along the SQ dimension for any spin state of A in the DQ dimension provides the active coupling which is marked for the cross section corresponding to the spin state . The displacement vectors marked for the spins M and X in the two SQ cross sections provide passive couplings and . The tilt of the displacement vectors for and are opposite indicating their signs are opposite. Other experimental details are given in the text. (B) two dimensional spectrum of 2,3-dibromopropionic acid correlating MX spin selected ZQ coherence to its SQ coherence along with the and projections. Although the ZQ evolves with the difference of the passive couplings, as the signs of and are opposite the doublet separation in the ZQ dimension is larger than in Fig. 5(A). This also indicates that and are opposite.

(A) two dimensional spectrum correlating MX spin selective DQ coherence to its SQ coherence in AMX spin system in 2,3-dibromopropionic acid along with the corresponding projections. The doublet separation in the dimension corresponds to . and corresponds to two spin states of A in the DQ dimension. M and X refers to the chemical shift positions of M and X, respectively. The cross section along the SQ dimension for any spin state of A in the DQ dimension provides the active coupling which is marked for the cross section corresponding to the spin state . The displacement vectors marked for the spins M and X in the two SQ cross sections provide passive couplings and . The tilt of the displacement vectors for and are opposite indicating their signs are opposite. Other experimental details are given in the text. (B) two dimensional spectrum of 2,3-dibromopropionic acid correlating MX spin selected ZQ coherence to its SQ coherence along with the and projections. Although the ZQ evolves with the difference of the passive couplings, as the signs of and are opposite the doublet separation in the ZQ dimension is larger than in Fig. 5(A). This also indicates that and are opposite.

Two dimensional spectrum of 2-fluoropyridine correlating proton 4Q coherence to its SQ coherence along with molecular structure. The spectrum at the chemical shift positions of all the four protons are plotted separately. The doublet in the 4Q dimension corresponds to the spin states and of fluorine. The individual passive coupling of fluorine to each proton is extracted from the indicated displacements, (i), (ii), (iii), and (iv) provides the coupling between fluorine at the protons numbered 3, 5, 4, and 6, respectively. From the displacement vectors it is obvious that signs of heteronuclear couplings and are opposite to that of and . The other experimental details are given in the text.

Two dimensional spectrum of 2-fluoropyridine correlating proton 4Q coherence to its SQ coherence along with molecular structure. The spectrum at the chemical shift positions of all the four protons are plotted separately. The doublet in the 4Q dimension corresponds to the spin states and of fluorine. The individual passive coupling of fluorine to each proton is extracted from the indicated displacements, (i), (ii), (iii), and (iv) provides the coupling between fluorine at the protons numbered 3, 5, 4, and 6, respectively. From the displacement vectors it is obvious that signs of heteronuclear couplings and are opposite to that of and . The other experimental details are given in the text.

two dimensional spin state selected DQ J resolved spectrum of 2-fluoropyridine in acetone-. The protons numbered 3 and 5 are selectively excited and detected for DQ-SQ correlation. A nonselective 180° pulse is applied on protons in the middle of dimension to retain only the sum of passive couplings to protons numbered 4 and 6 while the sum of passive couplings to fluorine spin is refocused. 180° pulse also decoupled fluorine from the protons. The spectrum at the chemical shift positions of 3 and 5 are separately plotted. Two doublets in DQ dimension provides and as indicated. The two displacement vectors indicated for proton 3 provide and . The displacement vectors indicated for proton 5 provide and .

two dimensional spin state selected DQ J resolved spectrum of 2-fluoropyridine in acetone-. The protons numbered 3 and 5 are selectively excited and detected for DQ-SQ correlation. A nonselective 180° pulse is applied on protons in the middle of dimension to retain only the sum of passive couplings to protons numbered 4 and 6 while the sum of passive couplings to fluorine spin is refocused. 180° pulse also decoupled fluorine from the protons. The spectrum at the chemical shift positions of 3 and 5 are separately plotted. Two doublets in DQ dimension provides and as indicated. The two displacement vectors indicated for proton 3 provide and . The displacement vectors indicated for proton 5 provide and .

two dimensional spectrum of 1-chloro-2-fluorobenzene in acetone- correlating proton 4Q coherence to its SQ coherence along with corresponding projections. The doublet in the 4Q dimension corresponds to the and spin states of fluorine and the separation provides the sum of all the couplings of protons to fluorine. Numbers 3, 4, 5, and 6 corresponds to chemical shifts of the protons numbered in the structure. The other experimental details are given in the text.

two dimensional spectrum of 1-chloro-2-fluorobenzene in acetone- correlating proton 4Q coherence to its SQ coherence along with corresponding projections. The doublet in the 4Q dimension corresponds to the and spin states of fluorine and the separation provides the sum of all the couplings of protons to fluorine. Numbers 3, 4, 5, and 6 corresponds to chemical shifts of the protons numbered in the structure. The other experimental details are given in the text.

Expanded region of spectrum corresponding to protons numbered 5 and 3 in Fig. 8. The spectrum on the right side is the expansion of part of the spectrum at one of the spin states in the 4Q dimension. From the separations marked (i), (ii), and (iii) on the right side of 5 one can determine , , and . From the separations marked (i), (ii), and (iii) on the right side of 3 one can determine and while being comparable to line width, it is difficult to determine.

Expanded region of spectrum corresponding to protons numbered 5 and 3 in Fig. 8. The spectrum on the right side is the expansion of part of the spectrum at one of the spin states in the 4Q dimension. From the separations marked (i), (ii), and (iii) on the right side of 5 one can determine , , and . From the separations marked (i), (ii), and (iii) on the right side of 3 one can determine and while being comparable to line width, it is difficult to determine.

Expanded region of spectrum corresponding to protons numbered 4 and 6 in Fig. 8. The spectrum on the right side is the expansion of part of the spectrum at one of the spin states in the 4Q dimension. From the separations marked (i), (ii), and (iii) on the right side of 4, one can determine , , and . From the separations marked (i) and (ii) on the right side of 6 one can determine and .

Expanded region of spectrum corresponding to protons numbered 4 and 6 in Fig. 8. The spectrum on the right side is the expansion of part of the spectrum at one of the spin states in the 4Q dimension. From the separations marked (i), (ii), and (iii) on the right side of 4, one can determine , , and . From the separations marked (i) and (ii) on the right side of 6 one can determine and .

Schematic representation of the behavior of magnetization in the DQ-SQ correlation spectra for an AMX spin system: (A) appearance of the spectrum from the first term of Eq. (A6), (B) appearance of the spectrum from the fourth term of Eq. (A6), and (C) the spectrum from the sum of the first and the fourth terms of Eq. (A6). The figure on the right side of C is the displacement vector , connecting peaks of like sign. Tilt angle can be used to predict the relative signs of the passive couplings.

Schematic representation of the behavior of magnetization in the DQ-SQ correlation spectra for an AMX spin system: (A) appearance of the spectrum from the first term of Eq. (A6), (B) appearance of the spectrum from the fourth term of Eq. (A6), and (C) the spectrum from the sum of the first and the fourth terms of Eq. (A6). The figure on the right side of C is the displacement vector , connecting peaks of like sign. Tilt angle can be used to predict the relative signs of the passive couplings.

## Tables

Acquisition and processing parameters used for the two dimensional selective and nonselective multiple quantum-single quantum correlation experiments in 2,3-dibromopropionic acid, 2-fluoropyridine, and 1-chloro-2-fluorobenzene. (For MX ZQ-SQ experiment, the parameters are identical to MX DQ-SQ, except for , which is .)

Acquisition and processing parameters used for the two dimensional selective and nonselective multiple quantum-single quantum correlation experiments in 2,3-dibromopropionic acid, 2-fluoropyridine, and 1-chloro-2-fluorobenzene. (For MX ZQ-SQ experiment, the parameters are identical to MX DQ-SQ, except for , which is .)

The spectral parameters in 2-fluoropyridine and 1-chloro-2-fluorobenzene in acetone- obtained from the analyses of the spectra in Figs. 6–8. (Errors on the parameters are of the order of digital resolution mentioned in the text.)

The spectral parameters in 2-fluoropyridine and 1-chloro-2-fluorobenzene in acetone- obtained from the analyses of the spectra in Figs. 6–8. (Errors on the parameters are of the order of digital resolution mentioned in the text.)

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