Solving problems with NMR spectroscopy 2nd ed

If a radiofrequency field is now applied in a direction perpendicular to the external magnetic field and at a fre-quency that exactly matches the precessional frequency “Larmor” frequenc

Solving Problems with NMR Spectroscopy

Second Edition

Atta-ur-Rahman

International Center for Chemical and Biological Sciences

(H E J Research Institute of Chemistry and Dr Panjwani Center for Molecular Medicine and Drug Research), University of Karachi, Karachi-75270, Pakistan

Muhammad Iqbal Choudhary

International Center for Chemical and Biological Sciences

(H E J Research Institute of Chemistry and Dr Panjwani Center for Molecular Medicine and Drug Research), University of Karachi, Karachi-75270, Pakistan

Atia-tul-Wahab

Dr Panjwani Center for Molecular Medicine and Drug Research(International Center for Chemical and Biological Sciences),

University of Karachi, Karachi-75270, Pakistan

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The second edition of the book Solving Problems with NMR Spectroscopy is

aimed to strengthen the understanding of how an NMR spectrometer functions This revised version of the book takes the same problem-solving approach as the highly praised first edition, published in 1996 The book focuses on describing the basic principles of NMR spectroscopy and explains in detail the functioning

of an NMR spectrometer The optimum use of this powerful technique is duced step by step, and common problems encountered by the practitioners and users of NMR spectroscopy are described in an easy-to-understand manner The real strength of the book is its highly practical approach in describing both the concepts and applications of NMR spectroscopy

intro-The second edition introduces a number of new topics, including ments in NMR hardware, such as cryogenically cooled probes, new probeheads, high-field magnets, and DNP–NMR, as well as innovative pulse sequences, such

develop-as DOSY, concatenated NMR techniques, and PANSY Particularly interesting

is a new chapter on sensitivity issues in NMR spectroscopy and their

current-ly available applications, which have driven most of the developments in this field Another chapter on recent developments in NMR spectroscopy updates the readers about the changing landscape in this field Over 180 penetrating problems and their well-described solutions help to reinforce and test the un-derstanding of the readers about various aspects of modern NMR spectroscopy Many of these problems focus on developing the interpretation skills of the readers in various types of NMR spectra toward structure determination The use of color printing and improved figures enhance the readability of the text

The revised edition of Solving Problems with NMR Spectroscopy by

Atta-ur-Rahman, M Iqbal Choudhary, and Atia-tul-Wahab is certainly a very useful addition to the NMR literature I am confident that the book will receive wide appreciation both from students as well as professionals

Professor Dr Richard R ErnstNobel Prize in Chemistry, 1991

Zurich, 2015

Solving Problems with NMR Spectroscopy http://dx.doi.org/10.1016/B978-0-12-411589-7.00001-2

Copyright © 2016 Elsevier Inc All rights reserved.

Nuclear magnetic resonance (NMR) spectroscopy is the study of molecules

by recording the interaction of radiofrequency (Rf ) electromagnetic radiations

with the nuclei of molecules placed in a strong magnetic field Zeeman first observed the strange behavior of certain nuclei when subjected to a strong mag-netic field at the end of the nineteenth century, but practical use of the so-called

“Zeeman effect” was made only in the 1950s when NMR spectrometers became commercially available

Like all other spectroscopic techniques, NMR spectroscopy involves the teraction of the material being examined with electromagnetic radiation Why

in-do we use the word “electromagnetic radiation”? This is so because each ray of light (or any other type of electromagnetic radiation) can be considered to be

a sine wave that is made up of two mutually perpendicular sine waves that are exactly in phase with each other, i.e., their maxima and minima occur at exactly the same point of line One of these two sine waves represents an oscillatory

electric field, while the second wave (that oscillates in a plane perpendicular to the first wave) represents an oscillating magnetic field – hence the term “elec- tromagnetic” radiation.

Cosmic rays, which have a very high frequency (and a short wavelength), fall

at the highest energy end of the known electromagnetic spectrum and involve frequencies greater than 3 × 1020 Hz Radiofrequency (Rf ) radiation, which is

the type of radiation that concerns us in NMR spectroscopy, occurs at the other (the lowest energy) end of the electromagnetic spectrum and involves energies

of the order of 100 MHz (1 MHz = 106 Hz) Gamma rays, X-rays, ultraviolet rays, visible light, infrared rays, microwaves and radiofrequency waves all fall between these two extremes The various types of radiations and the correspond-ing ranges of wavelength, frequency, and energy are presented in Table 1.1.Electromagnetic radiation also exhibits behavior characteristic of particles,

in addition to its wave-like character Each quantum of radiation is called a ton, and each photon possesses a discrete amount of energy, which is directly

pho-proportional to the frequency of the electromagnetic radiation The strength of

a chemical bond is typically around 400 kJ mol−1, so that only radiations above the visible region will be capable of breaking bonds But infrared, microwaves, and radio-frequency radiations will not be able to do so

Let us now consider how electromagnetic radiation can interact with a ticle of matter Quantum mechanics (the field of physics dealing with energy at the atomic level) stipulates that in order for a particle to absorb a photon of elec-tromagnetic radiation, the particle must first exhibit a uniform periodic motion with a frequency that exactly matches the frequency of the absorbed radiation

par-When these two frequencies exactly match, the electromagnetic fields can structively” interfere with the oscillations of the particle The system is then said to be “in resonance” and absorption of Rf energy can take place Nuclear

“con-magnetic resonance involves the immersion of nuclei in a “con-magnetic field, and

TABLE 1.1 The Electromagnetic Spectrum

Radiation Wavelength (nm) l Frequency (Hz)  Energy (kJ mol−1 )

(Rf ) waves 10

11 to 3 × 10 7 10 6 to 10 10 4 × 10 −7 to

4 × 10 −3

then matching the frequency at which they are precessing with electromagnetic

radiation of exactly the same frequency so that energy absorption can occur

1.1.1 The Birth of a Signal

Certain nuclei, such as 1H, 2H, 13C, 15N, and 19F, possess a spin angular

momen-tum and hence a corresponding magnetic moment m, given by

where h is Planck’s constant and g is the magnetogyric ratio (also called

gy-romagnetic ratio) When such nuclei are placed in a magnetic field B0, applied

along the z-axis, they can adopt one of 2I + 1 quantized orientations, where I is

the spin quantum number of the nucleus (Fig 1.1) Each of these orientations

corresponds to a certain energy level:

where m1 is the magnetic quantum number of the nucleus and mz is the magnetic

moment In the lowest energy orientation, the magnetic moment of the nucleus

is most closely aligned with the external magnetic field (B0), while in the

high-est energy orientation it is least closely aligned with the external field Organic

chemists are most frequently concerned with 1H and 13C nuclei, both of which

have a spin quantum number (I) of 1/2, and only two quantized orientations

are therefore allowed, in which the nuclei are either aligned parallel to the

ap-plied field (lower energy orientation) or antiparallel to it (higher energy

orienta-tion) The nuclei with only two quantized orientations are called dipolar nuclei

m=gh[I(I+1)]1/22π

E=−mzB0=−m1ghB02π

FIGURE 1.1 Representation of the precession of the magnetic moment about the axis of the

ap-plied magnetic field, B0 The magnitude m z, of the vector corresponds to the Boltzmann excess in

the lower energy (a) state.

Transitions from the lower energy level to the higher energy level can occur by absorption of radiofrequency radiation of the correct frequency The energy dif-ference ∆E between these energy levels is proportional to the external magnetic

field (Fig 1.2), as defined by the equation ∆E = ghB0/2π In frequency terms,

this energy difference corresponds to

it topples, when the two ends of its axis no longer remain stationary but trace circular paths in opposite directions (Fig 1.3) If a radiofrequency field is now applied in a direction perpendicular to the external magnetic field and at a fre-quency that exactly matches the precessional frequency (“Larmor” frequency)

of the nucleus, absorption of energy will occur and the nucleus will suddenly

“flip” from its lower energy orientation (in which its magnetic moment was processing in a direction aligned with the external magnetic field) to the higher energy orientation, in which it is aligned in the opposite direction It can then

relax back to the lower energy state through spin-lattice relaxation (T1) by transfer of energy to the assembly of surrounding molecules (“lattice”), or by

υ0=gB02π

FIGURE 1.2 The energy difference between the two energy states ∆E increases with increasing

value of the applied magnetic field B0 , with a corresponding increase in sensitivity.

spin-spin relaxation (T2), involving transfer of energy to a neighboring nucleus

The change in the impedance of the oscillator coils caused by the relaxation

is measured by the detector as a signal in the form of a decaying beat pattern,

known as a free induction decay (FID) (Fig 1.4), which is stored in the

com-puter memory and converted by a mathematical operation known as Fourier

transformation to the conventional NMR spectrum

Thus, excitations caused by absorption of radiofrequency energy cause

nu-clei to migrate to a higher energy level, while relaxations cause them to flip

back to the lower energy level, and an equilibrium state is soon established

Interestingly, the interaction with the radiofrequency causes certain nuclei to

excite to the higher energy state(s) and others to fall back to the lower

ener-gy state(s) This relaxation process is termed as induced relaxation (see the

Glossary section), which is different from spontaneous relaxation recorded as

an FID (Section 2.1.3) It is the net Rf absorption due to the difference in the

populations in the two states which leads to the NMR signal

In nuclei with positive magnetogyric ratios, such as 1H or 13C, the lower

energy state will correspond to the +1/2 state, and the higher energy state to the

−1/2 state, but in nuclei with negative magnetogyric states, for example, 29Si or

15N, the opposite will be true

Magnetogyric ratio (g) is not a “magic number.” It is a measurable quantity

for any charged particle (in case of NMR it is a rotating nucleus) Equation 1.4

is used for the measurement of magnetogyric ratio (g):

γ = q

m

2

FIGURE 1.3 Precessional or Larmor motion of an NMR active nucleus in magnetic field B0

Every nucleus has an inherently different range of precession frequencies, depending on its

mag-netogyric ratio (g).

where q is the charge and m is the mass of the charged particle The

magnetogy-ric ratios of some important nuclei are given in Table 1.2 (Harris, 1989)

If the populations of the upper and lower energy states were equal, then

no energy difference between the two states of the nucleus (in its parallel and antiparallel orientations) would exist and no NMR signal would be observed However, at equilibrium there is a slight excess (“Boltzmann excess”) of nuclei

TABLE 1.2 Magnetogyric Ratios of Some Important NMR-Active Nuclei

in the lower energy (a) state as compared to the upper energy (b) state, and it

is this difference in the populations of the two levels that is responsible for the

NMR signal (Fig 1.5) The ratio of the populations between the two states is

given by the Boltzmann equation:

= −∆ 

β α

N N

E k

exp

where N a is the population of the lower energy state, N b is the population of the

upper energy state k is the Boltzmann constant and T is the temperature.

On a 100 MHz instrument, if there are a million nuclei in the lower energy

level, there will be 999,987 in the upper energy level, yielding only a tiny excess

of 13 nuclei in the lower energy state It is this tiny excess that is detected by

the NMR spectrometer as a signal Since the signal intensity is dependent on the

population difference between nuclei in the upper and lower energy states, and

since the population difference depends on the strength of the applied magnetic

field (B0), the signal intensities will be significantly higher on instruments with

more powerful magnets Nuclear Overhauser enhancement (Section 6.2),

po-larization transfer (Section 4.2), or most recently dynamic nuclear popo-larization

(DNP) techniques (Section 3.6.1) can also be employed to enhance the

popula-tion of the ground state over that of the upper higher energy state to obtain a

more intense signal

Problem 1.1

Why are nuclei with odd atomic mass or number generally NMR active?

NbNa=exp−∆Ekt

FIGURE 1.5 (a) Vector representation displaying a greater number of spins aligned with the

mag-netic field B0 (b) Excess spin population (Boltzmann distribution excess) aligned with B0 results in

a bulk magnetization vector in the +z direction.

What is induced relaxation and how does it contribute in understanding the

popu-lation difference between lower (a) and upper (b) energy states?

Problem 1.6

What will happen if the radiofrequency pulse is applied for an unusually long time?

Problem 1.7

From the discussion in Section 1.1 , can you summarize the factors affecting the

population difference between the lower energy state (N a) and the upper energy

state (N b) How is the population difference related to the NMR signal strength?

Problem 1.8

As mentioned in the text, there is only a slight excess of nuclei in the ground state (about 13 protons in a million protons at 100 MHz) Would you expect that in the case of a 13 C-NMR experiment, the same population difference will prevail?

NMR spectrometer).

Problem 1.11

How magnetogyric ratios (g) of 1 H, 13 C, 15 N, and 2 H (deuterium) relate with their

Larmor frequencies ()?

Problem 1.12

What is “magnetogyric ratio” of a nucleus and how does it affect (1) the energy difference between two states, and (2) the sensitivity of the nuclear species to the NMR experiment?

1.2 INSTRUMENTATION

NMR spectrometers have improved significantly, particularly in the last few decades, with the development of very stable superconducting magnets and of computers that allow measurements over long time periods under homogeneous field conditions Repetitive scanning and signal accumulation allow NMR spec-tra to be obtained with very small sample quantities

There were two types of NMR spectrometers in the 1990s—continuous wave (CW) and pulsed Fourier transform (FT) The latter have now largely re-placed the CW instruments In the CW instruments, the oscillator frequency was kept constant while the magnetic field was changed gradually The value

of the magnetic field at which a match (in-resonance condition) is reached

be-tween the oscillator frequency and the frequency of nuclear precession depends

on the shielding effects that the protons experience (in the case of 1H-NMR) Different protons will therefore sequentially undergo transitions between their respective lower and upper energy levels at different values of the changing ap-plied magnetic field as and when the oscillator frequency matches exactly their respective Larmor frequencies during the scan, and corresponding absorption signals will be observed One limitation of this procedure was that at any given moment, only protons resonating at a particular chemical shift can be subjected

to excitation at the appropriate value of the magnetic field, and it is therefore

necessary to sequentially excite the protons that have differing precessional

fre-quencies in a given molecule A given set of protons will therefore be scanned for only a small fraction of the total scan time, with other protons or base line noise being scanned for the rest of the time

Fortunately, an alternative method of excitation was developed This volves the application of a short but intense radiofrequency pulse extending over the entire bandwidth of frequencies in which the nuclei to be observed res-onate, so that all the nuclei falling within the region are excited simultaneously

in-As a result, the total scan time is made independent of the sweep width W The

relaxations that occur immediately after this excitation process are measured

as exponentially decaying waves (FID) and are converted to NMR spectra by Fourier transformation Such instruments, called pulse Fourier transform (PFT) NMR spectrometers (Fig 1.6), have now replaced the earlier CW instruments

The NMR measurements on the earlier CW instruments were in the frequency domain, involving the measurement of the signal amplitude as a function of frequency The sample in such experiments was subjected to a weak field, and the energy absorbed was measured In pulse NMR, the sample is subjected to

a strong burst of radiofrequency energy; when the pulse is switched off, the

energy emitted by the relaxing nuclei is measured Thus, the CW NMR

experi-ment may be considered as providing an absorption spectrum, while the pulse NMR experiment affords an “emission” spectrum (nonradiative release of en-ergy, see Section 2.1.3)

Researchers need to be aware of some basic features of NMR spectrometers, briefly presented here

electrons becomes almost zero So, once charged, the “superconducting”

mag-nets become permanently magnetized and can exhibit a magnetic field without consuming electricity The liquid helium is housed in an inner container, with liquid nitrogen in an outer container to minimize the loss of helium by evapora-tion A large balloon can be connected to the magnet to collect the evaporated helium gas, for subsequent liquefaction and recycling In places where liquid helium is not readily available, it is advisable to order special magnet Dewars along with the instrument, with long helium hold times Fitted with such special Dewars, 500 MHz instruments need to be refilled only about once a year In

FIGURE 1.6 A 600 MHz NMR spectrometer The console is the computer-controlled recording and measuring system; the superconducting magnet is in front.

early 2000, ultrashielded and ultrashielded + ultrastabilized (US2) NMR nets were developed with long-term stable magnetic field, compact designs, and low helium evaporation/consumption This new technology also provides the added advantage of reducing the stray fields and protection against external electromagnetic field disturbances Superconducting magnets are very stable, allowing measurements to be made over long periods with little or no variation

mag-of the magnetic field (B0) With the advancements in superconducting magnets and refrigeration/insulation technologies, ultrahigh field NMR spectrometers have become available which are especially suited for the analysis of insensitive nuclei (13C, 15N, 31P, 17O) in structural biology research

More recently, earthfield NMR (EF-NMR) (270 mT) has been introduced for commercial applications EF-NMR uses the globally available, homog-enous magnetic field of the earth for detection (Ross et al., 2012; Melton and

a limited number of experiments can be performed (Katz et al., 2012; Liao

et al., 2010; Halse et al., 2009) This technology can make low field NMR able in countries and regions where availability of liquid helium is still an is-sue, although the experiments are of very limited use (Section 9.1.2) Similarly ultralow field and low field pulse NMR (LFP-NMR) spectrometers are being developed for various applications

avail-Similarly PFT-NMR spectrometers with permanent magnets (45–90 MHz) have returned back to the marketplace as robust machine for routine identifica-tion of known compounds or medium scale synthetic chemistry work (Sections 9.1.1, and 9.1.2)

Problem 1.13

Which of the following conditions will yield better NMR results?

1 More sample with measurement on a lower MHz NMR spectrometer.

2 Less sample with the use of a higher MHz NMR spectrometer.

Problem 1.14

Describe the effect of the magnet’s power B0 on the separation of the nuclei in the

frequency spectrum Do changes in magnetic power B0 also affect the coupling constant?

Problem 1.15

Do I get a higher resolution if I record the spectrum on a higher field instrument?

In other words, will the resolution be better on a 600 MHz instrument as pared to a 300 MHz instrument?

com-1.2.2 The Probe

The probe, situated between the field gradient coils in the bore of the magnet, consists of a cylindrical metal tube that transmits the pulses to the sample and

receives the resulting NMR signals The glass tube containing the sample lution is lowered gently onto a cushion of air from the top of the magnet into the upper regions of the probe The probe, which is inserted into the magnet from the bottom of the cryostat, is normally kept at room temperature, as is the sample tube The sample is spun on its axis in a stream of air to minimize the effects of any magnetic field inhomogeneities The gradient coils are also kept at room temperature For recording 1H-NMR and 13C-NMR spectra a dual

so-1H/13C probe is recommended, which, although having a somewhat (10–20%) lower sensitivity than the dedicated 1H probe, has the advantage of avoiding frequent changing of the probe, retuning, and reshimming If other nuclei (e.g.,

15N, 19F, 31P) are to be studied, then broad-band multinuclear probes can be used, although the sensitivity of such probes is lower than that of “dedicated” probes Special inverse probes were introduced to conduct inverse NMR ex-periments (Section 3.3.2.2) Solid-state NMR probes, more properly known as magic angle spinning (MAS) probes, are also readily available for special pur-poses (Section 9.2)

We also need to choose the probe diameter to accommodate 3, 5, 10, or

15 mm sample tubes In wide-bore magnets, the probes can be several ters in diameter, allowing insertion of larger sample tubes (and even small ani-mals, such as cockroaches and mice) Normally, the 5 mm probe is used, unless sample solubility is a critical limitation, when it may become necessary to use a larger quantity of sample solution to obtain a sufficiently strong signal The usual limitation is that of sample quantity rather than sample solubility, and it is often desirable to be able to record good spectra with very small sample quantities In such situations, we should use the smallest diameter probe possible that affords stronger signals than larger diameter probes with the same amount of sample Microprobes of diameter 1, 1.5, and 2.5 mm with special sample tubes are partic-ularly useful in such cases, and special NMR tubes are used with it If, however, the amount of sample available is not a limiting factor, then it may be preferable

centime-to use a larger diameter probe centime-to obtain good shim values and centime-to subject as much sample as possible to the NMR experiment so as to obtain a good spectrum in the shortest possible measuring time Such a situation may arise, for instance,

in INADEQUATE spectra (Section 7.7) in which 13C–13C couplings are ing observed, and it may be necessary to scan for days to obtain an acceptable spectrum

be-The significant improvements in sensitivity achieved during the last 5 years have been largely due to the development of magnets with higher magnetic field, improved probe design, and radiofrequency circuits Since the probe needs to be located very close to the sample, it must be made of a material with

a low magnetic susceptibility; otherwise, it would cause distortions of the static

magnetic field B0, thereby adversely affecting line shape and resolution Much research has, therefore, been undertaken by NMR spectrometer manufacturers

to develop materials that have low magnetic susceptibilities suitable for use in

probes The probe must also have a high field (B1) homogeneity; i.e., it must be

able to receive and transmit radiofrequency signals from and to different regions

of the sample solution in a uniform manner Besides these room temperature probes, new cryogenically cooled probe technology has also been introduced

in the last decade

In a cryogenically cooled probe, the Rf coils and preamplifiers are cooled

to 10 K (−263.15°C) by a uniform injection of gaseous helium, while the sample tube remains at room temperature This leads to a substantial increase

in sensitivity as the signal-to-noise (S/N) ratio increases with the reduction

of electronic noise at very low temperature Cryogenically cooled probes are now available in several configurations, such as dual (13C/1H), inverse, triple resonance or triple resonance inverse (15N/13C/1H), and magic angle spinning (MAS) solid-state probes, and in various sizes Introduction of cryogenically cooled probe technology is one of the most important milestones in NMR spectroscopy due to the tremendous boost in sensitivity achieved About four-fold sensitivity enhancement achievable by cryogenically cooled probe technology has made it possible to study very small quantities of samples as well as nuclei with low natural abundance (Section 3.3.2.1) Recently, liquid nitrogen cooled cryogenic probes were introduced which should further popu-larize the use of cryogenically cooled probe technology (Kovacs et al., 2005) (Section 9.1.4)

Typical probe assemblies, room temperature and cryogenically cooled, are shown in Fig 1.7, while Fig 1.8 shows the difference in the S/N ratio in the 1H-NMR spectra of oxandrolone (0.5 mg) recorded using a cryogenically cooled probe and a room temperature probe, respectively

Problem 1.16

Which types of NMR spectrometers would give the best sensitivity for recording carbon spectra?

Problem 1.17

Recommend the most suitable probe for each of the following laboratories:

1 A laboratory involved in biochemical work or in analytical studies on natural

products.

2 A laboratory involved in the synthesis of phosphorus compounds and

organo-metallic complexes.

3 A laboratory where large-scale synthesis of organic compounds is carried out.

4 A laboratory where various nitrogenous compounds are prepared and studied.

5 A laboratory where structures of labeled proteins of clinical importance in

liquid state are deduced.

Problem 1.18

What properties should an “ideal” NMR probe have?

trans-back from the sample The probe circuit is tuned to effectively transfer the Rf to

the sample and sensitively detect the precessing magnetization by matching the resonant frequency of the circuit to the precessional frequency of the nuclei It

is vital that the impedance of the wire be identical to those of the transmitter and receiver to properly perform the dual function of a pulse transmitter and a signal

FIGURE 1.7 (a) A typical probe assembly (b) Cryogenically cooled probe system (probe sembly not shown).

as-receiver In addition, the impedance of the coil must be matched with the ance of the spectrometer electronics (Bendet-Taicher et al., 2014) The probe is tuned and matched by adjusting the two capacitors present inside the probe resonant circuit by a long screw driver near the coil (Fig 1.9) Adjusting one

imped-of the capacitors changes the resonant frequency imped-of the circuit, and this ment is carried out so that the circuit resonant frequency precisely matches the precessional frequency of the observed nucleus The other capacitor controls the impedance of the circuit, and it is adjusted to match the probe impedance (Poeschko et al., 2014)

adjust-Normally, it is necessary to adjust these capacitors when the solvent is changed The two capacitors are adjusted in conjunction with one another, since adjustment of one tends to affect the other and an optimum combination of set-tings is required This process is facilitated by employing a directional coupler that is inserted between the probe and the transmitter output (Fig 1.10) The power of the pulse transmitter reflected from the probe is measured by the di-rectional coupler, and the probe is tuned so that the reflected power is kept to

a minimum to obtain the best performance (Poeschko et al., 2014; Daugaard

et al., 1981)

Problem 1.20

How does probe tuning affect the quality of the NMR spectrum?

FIGURE 1.8 1 H-NMR of oxandrolone (0.5 mg dissolved in 0.6 mL of CD3OD) was recorded on a (a) 500 MHz NMR spectrometer equipped with cryogenically cooled probe, and (b) 500 MHz NMR spectrometer equipped with room temperature probe using eight scans.

FIGURE 1.10 Use of directional coupler for probe tuning.

FIGURE 1.9 A schematic representation of a typical resonant circuit for a dual 1 H/ 13 C probe The pacitors A, B, C, and D perform various functions, such as symmetrization and matching of resonance.

ca-1.2.4 Shimming

Modern superconducting magnets have a set of superconducting gradient coils that are adjusted during installation of magnet (and never adjusted by the user) There is, however, another set of printed coils at room temperature that are wrapped around the magnet cylinder and these need to be adjusted from time

to time The weak magnetic fields produced by these coils can be adjusted to

simplify any errors in the static field, a process known as “shimming.” The

shim assembly contains many different coils, which have their respective fields

aligned with the x-, y-, and z-axes The NMR probe lies in between the shim sembly, with the sample tube being located in the center of the z-gradient coil The static field in superconducting magnets lies along the z-axis (in the older

as-iron magnets it was aligned horizontally) The proper adjustment of the vertical

z- and z2-gradients is important, particularly since most of the field

inhomo-geneities along the x- and y-axes are eliminated by the rapid spinning of the sample tube along the z-axis It is, therefore, necessary to correct the x- and y-gradients only to the third order (x, x2, x3, y, y2, y3), while the z-gradients need

to be corrected to the fourth or fifth order, particularly on high-field instruments

The axial shims, i.e., z, z2, etc that alter the field on the z-axis only, are

corrected while spinning the sample at 15–25 Hz The radial shims, i.e., ZXY

that affect the x and y coordinates should be shimmed without spinning the

sample

Since it is z- and z2-gradients that have to be adjusted most frequently, the operator had to become proficient in the rapid and optimum adjustment of these gradients each time the sample was changed on the older instruments This is now done automatically on the more modern instruments The adjust-ments afford maximum lock levels, which in turn lead to higher resolution and improved line shape The intensity of the lock signal (Section 1.2.5) dis-played on the lock-level meter or on some other gradient device indicates the field homogeneity, and it is therefore used to monitor the shimming process

In theory, the field generated by each shim coil is independent of the other, but practically there are considerable interactions and the shims must be ad-justed interactively

One feature of the shimming process is the interdependability of the dients; i.e., changing one set of gradients alters others, so that an already optimized gradient will need to be readjusted if other gradients have been sub-sequently altered Good shimming therefore requires patience and persever-ance, since there are several gradients to be adjusted and they affect each other Shimming of the various gradients is therefore not done randomly, since certain gradients affect other gradients to deferring extents The NMR operator soon recognizes these pairs or small groups of interdependent gradients that need

gra-to be adjusted gra-together The adjustment of x- and y-gradients corresponds gra-to first-order shimming, changes in xy-, xz-, yz-, and x2 − y2-gradients represent

second-order shimming, while optimization of xz2- and yz2-gradients is called

third-order shimming It is normally not necessary to alter the xy-, xz-, yz-, xy-,

or x2 − y2-gradients

Adjustment of the z-gradients affects the line widths, with changes in z-,

z3-, and z5-gradients altering the symmetrical line broadening and adjustments

of z2 and z4-gradients causing unsymmetrical line broadening Changes in the

lower order gradients, for example, z or z2, cause more significant effects than

changes in the higher order gradients (z3, z4, and z5) The height and shape of the

spinning side bands is affected by changing the horizontal x- and y-gradients,

adjustments to these gradients normally being carried out without spinning the

sample tube, since field inhomogeneity effects in the horizontal (xy) plane are

suppressed by spinning the sample tube A recommended stepwise procedure for shimming is as follows:

1 First optimize the z-gradient to maximum lock level Note the maximum

value obtained

2 Then adjust the z2-gradient, and note carefully the direction in which the z2gradient is changed

-3 Again adjust the z-gradient for maximum lock level.

4 Check if the strength of the lock level obtained is greater than that obtained

in step 1 If not, then readjust z2, changing the setting in a direction opposite

to that in step 2

5 Readjust the z-gradient for maximum lock level, and check if the lock level

obtained is greater than that in steps 1 and 3

6 Repeat the preceding adjustments till an optimum setting of z/z2-gradients

is achieved, adjusting the z2-gradient in small steps in the direction so that maximum lock level is obtained after subsequent adjustment of the

z-gradient.

7 If x-, y2-, or z2-gradients require adjustment, then follow this by

readjust-ment of the x- and y-gradients, making groups of three (x2, x, y; y2, x, y; z2,

x, y) This should be followed by readjustment of the z-gradient.

The main shim interactions are presented in Table 1.3 Note that since justments are made for maximum lock signal corresponding to the area of the single solvent line in the deuterium spectrum, a high lock signal will correspond

ad-to a high intensity of the NMR lines but will not represent improvement in the

line shape The duration and shape of the FID is a better indication of the line

shape Shimming should therefore create an exponential decay of the FID over

a long time to produce correct line shapes

The duration for which an FID is acquired also controls the resolution tainable in the spectrum Suppose we have two signals, 500.0 and 500.2 Hz away from the tetramethylsilane (TMS) signal To observe these two sig-nals separately, we must be able to see the 0.2-Hz difference between them This would be possible only if these FID oscillations were collected for long enough so that this difference became apparent If the FID was collected for

ob-only a second, then 500 oscillations (Hz) would be observed in this time, which would not allow a 0.2-Hz difference to be seen To obtain a resolu-

tion of signals separated by n Hz, we therefore need to collect data for 0.6/n

seconds Bear in mind, however, that if the intrinsic nature of the nuclei is

such that the signal decays rapidly, i.e., if a particular nucleus has a short T2* (Section 4.1.3), then the signals will be broad irrespective of the duration for which the data are collected As already stated, FIDs that decay over a long time produce sharp lines, whereas fast-decaying FIDs yield broad lines Thus,

to obtain sharp lines, we should optimize the shimming process so that the signal decays slowly

For longer experiments an automatic shimming system (AUTOSHIM) must

be turned on at the start of the experiment (in Bruker NMR spectrometers) This will keep the lock level to the same position

FIDs have to be accumulated and stored in the computer memory, often

over long periods, to obtain an acceptable S/N ratio During this time there may

be small drifts in the magnetic field due to a slight electrical resistance in the magnet solenoid, variations in room temperature, and other outside influences,

TABLE 1.3 Main Shimming Interactions

Gradient Adjusted* Main Interactions Subsidiary Interactions

*Alteration in any gradient in the first column will affect the gradients in the second column

markedly, while those in the third column will be less affected.

such as the presence of nearby metal objects It is therefore desirable to lock the signal onto a standard reference to compensate for these small changes.

The deuterium line of the deuterated solvent is used for this purpose, and the intensity of this lock signal is employed to monitor the shimming process The deuterium lock prevents any change in the static field or radiofrequency

by maintaining a constant ratio between the two This is achieved via a lock

feedback loop (Fig 1.11), which keeps a constant frequency of the deuterium signal The deuterium line has a dispersion-mode shape; i.e., its amplitude

is zero at resonance (at its center), but it is positive and negative on either side (Fig 1.12) If the receiver reference phase is adjusted correctly, then the signal will be exactly on resonance If, however, the field drifts in either di-rection, the detector will experience a positive or negative signal (Fig 1.13), which will be fed to a coil lying coaxially with the main magnet solenoid The coil will generate a field that will be added or subtracted from the main field to compensate for the effect of the field drift The deuterium lock therefore com-prises a simple deuterium spectrometer, operating in parallel to the nucleus being observed (Fig 1.11b)

am-1.2.5 Deuterium Lock

Two other parameters that need to be considered in the operation of the lock channel, besides adjusting the receiver reference phase as just described, are (1)

Rf power, and (2) the gain of the lock signal If too much Rf power is applied

to the deuterium nuclei, a state of saturation will result, since they will not be

able to dissipate the energy as quickly via relaxation processes, producing line

broadening and variation of the signal amplitude It is desirable to achieve the highest transmitter power level that is just below the saturation limit to obtain

a good lock signal amplitude The gain of the lock signal should also be mized, since too high a lock gain will result in over-amplification of the lock signal, thereby causing excessive noise

opti-It is important to ensure that the sample is properly locked For solvents with more than one peak in the proton/deuterium spectrum (ethanol, toluene, and THF are common solvents that have multiple peaks), it is necessary to make sure that the peak being used to lock corresponds to the peak that the software is processed to select The chemical shift of the solvent must therefore

be defined in the software It is possible to use a mixture of two deuterated vents, but it is best to avoid doing so unless one is trying to reproduce results reported in the literature obtained with mixed solvents This is because mixing two solvents will result in a perturbation of the chemical shifts of both solvents and it may cause problems in autolocking and gradient shimming One should also keep in mind the temperature dependence of the chemical shifts of some solvents One needs to be particularly careful when using D2O as a solvent as its chemical shift varies by 0.011 ppm per degree as the temperature is increased 4,4-Dimethyl-4-silapentane-1-sulfonic acid (DSS) can also be used as a solvent but its shift is also pH dependent Be careful not to be deceived by a peak at 0.08 ppm as the TMS peak—it is caused by silicone grease impurities in the sample

sol-1.2.6 Referencing NMR Spectra

There are three methods that are in use for referencing NMR spectra:

1 An internal standard is added to the solution

2 An external standard is used which is typically a neat liquid

3 The chemical shift of the lock solvent is used as a reference so that the vent itself serves as the internal standard This is now the usual method.The main problems associated with the use of internal standards are: (1) their chemical shifts change at different dilutions, and (2) removing the standard could become a problem if one wants to recover the sample after recording the NMR spectrum TMS was often added as an internal standard, but in spite of its relatively inert nature, its chemical shift can vary by more than 0.6 ppm in

sol-different organic solvents relative to neat TMS (e.g., benzene +0.30 ppm, roform −0.14 ppm).

chlo-A neat liquid (TMS) can also be used as a standard in a concentric insert in the NMR tube This allows the NMR measurement to be carried with two dif-ferent (unmixed) solvents, one of which is in a separate insert while the other is used for dissolving the solvent Both Varian, Bruker and Jeol spectrometers use the known absolute deuterium lock frequency, instead of the 1H TMS frequency,

as the basis for all multinuclear chemical shift calibrations This allows one to tablish chemical shifts without the need to have TMS in the sample tube If TMS

es-is present, then TMS can be used to set the absolute zero, but if it es-is not present, then the deuterium frequency can be used for the lock Nitrogen chemical shifts can be reported relative to neat liquid ammonia, neat nitromethane, and tetra-

methylammonium iodide in DMSO-d6 Biological NMR spectroscopists tend to report nitrogen shifts on the ammonia scale, while organic chemists normally use the nitromethane scale The two scales differ by 380.2 ppm Similarly, bio-NMR spectroscopists tend to report 13C shifts relative to DSS (4,4-dimethyl-4-silapen-tane-1-sulfonic acid) in D2O which is offset from TMS scale (1% in CDCl3) by a few hundredths of a ppm

10 mL of liquid sample) is normally used though NMR spectra of much smaller sample amounts can also be measured

NMR tubes are typically made of borosilicate glass Two important cations of NMR tubes are concentricity and camber Concentricity refers to the variation in the radial centers, when measured at the inner and outer walls, while

specifi-camber refers to the “straightness” of the NMR tube If values of either of these

are poor, then the homogeneity of the sample will be reduced, resulting in poor quality NMR spectra If the NMR tube has poor camber, it can wobble when spun, resulting in the appearance of spinning side bands

The sample is placed in the NMR sample tube which is usually a cal glass tube with a length of 17 cm and a diameter of 5 cm The reference

cylindri-compound, usually tetramethylsilane (TMS), is then added As TMS has a low boiling point (26°C) and a high vapor pressure, it may be difficult to handle,

so deuterated solvents containing 5% TMS are available which may be used Alternatively, the deuterated solvent itself can be used as a reference, and its frequency difference with respect to TMS inserted into the software If only a very small amount of sample is available, special NMR tubes with a smaller diameter (1–3 mm) or a Shigemi tube may be used (Section 3.4) These are shown in Fig 1.14

Problem 1.30

Why is the population difference between the two orientations (a and b for dipole

nuclei) very small, whereas in other spectrophotometric techniques (such as UV,

IR, Raman, etc.) the entire population is either in the ground energy state or in the excited energy state (after absorption of relevant electromagnetic radiation)?

FIGURE 1.14 NMR sample tubes: (a) for measurement with an internal standard; (b) and (c) with capillaries for measurements with an external standard; (d) for microsamples; and (e) Shigemi tubes.

SOLUTIONS TO PROBLEMS

1.1 Nuclei with odd atomic mass or number, i.e., with odd number of trons or protons create an inherent unsymmetry of nuclear spin Sub-atomic particles (electron, neutron, and proton) exist in spin pairs Their odd number leaves at least one of them as an unpaired species, creating an unsymmetry in the nuclear motion The resulting nuclear spin makes such nuclei NMR active Examples include 13C, 15N, 31P, 19F, 17O, 1H, etc

neu-1.2 Practically, every element in the periodic table has one or more isotopes with odd number of neutrons, which makes them NMR active For ex-ample, 17O and 13C isotopes of oxygen and carbon, respectively, are NMR active, whereas their main isotopes are NMR inactive It is therefore pos-sible to analyze almost every element in the periodic table by NMR spec-troscopy

1.3 All nuclei carry a charge because of the presence of protons In some nuclei, this charge may spin (such as in the 13C nucleus) while in other nuclei it may not spin and they will not be observed in the NMR spectrum (as in the 12C nucleus) In those nuclei in which the charge is spinning, the nuclei behave like tiny bar magnets, and they can become aligned either

in the direction parallel to the applied field (lower energy or a tion), or in the opposite direction (aligned against it (higher energy or b

orienta-orientation)

Nuclei such as 1H, 13C, and 31P and have a uniform spherical charge distribution and they are said to have a spin of 1/2 Nuclei in which the charge distribution is nonspherical (quadrupolar nuclei) have spin num-

ber I of 1, 3/2, or higher (in steps of1/2) As stated above, spin 1/2 nuclei

have two orientations (with or against the field), spin 1 nuclei will have three orientations, spin 3/2 nuclei will have four orientations, and so on Thus, deuterium which has spin 1 will exist in three different orientations

A carbon spectrum of CDCl3 therefore shows a 1:1:1 triplet of carbon because of its coupling with attached deuterium

1.4 After the application of a pulse, the nucleus takes a certain time to relax to its equilibrium position at an exponential rate The relaxation time is the

“time constant” of the exponential curve For a nucleus to relax to 95% of its equilibrium value, it will take five time constants

Relaxation can occur by two different processes In one process

(T1 or spin lattice relaxation), the excited nuclear spin relaxes by giving

up its energy to the surrounding lattice resulting in the magnetization

along the z-axis relaxing back to its equilibrium position In the second relaxation process (T2 relaxation), the magnetization in the x–y plane

spreads out by the excited spins exchanging energy with each other,

till the net magnetization in the x–y plane (transverse magnetization)

becomes zero

1.5 Applied radiofrequency (Rf), when in-phase with the varying range

of Larmor frequencies of a particular nucleus, can induce relaxation by accepting energy from in-phase nuclei and make them fall to lower en-ergy states As a result, absorption of applied radiofrequency leads to ex-citation of nuclei in the lower energy state(s) to the upper energy state(s) The release of radiofrequency from certain in-phase nuclei in upper en-ergy state(s) helps them to relax to lower energy state(s) It is the net dif-ference in absorption and release of energy due to population difference (Boltzmann distribution excess) which gives birth to an NMR signal This

is unlike other spectroscopic techniques (such as UV and IR tometry), where entire populations in the lower energy state are excited to the upper energy state through the absorption of specific electromagnetic radiation

spectropho-1.6 By absorption of continuous energy from the radiofrequency source,

tran-sitions of the nuclei occur to the higher energy state, b; then by relaxation processes, they revert to the lower energy state, a, and an equilibrium

is established with a slight Boltzmann excess in the lower a state This

slight excess of population in the lower state will be eliminated on

contin-uous irradiation, and a state of saturation will be reached, since the nuclei will not be able to dissipate the extra energy via relaxation processes.

1.7 The population difference between two energy levels a and b is directly

proportional to the energy difference ∆E.

= −∆ 

β α

N N

E k

expTThe energy difference ∆E depends on the strength of the external

magnetic field B0 and the magnetogyric ratio g A stronger applied netic field B0 will cause a correspondingly larger separation (∆E) between the two energy levels and result in a larger difference in the populations

mag-of the two levels Similarly, the energy difference ∆E also depends on the magnetogyric ratio of the nuclear species under observation:

γπ

∆ =E h B

2

0

Since the magnetogyric ratio determines the sensitivity of a

nucle-ar species to the external magnetic field, it has a profound effect on the strength of the NMR signals For instance, 1H nuclei will have a Larmor frequency of 300 MHz at an external magnetic field of 7.046 T, while

13C nuclei will resonate with a Larmor frequency of only 75.435 MHz

in the same magnetic field, since the g for 13C is about a quarter of the

g for 1H The signal strength is determined by g3, so a 13C signal will be about 64 times weaker than an 1H signal [(1/4)3 = 1/64] In practice, a 13C

NbNa=exp−∆Ekt

∆E=hgB02π

signal is over 6000 times weaker, because it occurs in only 1.1% natural

abundance

1.8 No Since the magnetogyric ratio of 13C is roughly one-fourth that of 1H,

the population difference between the two states (a and b) of 13C nuclei

will therefore be about 64 times [(1/4)3 = 1/64] less than that of the 1H

nuclei (13C enriched samples)

1.9 The frequency with which a nucleus precesses around the applied

mag-netic field is called its Larmor precessional frequency The Larmor

fre-quency depends on the strength of the applied magnetic field B0 and on

the magnetogyric ratio of the nucleus When the radiofrequency B1 is

applied in a direction perpendicular to the external magnetic field B0, and

when the value of B1 matches exactly the Larmor frequency, absorption of

energy occurs causing the nucleus to “flip” to a higher energy orientation

This represents the process of excitation Through a relaxation process,

the nuclei can then relax back to the lower energy level The energy

re-leased during the relaxation process is recorded as an FID (free induction

decay), which is then converted into NMR signals through a

mathemati-cal operation mathemati-called Fourier transformation

1.10 The Larmor or precession frequency of a nucleus depends on the

follow-ing two factors:

1 magnetic flux density (B0),

2 magnetogyric ratio (g).

As the magnetogyric ratios (g) of nuclei are different, they all have

specific Larmor frequencies which can be selectively studied without the

interference of the other nuclei For example, though both 13C and 1H in

an NMR sample tube experience the same (B0), but the magnetogyric

ra-tio of 13C is ¼ of the 1H As a result, while 1H resonates with the Larmor

frequency of 400 MHz, the 13C will resonate with the Larmor frequency

of 100 MHz This allows selective detection of one type of nucleus

pos-sible, without the interference of the other The same phenomenon applies

to selective detection of 17O, 15N, 19F, 31P, etc

1.11 Magnetogyric ratio (g) is related to the Larmor frequency through

where B0 is applied magnetic field and g magnetogyric ratio The

mag-netogyric ratios of 1H, 13C, 15N, and 2H are 26.7520, 6.7283, −2.712,

and 4.1065 (107 Rad T−1 s−1), respectively At a given magnetic field

(B0), let say in a 9.4 T (400 MHz), the 1H nuclei will resonate with the

highest Larmor frequency, i.e., 400 MHz, followed by 13C (∼100 MHz),

2H (∼61.5 MHz), and 15N (∼−40.5 MHz)

υ=g2πB0

1.12 The magnetogyric ratio of a nuclear spin represents its response toward the external magnetic field Nuclear species with larger magnetogyric ra-tios have larger differences in energy levels ∆E in comparison to nuclear

species of smaller magnetogyric ratios, when placed under an external

magnetic field of the same strength B0:

crease in T1 (FID will be short), and line broadening of the NMR signals will result Therefore, an optimum concentration (say, 25–50 millimolar solution) is recommended Of course, 1H-NMR spectra can be readily measured at much lower concentrations, though higher concentrations are necessary for recording 13C-NMR spectra

1.14 The magnetic field-strength B0 has a direct relationship with the Larmor frequencies of nuclei: the stronger the magnetic field, the greater the difference, in Hertz (not in ppm), between magnetically nonequivalent nuclei having differing chemical shifts Moreover, the population excess

of the lower energy level over the upper energy level increases with

in-creasing magnetic field, B0, leading to a corresponding increase in the sensitivity of the NMR experiment The magnitude of the coupling con-stants, however, remains unaffected by the magnetic field strength

1.15 No, this is a common misconception You do NOT necessarily improve resolution by going to a higher field instrument In fact, the resolution

on the higher field instrument may be poorer than that on the lower field

instrument By going to higher fields, you will achieve a greater sion of signals, so that nuclei with different chemicals shifts will spread

disper-farther apart, leading to simplification of multiplets by reduced order perturbations If the multiplets are overlapping in the low field in-strument, then they will separate at higher fields, making interpretation easier Some nuclei, such as 31P, may show worse resolution at higher fields because of an intrinsic property that they possess, such as chemical shift anisotropy, which increases with the field strength

second-1.16 The high field instruments give the best results For instance if you have the option to use 600 or 300 MHz instruments, then the 600 MHz instru-ment should be preferred, particularly if you have small sample quan-

tities, as the S/N (sensitivity) ratio on the 600 MHz instrument would

∆E=hgB02

be better than that on the 300 MHz instrument by a factor of 600/300 squared, or four times better The probe that you use is also important for optimum sensitivity If you are employing an indirect detection probe, then this has the proton observe coil closer to the sample, on the inside, and it would give a better proton signal but a weaker carbon signal (if you use it for directly detecting carbon) A standard probe however has the carbon coil on the inside, and it gives a better carbon signal but a weaker proton signal than the indirect detection probe.

The S/N ratios are normally measured by a single scan on a

con-centrated sample (standard sample supplied by manufacturer) In actual experiments, one is normally measuring a dilute sample for several hours, and the relaxation times of the nuclei need to be taken into account Also, nuclei take longer to relax at higher field strengths, so that the gain in the

S/N may be less than expected Carbons that do not have directly bonded

protons (such as quaternary carbons, carbonyls, etc.) will take much ger times to relax than protonated carbons and hence their signals may be expected to be weaker If one is interested in getting stronger signals for the quaternary carbons, then the D1 delay of 3 seconds or more should

lon-be employed to allow the quaternary carbons to relax after excitation lon-

be-fore experiencing another pulse Dramatic improvements in S/N ratios of

carbon spectra can be obtained if one records a short or long-range 2D heteronuclear (proton, carbon) correlation experiment (Luciano, 1979)

1.17 The probe selection should be based on the actual requirements of a laboratory

1 Small-diameter probes are generally suitable when the total ability of the sample is a limiting factor For natural products or bio-chemical studies, a 13C/1H probe of 5 mm size is probably the best choice, since the major requirement here is to analyze small quanti-ties of organic samples for the proton and carbon spectra A 2.5 mm microprobe is also available for use with special sample tubes having

avail-a diavail-ameter of 2.5 mm, avail-and it is highly recommended for smavail-all savail-am-ples Nanoprobes are available for very small samples quantities An inverse probe is highly desirable for 1H/13C inverse-shift correlation experiments (e.g., HMQC/HSQC, HMBC)

sam-2 For heteronuclear studies, where different types of nuclei are

investigat-ed routinely, the broad-band multinuclear probe is an excellent choice, since it can be tuned over a wide frequency range for various elements

3 In organic-synthesis laboratories, where sample quantity is not a iting factor, the larger probes provide a significant saving in time A

lim-13C/1H probe of 10–15 mm size is more appropriate

4 A laboratory where nitrogen is the main nucleus to be analyzed, with occasional 13C/1H analysis, a broad-band probe specific for nitrogen should be acquired

5 In a laboratory where structures of labeled proteins are studied, a triple resonance cryogenically cooled probe is ideal as it gives the capacity of measuring any of the labeled nuclei (2H, 15N, and 13C), as well as decoupling any one of them with improved sensitivity.

1.18 An ideal probe should have the following properties:

1 It should be made up of a material with a low magnetic susceptibility

so that it does not distort the static magnetic field B0 and adversely affect the line shape and resolution of the NMR signals

2 It should have a high field (B1) homogeneity so that it can receive and transmit radiofrequency signals uniformly from all parts of the sample solution

3 It should fulfill the needs of a maximum number of users

1.19 Cryogenically cooled probe technology has delivered the single largest increase in NMR sensitivity in the last four decades, after the advent of superconducting magnets Injection of gaseous helium in probe electron-ics decreases the resistance and increases the conductance This reduces

the noise contribution and yields an enhancement of the S/N by up to

five-fold, as compared to the comparable room temperature probe This 3-5 fold jump in sensitivity by use of the cryogenically cooled probe enables one to analyze smaller quantities of sample that are impractical with con-ventional probes Introduction of cryogenically cooled probe technology

in the arsenal of NMR spectroscopist has had a direct impact on research

in different fields Most profoundly, it is now possible to analyze and cord reasonably good quality NMR spectra of small quantities of proteins and other biomolecules, environmental contaminants, rare natural prod-ucts, etc Due to enhanced sensitivity, only a limited number of scans are required, increasing the sample throughput by up to 16-fold Similarly, with cryogenically cooled probes, it is possible to record high quality NMR spectra of insensitive or low natural abundance nuclei, such as 15N and 13C

re-1.20 The probe contains the electronics designed to detect the tiny NMR

sig-nal The central component of the probe is a wire that receives the Rf

pulse from the transmitter and dissipates it into the sample It also ceives the signal from the sample and transfers it to the receiver circuit

re-It is therefore necessary to tune the probe wire impedance to match it with those of the transmitter and the receiver The optimum sensitivity of the NMR experiment will be realized only when this adjustment is made accurately The probe tuning also minimizes the variable off-resonance effects, and it is therefore essential for the proper reproducibility of the pulse width

1.21 Poor shimming would lead to poor line shape and resolution, as trated here

illus-1.22 Shimming involves optimizing the homogeneity of the magnetic field by adjusting the resolution Tuning involves minimizing the impedance at the frequency to be studied by adjusting the variable capacitors in the probe If a probe is poorly tuned, it will result in the reflection of a lot of the power of the pulses, so that if we want to apply a 180° pulse, we may actually get only (say)

a 130° pulse This will not affect the resolution but it will lead to a poor S/N

ratio (sensitivity) Experiments, such as COSY and DEPT (that depend on the use of accurate 90° pulses), may then not work properly and produce noise

and artifact signals If the shimming of an instrument is poor, it will result in a

poor resolution, which will show up as a broadening of the NMR signals

1.23 You should not try and tune the probe unless you have been trained as

it is a specialized operation The Bruker instruments have an automatic system of tuning If you have an NMR spectrometer on which manual tuning is needed then you will need to bear in mind that tuning is affected

by frequency, solvent, and sample peak heights

1.24 1. This is probably because the lock is saturated Go to the shim window

and reduce the lock power by 4 in the lock power/gain/phase display This should result in a drop of the lock power If this does not happen, then keep reducing the lock power till the lock level has dropped

2. You may need to load the standard shims again as the previous user may have disturbed the shims.

3. If you have not already done so, load the standard values for the shims You do not know what sort of state the previous user left the shims in!

4. Make sure that the sample tube is not dirty or scratched, and that there

is no material floating in the sample If the concentration is too strong, then you may need to dilute the sample The sample tube needs to be properly centered in the coil

5. Shimming may also be difficult if you have paramagnetic ions in the sample which leads to line broadening Broad lines may be caused

by quadrupolar broadening with transition metals, or if chemical change is occurring

ex-1.25 Despite tremendous developments in the design of superconducting nets, high field magnets have greater possibilities of instability and inho-mogeneity The shimming system is designed to adjust only very minor errors or inhomogeneities In the case of high field NMR spectrometer, i.e., at 900 and 1000 MHz, the magnetic inhomogeneities are often much larger than what the shimming routine can adjust Therefore, it is more challenging to shim high field magnets

mag-1.26 The deuterium lock prevents changes in the static field (B0) and radio

frequency (B1) by maintaining a constant ratio between the two It fore ensures long-term stability of the magnetic field If the 2H lock is not applied, a drastic deterioration in the shape of the NMR lines is expected due to magnetic and radiofrequency inhomogeneities

there-1.27 1. Make sure that you are using a deuterated solvent.

2. Make sure that the tube is spinning properly, and that you have not broken it when inserting it into the probe

3. Switch off the lock in the lock display, increase the lock power and gain to the maximum value, and search for the sine wave by adjust-

ing z0 If a sine wave is found, then adjust z0 to zero value Now duce the lock power, in order to avoid saturation, and click the lock button to “ON.” If it loses lock when you lock on, then turn the lock off and adjust the lock phase (procedure should be described

1.29 No The signals from the lock transmitter would obliterate the signals we wish to observe

1.30 The energy difference between LUMO and HOMO in UV

spectrosco-py ranges from 29.87 to 155.35 kcal mol−1, while in IR spectroscopy the energy difference is of the order of 1.9–9.5 kcal mol−1 In NMR

spectroscopy, however, the energy difference between a and b states is

3 × 10−5 kcal mol−1 on a 300 MHz instrument Therefore, the tion and relaxation phenomena continue to occur simultaneously in NMR spectroscopy, leaving only a minor population difference (Boltzmann ex-cess) in the lower energy state which is detected

Chmurny, G.N., Hault, D.I., 1990 The ancient and honourable art of shimming Concepts Magn Reson 2 (3), 131–149

Daugaard, P., Jakobsen, H.J., Garber, A.R., Ellis, P.D., 1981 A simple method for NMR probe ing and some consequences of improper probe tuning J Magn Reson 44 (1), 224–227

tun-Haase, J., Kozlov, M., Mueller, K.-H., Siegel, H., Buechner, B., Eschrig, H., Webb, A.G., 2005 NMR in pulsed high magnetic fields at 1.3 GHz J Magn Magn Mater 290–291 (Pt 1), 438–441

Halse, M.E., Coy, A., Dykstra, R., Eccles, C.D., Hunter, M.W., Callaghan, P.T., 2009 sional earth’s field NMR In: Codd, S.L., Seymour, J.D (Eds.), Magnetic Resonance Micros- copy, WILEY-VCH Verlag GmbH&Co KGaA, Weinheim, Germany, pp 15–29

Multidimen-Harris, R.K., 1989 Nuclear Magnetic Resonance Spectroscopy Longman Scientific & Technical, Essex, England, p 5

Katz, I., Shtirberg, L., Shakour, G., Blank, A., 2012 Earth field NMR with chemical shift spectral resolution: theory and proof of concept J Magn Reson 219, 13–24

Kovacs, H., Moskau, D., Spraul, M., 2005 Cryogenically cooled probes: a leap in NMR ogy Prog Nucl Magn Reson Spectrosc 46, 131–155

technol-Liao, S.-H., Chen, M.-J., Yang, H.-C., Lee, S.-Y., Chen, H.-H., Horng, H.-E., Yang, S.-Y., 2010 A

study of J-coupling spectroscopy using the earth’s field nuclear magnetic resonance inside a

laboratory Rev Sci Instrum 81, 10410-1–104104-6

Luciano, M., 1979 Sensitivity enhanced detection of weak nuclei using heteronuclear multiple quantum coherence J Am Chem Soc 101 (16), 4481–4484

Melton, B.F., Pollak, V.L., 1971 Instrumentation for the earth’s field NMR technique Rev Sci Instrum 42 (6), 769–773

Pearson, G.A., 1991 Shimming an NMR magnet 17-Dec-1991, http://nmr.chem.uiowa.edu/ manuals/Shimming-GAP-NMR-magnet.pdf

Poeschko, M.T., Schlagnitweit, J., Huber, G., Nausner, M., Hornicakova, M., Desvaux, H., ler, N., 2014 On the tuning of high resolution NMR probes Chem Phys Chem 15 (16), 3639–3645

Muel-Ross, J.G., Holland, D.J., Blake, A., Sederman, A.J., Gladden, L.F., 2012 Extending the use of earth’s field NMR using Bayesian methodology Application of particle sizing J Magn Reson

Solving Problems with NMR Spectroscopy http://dx.doi.org/10.1016/B978-0-12-411589-7.00002-4

Copyright © 2016 Elsevier Inc All rights reserved.

As stated earlier, when placed in a magnetic field, the hydrogen nuclei adopt one

of two different orientations, aligned either with or against the applied magnetic

field B0 (Section 1.1.1) There is slight excess of nuclei in the lower energy (a)

orientation, in which the nuclei are aligned with the external field (B0) There

is a bulk or macroscopic magnetization M z0 corresponding to this difference

that points in the direction of the applied field (z-axis, by convention) and that

represents the sum of the magnetizations of the individual spins As long as the

bulk magnetization remains aligned along the z-axis, the precessional motion

of the nuclei, though present, will not become apparent This is the situation

prevailing at the thermal equilibrium

The NMR experiment is aimed at unveiling and measuring this precessional

motion of the nuclei One way to do this is to displace the magnetization from

its position along the z-axis by application of a radiofrequency pulse Once the

magnetization M0 is displaced from its position along the z-axis, it experiences

a force due to the applied magnetic field B0, causing it to “precess” about the

z-axis at a frequency of gB0 radians per second (or gB0/2π Hz) (Fig 2.1), a

Mz0

motion called “Larmor precession.” The aim of the NMR experiment is to sure this motion When the magnetization M0 is bent away from the z-axis, it will have a certain component in the xy-plane; it is this component that is mea-

mea-sured as the NMR signal

For a transition to occur from the lower energy state to the upper energy state, the precessing nuclei must absorb radiofrequency energy This can happen only

if the radiofrequency of the energy being emitted from the oscillator matches actly the precessional frequency of the nuclei Here is a simple analogy: imagine

ex-that you are holding a sandwich (an “energy packet,” if you like) in your right

hand while you are constantly rotating your left hand at a particular angular velocity To pass this sandwich from your right hand to your left hand without stopping the rotation of your left hand, your right hand must also rotate at exactly

the same angular velocity (in-resonance) The transfer of the sandwich (energy) between the two hands can take place only if they rotate synchronously Simi- larly, only when the oscillator frequency exactly matches the nuclear preces-

sional frequency can the nuclei absorb energy and flip-to the higher energy state

They can then relax back to their lower energy state via spin–lattice or spin–spin

relaxations The resulting change in the impedance of the detector coils during the relaxation process is recorded in the form of an NMR signal

The z-component of the magnetization (M z) corresponds to the population difference between the lower and upper energy states Any change in this popu-lation difference − for instance, by nuclear Overhauser enhancement or polar-

ization transfer − will result in a corresponding change in the magnitude of M z,

the NMR signal being strong when the magnitude of M z is large

Problem 2.1

Spin half nuclei (I = ½), such as 1 H, 13 C, 15 N, 19 F, and 13 P adopt one of two

differ-ent oridiffer-entations aligned either with or against the applied magnetic field B0 They are called dipole nuclei Is this also correct for other nuclei, such as 2H (I = 1), 14 N

(I = 1), 17O (I = 5/2), 35Cl (I = 3/2), etc.?

FIGURE 2.1 (a) Bulk magnetization vector, M z ∼, at thermal equilibrium (b) Magnetization

vector M0 after the application of a radiofrequency pulse.

Mz0

Problem 2.2

What is the bulk or macroscopic magnetization in terms of nuclear spins?

2.1.1 Effects of Pulses

A pulse is a burst of radiofrequency energy that may be applied by switching on

the Rf transmitter As long as the pulse is on, a constant force is exerted on the

sample magnetization, causing it to precess about the Rf vector.

The slight Boltzmann excess of nuclei aligned with the external magnetic

field corresponds to a net magnetization pointing toward the +z-axis We can

bend this magnetization in various directions by applying a pulse along one

of the axes (e.g., along the +x-, −x-, +y-, or −y-axis) If a pulse is applied along

the x-axis, a linear field is generated along the y-axis that is equivalent to two

vectors rotating in opposite directions in the xy-plane However, interaction with

the precessing nuclear magnetization occurs only with the vector that rotates

in the same direction and with exactly the same frequency

We can control the extent by which the +z-magnetization is bent by choosing

the duration for which the pulse is applied Thus, the term “90° pulse” actually

refers to the time period for which the pulse has to be applied to bend the

mag-netization by 90° If it takes, say, t ms to bend a pulse by 90°, it would require

half that time to bend the magnetization by 45°, i.e., t/2 ms A 180° pulse,

how-ever, will require double that time, i.e., 2t ms and cause the z-magnetization to

become inverted so that it comes to lie along the −z-axis (Fig 2.2) There will

then be a Boltzmann excess of nuclei in the upper energy state, and the spin

system is said to possess a “negative spin temperature.” A subscript such as x

or y is usually placed after the pulse angle to designate the direction in which

the pulse is applied A “90°x” pulse therefore refers to a pulse applied along the

+x-axis (in the direction +x to –x) that bends the nuclear magnetization by 90°,

while a 40°−y pulse is a pulse applied along the −y-axis (i.e., in the direction −y

to +y) for a duration just enough to bend the nuclear magnetization by 40° from

its previous position

The duration for which the pulse is applied is inversely proportional to the

bandwidth; i.e., if we wish to stimulate nuclei in a large frequency range, then

we must apply a pulse of a short duration Nuclear excitation will, of course,

only occur if the magnitude of the B1 field is large enough to produce the

re-quired tip angle Typically, if the transmitter power is adjusted to 100 W on a

high field instrument, then a 90° pulse width would have a duration of a few

microseconds This would also have a bandwidth of tens of kilohertz over which

the nuclei could be uniformly excited A “soft” pulse is one that has low power

or a long duration (milliseconds rather than microseconds), and such pulses can

be used to excite nuclei selectively in specific regions of the spectrum

For 1H-NMR experiments the pulse width is normally set at about 7–14 s

on the majority of instruments The field width or bandwidth (bw) of excitation

(in Hz) may be obtained from the formula:

90x0 40−y0