Chemical shift

In nuclear magnetic resonance (NMR) spectroscopy, the chemical shift is the resonant frequency of an atomic nucleus relative to a standard in a magnetic field. Often the position and number of chemical shifts are diagnostic of the structure of a molecule. Chemical shifts are also used to describe signals in other forms of spectroscopy such as photoemission spectroscopy.

Some atomic nuclei possess a magnetic moment (nuclear spin), which gives rise to different energy levels and resonance frequencies in a magnetic field. The total magnetic field experienced by a nucleus includes local magnetic fields induced by currents of electrons in the molecular orbitals (electrons have a magnetic moment themselves). The electron distribution of the same type of nucleus (e.g. ) usually varies according to the local geometry (binding partners, bond lengths, angles between bonds, and so on), and with it the local magnetic field at each nucleus. This is reflected in the spin energy levels (and resonance frequencies). The variations of nuclear magnetic resonance frequencies of the same kind of nucleus, due to variations in the electron distribution, is called the chemical shift. The size of the chemical shift is given with respect to a reference frequency or reference sample (see also chemical shift referencing), usually a molecule with a barely distorted electron distribution.

Operating frequency

The operating (or Larmor) frequency <math>\omega_{0}</math> of a magnet (usually quoted as absolute value in MHz) is calculated from the Larmor equation

: <math>\omega_{0} = -\gamma B_0,</math>

where is the induction of the magnet (SI units of tesla), and <math>\gamma</math> is the magnetogyric ratio of the nucleus an empirically measured fundamental constant determined by the details of the structure of each nucleus. For example, the proton operating frequency for a 1-tesla magnet is calculated as

: <math>\omega_0 = -4.258 \cdot 10^7~\frac{\text{Hz{\text{T \times 1.000~\text{T} = -42.58~\text{MHz}.</math>

MRI scanners are often referred to by their field strengths (e.g. "a 7&nbsp;T scanner"), whereas NMR spectrometers are commonly referred to by the corresponding proton Larmor frequency (e.g. "a 300&nbsp;MHz spectrometer", which has a of 7&nbsp;T). While chemical shift is referenced in order that the units are equivalent across different field strengths, the actual frequency separation in hertz scales with field strength (). As a result, the difference of chemical shift between two signals (ppm) represents a larger number of hertz on machines that have larger , and therefore the signals are less likely to be overlapping in the resulting spectrum. This increased resolution is a significant advantage for analysis. Higher-field machines are also favoured on account of having intrinsically higher signal arising from the Boltzmann distribution of magnetic spin states.

Chemical shift referencing

Chemical shift is usually expressed in parts per million (ppm) by frequency, because it is calculated from

: <math>\delta = \frac{\nu_\text{sample} - \nu_\text{ref{\nu_\text{ref,</math>

where is the absolute resonance frequency of the sample, and is the absolute resonance frequency of a standard reference compound, measured in the same applied magnetic field . Since the numerator is usually expressed in hertz, and the denominator in megahertz, is expressed in&nbsp;ppm.

The detected frequencies (in Hz) for ¹H, ¹³C, and ²⁹Si nuclei are usually referenced against TMS (tetramethylsilane), TSP (trimethylsilylpropanoic acid), or DSS, which by the definition above have a chemical shift of zero if chosen as the reference. Other standard materials are used for setting the chemical shift for other nuclei.

Thus an NMR signal observed at a frequency 300&nbsp;Hz higher than the signal from TMS, where the TMS resonance frequency is 300&nbsp;MHz, has a chemical shift of

: <math>\frac{300~\text{Hz{300 \times 10^6~\text{Hz = 1 \times 10^{-6} = 1~\text{ppm}.</math>

Although the absolute resonance frequency depends on the applied magnetic field, the chemical shift is independent of external magnetic field strength. On the other hand, the resolution of NMR will increase with applied magnetic field.

Tau scale

In early proton NMR publications, the scale was also used, defined as = 10 ppm - _TMS. It fell out of use around 1970.

Referencing methods

Practically speaking, diverse methods may be used to reference chemical shifts in an NMR experiment, which can be subdivided into indirect and direct referencing methods. If substances other than the solvent itself are used for internal referencing, the sample has to be combined with the reference compound, which may affect the chemical shifts.

1. External referencing, involving sample and reference contained separately in coaxial cylindrical tubes. If this method is used without field/frequency locking, shimming procedures between the sample and the reference need to be avoided as they change the applied magnetic field (and thereby influence the chemical shift). These may be negated by inclusion of calibrated reference compounds.

|-

!Isotope

! Occurrence<br> in nature<br> (%)

! Spin number

! Magnetic moment <br>()

! Electric quadrupole moment<br> (&nbsp;×&nbsp;10⁻²⁴&nbsp;cm²)

! Operating frequency at 7&nbsp;T<br> (MHz)

! Relative sensitivity

|-

|¹H

|99.984

|

|2.79628

|0

|300.13

|1

|-

|²H

|0.016

|1

|0.85739

|0.0028

|46.07

|0.0964

|-

|¹⁰B

|18.8

|3

|1.8005

|0.074

|32.25

|0.0199

|-

|¹¹B

|81.2

|

|2.6880

|0.026

|96.29

|0.165

|-

|¹²C

|98.9

|0

|0

|0

|0

|0

|-

|¹³C

|1.1

|

|0.70220

|0

|75.47

|0.0159

|-

|¹⁴N

|99.64

|1

|0.40358

|0.071

|21.68

|0.00101

|-

|¹⁵N

|0.37

|

|−0.28304

|0

|30.41

|0.00104

|-

|¹⁶O

|99.76

|0

|0

|0

|0

|0

|-

|¹⁷O

|0.0317

|

|−1.8930

|−0.0040

|40.69

|0.0291

|-

|¹⁹F

|100

|

|2.6273

|0

|282.40

|0.834

|-

|²⁸Si

|92.28

|0

|0

|0

|0

|0

|-

|²⁹Si

|4.70

|

|−0.5548

|0

|59.63

|0.0785

|-

|³¹P

|100

|

|1.1205

|0

|121.49

|0.0664

|-

|³⁵Cl

|75.4

|

|0.92091

|−0.079

|29.41

|0.0047

|-

|³⁷Cl

|24.6

|

|0.68330

|−0.062

|24.48

|0.0027

|}

¹H, ¹³C, ¹⁵N, ¹⁹F and ³¹P are the five nuclei that have the greatest importance in NMR experiments:

• ¹H because of high sensitivity and vast occurrence in organic compounds
• ¹³C because of being the key component of all organic compounds despite occurring at a low abundance (1.1%) compared to the major isotope of carbon ¹²C, which has a spin of 0 and therefore is NMR-inactive.
• ¹⁵N because of being a key component of important biomolecules such as proteins and DNA
• ¹⁹F because of high relative sensitivity
• ³¹P because of frequent occurrence in organic compounds and moderate relative sensitivity

Chemical shift manipulation

In general, the associated increased signal-to-noise and resolution has driven a move towards increasingly high field strengths. In limited cases, however, lower fields are preferred; examples are for systems in chemical exchange, where the speed of the exchange relative to the NMR experiment can cause additional and confounding linewidth broadening. Similarly, while avoidance of second order coupling is generally preferred, this information can be useful for elucidation of chemical structures. Using refocussing pulses placed between recording of successive points of the free induction decay, in an analogous fashion to the spin echo technique in MRI, the chemical shift evolution can be scaled to provide apparent low-field spectra on a high-field spectrometer. In a similar fashion, it is possible to upscale the effect of J-coupling relative to the chemical shift using pulse sequences that include additional J-coupling evolution periods interspersed with conventional spin evolutions.

Other chemical shifts

The Knight shift (first reported in 1949) and Shoolery's rule are observed with pure metals and methylene groups, respectively. The NMR chemical shift in its present-day meaning first appeared in journals in 1950. Chemical shifts with a different meaning appear in X-ray photoelectron spectroscopy as the shift in atomic core-level energy due to a specific chemical environment. The term is also used in Mössbauer spectroscopy, where similarly to NMR it refers to a shift in peak position due to the local chemical bonding environment. As is the case for NMR the chemical shift reflects the electron density at the atomic nucleus.

See also

• EuFOD, a shift agent
• MRI
• Nuclear magnetic resonance
• Nuclear magnetic resonance spectroscopy of carbohydrates
• Nuclear magnetic resonance spectroscopy of nucleic acids
• Nuclear magnetic resonance spectroscopy of proteins
• Random coil index
• Relaxation (NMR)
• Solid-state NMR
• TRISPHAT, a chiral shift reagent for cations
• Zeeman effect

References

External links

• chem.wisc.edu
• BioMagResBank
• NMR Table
• Proton chemical shifts
• Carbon chemical shifts
• Online tutorials (these generally involve combined use of IR, ¹H NMR, ¹³C NMR and mass spectrometry)
• Problem set 1 (see also this link for more background information on spin-spin coupling)
• Problem set 2

<!-- apparently a dead link **Problem set 3-->

• Problem set 4
• Problem set 5
• Combined solutions to problem set 5 (Problems 1&ndash;32) and (Problems 33&ndash;64)

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