In nuclear magnetic resonance (NMR), the chemical shift describes the dependence of nuclear magnetic energy levels on the electronic environment in a molecule. Chemical shifts are relevant in NMR spectroscopy techniques such proton NMR and carbon-13 NMR.

Introduction

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An atomic nucleus can have 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 (note that electrons have a magnetic moment themselves). The electron distribution of the same type of nucleus (e.g. ¹H, ¹³C, ¹⁵N) usually varies according to the local geometry (binding partners, bond lengths, angles between bonds, ...), 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.

The chemical shift is of great importance for NMR spectroscopy, a technique to explore molecular properties by looking at nuclear magnetic resonance phenomena.

Chemical shift referencing

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

$\backslash delta\; =\; \backslash frac\{\backslash mbox\{difference\; in\; precession\; frequency\; between\; two\; nuclei\}\}\{\backslash mbox\{operating\; frequency\; of\; the\; magnet\}\}$

Since the numerator is usually in hertz, and the denominator in megahertz, delta is expressed in ppm.

The detected frequencies (in Hz) for ¹H, ¹³C, and ²⁹Si nuclei are usually referenced against TMS (tetramethylsilane), which is assigned the chemical shift of zero. Other standard materials are used for setting the chemical shift for other nuclei.

The operating frequency of a magnet is calculate from the Larmor equation: $F\_\backslash mathrm\{larmor\}\; =\; \backslash gamma\; *\; B\_0$, where $B\_0$ is the actual strength of the magnet in units like teslas or gauss, and $\backslash gamma$ is the gyromagnetic ratio of the nucleus being tested.

Magnetic properties of most common nuclei

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¹H and ¹³C aren't the only nuclei susceptible to NMR experiments. A number of different nuclei can also be detected, although the use of such techniques is generally rare due to small relative sensitivities in NMR experiments (compared to ¹H) of the nuclei in question, the other factor for rare use being their slender representation in nature/organic compounds.

Isotope	Occurrence in nature (%)	spin number l	Magnetic moment μ (A·m²)	Electric quadrupole moment (e×10-24 cm2)	Frequency at 7 T (MHz)	Relative sensitivity
1H	99.984	1/2	2.79628		300.13	1
2H	0.016	1	0.85739	2.8 x 10-3	46.07	0.0964
10B	18.8	3	1.8005	7.4 x 10-2	32.25	0.0199
11B	81.2	3/2	2.6880	2.6 x 10-2	96.29	0.165
12C	98.9	0
13C	1.1	1/2	0.70220		75.47	0.0159
14N	99.64	1	0.40358	7.1 x 10-2	21.68	0.00101
15N	0.37	1/2	−0.28304		30.41	0.00104
16O	99.76	0
17O	0.0317	5/2	−1.8930	−4.0 x 10-3	40.69	0.0291
19F	100	1/2	2.6273		282.40	0.834
28Si	92.28	0
29Si	4.70	1/2	−0.55548		59.63	0.0785
31P	100	1/2	1.1205		121.49	0.0664
35Cl	75.4	3/2	0.92091	−7.9 x 10-2	29.41	0.0047
37Cl	24.6	3/2	0.68330	−6.2 x 10-2	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 abudance (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

The fastest way to understanding spectra

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Since the easiest way to obtain knowledge is by practice - that is, solving problems, a couple of external links are shown underneath. The problems are made of different combined spectra (IR, ¹H-NMR, ¹³C-NMR etc.), most of the links contain solutions to problems. The last URL is the best, with the solutions being on two separate pages.

• Problem set 1, advanced
• Problem set 2, moderate
• Problem set 3, for beginners
• Problem set 4, moderate, German language (don't let that scare you away!)
• Problem set 5, the best!
• Combined solutions to problem set 5 (answers 1-32)
• Combined solutions to problem set 5 (answers 33-64)

For Problem set 3, you will need Adobe Reader

In order to solve this problems, you must have some knowledge about IR spectroscopy and mass spectroscopy. Basic principles of spin-spin coupling are also required. You will find all information about the latter on this excellent link.

See also

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• Nuclear magnetic resonance
• NMR spectroscopy
• proton NMR
• carbon-13 NMR
• MRI
• Solid-state NMR
• Larmor equation
• Protein NMR

External links

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• www.chem.wisc.edu
• BioMagResBank
• wwwchem.csustan.edu
• Proton chemical shifts
• Carbon chemical shifts

Nuclear chemistry | Spectroscopy | Nuclear physics | Nuclear magnetic resonance