Chemical shift

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.

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.

Operating frequency

The operating frequency ω of a magnet is calculated from the Larmor equation

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

where <math>B_0</math> is the actual strength of the magnet in units like teslas or gauss, and γ is the gyromagnetic ratio of the nucleus being tested which is in turn calculated from its magnetic moment μ and spin number I with the nuclear magneton μ_N and the Planck constant h:

<math>\gamma = \frac{\mu\,\mu_N}{hI}\,</math>

Thus, the proton operating frequency for a 7 T magnet is calculated as:

<math>\omega_{0} = \frac{2.79*5.050\,10^{-27}\,J/T}{6.62\,10^{-34}\,J\cdot s*1/2}*7\,T*10^{-6}\, = 297 MHz\,</math>

Chemical shift referencing

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

<math>\delta = \frac{\mbox{difference in precession frequency between two nuclei}}{\mbox{operating frequency of the magnet}}</math>

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.

Thus, an NMR signal at 300 Hz from TMS at an applied frequency of 300MHz has a chemical shift of:

<math>\frac{300Hz}{300*10^6Hz}=1*10^{-6}= 1\,ppm \,</math>

Although the frequency depends on the applied field the chemical shift is independent of it. On the other hand the resolution of NMR will increase with applied magnetic field resulting in ever increasing chemical shift changes.

The induced magnetic field

The electrons around a nucleus will circulate in a magnetic field and create a secondary induced magnetic field. This field opposes the applied field as stipulated by Lenz's law and the nucleus is therefore said to be shielded. Trends in chemical shift are explained based on the degree of shielding or deshielding.

Nuclei are found to resonate in a wide range to the left (or more rare to the right) of the internal standard. When a signal is found with a higher chemical shift:

• the applied effective magnetic field is lower, if the resonance frequency is fixed, (as in old traditional CW spectrometers)
• the frequency is higher, when the applied magnetic field is static, (normal case in FT spectrometers)
• the nucleus is more deshielded
• the signal or shift is downfield or at low field or paramagnetic

Conversely a lower chemical shift is called a diamagnetic shift, and is upfield and more shielded.

Factors causing chemical shifts

Important factors influencing chemical shift are electron density, electronegativity of neighboring groups and anisotropic induced magnetic field effects.

Electron density shields a nucleus from the external field. For example in proton NMR the electron-poor tropylium ion has its protons downfield at 9.17 ppm, those of the electron-rich cyclooctatetraenyl anion move upfield to 6.75 ppm and its dianion even more upfield to 5.56 ppm.

A nucleus in the vicinity of an electronegative atom experiences reduced electron density and the nucleus is therefore deshielded. In proton NMR of methyl halides (CH₃X) the chemical shift of the methyl protons increase in the order I > Br > Cl > F from 2.16 ppm to 4.26 ppm reflecting this trend. In carbon NMR the chemical shift of the carbon nuclei increase in the same order from around -10 ppm to 70 ppm. Also when the electronegative atom is removed further away the effect diminishes until it can be observed no longer.

Anisotropic induced magnetic field effects are the result of a local induced magnetic field experienced by a nucleus resulting from circulating electrons that can either be paramagnetic when it is parallel to the applied field or diamagnetic when it is opposed to it. It is observed in alkenes where the double bond is oriented perpendicular to the external field with pi electrons likewise circulating at right angles. The induced magnetic field lines are parallel to the external field at the location of the alkene protons which therefore shift downfield to a 4.5 ppm - 7.5 ppm range. The three-dimensional space where a nucleus experiences diamagnetic shift is called the shielding zone with a cone-like shape aligned with the external field.

Induced magnetic field of alkenes in external magnetic fields, field lines in grey

The protons in aromatic compounds are shifted downfield even further with a signal for benzene at 7.73 ppm as a consequence of a diamagnetic ring current.

Alkyne protons by contrast resonate at high field in a 2-3 ppm range. For alkynes the most effective orientation in the external field in parallel with electrons circulation around the triple bond. In this way the acetylenic protons are located in the cone-shaped shielding zone hence the upfield shift.

Induced magnetic field of alkynes in external magnetic fields, field lines in grey

Magnetic properties of most common nuclei

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	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
Magnetic properties of common nuclei

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

Other chemical shifts

The related Knight shift (first reported in 1949) is observed with pure metals. 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

See also

• Carbon-13 NMR
• MRI
• NMR spectroscopy
• Nuclear magnetic resonance
• Protein NMR
• Proton NMR
• Solid-state NMR
• Zeeman effect

External links

• www.chem.wisc.edu
• BioMagResBank
• wwwchem.csustan.edu
• 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, advanced (see also this link for more background information on spin-spin coupling)
  • 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 (Problems 1–32) and (Problems 33–64)