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1.1 NMR Frequencies and Chemical Shifts
- NMR Spectrum is a plot of intensity of absorption (or emission) on the vertical aixs against frequency on the horizental axis.
- NMR frequencies: 10 to 800 MHz (radiofrequency/RF part), corresponding to from 30 m down to 40 cm in wavelength.
- Frequency (field dependent) --> Chemical Shift Scale (field independent)
1.1.1 Frequency
- : nuclear resonance frequency (in )
- : nuclear gyromagnetic ratio, for a proton ()，
- : the applied magnetic field strength (in )
For a common 400 MHz NMR instrument:
For a 600 MHz NMR instrument:
1.1.2 Chemical Shift Scales
Reference Compound: Tetramethylsilane (TMS) for and
- : Chemical Shift
- : parts per million
Conversion from Shifts to Frequencies:
mean while:
1.1.3 Receiver Reference Frequency
Peaks in spectrum were not measured absolutely but were determined relative to the receiver reference frequency (, rx for reciever), which called offset frequency .
Reason: The measurement coverage is rather small, ~ 4 kHz at 400 MHz
In most cases, chemical shifts can be calculated with sufficient accuracy:
1.2 Linewidths, Lineshape and Integrals
Spectral lines correspond to transitions in atoms, molecules or ions (nuclear spin energy level transition for NMR) and are associated with a specific energy. When this energy is measured using spectroscopic techniques, the spectral lines are not infinitely sharp. Many factors can cause the lines to broaden.
1.2.1 Principal Sources of Broadening
- Lifetime Broadening (Natural Broadening). According to the uncertainty principle, the energy uncertainty and lifetime of excited state are related by : . Therefore, the shorter the lifetime, the larger the energy uncertainty, resulting in a broader spectral peak. This effect produces a line with Lorentzian shape.
- (Thermal) Dopper Broadening. The movement of gas molecules or atoms relative to the observer will cause the frequency of the photons they emit to change (the frequency increases when they are close, and decreases when they are far away). The higher the temperature of the gas and the faster the speed relative to the observer, the more obvious the broadening of the spectral lines emitted by the gas. This effect produces a line with Gaussian shape.
- Pressure Broadening (Collision broadening). Collisions between gas molecules or atoms can shorten the lifetime of excited states, increase energy uncertainty , and cause spectral line broadening. Higher gas density (pressure) or temperature increases the collision probability. Typically, this broadening is Lorentzian.
- Inhomogeneous Broadening. Some particles are in a different local environment than others and therefore emit (or absorb) at a different frequency. This effect usually occurs in solid materials and is particularly noticeable in NMR and EPR. In liquids it is usually offset by motional narrowing. The broadening caused by this effect is Gaussian.
- Proximity Broadening. It is the dominant process for solids and liquids, causing both broadening and changes in line positions, such as the effect of hydrogen bonds on liquid NMR spectra.
- Instrument Factors. The observed line shape is a convolution of the intrinsic line shape with the instrument transfer function.
These effects can act individually or in combination. The combined lineshape is the convolution of the individual lineshapes. For example, the combination of the Doppler effect and the pressure effect produces the Voigt lineshape.
1.2.2 Lineshape and Integrals
- Lorentzian Type
The NMR spectrum derives from the free induction decay (FID) process, which approximates an exponential decay. The Fourier transform of this exponential decay results in a Lorentz function in the frequency domain, making the line shape a Lorentzion.
- Gaussian Type
centered, width for FWHM
- Voigtian Type
Convolution of Gaussian and Lorentzian