Weblab can be employed in principle for any type of interaction which can be described by a symmetric second rank tensor. In solid state NMR this is typically either chemical shielding, dipolar or quadrupolar coupling. Though any of these interactions is allowed, Weblab presents a menu depending on your choice for the spin, which is suitable for either shielding (I=1/2) or quadrupolar coupling (I=1).

There are several conventions in use for the description of tensor values. First order quadrupolar and dipolar couplings have symmetric traceless tensors, and thus can be characterized by only two components. In this case Weblab is using the so-called Haeberlen Notation. For the specification of chemical shielding, Weblab is following IUPAC conventions(a) and offers three choices, Chemical Shift Scale, Haeberlen Notation or Herzfeld-Berger Notation. The latter two are available in expert mode only.

Haeberlen Notation
When using the Haeberlen notation(b), Weblab calculates the two quantities δ and η, which are related to the principal values RXX,RYY,RZZ of the interaction tensor R by




together with the condition
which ensures that the Y-component is always between X and Z.

For dipolar and quadrupolar coupling the tensor is traceless, hence Riso = 0. Parameter η measures the asymmetry in the spectrum and thus is called asymmetry parameter. Parameter δ reflects the strength of the coupling and is a measure for the anisotropy of the interaction. Weblab is using the name coupling instead of anisotropy because the latter is reserved for the quantity Δ = 3/2 δ.

Chemical Shift Scale
For I=1/2 nuclei it is more common to enter the interaction values in terms of chemical shift instead of shielding σ.The chemical shift is defined following IUAPC conventions as

Since nmr frequencies are in in the order of MHz and their difference is in Hz, chemical shift values are in the order of 10-6 or ppm. In solids shielding is described by a tensor and so is chemical shift. According to IUPAC the shift tensor principal values are labled δ11, δ22, δ33 with the relationship

Herzfeld-Berger Notation
Another common possibility for specifying chemical shift tensor components is the Maryland or Herzfeld-Berger notation. Here one uses the quantities Ω (span) and κ (skew) as follows:




Ω is always positive and is the maximum width of the powder spectrum while skew κ measures amount and orientation of the asymmetry. It is between -1 and +1 and its sign gives the position of δ22 relative to δiso, the centre of gravity of the spectrum.

NMR Freqencies
The NMR frequencies in first order are given by the component of R along the external magnetic field and can be expressed using Haeberlen notation in terms of δ and η together with the polar angles Θ and Φ as


Averaging over all orientations yields the typical powder spectrum for I=1/2 with a total splitting of 3/2 δ or a Pake spectrum in case of I=1 where the total splitting is given by 2δ as shown below

If you choose I=1, Weblab is requesting the two values δ0 and η0, suitable for quadrupolar coupling where Riso=0, to characterize the interaction tensor without motion. According to its definition η0 is limited to values between 0 and 1 while δ0 can have any value. For deuterons in an aliphatic CH-bond one typically has δ0 ≈ 128 kHz and η0=0.

The option to choose between different tensor notations is available only for I=1/2 in expert mode.

Please note that Weblab assumes, that the greatest principal value RZZ-Riso, defined as above, is lying on the cone, and that the cone angle θ corresponds to the polar angle between the Z principal axis and the cone axis. When using the chemcial shift scale this can be either δ11 or δ33 depending on whether δ22 > δiso> (κ > 0) or vice versa.

a) Harris,R.K. et al., IUPAC Recommendations 2001, Pure Appl.Chem.73,1795.
b) Haeberlen, U. (1976), High Resolution NMR in Solids, Adv. Magn. Reson. Suppl. 1, Academic Press, San Diego