Requesting NMR properties

NMR calculations can generate the shielding tensor and/or electric field gradients for all of the atoms in the selected system. NMR properties are very sensitive to atomic positions, which makes NMR such a useful experimental tool for structure analysis. This means that it is highly recommended to perform a geometry optimization run before the NMR calculation. If the structure of a crystal or molecule under investigation is obtained from an experimental study, it is advisable to optimize positions of hydrogen atoms first of all. If the forces on heavy atoms as reported by CASTEP are high (in excess of 1 eV/Å), complete structure optimization is recommended.

A detailed review of the CASTEP NMR formalism and numerous examples of practical applications are discussed in Bonhomme et al. (2012).

NMR in CASTEP is part of the separately licensed module NMR CASTEP. NMR calculations can only be performed if you have purchased this module.

Chemical shielding tensor

The chemical shielding tensor, σ(r), is defined as the ratio between an external applied magnetic field, B, and the non-uniform induced magnetic field, B_in(r):

The isotropic shielding, σ_iso, is given by one third of the trace of σ(r). From the symmetric component of the shielding tensor, the chemical shielding anisotropy, σ_aniso and the asymmetry parameter, η, can be defined in terms of the principal components of the shielding tensor:

and:

where:

For values of σ_aniso close to zero the asymmetry parameter will be ill-defined.

Electric field gradient

The interaction of a quadrupolar nuclei with an external magnetic field can be characterized by the quadrupolar coupling constant, C_Q, and the asymmetry parameter, η_Q. If the principal components of the traceless electric field gradient tensor are labeled, V_xx, V_yy, and V_zz such that:

then:

where Q is the nuclear electric quadrupole moment, and:

For very small values of V_zz the asymmetry parameter will be ill-defined.

The value of the quadrupolar moment depends on the actual isotope; CASTEP makes a suggestion based on the most typical isotope used in solid state NMR experiments. The value of Q affects only the quadrupolar coupling constant, C_Q, calculated and printed out by CASTEP. If you find that the wrong value of Q was used you can rescale the generatedC_Q constant using a different Q value.

The list of default values is based on the compilation by Pyykkö (2008). CASTEP versions prior to the 5.0 release used an older compilation by Harris (1996), so some results for quadrupolar coupling constants may have changed in later versions.

J-couplings

NMR J-coupling or nuclear spin-spin coupling is an indirect interaction of the nuclear magnetic moments mediated by the bonding electrons. It is manifested as the fine structure in NMR spectra, providing a direct measure of bond strength and a map of the connectivities of the system.

Induced magnetization density and current density are expected to be short-ranged. This forms the basis of using J-coupling as a tool for probing the strength of interatomic bonds. However, in a periodic calculation the perturbing nucleus can be viewed as similar to a defect in a defect calculation. Hence, sometimes it might be necessary to construct a supercell which is large enough to inhibit the interaction between the periodic defects or perturbations. Convergence with respect to the cell size should represent an important test in establishing accuracy of J-coupling calculations in either periodic systems or in molecule in a box calculations.

J-coupling can be calculated only for non-magnetic systems. J-coupling calculations are supported only for systems with P1 symmetry. If your crystal has symmetry other than P1, you will be prompted to convert the crystal symmetry to P1 before you can continue.

To calculate NMR properties

1. Choose Modules | CASTEP | Calculation from the menu bar.
2. Choose the Electronic tab on the CASTEP Calculation dialog and select On the fly from the Pseudopotentials dropdown list.
3. On the Properties tab, check the NMR option on the list of properties.
4. Select the properties you wish to determine:
   • Shielding
   • EFG
   • J-coupling
   • G-tensor
5. Choose the method you wish to use to determine the NMR properties from the System type dropdown list (Crystal, Molecule, or Auto). The Molecule option refers to the supercell description of isolated molecules.
6. If J-coupling is selected, then there are some requirements:
   • At least one atom in the system must be selected, J-couplings will be calculated between the selected atom(s) and all other atoms in the system
   • On-the-fly-generated pseudopotentials must be used
   • The Relativistic treatment of the on-the-fly-generated pseudopotentials (on the Electronic tab of the CASTEP Calculation dialog) must be set to either Schroedinger for non-relativistic treatment or ZORA for scalar-relativistic effects to be taken into account.

NMR parameters will be calculated only for the elements for which the on-the-fly-generated pseudopotentials are chosen.

It is not recommended to use PW91 exchange-correlation functional when requesting NMR properties. PW91 functional may result in sharp real-space features of on-the-fly-generated pseudopotentials; PBE, RPBE, WC, BLYP, or PBESOL are better options when a GGA functional is required.

EPR G-tensor

Electron Spin Resonance (EPR - also known as Electron Paramagnetic Resonance) is a powerful experimental probe of the structure of defects in solids. EPR spectra of spin ½ centers are made up of two contributions:

• the hyperfine parameters
• the g-tensor

The g-tensor arises from the interaction of the electronic spin with external magnetic field. This term plays a somewhat similar role to the shielding in NMR; induced electronic currents in the sample modify the g tensor from its vacuum value.

EPR spectrum can be modeled using the following effective Hamiltonian, bilinear in the total electron spin S, and the applied uniform magnetic field or nuclear spins, B and I_I, respectively:

where:
atomic units are used
α is the fine structure constant
the summation I runs over the nuclei

The tensors A_I are the hyperfine parameters, and the tensor g is the EPR g-tensor.

See Also:

Calculating NMR shielding tensors using pseudopotentials
CASTEP Calculation dialog
NMR J couplings