dipolar_averages/vanVleckCalculator.py is a Python script for calculating the "second moment" of NMR lineshapes for organic molecules in the limiting conditions of no molecular motion or motion that is fast compared to the linewidth.

The script uses the Soprano library, which in itself is built on the Atomic Simulation Environment (ASE). Installing Soprano, e.g. with pip install soprano will automatically install ASE.

tests/AverageUnitTest.py is a test program that confirms that the analytical formula for the orientationally averaged root-mean-square dipolar coupling used in the main script gives the same result as an explicit numerical powder integration. It is supporting information only.

It's best to install the package in a virtual environment, e.g. using virtualenv or conda. Instructions for installing and using virtualenv can be found here.

Once you have a virtual environment set up, clone the repository with

git clone https://github.com/CCP-NC/dipolar_averages.git

After obtaining the code, install the dependencies with

pip install .

from the top-level directory (i.e. where this README.md file is).

Alternatively, you can install the package directly from GitHub with

pip install git+https://github.com/CCP-NC/dipolar_averages.git

This will install the dipolar_averages package, which contains the vanVleckCalculator script. It will add this script to the path, so it can be run from anywhere. You can check that it is installed correctly by running:

vanVleckCalculator --help

and you should see the usage information.

Rotation axes are expressed in terms of site labels, so it is necessary to supply a starting structure containing crystallographic site labels. In practice, this means using a CIF, since read_with_labels searches for CIF-specific data arrays.

It is assumed that the structure is of a three-dimensional molecular crystal. The lattice parameters and space group information are used to determine the atomic coordinates of molecules within a specified radius of the "origin" molecule.

The initial "use case" was motion in plastic crystals, where there is one molecule type which share the same dynamic process, with no significant correlation between the motion of different molecules. The code has recently been extended to improve support for systems with more than one molecule in the unit cell (Z' > 1).

Motions are currently limited to rotational diffusion of whole molecules about specified axes. Axis specifications are in terms of site labels within an individual molecule, with four specifications supported:

• Axes passing through a pair of atoms e.g. --axis C1,C2. Such axes must pass through the centre of mass (CoM) within a tolerance, currently 0.1 Å,
• Axes passing through the CoM, parallel to the interatomic vector between two atoms,
• Axes in a plane through the CoM and normal to a given interatomic vector (arbitrary orientation within plane),
• Axes bisecting a pair of atoms through the CoM.

Note that these axis specifications all resolve internally to specify a rotation in terms of a vector providing an origin and direction, i.e. it would be straightforward to extend the code to specify axes in different ways.

Multiple axes (of any type) can be provided. The motions are assumed to be uncorrelated, and since the motions are always fast, the order in which multiple axes are given is not important.

vanVleckCalculator --help will give the command line arguments and usage. A few clarifying points:

• Since H positioning is critical for quantitative results, either use neutron-diffraction structures,
• or DFT-optimised structures, with H positions relaxed.
• The symmetry of a rotation must be specified explictly, e.g. --axis C1,C2:2 denotes a two-fold jump motion about a vector between C1 and C2. No check is made against the symmetry of the molecule, so specifying a two-fold jump along an axis with 3-fold symmetry will not generate a warning!
• If an axis involves atoms with the same label, it is sufficient to give the label once, e.g. --CoMaxis C3:3 denotes a 3-fold rotation about an axis passing through both C3 atoms in a molecule. For this to work, the molecule must have exactly two atoms of type C3.
• The perpCoMaxis specification should only be used for truely "pseudo" axes, since the orientation of the axis is undefined in terms of individual atoms. Prefer the bisectorCoMaxis option if possible, for example, for C2 axes that are perpendicular to the principal symmetry axis.
• Uniquely the bisectorCoMaxis specification permits atom specifications that return more than two atoms. In this case, a pair of atoms that are closest together are identified and the bisector found by averaging these atomic positions. A warning is given if two equivalent short distances are not found; it is assumed that the set of atoms are related by symmetry, e.g. a C3 axis, and so a given atom should be equidistant to two others in the "ring".
• The calculation time will increase rapidly (roughly as the cube) with the radius parameter. Depending on the degree of convergence sought, there is little value in exceeding a radius of 20 Å. Note that a radius of 0 can be used to effetively calculate second moments on isolated molecules.
• The static (non-dynamic) limit is calculated when no axes are given.

The Examples directory contains DFT-optimised structures for diamantane (CSD refcode CONGRS) and triamantane (refcode TRIAMT01), hence

vanVleckCalculator --radius 15 --axis C1:3 Examples/CONGRSrelaxed_geomopt-out.cif

will output

Structure analysed: Z = 4, Z' = 1
Number of molecules for intermolecular interactions: 54
Label Intra-drss/kHz Inter-drss/kHz Total drss/kHz
H1 3.32 12.06 12.51
H9 13.56 8.25 15.87
H33 13.58 8.41 15.97
H57 11.17 8.47 14.02
Intramolecular contribution to mean d_SS: 148.98 kHz^2
Intermolecular contribution to mean d_SS at 15 Å: 77.68 kHz^2
Overall mean d_SS: 226.67 kHz^2 Mean d_RSS 15.06 kHz
Second moment: 102.00 (Intra: 67.04 Inter: 34.96) kHz^2

In other words, the structure contains four molecules of diamantane in the unit cell, one unique molecule. 54 molecules are within 15 Å of the reference molecule. The following table gives the intramolecular and intermolecular contributions to the root-sum-square dipolar coupling at the 4 crystallographically distinct H sites. The final lines give the mean sum-square and root-sum-square couplings, followed by the corresponding second moments (proportional to the mean sum-square-coupling).

The Experimental directory contains Python scripts to aid quantifying second moments from experimental data. See this directory for more information. Note that this directory can be downloaded independently of the rest of the repository. The scripts and examples it contains are not installed by the package installation script.

test/AverageUnitTest.py is a test script to validate the key result that the averaging of motionally averaged dipolar tensors can be carried out analytically.

The code is being made available through GitHub to encourage further development. You are welcome to contribute to development by raising issues or forking your own version to develop and potentially merge back (through a pull request).