Example: NMR Spin-spin coupling constants: C2H2¶
A calculation of NMR nuclear spin-spin coupling constants (NSCCs).
As explained in the ADF manual, the quality of a calculation for spin-spin coupling constants, using the program ‘CPL’, depends largely on the preceding ADF calculation, which produces the Kohn-Sham orbitals and orbital energies, used as a starting point.
One of the quality-determining factors is the chosen basis set. It should be sufficiently flexible near the nucleus. Although the all-electron basis TZ2P is chosen in this example, it is recommendable to add more functions to the basis sets near the nucleus in case of heavy elements. One could start from a ZORA/QZ4P basis for example.
The integration accuracy in the ADF calculation is chosen to be good.
BeckeGrid Quality good end
The NOSYM symmetry currently needs to be specified in ADF to enable the CPL program to work correctly.
The first call to cpl is as follows:
$ADFBIN/cpl <<eor nmrcoupling dso pso sd scf convergence 1e-7 nuclei 1 2 3 4 nuclei 3 4 end endinput eor
The CPL program can run in parallel.
The specification of what needs to be calculated is given in the nmrcoupling block key.
In this first example, the SD subkey is left out, as this would lead to a very strong increase in the required CPU time. The SD subkey is included in the second CPL run. That subkey controls the calculation of the so-called spin-dipole term.
The subkeys dso and pso specify that, respectively, the diamagnetic and paramagnetic orbital terms will be calculated. The often dominant Fermi contact term (FC) is calculated by default and therefore does not have to be specified explicitly.
The scf convergence subkey, in this context, refers to the convergence for the solution of the coupled-perturbed Kohn-sham equations which need to be solved to obtain to spin-spin couplings.
nuclei 1 2 3 4 nuclei 3 4
that one coupled-perturbed Kohn-Sham calculation is performed where nucleus number 1 (according to the ordering in the ADF output) is the perturbing nucleus, and nuclei 2, 3, and 4 are the perturbed nuclei, and another coupled-perturbed Kohn-Sham calculation is performed where nucleus 3 is the perturbing nucleus and nucleus 4 is the perturbed nucleus.
The second CPL run also includes the spin-dipole (SD) term, through the SD subkey.
The output of the CPL program first contains a lot of general information, a summary of the specified input, and then produces the desired numbers:
It prints separately the different contributions (FC, DSO, PSO, SD) if specified in input and sums them up to a total number. Experimental NSCCs between two nuclei A and B are usually reported as J(A,B) in Hertz. From a computational point of view, the so-called reduced NSCCs K(A,B) are more convenient for comparisons. CPL outputs both. In this example, the Fermi-contact term is indeed dominant.
The first part of the output refers to the line
nuclei 1 2 3 4
then the same thing is done for the second similar line where nucleus 3 is the perturbing nucleus.
The output for the second CPL run looks very similar, but now the SD term is added to the Fermi contact term, resulting in much longer execution times.
Scalar relativistic and spin-orbit calculations
The CPL program also enables calculations using scalar relativistic effects (ZORA) and/or spin-orbit effects.
Schematically, this requires the following changes to the input file with respect to a regular spin-orbit calculation and a non-relativistic CPL calculation:
- steep (1s) functions may need to be added to the standard basis sets.
- the full-potential option for ZORA is needed in the create runs and all further runs: relativistic zora scalar full
- the molecular ADF calculation should contain the line relativistic zora full spinorbit
- the CPL input is unmodified with respect to the example given here. Please check the ADF manual for details on relativistic input options.