Off-diagonal part shielding tensor not always calculated correctly
Important: the 2004.01 and older versions of the nmr module does not always calculate the off-diagonal part of the shielding tensors correctly. (This bug is fixed in the 2005.01 and later versions.) It means that in many cases the principal axes and principal values of the shielding tensors are calculated incorrectly. In the non-relativistic, ZORA scalar relativistic and ZORA spin-orbit coupled case the isotropic shieldings are calculated correctly. In the Pauli scalar relativistic and Pauli spin-orbit coupled case, the calculation of the isotropic part contains a (small) bug.
The calculation of nmr with the epr module does give correct numbers. This module epr can do non-relativistic and scalar relativistic Pauli calculations of the shielding tensor.
Next an example which shows what can go wrong with the nmr calculation. Here we look at HgCH3Br for two geometries A and B without symmetry, where the geometry of B is the same as geometry A, only translated 4 Angstrom in the x-direction, thus B=A+(4,0,0). In geometry A the nucleus Hg is close to the origin. These calculations should give the same shielding tensors. Results of non-relativistic frozen core calculations are shown, comparing epr and nmr calculations of the shielding tensor for the Hg nucleus and one of the H nuclei.
| principal values shielding | isotropic | |||||
| module | geometry | nucleus | 1 | 2 | 3 | shielding |
| nmr | A | Hg | 5484 | 5509 | 9616 | 6870 |
| nmr | B | Hg | 5321 | 5669 | 9619 | 6870 |
| epr | A | Hg | 5484 | 5510 | 9616 | 6870 |
| epr | B | Hg | 5484 | 5509 | 9616 | 6870 |
| nmr | A | H | 22.9 | 25.1 | 49.2 | 32.4 |
| nmr | B | H | 10.3 | 26.4 | 60.5 | 32.4 |
| epr | A | H | 25.1 | 28.4 | 43.7 | 32.4 |
| epr | B | H | 25.1 | 28.4 | 43.7 | 32.4 |
Conclusion: The calculation of the nmr shielding with the epr module does give the same results for geometry A and B, there is only a small difference due to numerical integration. The calculation of the nmr shielding with the nmr module on the other hand does not give the same principal values for geometry A and B. The isotropic part is calculated correctly. For Hg at geometry A the the results with the nmr module are still correct. However, for Hg at geometry B and H at geometry A and B, the results are incorrect. The errors with the nmr module become larger if the nucleus is further away from the origin. Not shown in this example are the principal axes, but in many cases they are also calculated incorrectly with the nmr module.
