I need to calculate a Dipolar Coupling Constants for some fancy triplet molecule that has been measured by EPR spectroscopy.

My "normal" output from Gaussian gives me the following:

  • Isotropic Fermi Contact Couplings
  • Spin Dipole Couplings
  • Anisotropic Spin Dipole Couplings in Principal Axis System

Am I right that none of these are Dipolar Coupling Constants? And If so ... how can I compute them either directly with the program or by hand through some formula?

  • $\begingroup$ Can you share your actual main line of keywords? $\endgroup$ Mar 30, 2016 at 14:23
  • $\begingroup$ @user1420303 currently nothing special, as those data are automatically printed when an open shell system is calculated. $\endgroup$ Mar 30, 2016 at 14:32
  • $\begingroup$ I am not sure, but I would try adding: NMR Prop(EPR) $\endgroup$ Mar 30, 2016 at 17:54
  • $\begingroup$ This doesn't change the output as far as I can see. $\endgroup$ Mar 31, 2016 at 12:16
  • $\begingroup$ I can not assure that it will give you the info. you need, but it must print a lot more of information. I've tried the NMR command by myself and it really worked for me. $\endgroup$ Mar 31, 2016 at 12:21

1 Answer 1


The output sections you mention are the major components of the electron-nuclear hyperfine interaction. There is also an orbital contribution, but this tends to be small compared to the Fermi contact and spin dipole terms, unless you go down the periodic table.

These are the terms in the effective spin Hamiltonian that contribute to the hyperfine interaction (from Wikipedia):

$$ \begin{align} \hat{H}_{\textrm{hyperfine}} = & 2 g_{I} \mu_{N} \mu_{\mathrm{B}} \frac{\mu_{0}}{4\pi} \frac{1}{L_{z}} \sum_{i}^{N_{\mathrm{elec}}} \frac{\hat{l}_{zi}}{r_{i}^{3}} \mathbf{I} \cdot \mathbf{L} \\ &+ g_{I} \mu_{N} g_{e} \mu_{\mathrm{B}} \frac{\mu_{0}}{4\pi} \frac{1}{S_{z}} \sum_{i}^{N_{\mathrm{elec}}} \frac{\hat{s}_{zi}}{r_{i}^{3}} \left\{ 3(\mathbf{I}\cdot\hat{\mathbf{r}})(\mathbf{S}\cdot\hat{\mathbf{r}}) - \mathbf{I} \cdot \mathbf{S} \right\} \\ &+ \frac{2}{3} g_{I} \mu_{N} g_{e} \mu_{\mathrm{B}} \mu_{0} \frac{1}{S_{z}} \sum_{i}^{N_{\mathrm{elec}}} \hat{s}_{zi} \delta^{3}(\hat{\mathbf{r}}_{i}) \mathbf{I} \cdot \mathbf{S} \end{align} $$

The first term is the orbital contribution due to spin-orbit coupling, the second term is the spin dipole term due to the electrons and nuclei behaving as dipoles in the presence of each other's magnetic fields, and the third term is the Fermi contact term arising from the non-zero probability of the unpaired electron(s) being inside the nucleus.

Isotropic Fermi Contact Couplings are the eigenvalues of the Fermi contact part of the effective spin Hamiltonian. Because of the presence of $\delta^{3}(\hat{\mathbf{r}}_{i})$, there is only one value, hence the "isotropic" descriptor.

Spin Dipole Couplings and Anisotropic Spin Dipole Couplings in Principal Axis System are two different presentations of the spin dipole term. Spin Dipole Couplings shows the eigenvalues of the spin dipole part of the effective spin Hamiltonian (in a.u.). Because this is a symmetric 3x3 tensor, only the 6 unique elements are shown. Diagonalizing the tensor gives the 3 principal values Baa, Bbb, Bcc as the eigenvalues and the vectors from the origin for each principal value as the eigenvectors. These are the values you're interested in, most commonly reported in MHz by the computational/theoretical chemistry community and in Gauss by the spectroscopy community.


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