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:
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?
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.
