Nuclear Spin-Spin Coupling Constants from Auxiliary Density Functional Theory

The working equations for the calculation of indirect spin-spin coupling constants (NSSCCs) within the framework of auxiliary density functional theory (ADFT) are presented. The individual contributions to the NSSCC, namely the Fermi-contact, spin-dipole, paramagnetic spin-orbit and diamagnetic spin-orbit terms, are calculated as analytic second-order ADFT energy derivatives. For the calculation of the perturbed density matrix elements, auxiliary density perturbation theory (ADPT) is used. To improve the computational performance, analytic kernel implementations for the local density approximation and the generalized gradient approximation are employed. To validate our new ADPT NSSCC implementation we compare ADFT calculated NSSCC values with results from other theoretical methods and experiments for a series of small molecules. This validation shows that ADPT NSSCCs are of similar quality as their Kohn-Sham counterparts and compare favorable with post Hartree-Fock results. To demonstrate the computational efficiency of our new implementation and its parallel scaling, benchmark calculations of ADPT NSSCCs in amylose chains are presented. These results show that NSSCCs of nanosystems with more than 1000 atoms can be routinely calculated with the here presented approach employing moderate-sized parallel architectures.