Indirect nuclear spin–spin couplings with third-order contributions added to the SOPPA method

In this article, a modification of the second-order polarization propagator approximation (SOPPA) method is introduced and illustrated for the calculation of the indirect nuclear spin–spin couplings. The standard SOPPA method, although cheaper in terms of computational cost, offers less accurate results than the ones obtained with coupled cluster methods. A new method, named SOPPA+A3-3, was therefore developed by adding the terms of the third-order A matrix that rely on the second-order double amplitudes. The performance of this third-order contribution was studied using the coupled cluster singles and doubles method as a reference, calculating the spin–spin couplings of molecules of diverse sizes and compositions, and comparing them to the SOPPA method. The results show that inclusion of this third-order contribution gives more accurate results than the standard SOPPA method with a level of accuracy close to that of the coupled cluster method with only a small increase in the computational cost of the response calculation that dominates the computational cost for small- to medium-sized molecules. The implementation of the first contributions to the third-order polarization propagator approximation in the Dalton program, thus, already shows a significant change in these molecular properties over those obtained with the standard SOPPA method.