Double-hybrid density functional theory for g-tensor calculations using gauge including atomic orbitals

An efficient implementation for calculations of the electronic g-tensor at the level of second-order Møller-Plesset perturbation theory (MP2) is presented. The resolution of identity (RI) approximation is applied for the efficient treatment of two-electron integrals, and gauge including atomic orbitals are used to circumvent the gauge problem present in all magnetic property calculations. Furthermore, given that MP2 is an ingredient in double-hybrid density functional theory (DHDFT), the latter is also featured in the implementation. Calculated g-shifts with RI-MP2 and DHDFT using the double-hybrid density functionals B2PLYP and DSD-PBEP86 are compared to experimental data and published data from other methods including coupled cluster singles doubles. Additionally, the computational performance for medium to large size molecular systems was studied using the RIJK and RIJCOSX approximations for the two-electron integral treatment in the formation of Fock and Fock-like matrices necessary for the calculation of analytic second derivatives.