Multireference perturbation theory (MRPT) geometry optimisations with scalar-relativistic effects: effective core potential (ECP) and spin-free X2C Hamiltonian.

In quantum chemistry calculations, molecular systems containing heavy elements require additional considerations compared with molecules comprising only light elements. In particular, accurate descriptions of both relativistic effects and static correlation are essential to obtain reliable wave functions and energies. Such calculations are computationally demanding due to the high cost of methods that properly incorporate relativistic effects and static correlation. This computational cost becomes even steeper when geometry optimisations or dynamical simulations are undertaken, as nuclear derivatives must be evaluated repeatedly. In this work, we combine the analytical gradients for the effective core potential (ECP), implemented in the LIBECPINT library, with the spin-free one-electron exact two-component (X2C) approach, implemented in our in-house version of BAGEL, for density-fitted MRPT2 methods. This enables scalar-relativistic geometry optimisations of molecules containing heavy elements, for both ground and electronically excited states, at a cost comparable to conventional (non-relativistic) MRPT2 calculations. We demonstrate the utility of the current computer program for optimising the geometries of Pd(IV) terminal oxo complexes and Fe(II) porphyrin.