X2C-inspired approximation of the Dirac coupling operator in a multiwavelet basis

We present a method to obtain the proven exact 2-component (X2C) method, normally applied to Gaussian-type fixed Hilbert bases, in an adaptative non-uniform grid basis of the Hilbert space, namely Multiwavelets. The X2C method manages to block-diagonalise the Dirac Hamiltonian restricted to the subspace of the basis, in an energy-independent manner. The method takes inspiration from the success of the atomic mean-field X2C method on the Gaussian bases to represent the coupling operator as a projector onto the small components of the eigenstates of the constituent atoms of the system.