In this work we develop a variational relativistic density
matrix
renormalization group (DMRG) approach within the exact-two-component
(X2C) framework (X2C-DMRG), using spinor orbitals optimized with the
two-component relativistic complete active space self-consistent field.
We investigate fine-structure splittings of p- (Ga, In, Tl) and d-block
(Sc, Y, La) atoms and excitation energies of monohydride molecules
(GeH, SnH, and TlH) with X2C-DMRG calculations using an all-electron
relativistic Hamiltonian in a Kramers-unrestricted basis. We find
that X2C-DMRG yields accurate 2P and 2D splittings
compared to multireference configuration interaction with singles
and doubles (MRCISD). We also investigated the degree of symmetry
breaking in the atomic multiplets and convergence of electron correlation
in the total energies. Symmetry breaking can be large in some cases
(∼30 meV); however, increasing the number of renormalized block
states m for the DMRG optimization recovers the symmetry
breaking by several orders of magnitude. Encouragingly, we find the
convergence of electron correlation to be close to MRCISDTQ5 quality.
Relativistic X2C-DMRG approaches are important for cases where spin–orbit
coupling is significant and the underlying reference wave function
requires a large determinantal space. We are able to obtain quantitatively
correct fine-structure splittings for systems up to 1019 number of determinants with traditional CI approaches, which are
currently unfeasible to converge for the field.