An efficient relativistic density-matrix renormalization group implementation in a matrix-product formulation.

We present an implementation of the relativistic quantum chemical density matrix renormalization group (DMRG) approach based on a matrix-product formalism. Our approach allows us to optimize matrix product state (MPS) wave functions including a variational description of scalar relativistic effects and spin orbit coupling from which we can calculate, for example, first-order electric and magnetic properties in a relativistic framework. While complementing our pilot implementation (Knecht, S. et al. J. Chem. Phys. 2014, 140, 041101), this work exploits all features provided by its underlying nonrelativistic DMRG implementation based on an matrix product state and operator formalism. We illustrate the capabilities of our relativistic DMRG approach by studying the ground-state magnetization, as well as current density of a paramagnetic f(9) dysprosium complex as a function of the active orbital space employed in the MPS wave function optimization.