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In this work we demonstrate that the heat bath configuration interaction(HCI) and its semistochastic extension can be used to treat relativisticeffects and electron correlation on an equal footing in large active spaces tocalculate the low energy spectrum of several systems including halogens groupatoms (F, Cl, Br, I), coinage atoms (Cu, Au) and the Neptunyl(VI) dioxideradical. This work demonstrates that despite a significant increase in the sizeof the Hilbert space due to spin symmetry breaking by the spin-orbit couplingterms, HCI retains the ability to discard large parts of the low importanceHilbert space to deliver converged absolute and relative energies. Forinstance, by using just over $10^7$ determinants we get converged excitationenergies for Au atom in an active space containing (150o,25e) which has over$10^{30}$ determinants. We also investigate the accuracy of five differenttwo-component relativistic Hamiltonians in which different levels ofapproximations are made in deriving the one-electron and two-electronsHamiltonians, ranging from Breit-Pauli (BP) to various flavors of exacttwo-component (X2C) theory. The relative accuracy of the different Hamiltoniansare compared on systems that range in atomic number from first row atoms toactinides.

One-step treatment of spin-orbit coupling and electron correlation in large active spaces