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We use the recently-developed Heat-bath Configuration Interaction (HCI)algorithm as an efficient active-space solver to perform multi-configurationself-consistent field calculations (HCISCF) with large active spaces. We give adetailed derivation of the theory and show that difficulties associated withnon-variationality of the HCI procedure can be overcome by making use of theLagrangian formulation to calculate the HCI relaxed two body reduced densitymatrix. HCISCF is then used to study the electronic structure of butadiene,pentacene, and Fe-porphyrin. One of the most striking results of our work isthat the converged active space orbitals obtained from HCISCF are relativelyinsensitive to the accuracy of the HCI calculation. This allows us to obtainnearly converged CASSCF energies with an estimated error of less than 1 mHausing the orbitals obtained from the HCISCF procedure in which the integraltransformation is the dominant cost. For example, an HCISCF calculation onFe-Porphyrin model complex with an active space of (44e, 44o) took only 412seconds per iteration on a single node containing 28 cores, out of which 185seconds were spent in the HCI calculation and the remaining 227 seconds weremainly used for integral transformation. Finally, we also show thatactive-space orbitals can be optimized using HCISCF to substantially speed upthe convergence of the HCI energy to the Full CI limit because HCI is notinvariant to unitary transformations within the active space.

Cheap and near exact CASSCF with large active spaces