Driven Similarity Renormalization Group with a Large Active Space: Applications to Oligoacenes, Zeaxanthin, and Chromium Dimer

We present a new implementation of the driven similarity renormalization group (DSRG) based on a density matrix renormalization group (DMRG) reference. The explicit build of high-order reduced density matrices is avoided by forming matrix-product-state compressed intermediates. This algorithm facilitates the application of DSRG second- and third-order perturbation theories to dodecacene with an active space of 50 electrons in 50 orbitals. This active space appears the largest employed to date within the framework of internally contracted multireference formalism. The DMRG-DSRG approach is applied to several challenging systems, including the singlet-triplet gaps (Δ_ST) of oligoacenes ranging from naphthalene to dodecacene, the vertical excitation energies of zeaxanthin, and the ground-state potential energy curve (PEC) of Cr₂ molecule. Our best estimate for the vertical Δ_ST of dodecacene is 0.22 eV, showing an excellent agreement with that of the linearized adiabatic connection method (0.24 eV). For zeaxanthin, all DSRG schemes suggest the order of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mn>2</mml:mn><mml:mspace></mml:mspace><mml:mmultiscripts><mml:msubsup><mml:mi>A</mml:mi><mml:mi>g</mml:mi><mml:mo>-</mml:mo></mml:msubsup><mml:mprescripts></mml:mprescripts><mml:none></mml:none><mml:mn>1</mml:mn></mml:mmultiscripts><mml:mo><</mml:mo><mml:mn>1</mml:mn><mml:mspace></mml:mspace><mml:mmultiscripts><mml:msubsup><mml:mi>B</mml:mi><mml:mi>u</mml:mi><mml:mo>+</mml:mo></mml:msubsup><mml:mprescripts></mml:mprescripts><mml:none></mml:none><mml:mn>1</mml:mn></mml:mmultiscripts><mml:mo><</mml:mo><mml:mn>1</mml:mn><mml:mspace></mml:mspace><mml:mmultiscripts><mml:msubsup><mml:mi>B</mml:mi><mml:mi>u</mml:mi><mml:mo>-</mml:mo></mml:msubsup><mml:mprescripts></mml:mprescripts><mml:none></mml:none><mml:mn>1</mml:mn></mml:mmultiscripts></mml:math> for excited states. Both the equilibrium and the shoulder regions of the Cr₂ PEC are reasonably reproduced by the linearized DSRG with one- and two-body operators.