  The density-matrix renormalization group (DMRG) method, which can deal with a
large active space composed of tens of orbitals, is nowadays widely used as an
efficient addition to traditional complete active space (CAS)-based approaches.
In this paper, we present the DMRG algorithm with a multi-level (ML) control of
the active space based on chemical intuition-based hierarchical orbital
ordering, which is called as ML-DMRG with its self-consistent field variant
ML-DMRG-SCF. Ground and excited state calculations of H2O, N2, indole, and Cr2
with comparisons to DMRG references using fixed number of kept states (M)
illustrate that MLtype DMRG calculations can obtain noticeable efficiency
gains. It is also shown that the orbital re-ordering based on hierarchical
multiple active subspaces may be beneficial for reducing computational time for
not only ML-DMRG calculations but also DMRG ones with fixed M values.
