Applications of the Density Matrix Renormalization Group …
111
The study of the manganese dimer concluded that the enormously increased cost
and effort of obtaining reasonably converged state-averaged DMRG-SCF results
for active spaces considerably larger than the full-valence (19, 16) space of Mn
3d and O 2p orbitals, particularly for active spaces that include virtual orbitals, is
neither justified by the limited numerical improvements nor expected to eventually
produce quantitatively satisfying results. Instead it was suggested that similarly to
the standard use of dynamic correlation methods such as CASPT2 and NEVPT2 on
top of a CASSCF reference, the full-valence DMRG-SCF wavefunction could be
used in subsequent DMRG-NEVPT2 calculations.
Indeed, DMRG-NEVPT2 calculations with the (19, 16) active space produced an
average J value of −85 cm
−1 (converged at M
1500), in very good agreement
with the experimental value. Compared to the DMRG-SCF calculations with the
same active space, a larger number of retained states were required for satisfactory
convergence of the NEVPT2 calculations, because of the requirement to calculate
reduced density matrices for more than two active electrons. Importantly, the variations of J values obtained from different spin-state pairs by DMRG-NEVPT2 was less
than 1 cm
−1 , confirming the prediction of Heisenberg behavior by the state-averaged
DMRG-SCF calculations.
5 General Remarks
5.1 Active Space Composition
A common choice in the case studies mentioned above is that the smallest useful
active space in practice contains the metal d orbitals as well as the valence orbitals of
the bridging ligands. Although the results obtained from DMRG-SCF calculations
with a metal-only active space are typically not numerically or qualitatively useful
in themselves, this does not mean that an active space composed of only metal-based
orbitals is a meaningless choice in principle. In certain types of application, this can
indeed form a well-defined starting point for certain computational approaches, such
as the difference-dedicated configuration interaction approach (DDCI) that attempts
to introduce a posteriori all the important corrections which are by definition absent
from the small reference wavefunction. However, these approaches lack generality
because of their extremely restricted field of application given their enormous cost.
The point of using DMRG is precisely that the severe restrictions on the size of
the active space can be lifted at the reference level, which not simply extends the
applicability of multireference methods to any exchange-coupled transition metal
system but, importantly, allows explicit inclusion of a large part of the required
physics directly into the reference wavefunction. Therefore, we consider the inclusion
of all metal and ligand valence orbitals to be the natural minimal choice in DMRGbased studies of exchange-coupled systems.
111
The study of the manganese dimer concluded that the enormously increased cost
and effort of obtaining reasonably converged state-averaged DMRG-SCF results
for active spaces considerably larger than the full-valence (19, 16) space of Mn
3d and O 2p orbitals, particularly for active spaces that include virtual orbitals, is
neither justified by the limited numerical improvements nor expected to eventually
produce quantitatively satisfying results. Instead it was suggested that similarly to
the standard use of dynamic correlation methods such as CASPT2 and NEVPT2 on
top of a CASSCF reference, the full-valence DMRG-SCF wavefunction could be
used in subsequent DMRG-NEVPT2 calculations.
Indeed, DMRG-NEVPT2 calculations with the (19, 16) active space produced an
average J value of −85 cm
−1 (converged at M
1500), in very good agreement
with the experimental value. Compared to the DMRG-SCF calculations with the
same active space, a larger number of retained states were required for satisfactory
convergence of the NEVPT2 calculations, because of the requirement to calculate
reduced density matrices for more than two active electrons. Importantly, the variations of J values obtained from different spin-state pairs by DMRG-NEVPT2 was less
than 1 cm
−1 , confirming the prediction of Heisenberg behavior by the state-averaged
DMRG-SCF calculations.
5 General Remarks
5.1 Active Space Composition
A common choice in the case studies mentioned above is that the smallest useful
active space in practice contains the metal d orbitals as well as the valence orbitals of
the bridging ligands. Although the results obtained from DMRG-SCF calculations
with a metal-only active space are typically not numerically or qualitatively useful
in themselves, this does not mean that an active space composed of only metal-based
orbitals is a meaningless choice in principle. In certain types of application, this can
indeed form a well-defined starting point for certain computational approaches, such
as the difference-dedicated configuration interaction approach (DDCI) that attempts
to introduce a posteriori all the important corrections which are by definition absent
from the small reference wavefunction. However, these approaches lack generality
because of their extremely restricted field of application given their enormous cost.
The point of using DMRG is precisely that the severe restrictions on the size of
the active space can be lifted at the reference level, which not simply extends the
applicability of multireference methods to any exchange-coupled transition metal
system but, importantly, allows explicit inclusion of a large part of the required
physics directly into the reference wavefunction. Therefore, we consider the inclusion
of all metal and ligand valence orbitals to be the natural minimal choice in DMRGbased studies of exchange-coupled systems.