116
V. Krewald and D. A. Pantazis
A potentially more powerful way of analyzing exchange coupling interactions
would be to use orbital entanglement measures, again in combination with localized
orbital subspaces. To our knowledge, the capabilities of such an approach for investigating and defining the magnetic topology of exchange-coupled transition metal
complexes are still unexplored.
6 Summary and Perspectives
The new capabilities offered by the DMRG algorithm in terms of handling large
active spaces in multiconfigurational SCF calculations of exchange-coupled transition metal systems have already led to pioneering applications in dinuclear complexes. The studies discussed in this chapter demonstrate that the active space limitations of traditional CASSCF approaches can largely be lifted. This promises that a
multireference description is in principle achievable for any transition metal dimer
regardless of the nature and oxidation state or electron configuration of the metal
ions, with active spaces that at the very least are “valence-complete” in terms of
including orbitals of all bridging ligands that could mediate superexchange. However, the existing in-depth studies on dinuclear complexes also highlight a number
of issues that need to be taken into account and some possible problems that need to
be addressed in future applications.
First of all, it is clear that in dealing with magnetic coupling orbital optimization is
essential and CI approaches do not lead to useful results. At the same time, it appears
that state-averaged calculations over all different spin states of the spin ladder are
required to obtain correct relative energies. This can be a major obstacle in extending
DMRG-SCF to systems of higher nuclearity, not necessarily because the active space
would become exceedingly large, but because state-averaged orbital optimization
might not be feasible over hundreds or thousands of roots encompassing all possible spin multiplicities. On the other hand, state-specific orbital optimizations, and
perhaps state-averaged but spin-specific orbital optimizations, run the risk of introducing large errors in the relative energetics that can seriously undermine the quality
of the results. It is not clear at this point how this conundrum can be answered, but it
will certainly be an important target of future studies. Finally, it should be recognized
that DMRG-SCF calculations reported to date have not demonstrably converged in a
systematically defined manner to the experimental exchange coupling constants for
all dinuclear complexes investigated. It is expected that, in general, quantitative predictions will still require treatment of dynamic electron correlation to achieve high
accuracy. The use of DMRG-NEVPT2 has already been demonstrated in the case of
a manganese dimer but other methods need to be explored and evaluated [127–132].
DMRG-based multiconfigurational approaches offer undoubtedly a new basis not
simply for obtaining numerically useful results for exchange-coupled systems but
for analyzing their electronic structure, investigating their magnetic topology, and
V. Krewald and D. A. Pantazis
A potentially more powerful way of analyzing exchange coupling interactions
would be to use orbital entanglement measures, again in combination with localized
orbital subspaces. To our knowledge, the capabilities of such an approach for investigating and defining the magnetic topology of exchange-coupled transition metal
complexes are still unexplored.
6 Summary and Perspectives
The new capabilities offered by the DMRG algorithm in terms of handling large
active spaces in multiconfigurational SCF calculations of exchange-coupled transition metal systems have already led to pioneering applications in dinuclear complexes. The studies discussed in this chapter demonstrate that the active space limitations of traditional CASSCF approaches can largely be lifted. This promises that a
multireference description is in principle achievable for any transition metal dimer
regardless of the nature and oxidation state or electron configuration of the metal
ions, with active spaces that at the very least are “valence-complete” in terms of
including orbitals of all bridging ligands that could mediate superexchange. However, the existing in-depth studies on dinuclear complexes also highlight a number
of issues that need to be taken into account and some possible problems that need to
be addressed in future applications.
First of all, it is clear that in dealing with magnetic coupling orbital optimization is
essential and CI approaches do not lead to useful results. At the same time, it appears
that state-averaged calculations over all different spin states of the spin ladder are
required to obtain correct relative energies. This can be a major obstacle in extending
DMRG-SCF to systems of higher nuclearity, not necessarily because the active space
would become exceedingly large, but because state-averaged orbital optimization
might not be feasible over hundreds or thousands of roots encompassing all possible spin multiplicities. On the other hand, state-specific orbital optimizations, and
perhaps state-averaged but spin-specific orbital optimizations, run the risk of introducing large errors in the relative energetics that can seriously undermine the quality
of the results. It is not clear at this point how this conundrum can be answered, but it
will certainly be an important target of future studies. Finally, it should be recognized
that DMRG-SCF calculations reported to date have not demonstrably converged in a
systematically defined manner to the experimental exchange coupling constants for
all dinuclear complexes investigated. It is expected that, in general, quantitative predictions will still require treatment of dynamic electron correlation to achieve high
accuracy. The use of DMRG-NEVPT2 has already been demonstrated in the case of
a manganese dimer but other methods need to be explored and evaluated [127–132].
DMRG-based multiconfigurational approaches offer undoubtedly a new basis not
simply for obtaining numerically useful results for exchange-coupled systems but
for analyzing their electronic structure, investigating their magnetic topology, and