106
V. Krewald and D. A. Pantazis
studies appears to be the method of orbital optimization: Harris et al. reported results
from state-specific calculations, whereas Spivak et al. used state-averaged orbitals,
i.e., a common set of orbitals for all spin states arising from the magnetic coupling
of the two ions. Among other methodological points, the study of the Mn dimer by
Roemelt et al. [23] to be discussed in the following investigated this issue explicitly,
strongly suggesting that the use of state-averaged orbital optimization is necessary to
avoid spurious and often unphysical deviations from the regular spacing of magnetic
levels.
4.2 Mn 2 Bis-µ-Oxo/µ-Acetato Complex
Another example of a detailed investigation of DMRG-based approaches comes
from Roemelt et al. [23], who presented an in-depth study of a mixed-valence bisμ-oxo/μ-acetato-bridged Mn(III/IV) dimer (Fig. 5). This complex was synthesized
and characterized by Bossek et al. [119], and features one 1, 4, 7-trimethyl-1, 4, 7triazacyclononane, and two additional acetates as terminal ligands. Owing to the combination of mixed-valence and asymmetric ligation, the Mn ions adopt distinct coordination environments. The Mn(III) site features a strong axial pseudo-Jahn–Teller
elongation, a hallmark of occupation of the σ-antibonding orbital of d(z
2 ) parentage,
that leads to an approximately square–pyramidal coordination geometry. This type
of system is of particular interest in inorganic and bioinorganic chemistry because
the high-valent nature of the Mn ions, the chemical nature of the ligands and the
bridging topology are of direct relevance to manganese systems encountered widely
in molecular magnetism and bioinorganic catalysis [108, 120, 121]. A prominent
example in the latter case is the oxo/carboxylato-bridged Mn 4 CaO 5 cluster of the
oxygen-evolving complex of photosystem II, the site of water oxidation in biological
photosynthesis [112, 122].
The two ions have local high-spin configurations, d
4 for Mn(III) and d
3 for Mn(IV),
with corresponding local spins S A 2 and S B 3/2. These couple to produce a ladder
of four spin states with total spin S 7/2, 5/2, 3/2, and 1/2. The complex exhibits
antiferromagnetic coupling, therefore the spin doublet is the ground state. Magnetic
susceptibility measurements led to a fitted value for the exchange coupling constant
of J −90.0 cm
−1 . Assuming the ideal case of an isotropic bilinear term in the
Heisenberg Hamiltonian, the energy splittings for the spin states correspond to the
Landé pattern, i.e., the S 3/2 state is 3J higher than the S 1/2 ground state, the
S 5/2 state is 5J higher than the S 3/2 state, and the ferromagnetic S 7/2 state
is 7J higher than the S 5/2 state, yielding a total span of 15J for the spin ladder.
The minimal active orbital space consists of the metal 3d orbitals, i.e., an active
space of 7 electrons in 10 orbitals, (7, 10). Regardless of the origin of the starting orbitals or of the method used in producing localized input orbitals (e.g.,
Pipek–Mezey or Foster–Boys), a simple CASCI treatment was reported to lead
always to strong ferromagnetic coupling (S 7/2 ground state) with an exchange
coupling constant J of almost +180 cm
−1 , in profound qualitative disagreement
V. Krewald and D. A. Pantazis
studies appears to be the method of orbital optimization: Harris et al. reported results
from state-specific calculations, whereas Spivak et al. used state-averaged orbitals,
i.e., a common set of orbitals for all spin states arising from the magnetic coupling
of the two ions. Among other methodological points, the study of the Mn dimer by
Roemelt et al. [23] to be discussed in the following investigated this issue explicitly,
strongly suggesting that the use of state-averaged orbital optimization is necessary to
avoid spurious and often unphysical deviations from the regular spacing of magnetic
levels.
4.2 Mn 2 Bis-µ-Oxo/µ-Acetato Complex
Another example of a detailed investigation of DMRG-based approaches comes
from Roemelt et al. [23], who presented an in-depth study of a mixed-valence bisμ-oxo/μ-acetato-bridged Mn(III/IV) dimer (Fig. 5). This complex was synthesized
and characterized by Bossek et al. [119], and features one 1, 4, 7-trimethyl-1, 4, 7triazacyclononane, and two additional acetates as terminal ligands. Owing to the combination of mixed-valence and asymmetric ligation, the Mn ions adopt distinct coordination environments. The Mn(III) site features a strong axial pseudo-Jahn–Teller
elongation, a hallmark of occupation of the σ-antibonding orbital of d(z
2 ) parentage,
that leads to an approximately square–pyramidal coordination geometry. This type
of system is of particular interest in inorganic and bioinorganic chemistry because
the high-valent nature of the Mn ions, the chemical nature of the ligands and the
bridging topology are of direct relevance to manganese systems encountered widely
in molecular magnetism and bioinorganic catalysis [108, 120, 121]. A prominent
example in the latter case is the oxo/carboxylato-bridged Mn 4 CaO 5 cluster of the
oxygen-evolving complex of photosystem II, the site of water oxidation in biological
photosynthesis [112, 122].
The two ions have local high-spin configurations, d
4 for Mn(III) and d
3 for Mn(IV),
with corresponding local spins S A 2 and S B 3/2. These couple to produce a ladder
of four spin states with total spin S 7/2, 5/2, 3/2, and 1/2. The complex exhibits
antiferromagnetic coupling, therefore the spin doublet is the ground state. Magnetic
susceptibility measurements led to a fitted value for the exchange coupling constant
of J −90.0 cm
−1 . Assuming the ideal case of an isotropic bilinear term in the
Heisenberg Hamiltonian, the energy splittings for the spin states correspond to the
Landé pattern, i.e., the S 3/2 state is 3J higher than the S 1/2 ground state, the
S 5/2 state is 5J higher than the S 3/2 state, and the ferromagnetic S 7/2 state
is 7J higher than the S 5/2 state, yielding a total span of 15J for the spin ladder.
The minimal active orbital space consists of the metal 3d orbitals, i.e., an active
space of 7 electrons in 10 orbitals, (7, 10). Regardless of the origin of the starting orbitals or of the method used in producing localized input orbitals (e.g.,
Pipek–Mezey or Foster–Boys), a simple CASCI treatment was reported to lead
always to strong ferromagnetic coupling (S 7/2 ground state) with an exchange
coupling constant J of almost +180 cm
−1 , in profound qualitative disagreement