104
V. Krewald and D. A. Pantazis
spin states, S 0, 1, 2, and 3. The experimentally determined exchange coupling
constant is −225 cm
−1 .
Similar to the iron dimer, a triple-ζ basis set for chromium and oxygen, and a
double-ζ basis set for the peripheral ammonia ligands was chosen. The minimal
active space is a (6, 6) active space containing only the magnetic orbitals. CASSCF
with this active space produces an exchange coupling constant of −52.4 cm
−1 . The
expansion of the active space to include occupied bridge orbitals as well as virtual
orbitals was described in this study as much more challenging. Upon inclusion of
the occupied 2p as well as the virtual 3p oxo-bridge orbitals, the exchange coupling
strength increases to −60 cm
−1 with CASSCF. The authors attempted to include the
empty Cr d orbitals in the active space, but only a (12, 13) CAS could be converged,
which contained an orbital delocalized over the entire core. It had d(z
2 ) character on
both metal centers, and symmetrical nodal planes with a lobe of s-character on the
oxo-bridge. Although still not containing all metal d orbitals, the exchange coupling
constant increases to −92.8 cm
−1 . The authors attributed this improvement to a more
balanced description of the Cr–O σ bonds, achieved by symmetrical mixing of the
orbitals dominated by O p(z) and Cr d(z
2 ) character. From a pure MO theory point
of view, one would expect three orbitals in total to be of importance for the σ bonds:
one dominated by the O p(z) atomic orbital (no nodal plane), and two dominated by
Cr d(z
2 ) character (one and two nodal planes).
Using an active space of (12, 25), containing the magnetic orbitals and their
double shells as well as the oxo-bridge 2p, 3p, and 3d orbitals, a stronger antiferromagnetic coupling can be achieved. With M 512 the exchange coupling constant
J is −166.9 cm
−1 , but increasing M to 1000 results in an exchange coupling constant that is significantly weaker, J −137.9 cm
−1 . Extrapolation of the individual
state energies to zero discarded weight results in an exchange coupling constant of
−123.6 cm
−1 , ca. 100 cm
−1 lower than the experimental value. In terms of possible
charge-transfer excitations with this active space, the MLCT excitations would be
expected to be adequately represented given that all magnetic orbitals and relevant
virtual ligand orbitals are included in the active space. In contrast, LMCT excitations
must be more limited, given that the virtual chromium 3d orbitals and their double
shells are not taken into account, and therefore dynamic correlation is recovered
incompletely compared to other systems.
An active space that contains a larger number of chromium 3d and 4d orbitals is
the (12, 32) active space. All 3d orbitals, the 4d(xy), 4d(xz), 4d(yz), and one 4d(z
2 )
orbital are included. Additionally, the 2p, 3s, 3p, 3d, and 4p orbitals of the central
oxo-bridge are taken into account. With this active space, an exchange coupling
constant of −165.9 cm
−1 is achieved, with M 1000 and a very small basis set (Cr:
double-ζ, O: triple-ζ, N, H: single-ζ). Extrapolation was not possible in this case due
to convergence problems of the M 512 calculation. It was also shown that the basis
set effect in this system is considerable. For the (12, 25) active space, a 11.8 cm
−1
difference results between the double-ζ and triple-ζ basis sets on Cr and O. With
a larger basis set, it might be hoped that an improved exchange coupling constant
could be achieved; however, the available results strongly indicate that this active
V. Krewald and D. A. Pantazis
spin states, S 0, 1, 2, and 3. The experimentally determined exchange coupling
constant is −225 cm
−1 .
Similar to the iron dimer, a triple-ζ basis set for chromium and oxygen, and a
double-ζ basis set for the peripheral ammonia ligands was chosen. The minimal
active space is a (6, 6) active space containing only the magnetic orbitals. CASSCF
with this active space produces an exchange coupling constant of −52.4 cm
−1 . The
expansion of the active space to include occupied bridge orbitals as well as virtual
orbitals was described in this study as much more challenging. Upon inclusion of
the occupied 2p as well as the virtual 3p oxo-bridge orbitals, the exchange coupling
strength increases to −60 cm
−1 with CASSCF. The authors attempted to include the
empty Cr d orbitals in the active space, but only a (12, 13) CAS could be converged,
which contained an orbital delocalized over the entire core. It had d(z
2 ) character on
both metal centers, and symmetrical nodal planes with a lobe of s-character on the
oxo-bridge. Although still not containing all metal d orbitals, the exchange coupling
constant increases to −92.8 cm
−1 . The authors attributed this improvement to a more
balanced description of the Cr–O σ bonds, achieved by symmetrical mixing of the
orbitals dominated by O p(z) and Cr d(z
2 ) character. From a pure MO theory point
of view, one would expect three orbitals in total to be of importance for the σ bonds:
one dominated by the O p(z) atomic orbital (no nodal plane), and two dominated by
Cr d(z
2 ) character (one and two nodal planes).
Using an active space of (12, 25), containing the magnetic orbitals and their
double shells as well as the oxo-bridge 2p, 3p, and 3d orbitals, a stronger antiferromagnetic coupling can be achieved. With M 512 the exchange coupling constant
J is −166.9 cm
−1 , but increasing M to 1000 results in an exchange coupling constant that is significantly weaker, J −137.9 cm
−1 . Extrapolation of the individual
state energies to zero discarded weight results in an exchange coupling constant of
−123.6 cm
−1 , ca. 100 cm
−1 lower than the experimental value. In terms of possible
charge-transfer excitations with this active space, the MLCT excitations would be
expected to be adequately represented given that all magnetic orbitals and relevant
virtual ligand orbitals are included in the active space. In contrast, LMCT excitations
must be more limited, given that the virtual chromium 3d orbitals and their double
shells are not taken into account, and therefore dynamic correlation is recovered
incompletely compared to other systems.
An active space that contains a larger number of chromium 3d and 4d orbitals is
the (12, 32) active space. All 3d orbitals, the 4d(xy), 4d(xz), 4d(yz), and one 4d(z
2 )
orbital are included. Additionally, the 2p, 3s, 3p, 3d, and 4p orbitals of the central
oxo-bridge are taken into account. With this active space, an exchange coupling
constant of −165.9 cm
−1 is achieved, with M 1000 and a very small basis set (Cr:
double-ζ, O: triple-ζ, N, H: single-ζ). Extrapolation was not possible in this case due
to convergence problems of the M 512 calculation. It was also shown that the basis
set effect in this system is considerable. For the (12, 25) active space, a 11.8 cm
−1
difference results between the double-ζ and triple-ζ basis sets on Cr and O. With
a larger basis set, it might be hoped that an improved exchange coupling constant
could be achieved; however, the available results strongly indicate that this active