102
V. Krewald and D. A. Pantazis
The above observations can be rationalized in terms of charge-transfer configurations when virtual orbitals are included in the active space. By adding bridge
3p orbitals, metal-to-ligand charge transfer (MLCT) configurations are considered.
Analogously, the inclusion of a metal “double shells” adds ligand-to-metal charge
transfer (LMCT) configurations and introduces radial dynamic correlation. In a traditional CASSCF calculation, the individual configurations and their relative contributions can be analyzed and quantified in a relatively straightforward manner;
however, the weights of contributing configurations [88, 115] were not reported
from the DMRG calculations. Nevertheless, as an indirect or summative effect of
all CT configurations, the orbital contour plots revealed the contribution of LMCT
states as a more pronounced delocalization on the bridging ligands.
The effect of basis set choice on the exchange coupling constant was studied in
some detail. The calculations employed relativistic atomic natural orbital basis sets
(ANO-RCC) with a series of contractions. For both the CASSCF(16, 13) and DMRGSCF(16, 26) calculations, a larger basis set led to weaker exchange coupling. For the
CASSCF approach, the results were converged with a quintuple-ζ basis set for iron
and oxo-bridge, and a quadruple-ζ basis set for the peripheral chloride ligands. For
the DMRG approach, the convergence behavior is less clear, as there is an additional
strong dependency on the M value: larger basis sets require a larger M, but as this
creates higher memory demands the calculations are not always feasible. The basis
set convergence is very similar for the CASSCF and DMRG approaches as long as
M is sufficiently large, i.e., up to a quadruple-ζ basis for all elements. It should be
noted that although no chloride orbitals enter the active space, increasing the basis
set size from double-ζ to quadruple-ζ was reported to change the predicted exchange
coupling constants by ca. 5 cm
−1 . This may be related to the π-bonding between
chloride and the iron ions. Taking both accuracy and efficiency into account, Harris
et al. [22] opted for a triple-ζ basis set for iron and oxygen, and a double-ζ basis set
for the peripheral chloride ligands.
The number of renormalized basis states, M, must be sufficiently large to ensure
that the energy converges to the correct value for a given choice of active space.
Furthermore, larger active spaces require larger values of M to converge properly,
implying that across a series of calculations with varying active space sizes for the
same system, different numbers of renormalized basis states will be needed. Because
the energy of a system converges to the exact value for increasing values of M, i.e.,
decreasing discarded weights, a linear extrapolation can be used to find the exact
energy based on several calculations with different numbers of renormalized basis
states.
The convergence with M is different for different spin states. This is apparent,
for example, in the case of the iron dimer (Fig. 3) [22]. The extrapolation of the S
0 state has a steeper slope than the extrapolation of the S 1 state, both based
on two energies calculated with M 512 and M 1000. It is also noted that the
corresponding discarded weights differ for calculations of different spin states with
the same M value.
When aiming to predict accurate energies of different spin states of an exchangecoupled system to subsequently extract coupling constants measured in cm
−1 units
V. Krewald and D. A. Pantazis
The above observations can be rationalized in terms of charge-transfer configurations when virtual orbitals are included in the active space. By adding bridge
3p orbitals, metal-to-ligand charge transfer (MLCT) configurations are considered.
Analogously, the inclusion of a metal “double shells” adds ligand-to-metal charge
transfer (LMCT) configurations and introduces radial dynamic correlation. In a traditional CASSCF calculation, the individual configurations and their relative contributions can be analyzed and quantified in a relatively straightforward manner;
however, the weights of contributing configurations [88, 115] were not reported
from the DMRG calculations. Nevertheless, as an indirect or summative effect of
all CT configurations, the orbital contour plots revealed the contribution of LMCT
states as a more pronounced delocalization on the bridging ligands.
The effect of basis set choice on the exchange coupling constant was studied in
some detail. The calculations employed relativistic atomic natural orbital basis sets
(ANO-RCC) with a series of contractions. For both the CASSCF(16, 13) and DMRGSCF(16, 26) calculations, a larger basis set led to weaker exchange coupling. For the
CASSCF approach, the results were converged with a quintuple-ζ basis set for iron
and oxo-bridge, and a quadruple-ζ basis set for the peripheral chloride ligands. For
the DMRG approach, the convergence behavior is less clear, as there is an additional
strong dependency on the M value: larger basis sets require a larger M, but as this
creates higher memory demands the calculations are not always feasible. The basis
set convergence is very similar for the CASSCF and DMRG approaches as long as
M is sufficiently large, i.e., up to a quadruple-ζ basis for all elements. It should be
noted that although no chloride orbitals enter the active space, increasing the basis
set size from double-ζ to quadruple-ζ was reported to change the predicted exchange
coupling constants by ca. 5 cm
−1 . This may be related to the π-bonding between
chloride and the iron ions. Taking both accuracy and efficiency into account, Harris
et al. [22] opted for a triple-ζ basis set for iron and oxygen, and a double-ζ basis set
for the peripheral chloride ligands.
The number of renormalized basis states, M, must be sufficiently large to ensure
that the energy converges to the correct value for a given choice of active space.
Furthermore, larger active spaces require larger values of M to converge properly,
implying that across a series of calculations with varying active space sizes for the
same system, different numbers of renormalized basis states will be needed. Because
the energy of a system converges to the exact value for increasing values of M, i.e.,
decreasing discarded weights, a linear extrapolation can be used to find the exact
energy based on several calculations with different numbers of renormalized basis
states.
The convergence with M is different for different spin states. This is apparent,
for example, in the case of the iron dimer (Fig. 3) [22]. The extrapolation of the S
0 state has a steeper slope than the extrapolation of the S 1 state, both based
on two energies calculated with M 512 and M 1000. It is also noted that the
corresponding discarded weights differ for calculations of different spin states with
the same M value.
When aiming to predict accurate energies of different spin states of an exchangecoupled system to subsequently extract coupling constants measured in cm
−1 units