Computational Versus Experimental Spectroscopy …
173
SMMs is related to the existence of two states separated by an energy barrier (U eff )
with U eff |D| · S
2 (S being the spin ground state of the complex and D describing
the magnetic anisotropy). SMMs have been proposed as potential candidates for several technological applications that require highly controlled thin films and patterns
(high-density information storage and quantum computing) [47, 48].
However, most of the existing molecular systems display extremely low transition temperatures to act as SMMs and then can not be used for applications [49, 50].
Recently, part of the origin of this problem has been unveiled as it has been shown
that the energy barrier does not depend on the total spin of the molecule as it was
previously believed, but on the magnetic anisotropy [51, 52]. Thus, the control of the
energy barrier is reduced to understand the so-called zero-field-splitting (ZFS) parameters that determine the magnetic anisotropy of an isolated transition-metal complex.
The ZFS parameter tensor is defined by the D and E parameters, which represent its
axial and rhombic contributions, respectively. Several experimental techniques have
been developed to determine D including indirect methods such as magnetometry, variable temperature, variable-field magnetic circular dichroism, and Mössbauer
spectroscopy, or direct methods such as inelastic neutron scattering and frequency
domain magnetic resonance spectroscopy [53]. However, the most appropriate technique to accurately define the ZFS parameters remains electronic paramagnetic resonance (EPR) spectroscopy. A precise determination of D generally necessitates
high-field limit conditions, i.e., when the energy provided by the EPR spectrometer
is much larger than the magnitude of D. Therefore, for systems with |D| > 0.2 cm
−1 ,
high-field EPR (HF-EPR) is required. In parallel, important theoretical efforts have
been carried out to develop suitable methodologies to predict the ZFS parameters and
to rationalize the experimental observations. For such investigations, both contributions to D, i.e., the spin-orbit coupling (SOC) and the electron–electron spin–spin
interaction (SS) have been accurately calculated [54]. Multiconfigurational wavefunction approaches [55], including ab initio frameworks, generally give satisfactory
predictions of D. Several multi-determinantal methods, especially like the complete
active space self-consistent field (CASSCF) and N-electron valence second-order
perturbation theory of second-order (NEVPT2) approaches lead to calculated D values in good agreement with the experimental data, but are computationally much
more expensive than density functional theory (DFT) [56], significantly hampering
their ability to apply them to medium and large transition-metal complexes. Two DFT
approaches rooted in very different physical foundations can be in principle used.
The first one is based on the coupled perturbed SOC method (CP-DFT) and closely
related to the work of Perderson and Khanna [57, 58]. It should be pointed out that
DFT perturbational approaches like, e.g., Pederson–Khanna, cannot be used when
orbital degeneracy is present. The second method is the ligand-field DFT (LF-DFT)
approach by Daul et al. [59], based on a multideterminant description of the transition metal’s multiplet fine structure that is able to tackle many difficult problems
including orbital degeneracy.
Since
the
most
famous
SMM
is
a
Mn-based
cluster,
[Mn 12 O 12 (CH 3 CO 2 ) 16 (H 2 O) 4 ], composed by eight Mn
III and four Mn
IV ions
[60], special interests have been devoted to these specific ions. However, while the
173
SMMs is related to the existence of two states separated by an energy barrier (U eff )
with U eff |D| · S
2 (S being the spin ground state of the complex and D describing
the magnetic anisotropy). SMMs have been proposed as potential candidates for several technological applications that require highly controlled thin films and patterns
(high-density information storage and quantum computing) [47, 48].
However, most of the existing molecular systems display extremely low transition temperatures to act as SMMs and then can not be used for applications [49, 50].
Recently, part of the origin of this problem has been unveiled as it has been shown
that the energy barrier does not depend on the total spin of the molecule as it was
previously believed, but on the magnetic anisotropy [51, 52]. Thus, the control of the
energy barrier is reduced to understand the so-called zero-field-splitting (ZFS) parameters that determine the magnetic anisotropy of an isolated transition-metal complex.
The ZFS parameter tensor is defined by the D and E parameters, which represent its
axial and rhombic contributions, respectively. Several experimental techniques have
been developed to determine D including indirect methods such as magnetometry, variable temperature, variable-field magnetic circular dichroism, and Mössbauer
spectroscopy, or direct methods such as inelastic neutron scattering and frequency
domain magnetic resonance spectroscopy [53]. However, the most appropriate technique to accurately define the ZFS parameters remains electronic paramagnetic resonance (EPR) spectroscopy. A precise determination of D generally necessitates
high-field limit conditions, i.e., when the energy provided by the EPR spectrometer
is much larger than the magnitude of D. Therefore, for systems with |D| > 0.2 cm
−1 ,
high-field EPR (HF-EPR) is required. In parallel, important theoretical efforts have
been carried out to develop suitable methodologies to predict the ZFS parameters and
to rationalize the experimental observations. For such investigations, both contributions to D, i.e., the spin-orbit coupling (SOC) and the electron–electron spin–spin
interaction (SS) have been accurately calculated [54]. Multiconfigurational wavefunction approaches [55], including ab initio frameworks, generally give satisfactory
predictions of D. Several multi-determinantal methods, especially like the complete
active space self-consistent field (CASSCF) and N-electron valence second-order
perturbation theory of second-order (NEVPT2) approaches lead to calculated D values in good agreement with the experimental data, but are computationally much
more expensive than density functional theory (DFT) [56], significantly hampering
their ability to apply them to medium and large transition-metal complexes. Two DFT
approaches rooted in very different physical foundations can be in principle used.
The first one is based on the coupled perturbed SOC method (CP-DFT) and closely
related to the work of Perderson and Khanna [57, 58]. It should be pointed out that
DFT perturbational approaches like, e.g., Pederson–Khanna, cannot be used when
orbital degeneracy is present. The second method is the ligand-field DFT (LF-DFT)
approach by Daul et al. [59], based on a multideterminant description of the transition metal’s multiplet fine structure that is able to tackle many difficult problems
including orbital degeneracy.
Since
the
most
famous
SMM
is
a
Mn-based
cluster,
[Mn 12 O 12 (CH 3 CO 2 ) 16 (H 2 O) 4 ], composed by eight Mn
III and four Mn
IV ions
[60], special interests have been devoted to these specific ions. However, while the