50
M. Stein
the calculation of EPR hyperfine interactions is exemplified here for this Ni(mnt)
−
2
model complex. Ligand
33 S,
13 C and
14 N hyperfine interactions a iso and A dip can be
calculated to within 1–2 MHz [71] from experimental EPR, HYSCORE and ESEEM
investigations [72] using a standard non-relativistic approach. Spin–orbit coupling
does not play a significant role here. In fact, quantum chemical calculations helped
to resolve ambiguities in the sign of the experimental
33 S hyperfine tensor.
For the anisotropic
61 Ni hyperfine interaction, however, a first order calculation
of the hyperfine interaction was clearly not sufficient. On the one hand, the isotropic
hyperfine coupling could be well-reproduced using scalar-relativistic ZORA calculations, even without considering spin–orbit coupling effects (a iso +18 MHz experimental; +17 MHz calculated). However, the experimental anisotropic
61 Ni hyperfine
interaction [70] of A dip (+27, −9, −18) MHz is not well reproduced in scalar relativistic calculations with (+53, −25, −28) MHz but overestimated by a factor of 2.
Here, the consideration of spin–orbit coupling reduces the dipolar part to (+25, −7,
−18) MHz and reproduces nicely the experimental
61 Ni hyperfine tensor. The hybrid
functional B3LYP does not perform superior to BP86 with calculated
61 Ni hyperfine
couplings of a iso +20 MHz and A dip (+29, −14, −15) MHz. This example demonstrates the necessity for an appropriate treatment of second-order spin–orbit coupling
contributions to the hyperfine interactions for transition metal ions (it makes up a
factor of 2 here). In particular, the covalency of the Ni–S bond and the subsequent
delocalization of the unpaired spin density are a challenge to describe correctly using
DFT methods. BP86 gives spin densities of ρ(Ni) 0.27 and ρ(S) 0.16; B3LYP
ρ(Ni) 0.28 and ρ(S) 0.17. The GGA results are closer to experimental results of
ρ(Ni) 0.25 and ρ(S) 0.13 [70, 72] and show that also GGA functionals are able
to correctly describe the degree of metal-ligand covalency.
55 Mo
V hyperfine interactions were calculated for a series of six small [75] and ten
larger [76] model complexes. For the large cis,trans-(L-N 2 S 2 )Mo
V OCl (L-N 2 S 2 =N,
N
-dimethyl-N, N
-bis(mercaptophenyl)ethylenediamine) complex, the calculated
isotropic Fermi-contact a iso hyperfine interaction ranges from 56 MHz for BP86 to
95 MHz for BPW91-40HF. Consideration of the pseudo-contact correction term A PC
due to spin–orbit corrections to the hyperfine tensor typically amounts to 14–17% of
a iso and adds an extra 11 and 15 MHz, respectively. The sum of the two contributions
to the isotropic
55 Mo hyperfine interaction gives 67 MHz for BP86 and 110 MHz
for BPW91-40HF which compares well with the experimental value of 107 MHz.
The consideration of second-order spin–orbit contributions to the metal hyperfine
interaction leads to only a minor change in relative g-tensor and the hyperfine tensor
orientation angles by 12, 7 and 13° for each of the principal axis.
M. Stein
the calculation of EPR hyperfine interactions is exemplified here for this Ni(mnt)
−
2
model complex. Ligand
33 S,
13 C and
14 N hyperfine interactions a iso and A dip can be
calculated to within 1–2 MHz [71] from experimental EPR, HYSCORE and ESEEM
investigations [72] using a standard non-relativistic approach. Spin–orbit coupling
does not play a significant role here. In fact, quantum chemical calculations helped
to resolve ambiguities in the sign of the experimental
33 S hyperfine tensor.
For the anisotropic
61 Ni hyperfine interaction, however, a first order calculation
of the hyperfine interaction was clearly not sufficient. On the one hand, the isotropic
hyperfine coupling could be well-reproduced using scalar-relativistic ZORA calculations, even without considering spin–orbit coupling effects (a iso +18 MHz experimental; +17 MHz calculated). However, the experimental anisotropic
61 Ni hyperfine
interaction [70] of A dip (+27, −9, −18) MHz is not well reproduced in scalar relativistic calculations with (+53, −25, −28) MHz but overestimated by a factor of 2.
Here, the consideration of spin–orbit coupling reduces the dipolar part to (+25, −7,
−18) MHz and reproduces nicely the experimental
61 Ni hyperfine tensor. The hybrid
functional B3LYP does not perform superior to BP86 with calculated
61 Ni hyperfine
couplings of a iso +20 MHz and A dip (+29, −14, −15) MHz. This example demonstrates the necessity for an appropriate treatment of second-order spin–orbit coupling
contributions to the hyperfine interactions for transition metal ions (it makes up a
factor of 2 here). In particular, the covalency of the Ni–S bond and the subsequent
delocalization of the unpaired spin density are a challenge to describe correctly using
DFT methods. BP86 gives spin densities of ρ(Ni) 0.27 and ρ(S) 0.16; B3LYP
ρ(Ni) 0.28 and ρ(S) 0.17. The GGA results are closer to experimental results of
ρ(Ni) 0.25 and ρ(S) 0.13 [70, 72] and show that also GGA functionals are able
to correctly describe the degree of metal-ligand covalency.
55 Mo
V hyperfine interactions were calculated for a series of six small [75] and ten
larger [76] model complexes. For the large cis,trans-(L-N 2 S 2 )Mo
V OCl (L-N 2 S 2 =N,
N
-dimethyl-N, N
-bis(mercaptophenyl)ethylenediamine) complex, the calculated
isotropic Fermi-contact a iso hyperfine interaction ranges from 56 MHz for BP86 to
95 MHz for BPW91-40HF. Consideration of the pseudo-contact correction term A PC
due to spin–orbit corrections to the hyperfine tensor typically amounts to 14–17% of
a iso and adds an extra 11 and 15 MHz, respectively. The sum of the two contributions
to the isotropic
55 Mo hyperfine interaction gives 67 MHz for BP86 and 110 MHz
for BPW91-40HF which compares well with the experimental value of 107 MHz.
The consideration of second-order spin–orbit contributions to the metal hyperfine
interaction leads to only a minor change in relative g-tensor and the hyperfine tensor
orientation angles by 12, 7 and 13° for each of the principal axis.