Anisotropic Magnetic Spin Interactions of Transition Metal …
37
oxidase (AO) and the mitochondrial amidoxime-reducing enzymes called mARC1
and 2 are present, the latter of which were only recently discovered. In bacteria,
the two-electron reduction of molecular nitrogen (N 2 ) to ammonia (NH 3 ) by the
heterotetrameric MoFe protein nitrogenase from cyanobacteria is an essential process
to sustain life on Earth [10] and has inspired the design and characterization of many
biomimetic complexes [11, 12]. The structure and function of mono-molybdenum
enzymes have been reviewed in [13, 14].
Mn superoxide dismutase is present in eukaryotic mitochondria, and also in most
bacteria. The Mn-SOD enzyme is the most ancient enzyme living in the presence of
oxygen and being able deal with the toxic effects of superoxide (O 2
− ) [15, 16]. The
oxygen-evolving complex (OEC) of photosystem II contains a Mn 4 CaO 5 cluster plus
two chloride ions with Mn oxidation states ranging from +2 to +4. Five oxygen atoms
serve as oxo bridges linking the five metal atoms and four water molecules bound
to the cluster which were structurally resolved, see reviews [17, 18] for PSII and
also biomimetic systems. Quantum chemical calculations for PSII are summarized
in reference [19] for example.
Whereas most computational benchmarks and comparison with experiment have
focused on calculating the principal values of the g- and hyperfine tensors, it is shown
here that the non-uniform distribution of electron spin and the anisotropy of magnetic
interactions provide additional valuable information such as the assignment of the
magnetic axes into a molecular or protein structure and the resolution of conformational states of ligands close to the spin center. This information is complementary
to the one that can be obtained from crystallography.
2 Electron Spin Interactions with an External Magnetic
Field
In the following, the discussion will be limited to a simple paramagnetic center with
one unpaired electron spin (S ½, M s ±½) and its interaction with nuclear spins
of the same spin state (I ½, M I ±½). For a discussion of more elaborate magnetic
systems, the reader is referred to textbooks about EPR and d-transition metals, such
as [1, 2].
In the absence of an external magnetic field, the electron magnetic moment is
randomly oriented and the two energy levels M s ±½ are energetically degenerate.
This degeneracy of α- and β-spin orbitals is removed in the presence of an external
magnetic field B 0 due to the electron Zeeman splitting:
H μ B S g e B 0
(1)
where g e is the g-factor of the free electron (g e 2.0023), μ B is the Bohr magneton
(9.274 × 10
−24 J T
−1 ), S is the spin operator and B 0 is the magnitude of the external
magnetic field in Tesla.
37
oxidase (AO) and the mitochondrial amidoxime-reducing enzymes called mARC1
and 2 are present, the latter of which were only recently discovered. In bacteria,
the two-electron reduction of molecular nitrogen (N 2 ) to ammonia (NH 3 ) by the
heterotetrameric MoFe protein nitrogenase from cyanobacteria is an essential process
to sustain life on Earth [10] and has inspired the design and characterization of many
biomimetic complexes [11, 12]. The structure and function of mono-molybdenum
enzymes have been reviewed in [13, 14].
Mn superoxide dismutase is present in eukaryotic mitochondria, and also in most
bacteria. The Mn-SOD enzyme is the most ancient enzyme living in the presence of
oxygen and being able deal with the toxic effects of superoxide (O 2
− ) [15, 16]. The
oxygen-evolving complex (OEC) of photosystem II contains a Mn 4 CaO 5 cluster plus
two chloride ions with Mn oxidation states ranging from +2 to +4. Five oxygen atoms
serve as oxo bridges linking the five metal atoms and four water molecules bound
to the cluster which were structurally resolved, see reviews [17, 18] for PSII and
also biomimetic systems. Quantum chemical calculations for PSII are summarized
in reference [19] for example.
Whereas most computational benchmarks and comparison with experiment have
focused on calculating the principal values of the g- and hyperfine tensors, it is shown
here that the non-uniform distribution of electron spin and the anisotropy of magnetic
interactions provide additional valuable information such as the assignment of the
magnetic axes into a molecular or protein structure and the resolution of conformational states of ligands close to the spin center. This information is complementary
to the one that can be obtained from crystallography.
2 Electron Spin Interactions with an External Magnetic
Field
In the following, the discussion will be limited to a simple paramagnetic center with
one unpaired electron spin (S ½, M s ±½) and its interaction with nuclear spins
of the same spin state (I ½, M I ±½). For a discussion of more elaborate magnetic
systems, the reader is referred to textbooks about EPR and d-transition metals, such
as [1, 2].
In the absence of an external magnetic field, the electron magnetic moment is
randomly oriented and the two energy levels M s ±½ are energetically degenerate.
This degeneracy of α- and β-spin orbitals is removed in the presence of an external
magnetic field B 0 due to the electron Zeeman splitting:
H μ B S g e B 0
(1)
where g e is the g-factor of the free electron (g e 2.0023), μ B is the Bohr magneton
(9.274 × 10
−24 J T
−1 ), S is the spin operator and B 0 is the magnitude of the external
magnetic field in Tesla.