The Electronic Determinants of Spin Crossover Described …
15
M–L bond enthalpies, relativistic effects typically surpass 5 kJ/mol [98]. It is of
fundamental scientific interest to understand whether relativistic effects contribute
to SCO. Also, from the point of view of theoretical prediction of SCO systems,
comparing nonrelativistic energy estimates directly to the experimental energy gaps
could cause an error in the conclusion on the quality of the applied nonrelativistic
method, whether it be CASPT2, CCSD(T), or DFT.
It has been shown [36] that scalar-relativistic corrections to the HS–LS energy
gap accurately reproduce relativistic effects computed using both second- and fourthorder Douglas–Kroll–Hess energies [99], which simplify the Dirac equation by separating the positive and negative energy states [100]. The success of scalar-relativistic
estimates arises from the small spin-orbit coupling of the light transition metal ions
(Mn, Fe, Co) that undergo SCO (~1 kJ/mol [101]), although spin-orbit coupling is
formally required for transition to occur in the first place and plays a qualitative role
in the process as seen, e.g., for light-induced SCO [102]. The Douglas–Kroll–Hess
two-component formalism with and without spin-orbit coupling only changes the
scalar-relativistic energies by typically ∼1 kJ/mol. Order 4 and 2 give similar results
within ∼1 kJ/mol, and the spin-orbit coupling corrections are 0–3 kJ/mol for the
HS–LS gap, justifying the use of scalar-relativistic corrections which can recover
most of the real relativistic LS stabilization by fast computation [36].
It turns out that there are significant relativistic contributions to SCO [36, 103,
104]. Interestingly, the relativistic energies tend to generally favor the LS state and are
quite systematic and not very variable, because they tend to be localized to the metal
center rather than other lighter atoms of the SCO system. The simplest explanation
for this relativistic SCO effect is that the LS state is more compact with lower spin and
angular momentum, and thus features stronger stabilization (reduction in inter-shell
electron repulsion) once the 1s-orbital on iron is relativistic stabilized and contracted.
In contrast, the reduced effective nuclear charge resulting from relativistic contraction
mainly destabilizes the diffuse higher-angular momentum d-orbitals, in particular,
the e g -type d-orbitals of the HS state [36]. This explanation of the relativistic SCO
effect follows closely the standard principles seen for other observables as outlined
and discussed by Pyykkö [105].
The relativistic LS stabilization averages to 9 kJ/mol for iron SCO systems [36].
This is, remarkably, of the same magnitude as the dispersion and ZPE corrections.
In other words, ZPE, dispersion, and relativistic effects work together to affect the
energy difference between the HS and LS states, which is of a net magnitude of
5–20 kJ/mol, and they all are of similar importance, on average ~10 kJ/mol or so
[36]. These three energy terms are systematic, i.e., they tend to favor one spin state
consistently. Accordingly, they need to be included if one strives toward quantitative
accuracy. To summarize this important conclusion, Fig. 4 displays the impact on a
hypothetical transition curve of the three energetic contributions discussed above,
i.e., ZPE (Fig. 4a), relativistic stabilization of LS (Fig. 4b), and the single-molecule
component of the dispersion forces (Fig. 4c). The systematic behavior of these terms
may aid us in the future rational design of powerful SCO systems with the exact
energy terms desired to contribute to H SCO of (2).
15
M–L bond enthalpies, relativistic effects typically surpass 5 kJ/mol [98]. It is of
fundamental scientific interest to understand whether relativistic effects contribute
to SCO. Also, from the point of view of theoretical prediction of SCO systems,
comparing nonrelativistic energy estimates directly to the experimental energy gaps
could cause an error in the conclusion on the quality of the applied nonrelativistic
method, whether it be CASPT2, CCSD(T), or DFT.
It has been shown [36] that scalar-relativistic corrections to the HS–LS energy
gap accurately reproduce relativistic effects computed using both second- and fourthorder Douglas–Kroll–Hess energies [99], which simplify the Dirac equation by separating the positive and negative energy states [100]. The success of scalar-relativistic
estimates arises from the small spin-orbit coupling of the light transition metal ions
(Mn, Fe, Co) that undergo SCO (~1 kJ/mol [101]), although spin-orbit coupling is
formally required for transition to occur in the first place and plays a qualitative role
in the process as seen, e.g., for light-induced SCO [102]. The Douglas–Kroll–Hess
two-component formalism with and without spin-orbit coupling only changes the
scalar-relativistic energies by typically ∼1 kJ/mol. Order 4 and 2 give similar results
within ∼1 kJ/mol, and the spin-orbit coupling corrections are 0–3 kJ/mol for the
HS–LS gap, justifying the use of scalar-relativistic corrections which can recover
most of the real relativistic LS stabilization by fast computation [36].
It turns out that there are significant relativistic contributions to SCO [36, 103,
104]. Interestingly, the relativistic energies tend to generally favor the LS state and are
quite systematic and not very variable, because they tend to be localized to the metal
center rather than other lighter atoms of the SCO system. The simplest explanation
for this relativistic SCO effect is that the LS state is more compact with lower spin and
angular momentum, and thus features stronger stabilization (reduction in inter-shell
electron repulsion) once the 1s-orbital on iron is relativistic stabilized and contracted.
In contrast, the reduced effective nuclear charge resulting from relativistic contraction
mainly destabilizes the diffuse higher-angular momentum d-orbitals, in particular,
the e g -type d-orbitals of the HS state [36]. This explanation of the relativistic SCO
effect follows closely the standard principles seen for other observables as outlined
and discussed by Pyykkö [105].
The relativistic LS stabilization averages to 9 kJ/mol for iron SCO systems [36].
This is, remarkably, of the same magnitude as the dispersion and ZPE corrections.
In other words, ZPE, dispersion, and relativistic effects work together to affect the
energy difference between the HS and LS states, which is of a net magnitude of
5–20 kJ/mol, and they all are of similar importance, on average ~10 kJ/mol or so
[36]. These three energy terms are systematic, i.e., they tend to favor one spin state
consistently. Accordingly, they need to be included if one strives toward quantitative
accuracy. To summarize this important conclusion, Fig. 4 displays the impact on a
hypothetical transition curve of the three energetic contributions discussed above,
i.e., ZPE (Fig. 4a), relativistic stabilization of LS (Fig. 4b), and the single-molecule
component of the dispersion forces (Fig. 4c). The systematic behavior of these terms
may aid us in the future rational design of powerful SCO systems with the exact
energy terms desired to contribute to H SCO of (2).