The Electronic Determinants of Spin Crossover Described …
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4 Performance of DFT for Describing SCO
4.1 The Massive Role of HF Exchange Favoring HS
In order to fully understand and predict SCO tendencies of molecular systems, the
various systematic effects discussed above need to be considered and added to the
electronic energy of the HS and LS states. The enthalpy of the process can be written
as:
H SCO E SCO + PV SCO
(5)
The last term is small (of the order of RT) for thermal SCO, and the energy term
is:
E SCO E el,SCO + E rel,SCO + E ZPE,SCO + E disp,SCO
(6)
where E el,SCO E el (HS) – E el (LS) is the direct nonrelativistic energy gap of the
HS and LS states computed by a density functional without dispersion included,
E rel,SCO E rel (HS) – E rel (LS) is the relativistic contribution to the HS–LS energy
gap (typically 5–10 kJ/mol in favor of LS and very constant), E ZPE,SCO is the
differential ZPE (typically 10 kJ/mol in favor of HS for SCO systems but very
dependent on metal and ligand type), and E disp,SCO is the differential dispersion
effect on SCO (typically 10 kJ/mol in favor of LS for single molecules, but augmented
with a variable contribution depending on intermolecular interactions). Commonly,
these three terms sum up to a correction of 0–20 kJ/mol in favor of LS. Once the
systematic effects of (5) are accounted for, it enables us to estimate the accuracy of
a theoretical method toward SCO and to identify truly spin-state-balanced density
functionals.
However, it turns out that the electronic Hamiltonian used to obtain the electronic
energies of the states, E el (HS) and E el (LS) of (6), is a major problem in itself.
In the world of DFT, there are hundreds of functionals with distinct acronyms to
choose from, and this diversity can easily overwhelm young researchers unless their
supervisors have very strong adherence to certain functionals. So which density
functionals produce accurate E el,SCO ?
The use of hybrid functionals, in particular B3LYP [126–128], greatly improved
the accuracy of computational main-group chemistry and have accordingly also been
widely applied to study inorganic chemistry. Paulsen et al. computed the energy gap
between HS and LS states for nine iron complexes using B3LYP and for some of them
also the non-hybrid GGA functionals PW91 and BLYP [34]. They observed that the
non-hybrid functionals produce energies much in favor of LS (by up to 104 kJ/mol
for PW91), whereas B3LYP favors HS. This observation that the 20% HF exchange
hybrid B3LYP favors HS and that 0% HF exchange favors LS probably inspired the
development of the B3LYP* functional by Reiher a year later [60, 129].
19
4 Performance of DFT for Describing SCO
4.1 The Massive Role of HF Exchange Favoring HS
In order to fully understand and predict SCO tendencies of molecular systems, the
various systematic effects discussed above need to be considered and added to the
electronic energy of the HS and LS states. The enthalpy of the process can be written
as:
H SCO E SCO + PV SCO
(5)
The last term is small (of the order of RT) for thermal SCO, and the energy term
is:
E SCO E el,SCO + E rel,SCO + E ZPE,SCO + E disp,SCO
(6)
where E el,SCO E el (HS) – E el (LS) is the direct nonrelativistic energy gap of the
HS and LS states computed by a density functional without dispersion included,
E rel,SCO E rel (HS) – E rel (LS) is the relativistic contribution to the HS–LS energy
gap (typically 5–10 kJ/mol in favor of LS and very constant), E ZPE,SCO is the
differential ZPE (typically 10 kJ/mol in favor of HS for SCO systems but very
dependent on metal and ligand type), and E disp,SCO is the differential dispersion
effect on SCO (typically 10 kJ/mol in favor of LS for single molecules, but augmented
with a variable contribution depending on intermolecular interactions). Commonly,
these three terms sum up to a correction of 0–20 kJ/mol in favor of LS. Once the
systematic effects of (5) are accounted for, it enables us to estimate the accuracy of
a theoretical method toward SCO and to identify truly spin-state-balanced density
functionals.
However, it turns out that the electronic Hamiltonian used to obtain the electronic
energies of the states, E el (HS) and E el (LS) of (6), is a major problem in itself.
In the world of DFT, there are hundreds of functionals with distinct acronyms to
choose from, and this diversity can easily overwhelm young researchers unless their
supervisors have very strong adherence to certain functionals. So which density
functionals produce accurate E el,SCO ?
The use of hybrid functionals, in particular B3LYP [126–128], greatly improved
the accuracy of computational main-group chemistry and have accordingly also been
widely applied to study inorganic chemistry. Paulsen et al. computed the energy gap
between HS and LS states for nine iron complexes using B3LYP and for some of them
also the non-hybrid GGA functionals PW91 and BLYP [34]. They observed that the
non-hybrid functionals produce energies much in favor of LS (by up to 104 kJ/mol
for PW91), whereas B3LYP favors HS. This observation that the 20% HF exchange
hybrid B3LYP favors HS and that 0% HF exchange favors LS probably inspired the
development of the B3LYP* functional by Reiher a year later [60, 129].