The Electronic Determinants of Spin Crossover Described …
3
illustrated by the spectrochemical series of the ligands and the corresponding series of
the metal ions [38, 39]. Thus, for example, most SCO systems contain moderate-field
nitrogen-donor ligands combined with Fe(II), as exemplified by the much studied,
first synthetic iron(II) SCO system Fe(Phen) 2 SCN 2 [40–43]. However, Fe(III) and
Co(II) are also relatively common SCO metal ions, with the first-reported Fe(III)
SCO systems being those of Cambi et al. [10] and the first Co(II) SCO system being
that of Stoufer et al. [44].
In this chapter, the basis for describing SCO accurately by chemical–physical
principles and the role of various contributions to the SCO tendency will be discussed. These include important systematic energy terms, i.e., the zero-point vibration energy, relativistic contributions to SCO, and dispersion forces that modulate
the HS–LS equilibrium already at the single-molecule level. The importance of modeling the vibrational entropy contribution in the theoretical study of SCO systems
is emphasized. The difference between the spectrochemical series and the “thermochemical series” of spin-state propensities are discussed. The performance of DFT
and various ingredients of the functionals that affect the accuracy are analyzed.
2 Fundamentals of Spin Crossover
2.1 The Dilemma and Choice Between LS and HS
As taught in basis inorganic chemistry, when ligands are placed around a metal ion,
the energies of the d-orbitals split into several energy levels due to the symmetry
breaking, i.e., the d-orbitals experience different environments. If the ligand field
is octahedral (O h symmetry), two levels occur: The two high-lying degenerate e g
orbitals are aligned toward the ligands and thus experience more electronic repulsion,
and the threefold degenerate low-lying t 2g orbital level becomes less repelled as these
orbitals (originating from d xy , d xz , and d yz ) distribute further from the ligands.
Depending on the energy splitting o between the two levels, the electrons face
a dilemma after occupying the three t 2g orbitals by one electron according to Hund’s
Rule: Either the additional electrons distribute in the normal fashion by pairing with
the three first t 2g electrons or, if the energy distance is small, they may in fact move
to the next level, e g . The solution to this dilemma partly (but not completely, as
discussed below) lies in resolving the relative magnitude of the penalty of moving up
to the e g orbitals, i.e., o , versus the penalty of occupying a t 2g orbital where another
electron is already residing close in space, i.e., the spin-pairing energy penalty P.
This situation is also entropically unfavorable, to be discussed below. If the fourth
and fifth electron decide to move to e g , the system will experience more aligned
electron spins; this state is the HS state. If it is more favorable to pair with the t 2g
electrons first, the resulting spin and magnetic moment becomes smaller; this is the
LS state.
3
illustrated by the spectrochemical series of the ligands and the corresponding series of
the metal ions [38, 39]. Thus, for example, most SCO systems contain moderate-field
nitrogen-donor ligands combined with Fe(II), as exemplified by the much studied,
first synthetic iron(II) SCO system Fe(Phen) 2 SCN 2 [40–43]. However, Fe(III) and
Co(II) are also relatively common SCO metal ions, with the first-reported Fe(III)
SCO systems being those of Cambi et al. [10] and the first Co(II) SCO system being
that of Stoufer et al. [44].
In this chapter, the basis for describing SCO accurately by chemical–physical
principles and the role of various contributions to the SCO tendency will be discussed. These include important systematic energy terms, i.e., the zero-point vibration energy, relativistic contributions to SCO, and dispersion forces that modulate
the HS–LS equilibrium already at the single-molecule level. The importance of modeling the vibrational entropy contribution in the theoretical study of SCO systems
is emphasized. The difference between the spectrochemical series and the “thermochemical series” of spin-state propensities are discussed. The performance of DFT
and various ingredients of the functionals that affect the accuracy are analyzed.
2 Fundamentals of Spin Crossover
2.1 The Dilemma and Choice Between LS and HS
As taught in basis inorganic chemistry, when ligands are placed around a metal ion,
the energies of the d-orbitals split into several energy levels due to the symmetry
breaking, i.e., the d-orbitals experience different environments. If the ligand field
is octahedral (O h symmetry), two levels occur: The two high-lying degenerate e g
orbitals are aligned toward the ligands and thus experience more electronic repulsion,
and the threefold degenerate low-lying t 2g orbital level becomes less repelled as these
orbitals (originating from d xy , d xz , and d yz ) distribute further from the ligands.
Depending on the energy splitting o between the two levels, the electrons face
a dilemma after occupying the three t 2g orbitals by one electron according to Hund’s
Rule: Either the additional electrons distribute in the normal fashion by pairing with
the three first t 2g electrons or, if the energy distance is small, they may in fact move
to the next level, e g . The solution to this dilemma partly (but not completely, as
discussed below) lies in resolving the relative magnitude of the penalty of moving up
to the e g orbitals, i.e., o , versus the penalty of occupying a t 2g orbital where another
electron is already residing close in space, i.e., the spin-pairing energy penalty P.
This situation is also entropically unfavorable, to be discussed below. If the fourth
and fifth electron decide to move to e g , the system will experience more aligned
electron spins; this state is the HS state. If it is more favorable to pair with the t 2g
electrons first, the resulting spin and magnetic moment becomes smaller; this is the
LS state.