Results

FcPyl⁺ X⁻ crystals were characterized from the structural point of view with XRD single crystal analysis, as reported in the Kondo work [78]. The crystal structures are available at two different temperatures for FcPyl⁺PF⁻₆ and FcPyl⁺ BF⁻₄: 113K (LT) and 273K (HT). For X= TFSI only the HT structure is given. For the LT and HT structures of FcPyl⁺PF⁻₆ and FcPyl⁺BF⁻₄ two conformations have been mapped (c₁and c₂). They are related to two orientation for the anion X.

Indeed, conformational disorder can affect BF₄and PF₆units and in particular the rotation around the central atom is possible, resulting in two different sets of atomic coordinates for each anion. Figures 2.18 to 2.20 show the overall arrangement in the crystal structure.

Calculating M and F for FcPyl

To estimate F and M in eq. 2.29 and 2.30 we need to estimate the atomic charges on the molecular anion relevant to both the DA⁺and the D⁺Astructures of FcPyl as well as the distribution of charges in counterions. For counterions we run a standard PM6 [97] calculation and, neglecting the (minimal) polar-izability of counterions, we assume that the resulting atomic charges q_χ do not change with the environment. To estimate atomic charges on FcPyl we follow a similar strategy as adopted for FcPTM. In particular we perform quantum chem-ical calculation on FcPyl under an applied electric field F as to drive the system from the DA⁺to the D⁺Astate.

Fig. 2.21 shows the properties of FcPyl as a function of an electric field oriented along the DA direction (from the Fe atom to the C atom in the carbonyl,

128 FcPyl⁺: bistability in molecular ion crystals

Figure 2.18: Monoclinic crystal structure in the unit cell of FcPyl⁺ TFSI⁻, from [78].

Figure 2.19: Orthorhombic crystal structure in the unit cell of FcPyl⁺ PF⁻₆ (HT), from [78]. Both c₁and c₂are shown.

linked to the external oxygen). The different curves are obtained adopting the FcPyl structure from the five crystal structures available. The results are very similar to those relevant to FcPTM. The region around F = 0 V/Å and F = 1 V/Å has almost flat polarizability, and we assume the charge distribution at F = 0 as {q⁰}, while the charge distribution at F = 1 V/Å describes Fc⁺Pyl state ({q(ρ = 1)}) . The calculation has been run on MOPAC2007 package, with PM6 model Hamiltonian, imposing the keyword^BIRADICAL, that actual mixes four microstates to include an eventual biradicalic character (this keyword is actually redundant and corresponds to the combination of the keywords^MECI

OPEN(2,2) SINGLETin the MOPAC2007 package). It implies a C.I. calculation

Figure 2.20: Orthorhombic structure in the unit cell of FcPyl⁺ BF⁻₄ (HT), from [78]. Both c₁and c₂are shown.

with the four configurations that arise considering the space of the HOMO and the LUMO.

As shown in the middle panel of fig. 2.21 the overall charge on the acceptor unit is close to 1 in the F ∼ 0 region and close to 0 in the region assumed for the CT state (F ∼ 1 V/Å), and vice versa on the donor Fc unit. The µ0 value that can be extracted here is about 40 D, corresponding to a dipole length of about 8 Å. This is really close to the crystallographic distances from the donor center (Fe atom) and the considered acceptor center (C of carbonyl group), being 7.6 - 7.7 Å in the reported structures. Moreover, the sigmoid curves for the five structures are similar, with minor differences (curves corresponding to the X= BF₄structure are smoother than the other curves). The information about atomic charges obtained from quantum chemical calculations is finally entered in eq. 2.29 and 2.30 to calculate F and M value: results are summarized in table 2.4 for the five crystal structures.

Table 2.4: Calculated value for electrostatic energies

anion X = T / K F / eV M /eV

TFSI⁻ 273 −0.05 −1.04

BF⁻₄ (LT) 113 0.04 (c₁) −0.01 (c2) −0.91 BF⁻₄ (HT) 273 −0.12 (c1) −0.26 (c2) −1.10 PF⁻₆ (LT) 113 −0.05 (c1) −0.04 (c2) −0.95 PF⁻₆ (HT) 273 −0.02 (c1) −0.07 (c2) −0.93

130 FcPyl⁺: bistability in molecular ion crystals

E V / Å

-20 0 20 40 60

µx (D)

X=TFSI^- (HT) X=PF₆^- (LT) X=PF₆^- (HT) X=BF₄^- (LT) X=BF₄^- (HT)

0 0.5 1

charge

0 0.5 1

E V / Å 0

50 100 150 200

α (10-24 cm3 )

Fc Pyl

Figure 2.21: Results of PM6 calculations for a FcPyl molecule with the crystal-lographic structures (see legend) under an external static electric field, F. F-dependence of the molecular dipole moment µ_x(top panel), molecular polarizabil-ity α (bottom panel), and total net charges (central panel) on the Fc (continuous line) and Pyl (dashed line) units. Dotted and dash-dotted vertical lines mark the DA⁺structure (F = 0) and the CT charge distribution, corresponding to flat regions of α.

0 0.5 1 1.5

0 0.5 1

0 0.5 1 1.5

z₀ / eV 0

0.5 1

c₁ 133K c₂ 133K c₁ 273K c₂ 273K 0.5

1

ρ

X^- = PF₆

-X^- = BF₄ -X^- = TFSI

-Figure 2.22: ρ(z₀) curves plotted for the M and F values calculated for each FcPylX structures (X= TFSI (top), X= PF₆(middle), X = BF₄(bottom)) as reported in tab. 2.4. Red lines and blue lines refer to low temperature (LT, 133K) and high temperature (HT, 273 K), respectively. Dashed lines refer to conformation c₂, where experimentally available.

132 FcPyl⁺: bistability in molecular ion crystals

The solution of the mf Hamiltonian in eq. 2.31 leads to results in figure 2.22, that shows the ρ(z₀)curves obtained for the M and F values in table 2.4; τ is set equal to 0.30 eV (see table 2.3). In all the cases a bistability region occurs.

For X=TFSI and X =PF₆the bistability occurs at z₀in the range 0.5 ÷ 0.6 eV, a value compatible with the parameters estimated in table 2.3.

A more exhaustive analysis including the fit of Mössbauer spectra is deferred to a subsequent work. We notice, however, that temperature dependent struc-tural data allows to calculate temperature dependent F and M values, suggest-ing a small increase of electrostatic interactions upon increassuggest-ing temperature.

This result can easily justify the experimental observation of Fc⁺Pyl / FcPyl⁺ concentration ratios larger than 1 ah high T, as extracted from Mössbuaer spec-tra [80].

The analysis of results relevant to FcPyl BF₄salt is more delicate. Remem-bering that for FcPyl⁺we estimate 0.5 ÷ 0.6 eV, data in fig. 2.22 suggest that at low T only the FcPyl⁺species is present in the crystal, so that, in agreement with experimental data, only in the neutral Fc signal is seen in Mössbauer spec-tra. However the same data, would predict in the high T phase a complete transformation of FcPyl⁺ to the Fc⁺Pyl, in contrast with experimental results.

While the delicate energy balance at the crossover and the fairly large uncer-tainties on molecular parameters and/or on electrostatic energies can explain this discrepancy, we also notice that the geometry of FcPyl⁺unit is different in the three salt, leading to slightly different molecular properties. In particular data in fig. 2.22 show the F-dependence of molecular properties as a function of the applied electric field. The results are different depending on the molec-ular geometry and in particmolec-ular the results obtained for the geometry relevant to the FcPylBF₄salts are much smoother than for the two other salts. This sug-gests a larger conjugation between Fc and Pyl fragments, i. e. a larger τ in the two state model for the FcPyl unit in the BF₄ salt. This observation is also in line with results from TDDFT calculations in ref. [78], that obtain a larger HOMO-LUMO gap for the FcPyl molecule in the geometry for the FcPylBF₄salt than for other geometries. A larger HOMO-LUMO gap definitively implies a larger conjugation (or possibly a large z₀value) and not a smaller conjugation as incorrectly suggested in ref. [78].

While we are not able to completely explain experimental observation for FcPylBF₄ crystals, results in fig. 2.22 exclude bistable behavior for this salt, at variance with FcPylTFSI and PF₆ salts. The M energies are similar for the three salts. In fact only electrostatic interaction energies between the FcPyl units enter the M expression (see eq. 2.30), and in view of the similar crystal

structures of the three salts, similar M values are calculated. The difference between the three salts is related to different F values. Interaction between FcPyl units and counterions explicitly enter the F expression (eq. 2.29), leading to a large variability of F with the counterion. This suggests that crystals of molecular ions, like DA⁺ or DA⁻, are particularly interesting for bistability. In these systems in fact a careful choice of the counterion offers a powerful tool to tune intermolecular electrostatic interactions as to guide the system towards bistability regions.

134 TTFPTM and related systems

2.3 TTFPTM

and related systems: bistability and