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For examples where through-space interactions dominate (but do not completely define) electronic communication in metal- and organic-based mixed-valence systems, see: (a) Elliott, C. M.; Derr, D. L.; Ferrere, S.; Newton, M. D.; Liu, Y. P. J. Am. Chem. Soc. 1996, 118, 5221-5228.
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33645362415
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note
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An energetic and geometric subtlety may exist here. Recall that van der Waals forces (responsible for assembly collapse) are exceptionally short-range forces. If they are counterbalanced by an electrostatic interaction sufficient enough to separate the porphyrin ligands slightly, significant further separation should occur, with minimal additional loss of favorable van der Waals interactions, because of the geometric stabilization (covalent bond stabilization) obtainable by restraightening the two bent ethynyl pyridine moieties. The fully expanded conformation then leads to smaller-than-otherwise- expected ligand/ligand electrostatic repulsions (and charge-state differences in repulsion) for the 2-, 3-, and 4- assemblies.
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33645357151
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Geometric differences also likely account for the absence of observable intervalence band intensity in the triply reduced form of 1. As discussed above, an open-cavity geometry (and therefore reduced orbital overlap and intervalence intensity) would be expected based on porphyrin-anion/porphyrin-anion electrostatic repulsion.
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0037451468
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We note that TD-DFT calculations should be used with care, since it is known that, because of inherent problems in the applied standard exchange-correlation functionals, TD-DFT fails to describe adequately the charge-transfer transitions in weakly electronic coupled systems. See for instance: (a) Grimme, S.; Parac, M. ChemPhysChem 2003, 4, 292-295.
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33645366936
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note
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Ligation of the Zn(II) centers by THF (as opposed to very weak ligation by methylene chloride) should increase the overall electron density on the porphyrin ligands, potentially accounting for the increase in electronic coupling.
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28
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33645378450
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note
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Unfortunately, baseline problems (probably due to the slow decomposition of the doubly reduced assembly) were encountered with the chemical reduction method. We suspect that these account for the slight difference between energies recorded following chemical vs electrochemical reduction. Most affected by baseline problems were measurements made in dimethylformamide as solvent, making these the least reliable entries in the table. The true energies in DMF are likely slightly smaller than those reported.
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The non-Liptay first-derivative contribution can appear regardless of whether vibronic coupling is important. Its origin is in the double-welled ground potential energy surface that characterizes symmetrical class II mixed-valence species. In the presence of a tiny applied field, essentially equal numbers of MV molecules will be oriented with dipole moments parallel to the field vs antiparallel to it. In the presence of a large field, one orientation will be significantly energetically stabilized and the other will be destabilized. Consequently, the intervalence band for one will be slightly blue-shifted, and the intervalence band for the other red-shifted. This is the origin of the standard Stark spectral broadening effect that appears as a second-derivative contribution to the electroabsorbance spectrum. A large field, however, can shift a significant portion of the population of one orientation (the energetically destabilized one) to the other orientation (the energetically stabilized one), with the shift being accomplished simply by intramolecular electron transfer. The field, therefore, generates more of the blue-shifted form. The blue shift appears in the difference spectrum (Stark spectrum) as a first-derivative contribution. The effect ought to show up, to a degree, whenever a completely symmetrical double-welled system is examined. In a low dielectric matrix, such as a glass used for Stark measurements, however, the mixed-valence species and its counterion will tend to pair. Ion pairing is well-known to introduce an energetic asymmetry in mixed-valence molecules because the ion preferentially interacts with the more highly charged half of the molecule. In extreme cases, the asymmetry can reach a few hundred millielectronvolts. (See, for example: Blackbourn, R. L.; Dong, Y.; Lyon, L. A.; Hupp, J. T. Inorg. Chem. 1994, 33, 4446-4452.) The non-Liptay blue-shift effect, therefore, will become important only when the external field is sufficient to offset the pairing-induced redox asymmetry. The system examined here may well be such a case since the charge of the mixed-valence assembly is low and the cation and anion sizes are relatively large. On the other hand, the effects of the external field are also low: about 24 meV for the conditions in Figure 6, if the molecule is perfectly aligned and a 3.4 Å charge-transfer distance is assumed. Notably, the spectrum measured at a quarter of this field strength yields the same values (within a few percent, i.e., smaller than the fitting uncertainties) for dipole moment changes and polarizability changes. Nevertheless, the values obtained here for polarizability changes probably should not be taken too seriously.
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