Optical transitions of symmetrical mixed-valence systems in the Class II-III transition regime

In the Robin and Day classification, mixed-valence systems are characterized as Class I, II or III depending on the strength of the electronic interaction between the oxidized and reduced sites, ranging from essentially zero (Class I), to moderate (Class II), to very strong electronic coupling (Class III). The properties of Class I systems are essentially those of the separate sites. Class II systems possess new optical and electronic properties in addition to those of the separate sites. However, the interaction between the sites is sufficiently weak that Class II systems are valence trapped or charge localized and can the be described by a double-well potential. In Class III systems the interaction of the donor and acceptor sites is so great that two separate minima are no longer discernible and the energy surface features a single minimum. The electron is delocalized and the system has its own unique properties. The Robin and Day classification has enjoyed considerable success and most of the redox systems studied to date are readily assigned to Class II. However the situation becomes much more complicated when the system shows borderline Class II/III behavior. Such "almost delocalized" mixed-valence systems are difficult to characterize. In this article spectral band shapes and intensities are calculated utilizing increasingly complex models including two to four states. Free-energy surfaces are constructed for harmonic diabetic surfaces and characterized as a function of increasing electronic coupling to simulate the Class II to III transition. The properties of the charge-transfer absorption bands predicted for borderline mixed-valence systems are compared with experimental data. The treatment is restricted to symmetrical (delta G0 = 0) systems.     

Ab initio calculations on some transition metal heptoxides by using effective core potentials

The ab initio molecular structures and vibrational frequencies for several transition metal heptoxides X₂O₇ⁿ⁻ (n=0, 2, 4) were calculated using effective core potentials at the HF and DFT (B3LYP) levels. The relative merits of different valence basis set arrangements were tested by comparison with experimental results available, in particular with gas-phase Re₂O₇ molecular structure and vibrational frequencies. The calculations were then extended to other heptoxides of the VB, VIB and VIIB transition metal groups. The results indicate that a staggered geometry (either D_3d or C₂) is the energy minimum for most of the heptoxides studied. The only exceptions are Mn₂O₇, which clearly prefers an eclipsed C_2v(syn) configuration, and Tc₂O₇, for which C₂ and C_2v(syn) geometries have nearly the same energy.

Particular attention was given to the magnitude of the X–O–X bond angle, as this structural parameter has been a matter of some controversy. The calculated values range from 125° (Mn₂O₇) to 180° (Group VB heptoxides) and depend on the position of the transition metal in the Periodic Table. A tendency for linearity of the X–O–X moiety on going both downwards the group and backwards the period was observed and discussed.     

Microwave spectroscopy measurements of rotational spectra and DFT calculations for two distinct structural isomers of 1,1'-dimethylferrocene

Microwave spectra were obtained for two distinct structural isomers of 1,1'-dimethylferrocene, an eclipsed synperiplanar isomer (phi = 0 degrees, the E0 isomer), with A = 1176.9003(2) MHz, B = 898.3343(2) MHz, C = 668.7469(2) MHz, and an eclipsed synclinal isomer (phi = 72 degrees, the E72 isomer) with A = 1208.7117(14) MHz, B = 806.4101(12) MHz, and C = 718.7179(8) MHz. The b-dipole, asymmetric-top spectra of both structural isomers were measured in the frequency range of 5-12 GHz using a Flygare-Balle type of spectrometer. A very good fit to observed transitions, with small distortion constants, was obtained for the E0 conformer, indicating that this conformer is nearly rigid. The deviations obtained in a similar least-squares fit for the E72 confomer are significantly larger, indicating possible fluxional behavior for this conformer. In addition, 7 out of the 26 transitions observed for the E72 isomer conformer clearly exhibit very small splittings, giving further evidence for internal motion. DFT calculations for the different possible conformations of 1,1'- dimethylferrocene arising from rotation of one methyl cyclopentadienyl ligand relative to the other about the nominal C5 axis by an angle phi (dihedral angle) were performed using the B3PW91 functional. The calculations converged and were optimized for five structures on this torsional potential energy surface corresponding to different dihedral angles phi; three yielded energy minima, and two gave energy maxima, corresponding to transition states. The experimental results are in very good agreement with the results of the DFT calculations.     

Odd-even oscillations in first hyperpolarizability of dipolar chromophores: role of conformations of spacers

Quantum chemical calculations on the linear and nonlinear electric polarizabilities of dipolar molecules separated by the alkyl spacers have been performed on O(2)N-Ph-N=N-Ph-(CH(2))(n)-Ph-N=N-Ph-NO(2), n = 1-12. These molecules exhibit a very strong odd-even behavior in the first hyperpolarizabilities (beta), with large (small) beta for n = odd (n = even). Such odd-even oscillations have been reported experimentally on similar systems, but the origin of such phenomena remains unclear. We propose it to be due to the role of the conformational orientation of the intervening alkyl spacers that leads to eclipsed orientation (parallel) of the dipoles for n = odd chains while staggered orientation (antiparallel) for n = even chains. The energy difference between the two extreme angular forms is approximately 6-8 kcal/mol, clearly more than the thermal fluctuations at room temperature. These conformational orientations will be preserved, leading to different packing arrangements at the macroscopic scale. We believe that it is this interaction at the molecular scale that controls such a macromolecular property.     

Through-bond versus through-space coupling in mixed-valence molecules: observation of electron localization at the single-molecule scale

Scanning tunneling microscopy (STM) is used to study two dinuclear organometallic molecules, meta-Fe2 and para-Fe2, which have identical molecular formulas but differ in the geometry in which the metal centers are linked through a central phenyl ring. Both molecules show symmetric electron density when imaged with STM under ultrahigh-vacuum conditions at 77 K. Chemical oxidation of these molecules results in mixed-valence species, and STM images of mixed-valence meta-Fe2 show pronounced asymmetry in electronic state density, despite the structural symmetry of the molecule. In contrast, images of mixed-valence para-Fe2 show that the electronic state density remains symmetric. Images are compared to constrained density functional (CDFT) calculations and are consistent with full localization of charge for meta-Fe2 on to a single metal center, as compared with charge delocalization over both metal centers for para-Fe2. The conclusion is that electronic coupling between the two metal centers occurs through the bonds of the organic linker, and through-space coupling is less important. In addition, the observation that mixed-valence para-Fe2 is delocalized shows that electron localization in meta-Fe2 is not determined by interactions with the Au(111) substrate or the position of neighboring solvent molecules or counterion species.     

Electrostatic Interactions That Determine the Rate of Pseudorotation Processes in Oxyphosphorane Intermediates: Implications with Respect to the Roles of Metal Ions in the Enzymatic Cleavage of RNA

The enzymatic cleavage of RNA takes place via a cyclic pentacoordinate oxyphosphorane intermediate/transition state. We carried out ab initio investigations on the neutral cyclic oxyphosphorane, which exists as a stable intermediate. As a consequence of the conformational preferences of the pentacoordinate trigonal bipyramidal intermediates, the rotation of the P-OH bonds is strongly coupled with the reaction coordinate for the pseudorotation process. In addition, the neutral PF(4)OH species has a higher barrier to pseudorotation than the corresponding anionic species PF(4)O(-). These findings are related to the positive charge of the hydrogen atoms on the equatorial oxygens in the trigonal bipyramidal structures: the hydrogen atoms preferably adopt eclipsed positions relative to the axial ligands. Fixing the cationic species in these regions causes an increase in the barrier heights for pseudorotation processes and, thus, prevents isomerization by pseudorotation. Consequently, metal coordination in the double-metal ion mechanism for enzymatic cleavage of RNA should serve to exclusively stabilize the trigonal bipyramidal intermediate/transition state for the in-line attack and departure process.     

Inter- or intramolecular electron transfer between triruthenium clusters: we’ll cross that bridge when we come to it

The purpose of this review is to examine the fundamental differences between intermolecular self-exchange vs. intramolecular ET in mixed-valence complexes based on similar triruthenium structural units. The role of orbital overlap between ancillary ligands of the electron donor and acceptor are considered in self-exchange reactions which are found to be strongly adiabatic and again in bridged mixed-valence systems. The method of infrared (IR) reflectance spectroelectrochemistry for the determination of extremely fast (10¹¹–10¹³ s^?1) ET rate constants is reviewed as a tool to provide quantitative information about the time scales of localization and delocalization. The role of internal vibrations of the bridging ligand in strongly delocalized mixed-valence ions is investigated by resonance Raman and IR spectroscopies. The role of solvent dipolar relaxation times in determining the rates of ultrafast intramolecular ET reactions is reviewed in the context of inorganic mixed-valence chemistry. Finally, the concept of Robin–Day Class II/III “borderline” complexes is considered, and a concise definition of the localized to delocalized transition is provided in terms of the relative contributions of external solvent and internal complex ion vibrational modes to ET.     

Multisite effects on intervalence charge transfer in a clusterlike trinuclear assembly containing ruthenium and osmium

The intervalence charge transfer (IVCT) properties of the mixed-valence forms of the diastereoisomers of the dinuclear [[Ru(bpy)2](mu-HAT)[M(bpy)2]]5+ (M = Ru or Os) complexes and the trinuclear heterochiral [[Ru(bpy)2]2[Os(bpy)2](mu-HAT)]n+ (n = 7, 8; HAT = 1,4,5,8,9,12-hexaazatriphenylene; bpy = 2,2'-bipyridine) species display a marked dependence on the nuclearity and extent of oxidation of the assemblies, while small differences are also observed for the diastereoisomers of the same complex in the dinuclear cases. The mixed-valence heterochiral [[Ru(bpy)2]2[Os(bpy)2](mu-HAT)]n+ (n = 7, 8) forms exhibit IVCT properties that are intermediate between those of the diastereoisomeric forms of the localized hetero-dinuclear complex [[Ru(bpy)2](mu-HAT)[Os(bpy)2]]5+ and the borderline localized-to-delocalized homo-trinuclear complex [[Ru(bpy)2]3(mu-HAT)]n+ (n = 7, 8). The near-infrared (NIR) spectrum of the +7 mixed-valence species exhibits both interconfigurational (IC) and IVCT transitions which are quantitatively similar to those in [[Ru(bpy)2](mu-HAT)[Os(bpy)2]]5+ and are indicative of the localized mixed-valence formulation [[Ru(II)(bpy)2]2[Os(III)(bpy)2](mu-HAT)]7+. The +8 state exhibits a new band attributable to an IVCT transition in the near-infrared region.     

Synthesis and characterization of K(38)Nb(7)As(24) and Cs(9)Nb(2)As(6): the first mixed-valence transition-metal Zintl phases

The two title compounds were prepared by direct reactions of the corresponding elements at high temperature, and their structures were determined from single-crystal X-ray diffraction data. The structure of K(38)Nb(7)As(24) (orthorhombic; Cmcm; Z = 4; a = 10.4974(6), b = 23.915(2), c = 36.046(2) A) comprises isolated tetrahedra of NbAs(4) and two types of dimers of edge-sharing tetrahedra: dimers containing only Nb(V), [Nb(V)2As(6)](8-), and mixed-valence dimers with both Nb(IV) and Nb(V), [Nb(IV)Nb(V)As(6)](9-). The structure of Cs(9)Nb(2)As(6) (orthorhombic; Pbca; Z = 8; a = 17.5848(7), b = 16.940(2), c = 18.183(4) A) contains only the latter dimers. Magnetic measurements showed Curie-Weiss paramagnetic behavior for both compounds consistent with one unpaired electron/mixed-valence dimer. Cs(9)Nb(2)As(6) exhibits also an antiferromagnetic transition at about 36 K. The two compounds are the first mixed-valence (of class III) transition-metal Zintl phases.     

Dynamical Cooperativity in Electron Delocalization of Mixed-Valence Biferrocenium Complexes

Abstract

Intramolecular electron transfer in the mixed-valence biferrocenium complexes in crystals shows qualitatively different behavior from that in the complexes in solutions. The ‘extra’ electron in a mixed-valence complex in the crystal may be localized at low temperature and delocalized at higher temperature. The electron localization-delocalization transition induced thermally corresponds to a kind of order-disorder phase transition. In order to clarify the mechanism of the transition, a statistical mechanical model has been proposed (T. Kambara, D.N. Hendrickson, T.-Y. Dong, and M. J. Cohn, J. Chem. Phys., 86, 2362 (1987)). The temperature dependences of the physical quantities relevant to the cooperative electron localization-delocalization transition are calculated base on the model. In the calculation a more elaborate treatment is adopted for the intermolecular interactions. Those calculated values are compared with the observed ones for various kinds of mixed-valence biferrocenium trihalide crystals and reasonable agreements are obtained.     

Self‐Sorting of Cyclic Peptide Homodimers into a Heterodimeric Assembly Featuring an Efficient Photoinduced Intramolecular Electron‐Transfer Process

We describe the thermodynamic characterisation of the self‐sorting process experienced by two homodimers assembled by hydrogen‐bonding interactions through their cyclopeptide scaffolds and decorated with Zn–porphyrin and fullerene units into a heterodimeric assembly that contains one electron‐donor (Zn–porphyrin) and one electron‐acceptor group (fullerene). The fluorescence of the Zn–porphyrin unit is strongly quenched upon heterodimer formation. This phenomenon is demonstrated to be the result of an efficient photoinduced electron‐transfer (PET) process occurring between the Zn–porphyrin and the fullerene units of the heterodimeric system. The recombination lifetime of the charge‐separated state of the heterodimer complex is in the order of 180 ns. In solution, both homo‐ and heterodimers are present as a mixture of three regioisomers: two staggered and one eclipsed. At the concentration used for this study, the high stability constant determined for the heterodimer suggests that the eclipsed conformer is the main component in solution. The application of the bound‐state scenario allowed us to calculate that the heterodimer exists mainly as the eclipsed regioisomer (75–90 %). The attractive interaction that exists between the donor and acceptor chromophores in the heterodimeric assembly favours their arrangement in close contact. This is confirmed by the presence of charge‐transfer bands centred at 720 nm in the absorption spectrum of the heterodimer. PET occurs in approximately 75 % of the chromophores after excitation of both Zn–porphyrin and fullerene chromophores. Conversely, analogous systems, reported previously, decorated with extended tetrathiafulvalene and fullerene units showed a PET process in a significantly reduced extent (33 %). We conclude that the strength (stability constant (K)×effective molarity (EM)) of the intramolecular interaction established between the two chromophores in the Zn–porphyrin/fullerene cyclopeptide‐based heterodimers controls the regioisomeric distribution and regulates the high extent to which the PET process takes place in this system.     

π‐Electron Systems That Form Planar and Interlocked Anion Complexes and Their Ion‐Pairing Assemblies

Interactions between designed charged species are important for the ordered arrangements of π‐electron systems in assembled structures. As precursors of π‐electron anion units, new arylethynyl‐substituted dipyrrolyldiketone boron complexes, which showed anion‐responsive behavior, were synthesized. They formed a variety of receptor–anion complexes ([1+1] and [2+1] types) in solution, and the stabilities of these complexes were discussed in terms of their thermodynamic parameters. Solid‐state ion‐pairing assemblies of [1+1]‐ and [2+1]‐type complexes with countercations were also revealed by single‐crystal X‐ray analysis. In particular, a totally charge‐segregated assembly was constructed based on negatively and positively charged layers fabricated from [2+1]‐type receptor–anion complexes and tetrabutylammonium cations, respectively. Furthermore, the [1+1]‐type anion complex of the receptor possessing long alkyl chains exhibited mesophases based on columnar assembled structures with contributions from charge‐by‐charge and charge‐segregated arrangements, which exhibited charge‐carrier transporting properties.     

On the Low-Lying Electronically Excited States of Azobenzene Dimers: Transition Density Matrix Analysis

Azobenzene-containing molecules may associate with each other in systems such as self-assembled monolayers or micelles. The interaction between azobenzene units leads to a formation of exciton states in these molecular assemblies. Apart from local excitations of monomers, the electronic transitions to the exciton states may involve charge transfer excitations. Here, we perform quantum chemical calculations and apply transition density matrix analysis to quantify local and charge transfer contributions to the lowest electronic transitions in azobenzene dimers of various arrangements. We find that the transitions to the lowest exciton states of the considered dimers are dominated by local excitations, but charge transfer contributions become sizable for some of the lowest ππ* electronic transitions in stacked and slip-stacked dimers at short intermolecular distances. In addition, we assess different ways to partition the transition density matrix between fragments. In particular, we find that the inclusion of the atomic orbital overlap has a pronounced effect on quantifying charge transfer contributions if a large basis set is used.     

Charge localization in a 17-bond mixed-valence quinone radical anion

Optical spectra in dimethylformamide are reported for the radical anions of benzoquinone, its tetramethyl and tetrachloro analogues, and tetra-ortho-alkyl derivatives of biphenyl, stilbene, terphenyl, quadriphenyl, and 1,4-bis(2-phenylethenyl)benzene quinones. The first absorption bands for all but the quadriphenyl quinone show vibrational fine structure, demonstrating that they are delocalized (Class III) mixed-valence compounds. The quadriphenyl quinone radical anion shows a wide Gaussian-shaped band having a band maximum that is strongly dependent on solvent, typical of localized (Class II) mixed-valence compounds. The simple O charge-bearing unit of these compounds maintains charge delocalization in examples with unusually large bridges.     

Excited-state mixed valence in a diphenyl hydrazine cation: Spectroscopic consequences of coupling and transition dipole moment orientation

A quantitative model of mixed-valence excited-state spectroscopy is developed and applied to 2,3-diphenyl-2,3-diazabicyclo[2.2.2]octane. The lowest-energy excited state of this molecule arises from a transition from the ground state, where the charge is located on the hydrazine bridge, to an excited state where the charge is associated with one phenyl group or the other. Coupling splits the absorption band into two components with the lower-energy component being the most intense. The sign of the coupling, derived by using a neighboring orbital model, is positive. The transition dipole moments consist of parallel and antiparallel vector components, and selection rules for each are derived. Bandwidths are caused by progressions in totally symmetric modes determined from resonance Raman spectroscopic analysis. The absorption, emission, and Raman spectra are fit simultaneously with one parameter set.     

Solvent induced channel interference in the two-photon absorption process--a theoretical study with a generalized few-state-model in three dimensions

For the first time, we report the effect of interference between different optical channels on the two-photon absorption (TPA) process in three dimensions. We have employed response theory as well as a sum-over-states (SOS) approach involving few intermediate states to calculate the TPA parameters like transition probabilities (δ(TP)) and TPA tensor elements. In order to use the limited SOS approach, we have derived a new formula for a generalized few-state-model (GFSM) in three dimensions. Due to the presence of additional terms related to the angle between different transition moment vectors, the channel interference associated with the TPA process in 3D is significantly different and much more complicated than that in 1D and 2D cases. The entire study has been carried out on the two simplest Reichardt's dyes, namely 2- and 4-(pyridinium-1-yl)-phenolate (ortho- and para-betain) in gas phase, THF, CH(3)CN and water solvents. We have meticulously inspected the effect of the additional angle related terms on the overall TPA transition probabilities of the two 3D isomeric molecules studied and found that the interfering terms involved in the δ(TP) expression contribute both constructively and destructively as well to the overall δ(TP) value. Moreover, the interfering term has a more conspicuous role in determining the net δ(TP) associated with charge transfer transition in comparison to that of π-π* transition of the studied systems. Interestingly, our model calculations suggest that, for o- and p-betain, the quenching of destructive interference associated with a particular two-photon process can be done with high polarity solvents while the enhancement of constructive interference will be achieved in solvents having relatively small polarity. All the one- and two-photon parameters are evaluated using a range separated CAMB3LYP functional.     

TTF-Annulated Silicon Phthalocyanine Oligomers and Their External-Stimuli-Responsive Orientational Ordering

Orientational control of functional molecules is essential to create complex functionalities as seen in nature; however, such artificial systems have remained challenge. Herein, we have succeeded in controlling rotational isomerism of μ-oxo silicon phthalocyanine (SiPc) oligomers to achieve an external-stimuli-responsive orientational ordering using intermolecular interactions of tetrathiafulvalene (TTF). In this system, three modes of orientations, free rotation, eclipsed conformation, and staggered conformation, were interconverted in response to the oxidation states of TTF, which varied interactions from association due to formation of mixed-valence TTF dimer to dissociation due to electrostatic repulsion between TTF dications. Furthermore, a stable performance of oligomers as a cathode material in a Li-ion battery proved that the one-dimensionally stacked, rotatable structure of SiPc oligomers is useful to control the orientation of functional molecules toward molecular electronics.     

An unusual dinuclear ruthenium(III) complex with a conjugated bridging ligand derived from cleavage of a 1,4-dihydro-1,2,4,5-tetrazine ring. Synthesis,structure, and UV-vis-NIR spectroelectrochemical characterization of a five-membered redox chain incorporating two mixed-valence states

Reaction of [Ru(acac)(2)(CH(3)CN)(2)] with 3,6-bis(3,5-dimethylpyrazol-1-yl)-1,4-dihydro-1,2,4,5-tetrazine (H(2)L) results in formation of an unexpected dinuclear complex [(acac)(2)Ru(III)(L(1))Ru(III)(acac)(2)] (1) in which the bridging ligand [L(1)](2)(-) contains an (-)HN[bond]C[double bond]N[bond]N[double bond]C[bond]NH(-) unit arising from two-electron reduction of the 1,4-dihydro-1,2,4,5-tetrazine component of H(2)L. The crystal structure of complex 1 confirms the oxidation assignment of the metal ions as Ru(III) and clearly shows the consequent arrangement of double and single bonds in the bridging ligand, which acts as a bis-bidentate chelate having two pyrazolyl/amido chelating sites. Cyclic voltammetry of the complex shows the presence of four reversible one-electron redox couples, assigned as two Ru(III)/Ru(IV) couples (oxidations with respect to the starting material) and two Ru(II)/Ru(III) couples (reductions with respect to the starting material). The separation between the two Ru(III)/Ru(IV) couples (Delta E(1/2) = 700 mV) is much larger than that between the two Ru(II)/Ru(III) couples (Delta E(1/2) = 350 mV) across the same bridging pathway, because of the better ability of the dianionic bridging ligand to delocalize an added hole (in the oxidized mixed-valence state) than an added electron (in the reduced mixed-valence state), implying some ligand-centered character for the oxidations. UV-vis-NIR spectroelectrochemical measurements were performed in all five oxidation states; the Ru(II)-Ru(III) mixed-valence state of [1](-) has a strong IVCT transition at 2360 nm whose parameters give an electronic coupling constant of V(ab) approximately 1100 cm(-1), characteristic of a strongly interacting but localized (class II) mixed-valence state. In the Ru(III)-Ru(IV) mixed-valence state [1](+), no low-energy IVCT could be detected despite the strong electronic interaction, possibly because it is in the visible region and obscured by LMCT bands.