Charge-transfer transitions in triarylamine mixed-valence systems: a joint density functional theory and vibronic coupling study

A theoretical model is developed to describe the intramolecular transfer in organic mixed-valence systems. It is applied to rationalize the intervalence charge-transfer transitions in triarylamine mixed-valence compounds. The electronic coupling parameter is evaluated at the density functional theory (DFT) and time-dependent density functional theory (TD-DFT) levels. The shapes of the charge-transfer absorption bands are analyzed in the framework of a dynamic vibronic model. The influence on the optical properties of diagonal and nondiagonal vibronic couplings is discussed. Our results are compared to recent experimental data.     

Charge delocalization in a homologous series of α,α'-bis(dianisylamino)-substituted thiophene monocations

A homologous series of three molecules containing thiophene, bithiophene, and terthiophene bridges between two redox-active tertiary amino groups was synthesized and explored. Charge delocalization in the one-electron-oxidized forms of these molecules was investigated by a combination of cyclic voltammetry, near-infrared optical absorption spectroscopy, and EPR spectroscopy. All three cation radicals can be described as organic mixed-valence species, and for all of them the experimental data are consistent with strong delocalization of the unpaired electron. Depending on what model is used for analysis of the optical absorption data, estimates for the electronic coupling matrix element (H(AB)) range from ～5000 to ～7000 cm(-1) for the shortest member of the homologous series. According to optical absorption and EPR spectroscopy, even the terthiophene radical appears to belong either to Robin-Day class III or to a category of radicals commonly denominated as borderline class II/class III systems. The finding of such a large extent of charge delocalization over up to three adjacent thiophene units is remarkable.     

Calculation of the vibronic structure of the photodetachment spectra of CCCl- and CCBr-

The vibronic structure of the closely spaced and strongly coupled X 2Sigma+ and A 2Pi states in the photodetachment spectra of CCCl- and CCBr- has been calculated by considering Sigma-Pi vibronic coupling together with spin-orbit coupling. The stretching modes are treated within the so-called linear-vibronic-coupling model. The vibronic and spin-orbit parameters have been determined by accurate ab initio electronic-structure calculations. While the nonrelativistic vibronic-coupling parameters are of approximately equal strength in CCCl and CCBr, the vibronic-coupling parameters of spin-orbit origin are found to be larger in the latter. The calculated photodetachment spectra of both systems are shown to exhibit a complicated vibronic structure due to strong Sigma-Pi vibronic coupling. The spectral envelopes of the calculated photodetachment spectra exhibit a double-hump reminiscent of strongly coupled Exe Jahn-Teller systems.     

Donor-acceptor (electronic) coupling in the precursor complex to organic electron transfer: intermolecular and intramolecular self-exchange between phenothiazine redox centers

Intermolecular electron transfer (ET) between the free phenothiazine donor (PH) and its cation radical (PH*+) proceeds via the [1:1] precursor complex (PH)(2)*+ which is transiently observed for the first time by its diagnostic (charge-resonance) absorption band in the near-IR region. Similar intervalence (optical) transitions are also observed in mixed-valence cation radicals with the generic representation: P(br)P*+, in which two phenothiazine redox centers are interlinked by p-phenylene, o-xylylene, and o-phenylene (br) bridges. Mulliken-Hush analysis of the intervalence (charge-resonance) bands afford reliable values of the electronic coupling element H(IV) based on the separation parameters for (P/P*+) centers estimated from some X-ray structures of the intermolecular (PH)(2)*+ and the intramolecular P(br)P*+ systems. The values of H(IV), together with the reorganization energies lambda derived from the intervalence transitions, yield activation barriers DeltaG(ET)() and first-order rate constants k(ET) for electron-transfer based on the Marcus-Hush (two-state) formalism. Such theoretically based values of the intrinsic barrier and ET rate constants agree with the experimental activation barrier (E(a)) and the self-exchange rate constant (k(SE)) independently determined by ESR line broadening measurements. This convergence validates the use of the two-state model to adequately evaluate the critical electronic coupling elements between (P/P*+) redox centers in both (a) intermolecular ET via the precursor complex and (b) intramolecular ET within bridged mixed-valence cation radicals. Important to intermolecular ET mechanism is the intervention of the strongly coupled precursor complex since it leads to electron-transfer rates of self-exchange that are 2 orders of magnitude faster (and activation barrier that is substantially lower) than otherwise predicted solely on the basis of Marcus reorganization energy.     

Dications of bis-triarylamino-[2.2]paracyclophanes: Evaluation of excited state couplings by GMH analysis

In this paper, we present the absorption properties of a series of bis-triarylamino-[2.2]paracyclophane diradical dications. The localized pi-pi and the charge-transfer (CT) transitions of these dications are explained and analyzed by an exciton coupling model that also considers the photophysical properties of the "monomeric" triarylamine radical cations. Together with AM1-CISD-calculated transition moments, experimental transition moments and transition energies of the bis-triarylamine dications were used to calculate electronic couplings by a generalized Mulliken-Hush (GMH) approach. These couplings are a measure for interactions of the excited mixed-valence CT states. The modification of the diabatic states reveals similarities of the GMH three-level model and the exciton coupling model. Comparison of the two models shows that the transition moment between the excited mixed-valence states mu(ab) of the dimer equals the dipole moment difference Delta of the ground and the excited bridge state of the corresponding monomer.     

X-ray structure analysis and the intervalent electron transfer in organic mixed-valence crystals with bridged aromatic cation radicals

X-ray crystallography identifies the aromatic donor group D = 2,5-dimethoxy-4-methylphenyl to be a suitable redox center for the construction of organic mixed-valence crystals owing to its large structural change attendant upon 1e oxidation to the cation-radical (D*(+)). The combination of cyclic voltammetry, dynamic ESR line broadening, and electronic (NIR) spectroscopy allows the intervalence electron transfer between the redox centers in the mixed-valence system D-br-D*(+) [where br can be an aliphatic trimethylene or an aromatic (poly)phenylene bridge] to be probed quantitatively. Independent measures of the electronic coupling matrix element (H) for D/D*(+) electron exchange via Mulliken-Hush theory accord with the X-ray crystallographic data-both sufficient to consistently identify the various D-br-D*(+) according to the Robin-Day classification. Thus, the directly coupled biaryl D-D*(+) is a completely delocalized cation in class III with the charge distributed equally over both redox centers. The trimethylene- and biphenylene-bridged cations D(CH(2))(3)D*(+) and D(ph)(2)D*(+) with highly localized charge distributions are prototypical class II systems involving moderately coupled redox centers with H approximately equal to 400 cm(-1). The borderline region between class II/III is occupied by the phenylene-bridged cation D(ph)D*(+); and the X-ray, CV, and NIR analyses yield ambivalent H values (which we believe to be) largely a result of an unusually asymmetric (20/80) charge distribution that is polarized between the D/D*(+) redox centers.     

Ab initio study of dynamical E × e Jahn-Teller and spin-orbit coupling effects in the transition-metal trifluorides TiF3, CrF3, and NiF3

Multiconfiguration ab initio methods have been employed to study the effects of Jahn-Teller (JT) and spin-orbit (SO) coupling in the transition-metal trifluorides TiF(3), CrF(3), and NiF(3), which possess spatially doubly degenerate excited states ((M)E) of even spin multiplicities (M = 2 or 4). The ground states of TiF(3), CrF(3), and NiF(3) are nondegenerate and exhibit minima of D(3h) symmetry. Potential-energy surfaces of spatially degenerate excited states have been calculated using the state-averaged complete-active-space self-consistent-field method. SO coupling is described by the matrix elements of the Breit-Pauli operator. Linear and higher order JT coupling constants for the JT-active bending and stretching modes as well as SO-coupling constants have been determined. Vibronic spectra of JT-active excited electronic states have been calculated, using JT Hamiltonians for trigonal systems with inclusion of SO coupling. The effect of higher order (up to sixth order) JT couplings on the vibronic spectra has been investigated for selected electronic states and vibrational modes with particularly strong JT couplings. While the weak SO couplings in TiF(3) and CrF(3) are almost completely quenched by the strong JT couplings, the stronger SO coupling in NiF(3) is only partially quenched by JT coupling.     

Intermolecular coulomb couplings from ab initio electrostatic potentials: application to optical transitions of strongly coupled pigments in photosynthetic antennae and reaction centers

An accurate and numerically efficient method for the calculation of intermolecular Coulomb couplings between charge densities of electronic states and between transition densities of electronic excitations is presented. The coupling of transition densities yields the F?rster type excitation energy transfer coupling, and from the charge density coupling, a shift in molecular excitation energies results. Starting from an ab initio calculation of the charge and transition densities, atomic partial charges are determined such as to fit the resulting electrostatic potentials of the different states and the transition. The different intermolecular couplings are then obtained from the Coulomb couplings between the respective atomic partial charges. The excitation energy transfer couplings obtained in the present TrEsp (transition charge from electrostatic potential) method are compared with couplings obtained from the simple point-dipole and extended dipole approximations and with those from the ab initio transition density cube method of Krüger, Scholes, and Fleming. The present method is of the same accuracy as the latter but computationally more efficient. The method is applied to study strongly coupled pigments in the light-harvesting complexes of green sulfur bacteria (FMO), purple bacteria (LH2), and higher plants (LHC-II) and the "special pairs" of bacterial reaction centers and reaction centers of photosystems I and II. For the pigment dimers in the antennae, it is found that the mutual orientation of the pigments is optimized for maximum excitonic coupling. A driving force for this orientation is the Coulomb coupling between ground-state charge densities. In the case of excitonic couplings in the "special pairs", a breakdown of the point-dipole approximation is found for all three reaction centers, but the extended dipole approximation works surprisingly well, if the extent of the transition dipole is chosen larger than assumed previously. For the "special pairs", a large shift in local transition energies is found due to charge density coupling.     

Substituent effects on the vibronic coupling for the phenoxyl/phenol self-exchange reaction

The impact of substituents on the vibronic coupling for the phenoxyl/phenol self-exchange reaction, which occurs by a proton-coupled electron transfer mechanism, is investigated. The vibronic couplings are calculated with a grid-based nonadiabatic method and a nuclear-electronic orbital nonorthogonal configuration interaction method. The quantitative agreement between these two methods for the unsubstituted phenoxyl/phenol system and the qualitative agreement in the predicted trends for the substituted phenoxyl/phenol systems provides a level of validation for both methods. Analysis of the results indicates that electron-donating groups enhance the vibronic coupling, while electron-withdrawing groups attenuate the vibronic coupling. Thus, if all other aspects of the reaction are the same, then electron-donating groups will increase the rate, while electron-withdrawing groups will decrease the rate. Correlations between the vibronic coupling and physical properties of the phenol are also analyzed. Negative Hammett constants correspond to higher vibronic couplings, while positive Hammett constants correspond to similar or slightly lower vibronic couplings relative to the unsubstituted phenoxyl/phenol system. In addition, lower bond dissociation enthalpies, ionization potentials, and redox potentials, as well as higher pKa values, tend to correspond to higher vibronic couplings relative to the unsubstituted phenoxyl/phenol system. The observed trends enable the prediction of the impact of general substituents on the vibronic coupling, and hence the rate, for the phenoxyl/phenol self-exchange reaction. The fundamental physical insights obtained from these studies are applicable to other proton-coupled electron transfer systems.     

Vibronic coupling in cyclopentadienyl radical: a method for calculation of vibronic coupling constant and vibronic coupling density analysis

A method of calculation of vibronic or electron-phonon coupling constant is presented for a Jahn-Teller molecule, cyclopentadienyl radical. It is pointed out that symmetry breaking at degenerate point and violation of Hellmann-Feynman theorem occur in the calculations based on a single Slater determinant. In order to overcome these difficulties, the electronic wave functions are calculated using generalized restricted Hartree-Fock and complete active space self-consistent-field method and the couplings are computed as matrix elements of the electronic operator of the vibronic coupling. Our result agrees well with the experimental and theoretical values. A concept of vibronic coupling density is proposed in order to explain the order of magnitude of the coupling constant from view of the electronic and vibrational structures. It illustrates the local properties of the coupling and enables us to control the interaction. It could open a way to the engineering of vibronic interactions.     

On the construction of quasidiabatic state representations of bound adiabatic state potential energy surfaces coupled by accidental conical intersections: incorporation of higher order terms

The quadratic vibronic coupling model is an important computational tool for simulating photoelectron spectra involving strongly coupled electronic states in polyatomic molecules. However, recent work has indicated the need for higher order terms, with most of the initial studies focusing on molecules with symmetry-required degeneracies. In this study we report an extension of our approach for constructing fully quadratic representations of bound electronic states coupled by conical intersections, which allows for the inclusion of higher order terms, demonstrated here employing a quartic expansion. Procedures are developed that eliminate unphysical behavior for large displacements, a problem likely to be an endemic to anharmonic expansions. Following work on representing dissociative electronic states, Lagrange multipliers are used to constrain the constructed representation to reproduce exactly the energy, energy gradients, and∕or derivative couplings at specific points, or nodes, in nuclear coordinate space. The approach is illustrated and systematically studied using the four lowest electronic states of triazolyl, (CH)(2)N(3).     

Influences of Quantum Mechanically Mixed Electronic and Vibrational Pigment States in 2D Electronic Spectra of Photosynthetic Systems: Strong Electronic Coupling Cases

In 2D electronic spectroscopy studies, long‐lived quantum beats have recently been observed in photosynthetic systems, and several theoretical studies have suggested that the beats are produced by quantum mechanically mixed electronic and vibrational states. Concerning the electronic‐vibrational quantum mixtures, the impact of protein‐induced fluctuations was examined by calculating the 2D electronic spectra of a weakly coupled dimer with the Franck‐Condon active vibrational modes in the resonant condition [Fujihashi et al., J. Chem. Phys.­ 2015 , 142, 212403.]. This analysis demonstrated that quantum mixtures of the vibronic resonance are rather robust under the influence of the fluctuations at cryogenic temperatures, whereas the mixtures are eradicated by the fluctuations at physiological temperatures. However, this conclusion cannot be generalized because the magnitude of the coupling inducing the quantum mixtures is proportional to the inter‐pigment electronic coupling. In this study, we explore the impact of the fluctuations on electronic‐vibrational quantum mixtures in a strongly coupled dimer with an off‐resonant vibrational mode. Toward this end, we calculate energy transfer dynamics and 2D electronic spectra of a model dimer that corresponds to the most strongly coupled bacteriochlorophyll molecules in the Fenna‐Matthews‐Olson complex in a numerically accurate manner. The quantum mixtures are found to be robust under the exposure of protein‐induced fluctuations at cryogenic temperatures, irrespective of the resonance. At 300 K, however, the quantum mixing is disturbed more strongly by the fluctuations, and therefore, the beats in the 2D spectra become obscure even in a strongly coupled dimer with a resonant vibrational mode. Further, the overall behaviors of the energy transfer dynamics are demonstrated to be dominated by the environment and coupling between the 0 0 vibronic transitions as long as the Huang‐Rhys factor of the vibrational mode is small. The electronic‐vibrational quantum mixtures do not necessarily play a significant role in electronic energy transfer dynamics despite contributing to the enhancement of long‐lived quantum beating in the 2D spectra.     

Zero-point fluctuations in naphthalene and their effect on charge transport parameters

We calculate the effect of vibronic coupling on the charge transport parameters in crystalline naphthalene, between 0 and 400 K. We find that nuclear fluctuations can cause large changes in both the energy of a charge on a molecule and on the electronic coupling between molecules. As a result, nuclear fluctuations cause wide distributions of both energies and couplings. We show that these distributions have a small temperature dependence and that, even at high temperatures, vibronic coupling is dominated by the effect of zero-point fluctuations. Because of the importance of zero-point fluctuations, we find that the distributions of energies and couplings have substantial width, even at 0 K. Furthermore, vibronic coupling with high energy modes may be significant, even though these modes are never thermally activated. Our results have implications for the temperature dependence of charge mobilities in organic semiconductors.     

Contributions of symmetric and asymmetric normal coordinates to the intervalence electronic absorption and resonance Raman spectra of a strongly coupled p-phenylenediamine radical cation

Resonance Raman spectroscopy, electronic absorption spectroscopy, and the time-dependent theory of spectroscopy are used to analyze the intervalence electron transfer properties of a strongly delocalized class III molecule, the tetraalkyl-p-phenylene diamine radical cation bis(3-oxo-9-azabicyclo[3.3.1]non-9-yl)benzene ((k33)(2)PD(+)). This molecule is a prototypical system for strongly coupled organic intervalence electron transfer spectroscopy. Resonance Raman excitation profiles in resonance with the lowest energy absorption band are measured. The normal modes of vibration that are most strongly coupled to the intervalence transition are identified and assigned by using UB3LYP/6-31G(d) calculations. Excited state distortions are obtained, and the resonance Raman intensities and excitation profiles are calculated by using the time-dependent theory of Raman spectroscopy. The most highly distorted normal modes are all totally symmetric, but intervalence electron transfer absorption spectra are usually interpreted in terms of a model based on coupling between potential surfaces that are displaced along an asymmetric normal coordinate. This model provides a convenient physical picture for the intervalence compound, but it is inadequate for explaining the spectra. The absorption spectrum arising from only the strongly coupled surfaces consists of a single narrow band, in contrast to the broad, vibronically structured experimental spectrum. The electronic absorption spectrum of (k33)(2)PD(+) is calculated by using exactly the same potential surfaces as those used for the Raman calculations. The importance of symmetric normal coordinates, in addition to the asymmetric coordinate, is discussed. The observed vibronic structure is an example of the missing mode effect; the spacing is interpreted in terms of the time-dependent overlaps in the time domain.     

Vibronic coupling in benzene cation and anion: vibronic coupling and frontier electron density in Jahn-Teller molecules

Vibronic coupling constants of Jahn-Teller molecules, benzene radical cation and anion, are computed as matrix elements of the electronic part of the vibronic coupling operator using the electronic wave functions calculated by generalized restricted Hartree-Fock and state-averaged complete active space self-consistent-field methods. The calculated vibronic coupling constants for benzene cation agree well with the experimental and theoretical values. Vibronic coupling density analysis, which illustrates the local properties of the coupling, is performed in order to explain the order of magnitude of the coupling constant from view of the electronic and vibrational structures. This analysis reveals that the couplings of the e2g2 and e2g3 modes in which the large displacements locate on C-C bonds are strong in the cation. On the other hand, they are greatly weakened in the anion because of the decrease of electron density in the region of the C-C bonds, which originates from the antibonding nature of the singly occupied molecular orbital of the anion. However, the difference of the electronic structure has a little influence on the vibronic coupling of the e2g4 mode. These results indicate that the vibronic coupling depends not only on the direction of the nuclear displacement but also on the frontier electron density.     

Model aluminum-poly(p-phenylenevinylene) interfaces studied by surface raman spectroscopy

Polymeric organic light-emitting diodes (OLEDs) have emerged as inexpensive and versatile alternatives to traditional inorganic-based display technologies. Further advances in this field depend on extending device lifetimes and improving electroluminescence efficiencies, both of which are strongly coupled to the integrity of the electrode/organic contacts. Therefore, the deposition of low-work function metals on organic materials has been extensively studied by X-ray photoelectron spectroscopy (XPS), ultraviolet photoemission spectroscopy (UPS), and near-edge X-ray adsorption fine structure (NEXAFS) to ascertain information about the chemical and electronic states within the interfacial region. However, to date, the only molecular structural information about metal-organic species formed in these regions has come from fits of theoretical models to existing XPS and UPS data. Very little direct structural information exists about the potential multitude of metal-organic species formed during cathode deposition. We report the use of surface Raman spectroscopy to study the interactions between aluminum and trans-stilbene, a model for poly(p-phenylenevinylene) (PPV). The Raman spectral data suggest preferential formation of covalent Al-C bonds at the vinylene carbons as opposed to the phenyl carbons of PPV.     

An ab initio study of the vibronic, spin-orbit, and magnetic hyperfine structure in the X2Pi electronic state of NCO

In the present study we give the results of the ab initio calculations on the vibronic, spin-orbit, and magnetic hyperfine structure in the X (2)Pi electronic state of the NCO radical. The calculations of the potential surfaces and the electronic mean values of the hyperfine coupling constants are carried out by means of the density functional theory approach (B3LYP functional combined with an atomic orbital basis set suitable for calculations of the hyperfine structure). The vibronic levels, spin-orbit splitting, and the vibronic mean values of the components of the hyperfine tensor in the vibronic species are calculated using a variational method. The results of the calculations are in good agreement with the available experimental data.     

Vibrational quenching of excitonic splittings in H-bonded molecular dimers: the electronic Davydov splittings cannot match experiment

The S(1)/S(2) state exciton splittings of symmetric doubly hydrogen-bonded gas-phase dimers provide spectroscopic benchmarks for the excited-state electronic couplings between UV chromophores. These have important implications for electronic energy transfer in multichromophoric systems ranging from photosynthetic light-harvesting antennae to photosynthetic reaction centers, conjugated polymers, molecular crystals, and nucleic acids. We provide laser spectroscopic data on the S(1)/S(2) excitonic splitting Δ(exp) of the doubly H-bonded o-cyanophenol (oCP) dimer and compare to the splittings of the dimers of (2-aminopyridine)(2), [(2AP)(2)], (2-pyridone)(2), [(2PY)(2)], (benzoic acid)(2), [(BZA)(2)], and (benzonitrile)(2), [(BN)(2)]. The experimental S(1)/S(2) excitonic splittings are Δ(exp) = 16.4 cm(-1) for (oCP)(2), 11.5 cm(-1) for (2AP)(2), 43.5 cm(-1) for (2PY)(2), and <1 cm(-1) for (BZA)(2). In contrast, the vertical S(1)/S(2) energy gaps Δ(calc) calculated by the approximate second-order coupled cluster (CC2) method for the same dimers are 10-40 times larger than the Δ(exp) values. The qualitative failure of this and other ab initio methods to reproduce the exciton splitting Δ(exp) arises from the Born-Oppenheimer (BO) approximation, which implicitly assumes the strong-coupling case and cannot be employed to evaluate excitonic splittings of systems that are in the weak-coupling limit. Given typical H-bond distances and oscillator strengths, the majority of H-bonded dimers lie in the weak-coupling limit. In this case, the monomer electronic-vibrational coupling upon electronic excitation must be accounted for; the excitonic splittings arise between the vibronic (and not the electronic) transitions. The discrepancy between the BO-based splittings Δ(calc) and the much smaller experimental Δ(exp) values is resolved by taking into account the quenching of the BO splitting by the intramolecular vibronic coupling in the monomer S(1) ← S(0) excitation. The vibrational quenching factors Γ for the five dimers (oCP)(2), (2AP)(2), (2AP)(2), (BN)(2), and (BZA)(2) lie in the range Γ = 0.03-0.2. The quenched excitonic splittings Γ[middle dot]Δ(calc) are found to be in very good agreement with the observed splittings Δ(exp). The vibrational quenching approach predicts reliable Δ(exp) values for the investigated dimers, confirms the importance of vibrational quenching of the electronic Davydov splittings, and provides a sound basis for predicting realistic exciton splittings in multichromophoric systems.