Strong Vibronic Coupling Research Articles

Electrochemical proton-coupled electron transfer: Beyond the golden rule

Electrochemical proton-coupled electron transfer rate constant expressions that interpolate between the golden rule and solvent-controlled limits are derived. These expressions include the effects of solvent dynamics and thus are applicable for a wide range of vibronic couplings and solvent relaxation times. The golden rule limit is defined in terms of weak vibronic coupling and fast solvent relaxation, and the solvent-controlled limit is defined in terms of strong vibronic coupling and slow solvent relaxation. In the golden rule limit, the rate constant is proportional to the square of the vibronic coupling and is independent of the solvent relaxation time. In the solvent-controlled limit, the rate constant is independent of the vibronic coupling and increases as the solvent relaxation time decreases. The interconversion between the solvent-controlled and golden rule limits can be induced by altering the proton donor-acceptor mode frequency and the overlap between the reactant and product proton vibrational wave functions, as well as the electronic coupling, the solvent relaxation time, and the overpotential. The kinetic isotope effect behaves differently in the solvent-controlled and golden rule limits and thus provides a unique probe for characterizing electrochemical proton-coupled electron transfer processes. The analogous rate constant expressions for electrochemical electron transfer and homogeneous proton-coupled electron transfer are also presented. The impact of electrode overpotential, solvent relaxation time, and proton donor-acceptor mode frequency on the rate constants are analyzed for model systems.

On the determination of optimized, fully quadratic, coupled state quasidiabatic Hamiltonians for determining bound state vibronic spectra

The quasidiabatic, coupled electronic state, fully quadratic Hamiltonian (H(d)), suitable for the simulation of spectra exhibiting strong vibronic couplings and constructed using a recently introduced pseudonormal equations approach, is studied. The flexibility inherent in the normal equations approach is shown to provide a robust means for (i) improving the accuracy of H(d), (ii) extending its domain of utility, and (iii) determining the limits of the fully quadratic model. The two lowest electronic states of pyrrolyl which are coupled by conical intersections are used as a test case. The requisite ab initio data are obtained from large multireference configuration interaction expansions comprised of 108.5x10(6) configuration state functions and based on polarized triple zeta quality atomic orbital bases.

High-resolution spectroscopy of weak and short-lived bands of the S1 B13u←S A1g transition of naphthalene

Rotationally resolved high-resolution spectra and fluorescence decay curves have been observed for weak and short-lived vibronic bands of the S(1) (1)B(3u) <-- S(0) (1)A(g) transition of naphthalene. Fluorescence lifetime of the vibronic band with an excess energy of 1390 cm(-1) (0(0)(0) + 1390 cm(-1) band) is remarkably shorter than that of other bands. Zeeman splitting of rotational lines is very small, so that the main radiationless process is not intersystem crossing to the triplet state but internal conversion to the ground state. The lifetime is thought to be governed by the strength of vibronic coupling between vibrational levels of the S(0) and S(1) states. As for the 0(0)(0) + 2570 cm(-1) band, energy shifts were found in only a few rotational levels although the excess energy was higher than the threshold of intramolecular vibrational redistribution. We conclude that all of the rotational levels are mixed with other vibrational levels. The 0(0)(0) + 3068 cm(-1) band spectrum is fairly complicated with numerous rotational lines, which is attributed to strong vibronic coupling with the S(2) (1)B(2u) state.

Beyond the strong vibronic coupling approximation – sexithiophene single crystal

AbstractA new approach to vibronic coupling in molecular crystals is proposed. The underlying model describes an infinite 3‐dimensional crystal with two or four molecules in the unit cell. One Frenkel state and one vibrational mode per molecule is taken into account. The approach is rooted in the approximation of strong vibronic coupling, which is extended by taking into account the 2‐particle and 3‐particle contributions in order to cover the intermediate‐coupling region. The results of numerical calculations are presented for sexithiophene; they are discussed in the context of finite cluster models and their validity. (© 2009 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Sub-millimeter wave spectroscopy of the C 3H radical: Ro-vibrational transitions from ground to the lowest bending state

Linear C 3H in its (X 2 Π) electronic ground state possesses strong Renner–Teller coupling in the two lowest bending modes, ν 4 and ν 5. The 2 Σ μ level of the v 4 = 1 bending mode is shifted towards lower energies and is supposed to lie only 20.3 cm −1 above the ground state [S. Yamamoto, S. Saito, H. Suzuki, S. Deguchi, N. Kaifu, S. Ishikawa, M. Ohishi, Astrophys. J. 348 (1990) 363]. In the present study, first measurements of ro-vibrational transitions from the 2 Π 3/2 ground state to the 2 Σ μ lowest vibrational state were performed using a Terahertz spectrometer equipped with a supersonic jet nozzle. Rotational levels of the 2 Π 3/2 and v 4 = 1( 2 Σ μ ) state are close in energy and a crossing of the rotational energy ladders occurs between J = 24.5 and 25.5. A strong vibronic coupling leads to a significant intensity enhancement of 2 Π 3/2 − 2 Σ μ ro-vibrational transitions. The search for ro-vibrational transitions was facilitated by measurements on pure rotational transitions in the 2 Π 1/2, 2 Π 3/2 and v 4 = 1( 2 Σ μ ) states, substantially extending the former data set published by Yamamoto et al. Data analysis yields an accurate value for the v 4 = 1( 2 Σ μ ) energy level which has been found to lie 609.9771(42) GHz or 20.34664(14) cm −1 above the 2 Π ground state. Furthermore, the value of the vibronic coupling constant β has been improved significantly and determined as 1231.77(51) MHz. The new set of spectroscopic parameters obtained in the present study permits very reliable frequency predictions into the Terahertz region.

Multistate vibronic interactions in difluorobenzene radical cations. I. Electronic structure calculations

The multimode multistate vibronic interactions between the five lowest electronic states of all three isomers of the difluorobenzene radical cation are investigated theoretically, based on ab initio electronic structure data, and employing a well-established vibronic coupling model. The approach rests on the linear vibronic coupling scheme, augmented by quadratic coupling terms for the totally symmetric modes. The underlying ionization potentials and coupling constants are obtained from ab initio coupled-cluster calculations. Low-energy conical intersections and strong vibronic couplings are found to prevail within the sets of X-A and B-C-D cationic states, while the interactions between these two sets of states are found to be weaker and depend on the isomer. The inclusion of the aforementioned quadratic couplings is found to be essential to correctly reproduce the lowest-energy conical intersections between the two different sets of electronic states. Differences between the three isomers regarding these quantities are pointed out. The results will be used as basis for multidimensional wave-packet dynamical simulations for these coupled potential energy surfaces to be presented in the following paper (Paper II).

Molecular beam resonant two-photon ionization study of caffeine and its hydrated clusters

We investigated electronically excited states of caffeine and its 1:1 complex with water by using resonant two-photon ionization (R2PI) and UV-UV hole-burning techniques. Strong vibronic coupling between a pair of close-lying pi-pi* and n-pi* transitions is proposed to be responsible for the broad spectral feature observed. By comparing the experimental results with those of theoretical calculations, both the O-bonded and N-bonded forms were suggested to be initially produced for the 1:1 complex. The electronic transitions of the O-bonded complex were blueshifted in the R2PI spectrum. For the N-bonded complex, the excited state undergoes an ultrafast decay process, followed by dissociation on a repulsive potential energy surface, which gives rise to a characteristically anomalous cluster distribution in nanosecond experiments.

Two photon absorption of extended substituted phenylenevinylene oligomers: A TDDFT study

Time dependent density functional theory has been applied to analyze the effect of substituent groups on one-photon (OPA) and two-photon (TPA) absorption properties of extended amine-terminated phenylenevinylene oligomers. All investigated molecules are characterized by increased TPA activity. Calculated TPA cross-sections for these compounds do not show TPA enhancements observed in experimental measurements. Stabilization of the TPA active excited state in these chromophores leads to the small (∼0.2 eV) energy separation between the OPA and TPA allowed excited states, which agrees well with experimental data and may lead to the enhancement of the TPA response due to the strong vibronic couplings.

Potential-Induced Redox Switching in Viologen Self-Assembled Monolayers: An ATR−SEIRAS Approach

Monolayers of viologens (N-alkyl-N‘-(n-thioalkyl)-4,4‘-bipyridinium bromide, n = 6, 8, 10) have been self-assembled from ethanolic solution onto gold substrates. Their structure and redox functionality were studied by cyclic voltammetry and in situ ATR−SEIRAS. Voltammetric experiments revealed that the first redox process, V2+ ↔ V•+, is reversible, whereas the second redox process, V•+ ↔ V0, is quasi reversible. The V2+ adlayer exhibits a sandwich-like structure. Van der Waals interactions between the alkyl chains lead to two well-ordered hydrophobic layers, with the redox-active bipyridinium unit enclosed in between. The alkyl chains are aligned in an all-trans configuration in a tilted orientation with respect to the surface normal and exhibit a slight conformational disorder. The long axis of the central bipyridinium rings is also tilted. The alignment of V2+ is stabilized by interplanar π−π stacking and electrostatic coulomb interactions. Both monomers and dimers of V•+ coexist in the V•+adlayer. The molecular alignment of the V•+ adlayer is stabilized by the strong vibronic coupling within the dimers and the π−π stacking between the monomers. Increasing length of the alkyl chain results in more tilted bipyridinium units, and favors both the dimerization and the alignment of V•+ within the SAMs. The complex reaction, V2+ → V•+, is described as electron transport from the electrode to the V2+ moiety followed by the dimerization of V•+, the delocalization of the radical electrons, and the migration of coadsorbed ClO4- anions.

Slow electron velocity-map imaging spectroscopy of the 1-propynyl radical

High resolution photoelectron spectra of the 1-propynyl and 1-propynyl-d(3) anions acquired with slow electron velocity-map imaging are presented. The electron affinity is determined to be 2.7355+/-0.0010 eV for the 1-propynyl radical and 2.7300+/-0.0010 eV for 1-propynyl-d(3). Several vibronic transitions are observed and assigned using the isotopic shifts and results from ab initio calculations. Good agreement between experimental spectra and calculations suggests a C(3v) geometry for the 1-propynyl radical. No evidence is found for strong vibronic coupling between the ground electronic state and the low-lying first excited state.

Strong vibronic coupling effects in polarized IR spectra of the hydrogen bond in N-methylthioacetamide crystals

This paper presents the investigation results of the polarized IR spectra of the hydrogen bond in crystals of N-methylthioacetamide. The spectral studies were preceded by the determination of the crystal X-ray structure. The spectra were measured at 283 K and at 77 K by a transmission method, using polarized light. Theoretical analysis of the results concerned the linear dichroic effects, the H/D isotopic and temperature effects, observed in the solid-state IR spectra of the hydrogen and of the deuterium bond at the frequency ranges of the ν N–H and the ν N–D bands, respectively. The main spectral properties of the crystals can be interpreted satisfactorily in terms of the simple quantitative theory of the IR spectra of the hydrogen bond, i.e., the “ strong-coupling” theory on the basis of the hydrogen bond centrosymmetric dimer model. The spectra revealed that the strongest vibrational exciton coupling involved the closely spaced hydrogen bonds, each belonging to a different chain of associated N-methylthioacetamide molecules. The crystal spectral properties, along with an abnormal H/D isotopic effect in the spectra, were found to be strongly influenced by vibronic coupling mechanisms in these dimers. These mechanisms were considered as responsible for the activation in IR of the totally symmetric proton stretching vibrations in the dimers. On analyzing the spectra of isotopically diluted crystalline samples of N-methylthioacetamide, it was proved that a non-random distribution of the protons and deuterons took place in the hydrogen bond lattices. In an individual hydrogen-bonded chain in the crystals distribution of the hydrogen isotope atoms H and D was fully random. The H/D isotopic “ self-organization” mechanism, of a vibronic nature, involved a pair of hydrogen bonds from a unit cell, where each hydrogen bond belonged to a different chain of the associated molecules.

Solvent Effect on Conical Intersections in Excited-State 9H-Adenine: Radiationless Decay Mechanism in Polar Solvent

The ground- and excited-state free energy minima and the conical intersections among these states of 9H-adenine in aqueous and acetonitrile solutions are studied theoretically to elucidate the mechanism of radiationless decay. We employ the recently proposed linear-response free energy (LRFE) to locate the energy minima and conical intersections in solution. The LRFE is calculated by using the reference interaction site model self-consistent field method. The geometry optimizations are carried out at the complete active space self-consistent field level, and the dynamic electron correlation energies are estimated by the multireference Møller-Plesset method. We find that the conical intersection between the (1)L(a) and (1)L(b) states in aqueous solution occurs at a wide area of the free energy surface, indicating a strong vibronic coupling between them. On the other hand, the (1)npi(*) state is largely blue-shifted at planar geometries in solution, which suggests that the nonadiabatic transition to this state is suppressed. The importance of the (1)pisigma(*) channel is also examined in both the gas phase and solution. Based on the free energy characteristics obtained by the calculations, we intend to explain the experimental observations that the excited state of 9H-adenine decays monoexponentially with shorter lifetimes in polar solvents than that in the gas phase.

Vibronic reduction factors in E ⊗ ( β1 + β2) and their Berry’s phase manifestations

In a linearly coupled dihedral E ⊗ ( β 1 + β 2) Jahn–Teller system one finds two different q-factors (say, q 1 and q 2) and a p-factor. For stronger β 1- than β 2-coupling, one obtains q 1 > q 2 and in the strong linear vibronic coupling limit, q 1 → 0.5, q 2 → 0. At all strengths, the historical relation “ p = 2 q − 1” turns into p = q 1 + q 2 − 1. A slowly rotating external field induces in the electronic wave-functions, upon a full turn, a Berry’s phase equal to the solid angle subtended by the field’s vector at the origin. We have calculated (by employing a quasi-classical approximation to solve the dynamic problem for the ground vibronic state) the corresponding phase change, now diminished by the vibronic reduction factors.

Jet-cooled infrared spectrum of methoxy in the CH stretching region

Observations of the jet-cooled infrared spectrum of CH(3)O in the CH stretching region have been extended, down to 2756 cm(-1) and up to 3003 cm(-1). In the lower frequency extension, a single vibronic band has been assigned. In the higher frequency region, the spectrum becomes complex above 2900 cm(-1) and remains so until near 2970 cm(-1) where it rapidly becomes sparse. Including the single vibronic band previously reported, a total of four bands have been assigned. Two bands including the original one follow a perpendicular DeltaP = +1 rotational selection rule and the other two bands follow a parallel DeltaP = 0 selection rule. In addition to these in the congested region between 2900 and 2970 cm(-1), ten isolated sub-bands (two P'' = -1/2, two P'' = +1/2, and six P'' = +1.5) have been assigned, but it has so far not been possible to connect these together to form bands. Taken together these observations suggest that there are strong vibronic couplings between the two CH stretching vibrations and the overtone and combination levels in the region.

Temperature dependence of very deep emission from an exciton bound to an isoelectronic defect in polycrystalline CuInS2

Zero-phonon lines (ZPLs) of deep exciton bound to isoelectronic deep-donor–deep-acceptor pair in CuInS2 are studied by photoluminescence. These ZPLs have peak positions at 0.6241eV (A line) and 0.6220eV (B line), followed by two series of phonon replicas with phonon energies of 8 and 40.5meV. Temperature dependence of the intensity of these ZPLs is explained by electron-phonon coupling to a single phonon mode with energy of 8meV and shows that the lines are originated from two excited state levels of the same exciton. The (anomalously strong) temperature broadening of ZPLs follows ∼T2.6 law and can be explained by assuming a strong vibronic coupling between two excited states.

Multi-mode vibronic interactions in the five lowest electronic states of the fluorobenzene radical cation

The multi-mode vibronic interactions between the five lowest electronic states of the fluorobenzene radical cation are investigated theoretically, based on ab initio electronic structure data, and employing the linear vibronic coupling model. Low-energy conical intersections, and strong vibronic couplings are found to prevail within the set of X ∼ – A ∼ and B ∼ – C ∼ – D ∼ cationic states, while the interactions between these two sets of states are found to be rather weak (owing to high-energy conical intersections). The overall intensity distribution of the experimental photoelectron spectrum, as well as the line positions observed in the MATI spectrum, are well reproduced. The vibronic interactions in the X ∼ – A ∼ states are found to be a replica of the multi-mode dynamical Jahn–Teller effect in the parent system, the X ∼ 2 E 1 g ground state of the benzene radical cation. Ultrafast internal conversion processes within the electronic manifolds in question demonstrate the strength of the nonadiabatic coupling effects and complement the analogous findings for the electronic spectra. The implications for the fluorescence dynamics of the fluorobenzene radical cation are discussed.

Resonant inelastic tunneling in molecular junctions

Within a phonon-assisted resonance level model we develop a self-consistent procedure for calculating electron transport currents in molecular junctions with intermediate to strong electron-phonon interaction. The scheme takes into account the mutual influence of the electron and phonon subsystems. It is based on the second order cumulant expansion, used to express the correlation function of the phonon shift generator in terms of the phonon momentum Green function. Equation of motion (EOM) method is used to obtain an approximate analog of the Dyson equation for the electron and phonon Green functions in the case of many-particle operators present in the Hamiltonian. To zero order it is similar in particular cases (empty or filled bridge level) to approaches proposed earlier. The importance of self-consistency in resonance tunneling situations (partially filled bridge level) is stressed. We confirm, even for strong vibronic coupling, a previous suggestion concerning the absence of phonon sidebands in the current versus gate voltage plot when the source-drain voltage is small [Mitra et al., Phys. Rev. B 69, 245302 (2004)].

Solid-state optical properties of linear polyconjugated molecules: π-stack contra herringbone

The intermolecular arrangement in the solid state and the consequences on the optical and photophysical properties are studied on different derivatives of oligophenylenevinylenes by UV/VIS absorption and angular-resolved polarized fluorescence spectroscopy. Unsubstituted distyrylbenzene (DSB) organizes in a herringbone manner, with the long axes of the molecules oriented in parallel, but the short axes almost perpendicular to each other. Fluorinated distyrylbenzene (F(12)DSB) as well as the DSB:F(12)DSB cocrystals prefer cofacial pi-stacking in the solid state. For all structures, the consequence of the parallel alignment of the transition moments is a strongly blueshifted H-type absorption spectrum and a low radiative rate constant k(F). Significant differences are observed for the emission spectra: the perpendicular arrangement of the short axes in DSB crystals leads to only very weak intermolecular vibronic coupling. Hence the emission spectrum is well structured, very similar to the one in solution. For F(12)DSB and DSB:F(12)DSB, the cofacial arrangement of the adjacent molecules enables strong intermolecular vibronic coupling of adjacent molecules. Thus, an unstructured and strongly redshifted excimerlike emission spectrum is observed. The differences in the electronic nature of the excited states are highlighted by quantum-chemical calculations, revealing the contribution of interchain excitations to the electronic transitions.

Molecular electronics: Some views on transport junctions and beyond

The field of molecular electronics comprises a fundamental set of issues concerning the electronic response of molecules as parts of a mesoscopic structure and a technology-facing area of science. We will overview some important aspects of these subfields. The most advanced ideas in the field involve the use of molecules as individual logic or memory units and are broadly based on using the quantum state space of the molecule. Current work in molecular electronics usually addresses molecular junction transport, where the molecule acts as a barrier for incoming electrons: This is the fundamental Landauer idea of "conduction as scattering" generalized to molecular junction structures. Another point of view in terms of superexchange as a guiding mechanism for coherent electron transfer through the molecular bridge is discussed. Molecules generally exhibit relatively strong vibronic coupling. The last section of this overview focuses on vibronic effects, including inelastic electron tunneling spectroscopy, hysteresis in junction charge transport, and negative differential resistance in molecular transport junctions.

The Band 12 Issue in the Electron Momentum Spectra of Norbornane: A Comparison with Additional Green's Function Calculations and Ultraviolet Photoemission Measurements

In continuation of a recent study of the electronic structure of norbornane [J. Chem. Phys., 2004, 121, 10525] by means of electron momentum spectroscopy (EMS), we present Green's Function calculations of the ionization spectrum of this compound at the ADC(3) level using basis sets of varying quality, along with accurate evaluations at the CCSD(T) level of the vertical (26.5 eV) and adiabatic (22.1 eV) double ionization thresholds under C(2v) symmetry. The obtained results are compared with newly recorded ultraviolet photoemission spectra (UPS), up to binding energies of 40 eV. The theoretical predictions are entirely consistent with experiment and indicate that, in a vertical depiction of ionization, shake-up states at binding energies larger than approximately 26.5 eV tend to decay via emission of a second electron in the continuum. A band of s-type symmetry that has been previously seen at approximately 25 eV in the electron impact ionization spectra of norbornane is entirely missing in the UPS measurements and theoretical ADC(3) spectra. With regard to these results and to the time scales characterizing electron-electron interactions in EMS (10(-17) s) as compared with that (10(-13) s) of photon-electron interactions in UPS, and considering the p-type symmetry of the electron momentum distributions for the nearest 1b(1) and 1b(2) orbitals, this additional band can certainly not be due to adiabatic double ionization processes starting from the ground electronic state of norbornane, or to exceptionally strong vibronic coupling interactions between cationic states derived from ionization of the latter orbitals. It is therefore tentatively ascribed to autoionization processes via electronically excited and possibly dissociating states.