Electron-vibration Interaction Research Articles

One- and two-photon absorption spectra of the yellow fluorescent protein citrine: effects of intramolecular electron-vibrational coupling and intermolecular interactions

ABSTRACTBoth the vibrationally resolved and statistically averaged one-photon absorption (OPA) and two-photon absorption (TPA) spectra of the anionic form of chromophore (AC) in its micro-environment of yellow fluorescent protein (YFP) Citrine have been calculated. The result comparison has been made with those of the AC model compounds in vacuo and methanol solution, which allows us to allocate the individual contribution of the intramolecular electron-vibrational coupling, the electrostatic π-stacking interaction between Tyr203 and AC, and the interaction between AC and its micro-environment to the spectra. The results reveal that the non-Condon vibronic coupling effect is responsible for the blue shift of TPA absorption maximum compared with its OPA counterpart corresponding to S0 → S1, and that the π-stacking interaction between Tyr203 and AC alters the relative intensities of TPA maxima, which further enhances the higher-energy vibronic peaks and weakens the lowest-energy peak. The statically averaged OPA and TPA spectra calculated by quantum mechanics/molecular mechanics (QM/MM) methods based on Born–Oppenheimer molecular dynamics simulation largely deviate the experimental spectral lineshapes, which further verifies the significant contribution of non-Condon vibronic coupling effect on the spectra. The interaction of individual amino acid residue or water close to AC+Tyr203 has different effects on the spectra, which may increase/decrease the excitation energy depending on its position and electronic property.

Perspective: Theory of quantum transport in molecular junctions.

Molecular junctions, where single molecules are bound to metal or semiconductor electrodes, represent a unique architecture to investigate molecules in a distinct nonequilibrium situation and, in a broader context, to study basic mechanisms of charge and energy transport in a many-body quantum system at the nanoscale. Experimental studies of molecular junctions have revealed a wealth of interesting transport phenomena, the understanding of which necessitates theoretical modeling. The accurate theoretical description of quantum transport in molecular junctions is challenging because it requires methods that are capable to describe the electronic structure and dynamics of molecules in a condensed phase environment out of equilibrium, in some cases with strong electron-electron and/or electronic-vibrational interaction. This perspective discusses recent progress in the theory and simulation of quantum transport in molecular junctions. Furthermore, challenges are identified, which appear crucial to achieve a comprehensive and quantitative understanding of transport in these systems.

Origin of Spectral Band Patterns in the Cosmic Unidentified Infrared Emission.

The cosmic unidentified infrared emission (UIE) band phenomenon is generally considered as indicative of free-flying polycyclic aromatic hydrocarbon molecules in space. However, a coherent explanation of emission spectral band patterns depending on astrophysical source is yet to be resolved under this attribution. Meanwhile astronomers have restored the alternative origin as due to amorphous carbon particles, but assigning spectral patterns to specific structural elements of particles is equally challenging. Here we report a physical principle in which inclusion of nonplanar structural defects in aromatic core molecular structures (π domains) induces spectral patterns typical of the phenomenon. We show that defects in model π domains modulate the electronic-vibration coupling that activates the delocalized π-electron contribution to aromatic vibrational modes. The modulation naturally disperses C=C stretch modes in band patterns that readily resemble the UIE bands in the elusive 6-9 μm range. The electron-vibration interaction mechanics governing the defect-induced band patterns underscores the importance of π delocalization in the emergence of UIE bands. We discuss the global UIE band regularity of this range as compatible with an emission from the delocalized sp^{2} phase, as π domains, confined in disordered carbon mixed-phase aggregates.

Non-renewal statistics for electron transport in a molecular junction with electron-vibration interaction.

Quantum transport of electrons through a molecule is a series of individual electron tunneling events separated by stochastic waiting time intervals. We study the emergence of temporal correlations between successive waiting times for the electron transport in a vibrating molecular junction. Using the master equation approach, we compute the joint probability distribution for waiting times of two successive tunneling events. We show that the probability distribution is completely reset after each tunneling event if molecular vibrations are thermally equilibrated. If we treat vibrational dynamics exactly without imposing the equilibration constraint, the statistics of electron tunneling events become non-renewal. Non-renewal statistics between two waiting times τ1 and τ2 means that the density matrix of the molecule is not fully renewed after time τ1 and the probability of observing waiting time τ2 for the second electron transfer depends on the previous electron waiting time τ1. The strong electron-vibration coupling is required for the emergence of the non-renewal statistics. We show that in the Franck-Condon blockade regime, extremely rare tunneling events become positively correlated.

White light emission through efficient energy transfer from Ce3+ to Dy3+ ions in Ca3Mg3(PO4)4 matrix aided by Li+ charge compensator

In this work, we have comprehensively explored the energy transfer process between Ce3+ and Dy3+ ions doped in Ca3Mg3(PO4)4 host lattice. The phosphors were synthesized by facile urea-assisted combustion method. The charge imbalance, produced due to doping of trivalent lanthanides in the divalent sites of the host lattice, has been compensated by adding Li+ charge compensator. The structural characterization by Rietveld refinement, morphological and FTIR studies were performed on the as-prepared Ca2.96Mg3(PO4)4:0.01Ce3+, 0.01Dy3+, 0.02Li+ phosphor. The diffuse reflectance spectra and the photoluminescence spectra of the prepared phosphors and the electron-vibration interaction (EVI) parameters of Ca3Mg3(PO4)4:Ce3+,Li+ phosphor were thoroughly analysed. Ca3Mg3(PO4)4:Ce3+,Dy3+,Li+ phosphor exhibited its ability to produce white light emission at UV excitation wavelength 316nm. The codoping of Ce3+ ions enhanced the PL emission intensity of Dy3+ by ten times as compared to the intensity obtained for the samples that were singly-doped with Dy3+. The results suggest the use of single-phased Ca2.96Mg3(PO4)4:0.01Ce3+, 0.01Dy3+, 0.02Li+ phosphor as potential white light emitting phosphor.

Theoretical analysis of electron vibration interactions and study of photo physical properties in Ce3+ doped Ca2P2O7 nano phosphor capped with SHMP

In the present manuscript, Calcium diphosphate phosphor doped with Cerium and capped with sodium hexametaphosphate has been reported. A theoretical analysis of electron vibration interactions in optical transitions of Ce3+ ions in Ca2P2O7 has been elaborated in brief. The main EVI parameters such as Huang’s Rhys factor and effective phonon energy were determined by evaluating the lowest 5d level of Ce3+ spectrum. The obtained values were used to model the shape of emission band along with estimation of zero phonon line. The fabricated nano phosphor was characterized by powder X-ray diffraction technique. Studies revealed that Ca2P2O7 crystallizes in tetragonal group with square anti prism symmetry. The crystal structure arrangement was found to be non linear in nature with two PO3 groups linked by bridging oxygen forming the diphosphate group. Transmission electron microscopy observations explored nano structural features of the synthesized nano phosphor compound. A study involving SAED and HRTEM on isolated particles was carried out to validate the stabilization of the tetragonal phase. The phosphate functional group of the host was probed by Fourier transform infrared microscopy. Optical properties were examined by evaluating the photoluminescence excitation and emission spectra. Broad emission peaks were observed around 326 nm and 347 nm because of 4f-5d transitions of rare earth activator Ce3+. With the help of TL glow curve measurements, the trap depths were calculated employing peak shape method. Lifetime calculation for the nano phosphor indicates that the aforementioned compound has promising potential for solid state lighting and optoelectronic applications.

Controlling charge transport mechanisms in molecular junctions: Distilling thermally induced hopping from coherent-resonant conduction.

The electrical conductance of molecular junctions may depend strongly on the temperature and weakly on molecular length, under two distinct mechanisms: phase-coherent resonant conduction, with charges proceeding via delocalized molecular orbitals, and incoherent thermally assisted multi-step hopping. While in the case of coherent conduction, the temperature dependence arises from the broadening of the Fermi distribution in the metal electrodes, in the latter case it corresponds to electron-vibration interaction effects on the junction. With the objective to distill the thermally activated hopping component, thus exposing intrinsic electron-vibration interaction phenomena on the junction, we suggest the design of molecular junctions with "spacers," extended anchoring groups that act to filter out phase-coherent resonant electrons. Specifically, we study the electrical conductance of fixed-gap and variable-gap junctions that include a tunneling block, with spacers at the boundaries. Using numerical simulations and analytical considerations, we demonstrate that in our design, resonant conduction is suppressed. As a result, the electrical conductance is dominated by two (rather than three) mechanisms: superexchange (deep tunneling) and multi-step thermally induced hopping. We further exemplify our analysis on DNA junctions with an A:T block serving as a tunneling barrier. Here, we show that the electrical conductance is insensitive to the number of G:C base-pairs at the boundaries. This indicates that the tunneling-to-hopping crossover revealed in such sequences truly corresponds to the properties of the A:T barrier.

Closed systems of equations of correlation functions of currents for heterogeneous DNA fragments and polarons

A closed system of nonlinear differential equations is proposed for current correlation functions of the Kubo expression for conductivity. The chain of equations is closed by dropping the correlations of higher order. The approach allows estimating an error of the dropped correlations. A successive approximation technique can take account of the corrections and allow for subtle effects caused by DNA structure and identifies areas, where these corrections are significant. The local conductivity in one-dimensional case was shown to be defined by adjacent sites. Zone conductivity takes place for small electron-vibrational interactions. The conductivity decreases with temperature rise, but it may increase or decrease at low temperatures because of finiteness of polymer fragment. At low temperatures the zone conductivity persists for large electron-vibrational interactions, however the possibility of hopping appears, and hopping conductivity increases with temperature rise and becomes determinant at some temperature but starts decreasing with temperature rise at high temperatures.

Waiting time distribution for electron transport in a molecular junction with electron-vibration interaction.

On the elementary level, electronic current consists of individual electron tunnelling events that are separated by random time intervals. The waiting time distribution is a probability to observe the electron transfer in the detector electrode at time t+τ given that an electron was detected in the same electrode at an earlier time t. We study waiting time distribution for quantum transport in a vibrating molecular junction. By treating the electron-vibration interaction exactly and molecule-electrode coupling perturbatively, we obtain the master equation and compute the distribution of waiting times for electron transport. The details of waiting time distributions are used to elucidate microscopic mechanism of electron transport and the role of electron-vibration interactions. We find that as nonequilibrium develops in the molecular junction, the skewness and dispersion of the waiting time distribution experience stepwise drops with the increase of the electric current. These steps are associated with the excitations of vibrational states by tunnelling electrons. In the strong electron-vibration coupling regime, the dispersion decrease dominates over all other changes in the waiting time distribution as the molecular junction departs far away from the equilibrium.

AC transport and full-counting statistics of molecular junctions in the weak electron-vibration coupling regime

The coupling of the charge carriers passing through a molecule bridging two bulky conductors with local vibrational modes of the molecule gives rise to distinct features in the electronic transport properties on one hand and to nonequilibrium features in the vibrations’ properties, e.g., their population, on the other. Here we explore theoretically a generic model for a molecular junction biased by an arbitrary dc voltage in the weak-coupling regime. We succinctly summarize parts of our past work related to the signature of the electron-vibration interaction on the full-counting statistics of the current fluctuations (i.e., the cumulant generating-function of the current correlations). In addition, we provide a novel account of the response to an ac field exerted on the junction (on top of the dc bias voltage); in particular, we study the nonequilibrium distribution and the displacement fluctuations of the vibrational modes. Remarkably, we find a behavior pattern that cannot be accounted for by classical forced oscillations. The calculations use the technique of nonequilibrium Green’s functions and treat the electron-vibration coupling in perturbation theory, within the random-phase approximation when required.

Effects of vibrational anharmonicity on molecular electronic conduction and thermoelectric efficiency

We study inelastic vibration-assisted charge transfer effects in two-site molecular junctions, focusing on signatures of vibrational anharmonicity on the electrical characteristics and the thermoelectric response of the junction. We consider three types of oscillators: harmonic, anharmonic-Morse allowing bond dissociation, and harmonic-quartic, mimicking a confinement potential. Using a quantum master equation method which is perturbative in the electron-vibration interaction, we find that the (inelastic) electrical and thermal conductances can be largely affected by the nature of the vibrational potential. In contrast, the Seebeck coefficient, the thermoelectric figure-of-merit, and the thermoelectric efficiency beyond linear response conceal this information, showing a rather weak sensitivity to vibrational anharmonicity. Our work illustrates that anharmonic (many-body) effects, consequential to the current-voltage characteristics, are of little effect for the thermoelectric performance in the present model.

Cavity-Controlled Chemistry in Molecular Ensembles.

The demonstration of strong and ultrastrong coupling regimes of cavity QED with polyatomic molecules has opened new routes to control chemical dynamics at the nanoscale. We show that strong resonant coupling of a cavity field with an electronic transition can effectively decouple collective electronic and nuclear degrees of freedom in a disordered molecular ensemble, even for molecules with high-frequency quantum vibrational modes having strong electron-vibration interactions. This type of polaron decoupling can be used to control chemical reactions. We show that the rate of electron transfer reactions in a cavity can be orders of magnitude larger than in free space for a wide class of organic molecular species.

Replicas of the Kondo peak due to electron-vibration interaction in molecular transport properties

The low temperature properties of single level molecular quantum dots including both, electron-electron and electron-vibration interactions, are theoretically investigated. The calculated differential conductance in the Kondo regime exhibits not only the zero bias anomaly but also side peaks located at bias voltages which coincide with multiples of the energy of vibronic mode $V \sim \hbar\Omega/e$. We obtain that the evolution with temperature of the two main satellite conductance peaks follows the corresponding one of the Kondo peak when $\hbar\Omega \gg k_B T_K$, being $ T_K$ the Kondo temperature, in agreement with recent transport measurements in molecular junctions. However, we find that this is no longer valid when $ \hbar\Omega$ is of the order of a few times $k_B T_K$.

Microscopic insight into the pump–probe relaxation dynamics of superconductors: Model study of MgB2 relaxation within nonlinear response theory

Here we present a quantum‐statistical formulation of relaxation dynamics of superconductors related to pump–probe (PP) spectroscopy. The method is based on the perturbation expansion of the non‐equilibrium density matrix for calculation of multi‐time correlation functions, and the corresponding response function. As a model for our study, the high‐temperature superconductor MgB2 has been selected. Knowledge of the electronic structure and of the corresponding Eliashberg function of electron–phonon (EP) interactions enabled us to distinguish non‐equilibrium processes in a sequence of interactions with laser pulses on a microscopic level. Temperature‐dependent relaxation dynamics as a function of delay time between the pump and probe pulses have been derived. We have shown that an abrupt increase of the relaxation time at Tc is the direct consequence of sudden changes in the character of EP coupling in transition from an adiabatic to a stabilized superconducting anti‐adiabatic state, as it predicts the anti‐adiabatic theory of electron–vibration interactions. The BCS model, which is based on adiabatic character of EP coupling, is basically unable to reflect the enormous sudden increase of the relaxation time at Tc. Differences in the optical pump–optical probe and the optical pump–terahertz probe settings of PP relaxation dynamics are discussed within diagrammatic perturbation theory.

Revisiting the inelastic electron tunneling spectroscopy of single hydrogen atom adsorbed on the Cu(100) surface.

Inelastic electron tunneling spectroscopy (IETS) of a single hydrogen atom on the Cu(100) surface in a scanning tunneling microscopy (STM) configuration has been investigated by employing the non-equilibrium Green's function formalism combined with density functional theory. The electron-vibration interaction is treated at the level of lowest order expansion. Our calculations show that the single peak observed in the previous STM-IETS experiments is dominated by the perpendicular mode of the adsorbed H atom, while the parallel one only makes a negligible contribution even when the STM tip is laterally displaced from the top position of the H atom. This propensity of the IETS is deeply rooted in the symmetry of the vibrational modes and the characteristics of the conduction channel of the Cu-H-Cu tunneling junction, which is mainly composed of the 4s and 4pz atomic orbitals of the Cu apex atom and the 1s orbital of the adsorbed H atom. These findings are helpful for deepening our understanding of the propensity rules for IETS and promoting IETS as a more popular spectroscopic tool for molecular devices.

Vibrational properties of organic donor-acceptor molecular crystals: Anthracene-pyromellitic-dianhydride (PMDA) as a case study.

We establish a reliable quantum-mechanical approach to evaluate the vibrational properties of donor-acceptor molecular crystals. The anthracene-PMDA (PMDA = pyromellitic dianhydride) crystal, where anthracene acts as the electron donor and PMDA as the electron acceptor, is taken as a representative system for which experimental non-resonance Raman spectra are also reported. We first investigate the impact that the amount of nonlocal Hartree-Fock exchange (HFE) included in a hybrid density functional has on the geometry, normal vibrational modes, electronic coupling, and electron-vibrational (phonon) couplings. The comparison between experimental and theoretical Raman spectra indicates that the results based on the αPBE functional with 25%-35% HFE are in better agreement with the experimental results compared to those obtained with the pure PBE functional. Then, taking αPBE with 25% HFE, we assign the vibrational modes and examine their contributions to the relaxation energy related to the nonlocal electron-vibration interactions. The results show that the largest contribution (about 90%) is due to electron interactions with low-frequency vibrational modes. The relaxation energy in anthracene-PMDA is found to be about five times smaller than the electronic coupling.

Center Line Slope Analysis in Two-Dimensional Electronic Spectroscopy.

Center line slope (CLS) analysis in 2D infrared spectroscopy has been extensively used to extract frequency–frequency correlation functions of vibrational transitions. We apply this concept to 2D electronic spectroscopy, where CLS is a measure of electronic gap fluctuations. The two domains, infrared and electronic, possess differences: In the infrared, the frequency fluctuations are classical, often slow and Gaussian. In contrast, electronic spectra are subject to fast spectral diffusion and affected by underdamped vibrational wavepackets in addition to Stokes shift. All these effects result in non-Gaussian peak profiles. Here, we extend CLS-analysis beyond Gaussian line shapes and test the developed methodology on a solvated molecule, zinc phthalocyanine. We find that CLS facilitates the interpretation of 2D electronic spectra by reducing their complexity to one dimension. In this way, CLS provides a highly sensitive measure of model parameters describing electronic–vibrational and electronic–solvent interaction.

Static and Dynamic Energetic Disorders in the C60, PC61BM, C70, and PC71BM Fullerenes.

We use a combination of molecular dynamics simulations and density functional theory calculations to investigate the energetic disorder in fullerene systems. We show that the energetic disorder evaluated from an ensemble average contains contributions of both static origin (time-independent, due to loose packing) and dynamic origin (time-dependent, due to electron-vibration interactions). In order to differentiate between these two contributions, we compare the results obtained from an ensemble average approach with those derived from a time average approach. It is found that in both amorphous C60 and C70 bulk systems, the degrees of static and dynamic disorder are comparable, while in the amorphous PC61BM and PC71BM systems, static disorder is about twice as large as dynamic disorder.

Interplay between electron–electron and electron–vibration interactions on the thermoelectric properties of molecular junctions

The linear and non-linear thermoelectric properties of molecular junctions are theoretically studied close to room temperature within a model including electron–electron and electron–vibration interactions on the molecule. A non-equilibrium adiabatic approach is devised to include a strong Coulomb repulsion and applied to the self-consistent calculation of electron and phonon transport properties of massive molecules, such as fullerenes, within the Coulomb blockade regime. We show that the phonon thermal conductance is quite sensitive to strong electron–electron interactions within the intermediate electron–vibration coupling regime. Furthermore, the electron–vibration interaction enhances both phonon and electron thermal conductance, and it reduces not only the charge conductance, but also the thermopower. The effect of the strong electron–electron interactions provides a peculiar double-peak structure to the thermopower versus charge conductance curve. Finally, within the regime of weak to intermediate electron–vibration and vibration–lead phonon coupling, the peak values of the thermoelectric figure of merit are slightly less than unity, and the maximal efficiency of the junction can reach values slightly less than half of the Carnot limit for large temperature differences between the leads.

Effect of nonadiabatic electronic-vibrational interactions on the transport properties of single-molecule junctions

The interaction between electronic and vibrational degrees of freedom in single-molecule junctions may result from the dependence of the electronic energies or the electronic states of the molecular bridge on the nuclear displacement. The latter mechanism leads to a direct coupling between different electronic states and is referred to as nonadiabatic electronic-vibrational coupling. Employing a perturbative nonequilibrium Green's function approach, we study the influence of nonadiabatic electronic-vibrational coupling in model molecular junctions. Thereby, we distinguish between systems with well-separated and quasidegenerate electronic levels. The results show that the nonadiabatic electronic-vibrational interaction can have a significant influence on the transport properties. The underlying mechanisms, in particular the difference between nonadiabatic and adiabatic electronic-vibrational couplings, are analyzed in some detail.