Homogeneous Line Shape Research Articles

Probing Ion Configurations in the KcsA Selectivity Filter with Single-Isotope Labels and 2D IR Spectroscopy.

The potassium ion (K+) configurations of the selectivity filter of the KcsA ion channel protein are investigated with two-dimensional infrared (2D IR) spectroscopy of amide I vibrations. Single 13C-18O isotope labels are used, for the first time, to selectively probe the S1/S2 or S2/S3 binding sites in the selectivity filter. These binding sites have the largest differences in ion occupancy in two competing K+ transport mechanisms: soft-knock and hard-knock. According to the former, water molecules alternate between K+ ions in the selectivity filter while the latter assumes that K+ ions occupy the adjacent sites. Molecular dynamics simulations and computational spectroscopy are employed to interpret experimental 2D IR spectra. We find that in the closed conductive state of the KcsA channel, K+ ions do not occupy adjacent binding sites. The experimental data is consistent with simulated 2D IR spectra of soft-knock ion configurations. In contrast, the simulated spectra for the hard-knock ion configurations do not reproduce the experimental results. 2D IR spectra of the hard-knock mechanism have lower frequencies, homogeneous 2D lineshapes, and multiple peaks. In contrast, ion configurations of the soft-knock model produce 2D IR spectra with a single peak at a higher frequency and inhomogeneous lineshape. We conclude that under equilibrium conditions, in the absence of transmembrane voltage, both water and K+ ions occupy the selectivity filter of the KcsA channel in the closed conductive state. The ion configuration is central to the mechanism of ion transport through potassium channels.

Theory of Photoluminescence Spectral Line Shapes of Semiconductor Nanocrystals.

Single-molecule photoluminescence (PL) spectroscopy of semiconductor nanocrystals (NCs) reveals the nature of exciton-phonon interactions in NCs. Understanding the homogeneous spectral line shapes and their temperature dependence remains an open problem. Here, we develop an atomistic model to describe the PL spectrum of NCs, accounting for excitonic effects, phonon dispersion relations, and exciton-phonon couplings. We validate our model using single-NC measurements on CdSe/CdS NCs from T = 4 to 290 K, and we find that the slightly asymmetric main peak at low temperatures is comprised of a narrow zero-phonon line (ZPL) and acoustic phonon sidebands. Furthermore, we identify the specific phonon modes that give rise to the optical phonon sidebands. At temperatures above 200 K, the spectral line width shows a stronger dependence upon the temperature, which we demonstrate to be correlated with higher order exciton-phonon couplings. We also identify the line width dependence upon reorganization energy, NC core sizes, and shell thicknesses.

Modeling the Effect of Disorder in the Two-Dimensional Electronic Spectroscopy of Poly-3-hexyltiophene in an Organic Photovoltaic Blend: A Combined Quantum/Classical Approach.

We introduce a first-principles model of the 12-mer poly-3-hexyltiophene (P3HT) polymer system in the realistic description of an organic photovoltaic blend environment. We combine Molecular Dynamics (MD) simulations of a thin-film blend of P3HT and phenyl-C61-butyric acid methyl ester (PCBM) to model the interactions with a fluctuating environment with Time-Dependent Density Functional Theory (TDDFT) calculations to parametrize the effect of the torsional flexibility in the polymer and construct an exciton-type Hamiltonian that describes the photoexcitation of the polymer. This allows us to reveal the presence of different flexibility patterns governed by the torsional angles along the polymer chain which, in the interacting fluctuating environment, control the broadening of the spectral observables. We identify the origin of the homogeneous and inhomogeneous line shape of the simulated optical signals. This is paramount to decipher the spectroscopic nature of the ultrafast electron-transfer process occurring in organic photovoltaic (OPV) materials.

Homogeneous and inhomogeneous line shape of the electronic excitation of a single molecule on a surface

Here, the authors perform a single-molecule spectroscopy experiment on an organic molecule (PTCDA) adsorbed on a KCl surface. The homogeneous line profile is approximately of Lorentzian shape. Although the molecule is slightly out-of-plane distorted due to the adsorption, the dephasing time is 0.70 ns, yielding sharp zero phonon lines. The inhomogeneous line profile of the ensemble is broader by a factor of about 200 and also of Lorentzian shape. This is due to the stochastic interaction with surface defects.

Studying the size-selective precipitation of colloidal quantum dots by decomposing the excitation-emission matrix.

The exciton peak in the excitation-emission matrix (EEM) of colloidal quantum dots implicitly contains information about inhomogeneous broadening and the photoluminescence (PL) and photoluminescence excitation (PLE) spectra of individual particles in the vicinity of the absorption onset. A numerical procedure for extracting this information has been developed and applied to the EEMs of polydisperse InP/ZnS core/shell colloidal quantum dots and their supernatant solutions obtained by partial precipitation with a non-solvent. The inhomogeneous broadenings obtained in this way have been converted by the sizing curve into particle-size distributions. These distributions have been found to be in agreement with the size-selective precipitation theory proposed recently. The homogeneous PL and PLE line shapes obtained by analyzing the EEMs were found to satisfy the Kennard-Stepanov relation, which is the first more or less direct evidence of its validity for colloidal quantum dots.

A Unified Pervasive Linebroadening Function for Quantum Wells in Light Emitting Diodes

The broadening functions for quantum wells in LEDs and laser diodes below the lasing threshold are examined. Inhomogeneous and homogeneous broadening mechanisms are included. Hydrogen-atom-like exciton and the electron-hole plasma recombination models are considered. Material disorder and the Urbach tail are reviewed as the main reasons for the inhomogeneous broadening. Charge carrier scattering and relaxation times in the conduction and valence bands are examined as the origin for the homogeneous lifetime broadening. Two homogeneous lineshapes are compared using the momentum relaxation times obtained from the electron and hole mobilities available for GaAs. In addition to crystal disorder, the mutual collision of charge carriers in the quantum wells is examined as the reason for the relaxation time shortening. The analogy to pressure broadening in gases is used to combine the proper homogeneous and inhomogeneous broadening functions to a unified quantum well lineshape.

Two-dimensional electronic spectroscopy reveals liquid-like lineshape dynamics in CsPbI3 perovskite nanocrystals

Lead-halide perovskites have attracted tremendous attention, initially for their performance in thin film photovoltaics, and more recently for a variety of remarkable optical properties. Defect tolerance through polaron formation within the ionic lattice is a key aspect of these materials. Polaron formation arises from the dynamical coupling of atomic fluctuations to electronic states. Measuring the properties of these fluctuations is therefore essential in light of potential optoelectronic applications. Here we apply two-dimensional electronic spectroscopy (2DES) to probe the timescale and amplitude of the electronic gap correlations in CsPbI3 perovskite nanocrystals via homogeneous lineshape dynamics. The 2DES data reveal irreversible, diffusive dynamics that are qualitatively inconsistent with the coherent dynamics in covalent solids such as CdSe quantum dots. In contrast, these dynamics are consistent with liquid-like structural dynamics on the 100 femtosecond timescale. These dynamics are assigned to the optical signature of polaron formation, the conceptual solid-state analogue of solvation.

Wavelength-Dependent Exciton-Vibrational Coupling in the Water-Soluble Chlorophyll Binding Protein Revealed by Multilevel Theory of Difference Fluorescence Line-Narrowing.

One of the most powerful line-narrowing techniques used to unravel the homogeneous lineshapes of inhomogeneously broadened systems is difference fluorescence line-narrowing spectroscopy. When this spectroscopy was applied to multichromophoric systems so far, the spectra were analyzed by an effective two-level system approach, composed of the electronic ground state and the lowest exciton state. An effective Huang-Rhys factor was assigned for the coupling of this state to the vibrations. Here, we extend this approach by including a multilevel line shape theory, which takes into account the excitonic coupling between pigments and thereby the effect of the delocalization of the excited states explicitly. In this way, it becomes possible to extract the spectral density of the local exciton-vibrational coupling. The theory is applied to the recombinant water-soluble chlorophyll binding protein reconstituted with chlorophyll a or b and reveals a significant decrease of the Huang-Rhys factor of the local exciton-vibrational coupling with decreasing transition energy of the chlorophylls. This decrease could be due to the increase in steric interactions reducing the flexibility of the environment and red-shifting the site energy of the pigments.

Few-second-long correlation times in a quantum dot nuclear spin bath probed by frequency-comb nuclear magnetic resonance spectroscopy

One of the key challenges in spectroscopy is inhomogeneous broadening that masks the homogeneous spectral lineshape and the underlying coherent dynamics. A variety of techniques including four-wave mixing and spectral hole-burning are used in optical spectroscopy while in nuclear magnetic resonance (NMR) spin-echo is the most common way to counteract inhomogeneity. However, the high-power pulses used in spin-echo and other sequences often create spurious dynamics obscuring the subtle spin correlations that play a crucial role in quantum information applications. Here we develop NMR techniques that allow the correlation times of the fluctuations in a nuclear spin bath of individual quantum dots to be probed. This is achieved with the use of frequency comb excitation which allows the homogeneous NMR lineshapes to be measured avoiding high-power pulses. We find nuclear spin correlation times exceeding 1 s in self-assembled InGaAs quantum dots - four orders of magnitude longer than in strain-free III-V semiconductors. The observed freezing of the nuclear spin fluctuations opens the way for the design of quantum dot spin qubits with a well-understood, highly stable nuclear spin bath.

Pulse Propagation Effects in Optical 2D Fourier-Transform Spectroscopy: Theory.

A solution to Maxwell's equations in the three-dimensional frequency domain is used to calculate rephasing two-dimensional Fourier transform (2DFT) spectra of the D2 line of atomic rubidium vapor in argon buffer gas. Experimental distortions from the spatial propagation of pulses through the sample are simulated in 2DFT spectra calculated for the homogeneous Bloch line shape model. Spectral features that appear at optical densities of up to 3 are investigated. As optical density increases, absorptive and dispersive distortions start with peak shape broadening, progress to peak splitting, and ultimately result in a previously unexplored coherent transient twisting of the split peaks. In contrast to the low optical density limit, where the 2D peak shape for the Bloch model depends only on the total dephasing time, these distortions of the 2D peak shape at finite optical density vary with the waiting time and the excited state lifetime through coherent transient effects. Experiment-specific conditions are explored, demonstrating the effects of varying beam overlap within the sample and of pseudo-time domain filtering. For beam overlap starting at the sample entrance, decreasing the length of beam overlap reduces the line width along the ωτ axis but also reduces signal intensity. A pseudo-time domain filter, where signal prior to the center of the last excitation pulse is excluded from the FID-referenced 2D signal, reduces propagation distortions along the ωt axis. It is demonstrated that 2DFT rephasing spectra cannot take advantage of an excitation-detection transformation that can eliminate propagation distortions in 2DFT relaxation spectra. Finally, the high optical density experimental 2DFT spectrum of rubidium vapor in argon buffer gas [J. Phys. Chem. A 2013, 117, 6279-6287] is quantitatively compared, in line width, in depth of peak splitting, and in coherent transient peak twisting, to a simulation with optical density higher than that reported.

Ultrafast phosphate hydration dynamics in bulk H2O.

Phosphate vibrations serve as local probes of hydrogen bonding and structural fluctuations of hydration shells around ions. Interactions of H2PO4(-) ions and their aqueous environment are studied combining femtosecond 2D infrared spectroscopy, ab-initio calculations, and hybrid quantum-classical molecular dynamics (MD) simulations. Two-dimensional infrared spectra of the symmetric (νS(PO2(-))) and asymmetric (νAS(PO2(-))) PO2(-) stretching vibrations display nearly homogeneous lineshapes and pronounced anharmonic couplings between the two modes and with the δ(P-(OH)2) bending modes. The frequency-time correlation function derived from the 2D spectra consists of a predominant 50 fs decay and a weak constant component accounting for a residual inhomogeneous broadening. MD simulations show that the fluctuating electric field of the aqueous environment induces strong fluctuations of the νS(PO2(-)) and νAS(PO2(-)) transition frequencies with larger frequency excursions for νAS(PO2(-)). The calculated frequency-time correlation function is in good agreement with the experiment. The ν(PO2(-)) frequencies are mainly determined by polarization contributions induced by electrostatic phosphate-water interactions. H2PO4(-)/H2O cluster calculations reveal substantial frequency shifts and mode mixing with increasing hydration. Predicted phosphate-water hydrogen bond (HB) lifetimes have values on the order of 10 ps, substantially longer than water-water HB lifetimes. The ultrafast phosphate-water interactions observed here are in marked contrast to hydration dynamics of phospholipids where a quasi-static inhomogeneous broadening of phosphate vibrations suggests minor structural fluctuations of interfacial water.

Expression and purification of mouse peptide ESP4 in Escherichia coli

Pheromones are species-specific chemical signals that regulate a wide range of social and sexual behaviors in many animals. In mice, the male-specific peptide ESP1 (exocrine gland-secreting peptide 1) is secreted into tear fluids and enhances female sexual receptive behavior. ESP1 belongs to the ESP family, a multigene family with 38 genes in mice. ESP1 shares the highest homology with ESP4. ESP1 is expressed in the extraorbital lacrimal gland, whereas ESP4 is expressed in some exocrine glands. Thus, ESP4 is expected to have a function that has not been elucidated yet. Large amounts of the purified ESP4 protein are required for structural and biochemical studies. Here we present an expression and purification scheme for the recombinant ESP4 protein. The N-terminally histidine-tagged ESP4 fusion protein was expressed in Escherichia coli as inclusion bodies, which were solubilized and purified by nickel affinity chromatography. The histidine tag was cleaved with thrombin and removed by a second nickel affinity chromatography step. The ESP4 protein was isolated with high purity by reversed-phase chromatography. For NMR analyses, we prepared a stable isotope-labeled ESP4 protein. Three repeated freeze-drying steps after the reversed-phase chromatography were required, to remove a volatile contaminating compound and to obtain an NMR spectrum with a homogeneous line shape. AMS-modification and far-UV CD spectroscopic analyses suggested that ESP4 has an intramolecular disulfide bridge and a helical structure, respectively. The present study provides a powerful tool for structural and biochemical studies of ESP4, leading toward the elucidation of the roles of the ESP family members.

Dynamic nuclear polarization-enhanced 13C NMR spectroscopy of static biological solids

We explore the possibility of using dynamic nuclear polarization (DNP) to enhance signals in structural studies of biological solids by solid state NMR without sample spinning. Specifically, we use 2D 13C–13C exchange spectroscopy to probe the peptide backbone torsion angles (ϕ, ψ) in a series of selectively 13C-labeled 40-residue β-amyloid (Aβ1–40) samples, in both fibrillar and non-fibrillar states. Experiments are carried out at 9.39T and 8K, using a static double-resonance NMR probe and low-power microwave irradiation at 264GHz. In frozen solutions of Aβ1–40 fibrils doped with DOTOPA-TEMPO, we observe DNP signal enhancement factors of 16–21. We show that the orientation- and frequency-dependent spin polarization exchange between sequential backbone carbonyl 13C labels can be simulated accurately using a simple expression for the exchange rate, after experimentally determined homogeneous 13C lineshapes are incorporated in the simulations. The experimental 2D 13C–13C exchange spectra place constraints on the ϕ and ψ angles between the two carbonyl labels. Although the data are not sufficient to determine ϕ and ψ uniquely, the data do provide non-trivial constraints that could be included in structure calculations. With DNP at low temperatures, 2D 13C–13C exchange spectra can be obtained from a 3.5mg sample of Aβ1–40 fibrils in 4h or less, despite the broad 13C chemical shift anisotropy line shapes that are observed in static samples.

N–H Stretching Vibrations of Guanosine–Cytidine Base Pairs in Solution: Ultrafast Dynamics, Couplings, and Line Shapes

Dynamics and couplings of N-H stretching vibrations of chemically modified guanosine-cytidine (G·C) base pairs in chloroform are investigated with linear infrared spectroscopy and ultrafast two-dimensional infrared (2D-IR) spectroscopy. Comparison of G·C absorption spectra before and after H/D exchange reveals significant N-H stretching absorption in the region from 2500 up to 3300 cm(-1). Both of the local stretching modes ν(C)(NH(2))(b) of the hydrogen-bonded N-H moiety of the cytidine NH(2) group and ν(G)(NH) of the guanosine N-H group contribute to this broad absorption band. Its complex line shape is attributed to Fermi resonances of the N-H stretching modes with combination and overtones of fingerprint vibrations and anharmonic couplings to low-frequency modes. Cross-peaks in the nonlinear 2D spectra between the 3491 cm(-1) free N-H oscillator band and the bands centered at 3145 and 3303 cm(-1) imply N-H···O═C hydrogen bond character for both of these transitions. Time evolution illustrates that the 3303 cm(-1) band is composed of a nearly homogeneous band absorbing at 3301 cm(-1), ascribed to ν(G)(NH(2))(b), and a broad inhomogeneous band peaking at 3380 cm(-1) with mainly guanosine carbonyl overtone character. Kinetics and signal strengths indicate a <0.2 ps virtually complete population transfer from the excited ν(G)(NH(2))(b) mode to the ν(G)(NH) mode at 3145 cm(-1), suggesting lifetime broadening as the dominant source for the homogeneous line shape of the 3301 cm(-1) transition. For the 3145 cm(-1) band, a 0.3 ps population lifetime was obtained.

Polarized atomic radiative emission in electric and magnetic fields1This article is part of a Special Issue on the 10th International Colloquium on Atomic Spectra and Oscillator Strengths for Astrophysical and Laboratory Plasmas.

A reduced density matrix approach is employed to provide a general theoretical description of polarized radiative emission during single-photon transitions from bound and auto-ionizing states of many-electron atomic systems in the presence of a general arrangement of static (or quasi-static) electric and magnetic fields. Polarized radiative emission from partially ionized atomic systems can occur as a result of the excitation of the radiating atomic states by electrons or ions with an anisotropic velocity distribution, which can be produced in an electron or ion beam experiment, and in a non-equilibrium plasma environment. Polarized radiative emission can also be produced or modified during the excitation of the atomic system in the presence of electric and magnetic fields, and electromagnetic fields. In electric and magnetic fields, the normally overlapping angular momentum projection components of atomic spectral lines can be substantially shifted from their field-free positions and split into spectroscopically resolvable (and inherently polarized) features. Because of the breakdown of the field-free angular momentum and parity selection rules, otherwise forbidden components of atomic spectral lines can be generated. Using a representation based on the field-free many-electron atomic states, the Stark–Zeeman patterns can be determined by a diagonalization of the atomic Hamiltonian in the presence of electric and magnetic fields. In the density operator approach, account can be taken of the coherent excitation of a particular subspace of the initial atomic bound or auto-ionizing states. A general expression for the matrix elements of the detected-photon density operator is obtained and provides a unified framework for the analysis of the spectral intensity, angular distribution, and polarization of the Stark–Zeeman patterns. From a unified development of time-domain (equation-of-motion) and frequency-domain (resolvent-operator) formulations of the more comprehensive reduced density matrix approach, the non-equilibrium atomic state kinetics and the homogeneous spectral line shapes can be systematically and self-consistently described.

Demonstration and interpretation of significant asymmetry in the low-resolution and high-resolution Q y fluorescence and absorption spectra of bacteriochlorophyll a

Low- and high-resolution absorption and fluorescence emission Q(y) spectra of bacteriochlorophyll a (BChl a) were recorded, along with homogeneous band line shapes, revealing significant asymmetry between the absorption and emission profiles that are interpreted using a priori spectral calculations. The spectra were recorded in a range of organic solvents facilitating both penta- and hexa-coordination of Mg at ambient and cryogenic temperatures. Detailed vibrational structure in the ground electronic state, virtually independent of Mg coordination, was revealed at 4.5 K by a hole-burning fluorescence line-narrowing technique, complementing the high-resolution spectrum of the excited state measured previously by hole burning to provide the first complete description of the Q(y) absorption and fluorescence spectra of BChl a. Spectral asymmetry persists from 4.5 to 298 K. Time-dependent density-functional theory calculations of the gas-phase absorption and emission spectra obtained using the CAM-B3LYP density functional, curvilinear coordinates, and stretch-bend-torsion scaling factors fitted to data for free-base porphyrin quantitatively predict the observed frequencies of the most-significant vibrational modes as well as the observed absorption∕emission asymmetry. Most other semi-empirical, density-functional, and ab initio computational methods severely overestimate the electron-vibrational coupling and its asymmetry. It is shown that the asymmetry arises primarily through Duschinsky rotation.

Anharmonic Electron−Phonon Coupling in Condensed Media: 1. Formalism

Three different schemes for calculating anharmonic line shape functions are reported and discussed for the first time in this article using eigenstate representation. First, the linear dipole-moment time correlation function (DMTCF), homogeneous (single-site) absorption line shape function, and the respective Franck-Condon factors (FCF) are derived and explored as a molecule makes a transition from a harmonic to an anharmonic (Morse potential) electronic state. Second, the linear DMTCF, homogeneous absorption line shape function, and FCFs are also derived as a molecule makes a transition from one anharmonic to another linearly displaced anharmonic state; FCFs in this case are reported in an exact closed-form expressed in terms of Appell's hypergeometric function. Third, same as the latter set of results are reported but with both linearly displaced and distorted shape of the upper Morse potential. FCFs of the zero-phonon line in all three cases are reported. The first case is rather mathematically complex as a result of taking the overlap integral of the Morse oscillator eigenfunctions, whose spatial decay is a simple exponential, with those of harmonic oscillator, whose decay is a Gaussian. This form of a functional disparity gives rise to some challenges. Model calculations are presented and discussed.

Exciton dynamics in photosynthetic complexes: excitation by coherent and incoherent light

In this paper, we consider the dynamics of a molecular system subjected to external pumping by a light source. Within a completely quantum mechanical treatment, we derive a general formula, which enables us to assess the effects of different light properties on the photo-induced dynamics of excitations in a molecular system. We show that, once the properties of light are known in terms of a certain two-point correlation function, the only information needed to reconstruct the system dynamics is the reduced evolution superoperator. The latter quantity is, in principle, accessible through ultrafast nonlinear spectroscopy. Considering a direct excitation of a small molecular antenna by incoherent light, we find that excitation of coherences is possible due to the overlap of homogeneous line shapes associated with different excitonic states. In Markov and secular approximations, the amount of coherence is significant only under fast relaxation, and both the populations and coherences between exciton states become static at long times. We also study the case when the excitation of a photosynthetic complex is mediated by a mesoscopic system. We find that such a case can be treated by the same formalism with a special correlation function characterizing ultrafast fluctuations of the mesoscopic system. We discuss bacterial chlorosome as an example of such a mesoscopic mediator and propose that the properties of energy-transferring chromophore–protein complexes might be specially tuned to the fluctuation properties of their associated antennae.

Modeling non-Lorentzian two-photon absorption line shape in dipolar chromophores

We present a new approach to modeling of homogeneous line shape in two-photon absorption (2PA) spectra of chromophores with large permanent dipole moment difference between the ground- and excited electronic states using numerical solution of stochastic two-level density matrix equation of motion. Good agreement with experimental 2PA line shapes is obtained for S 1←S 0 transition of Styryl 9 M, which allows us to estimate that the permanent dipole moment difference varies in this chromophore within the S 1←S 0 band in the range, Δ μ=12–25 D.

Parallels between multiple population-period transient spectroscopy and multidimensional coherence spectroscopies

We have recently shown that homogeneous and heterogeneous kinetics can be distinguished by experiments that compare the evolution of the population of a state over two time intervals [E. van Veldhoven et al., ChemPhysChem 8, 1761 (2007)]. This paper elaborates on the analogy between these multiple population-period transient spectroscopy (MUPPETS) experiments and more familiar spectroscopies based on the evolution of coherences. Using a modified inverse-Laplace transform, a standard kinetics decay is re-expressed as a "rate spectrum." A nonexponential decay creates a linewidth in this spectrum. Mechanisms for line broadening in rate spectra are compared to those for line broadening in frequency-domain spectra. Homogeneous and heterogeneous kinetics are defined precisely and are shown to be the counterparts of homogeneous and inhomogeneous line broadenings in frequency-domain spectra. Homogeneous line broadening mechanisms are further divided into equilibrium and nonequilibrium mechanisms, with equilibrium mechanisms more prevalent in frequency spectra and nonequilibrium mechanisms more prevalent in rate spectra. Spectral representations of two-dimensional MUPPETS experiments are developed that are equivalent to two-dimensional coherence spectroscopies. In particular, spectra equivalent to hole-burning and to correlation spectra are defined. Frequency-domain spectra are often modeled as an inhomogeneous distribution of identical homogeneous line shapes. A parallel homogeneous-heterogeneous model for kinetics is defined. Within this model, MUPPETS has sufficient information to completely separate the homogeneous and heterogeneous contributions to a nonexponential decay, even when the homogeneous contribution is nonexponential.