Lorentzian line shape due to an inhomogeneous size distribution without relaxation

In this paper, it is demonstrated that a Lorentzian line shape is predicted for a resonance interacting with a bath of equally spaced levels, even in the sparse, low density of states limit, if one performs an inhomogeneous average over the position of the bath states relative to the bright state. The implication for the spectroscopy of molecules in helium nanodroplets and possibly other samples with a significant size distribution is that coupling of excitations to phonons can lead to Lorentzian shaped transitions entirely from inhomogeneous broadening with no population relaxation in the sample.     

The model of level broadening in condensed phase

We study a model of non-Markovian kinetics for a harmonic oscillator embedded in a harmonic heat bath. We present a new scheme for approximately solving the quantum relaxation equation for the density matrix to find a distribution of level populations. It is found to be an extended Lorentzian with the width depending on the energy. A more convenient non-Markovian distribution called square root Fourier distribution that was implemented in the preceding paper [M. V. Basilevsky et al., J. Chem. Phys. 125, 194513 (2006)] is closely related to this extended Lorentzian model. Both distributions decay exponentially far away from their centers and reproduce well standard Lorentzian widths in the vicinity of the central region. A conventional Lorentzian model with such widths results when the Redfield approximation is applied in the frame of the present procedure.     

ESR line width and line shape dependence of Overhauser‐enhanced magnetic resonance imaging

Electron spin resonance and Overhauser‐enhanced magnetic resonance imaging studies were carried out for various concentrations of ¹⁴N‐labeled 3‐carbamoyl‐2,2,5,5‐tetramethyl‐pyrrolidine‐1‐oxyl in pure water. Overhauser‐enhancement factor attains maxima in the range of 2.5–3 mm concentration. The leakage factor showed an asymptotic increase with increasing agent concentration. The coupling parameter showed the interaction between the electron and nuclear spins to be mainly dipolar in origin. The electron spin resonance parameters, such as the line width, line shape and g‐factor, were determined. The line width analysis confirms that the line broadening is proportional to the agent concentration, and also the agent concentration is optimized in the range of 2.5–3 mm . The line shape analysis shows that the observed electron spin resonance line shape is a Voigt line shape, in which the Lorentzian component is dominant. The contribution of Lorentzian component was estimated using the winsim package. The Lorentzian component of the resonance line attains maxima in the range of 2.5–3 mm concentration. Therefore, this study reveals that the agent concentration, line width and Lorentzian component are the important factors in determining the Overhauser‐enhancement factor. Hence, the agent concentration was optimized as 2.5–3 mm for in vivo/in vitro electron spin resonance imaging and Overhauser‐enhanced magnetic resonance imaging phantom studies. Copyright © 2016 John Wiley & Sons, Ltd.     

Lineshape of rotational spectrum of CO in (4)He droplets

In a recent experiment the rovibrational spectrum of CO isotopomers in superfluid helium-4 droplets was measured, and a Lorentzian lineshape with a large line width of 0.024 K (half width at half maximum) was observed [von Haeften et al., Phys. Rev. B 73, 054502 (2006)]. In the accompanying theoretical analysis it was concluded that the broadening mechanism may be homogeneous and due to coupling to collective droplet excitations (phonons). Here we generalize the lineshape analysis to account for the statistical distribution of droplet sizes present in nozzle expansion experiments. These calculations suggest an alternative explanation for the spectral broadening, namely, that the coupling to phonons can give rise to an inhomogeneous broadening as a result of averaging isolated rotation-phonon resonances over a broad cluster size distribution. This is seen to result in Lorentzian lineshapes, with a width and peak position that depend weakly on the size distribution, showing oscillatory behavior for the narrower size distributions. These oscillations decrease with droplet size and for large enough droplets ( approximately 10(4)) the line widths saturate at a value equal to the homogeneous line width calculated for the bulk limit.     

Motional narrowing of the rotational spectrum of trifluoropropyne at 6550 cm(-1) by intramolecular vibrational energy redistribution

We present the basic principles of dynamic rotational spectroscopy for the highly vibrationally excited symmetric top molecule trifluoropropyne (TFP,CF3CCH). Single molecular eigenstate rotational spectra of TFP were recorded in the region of the first overtone of the nu(1) acetylenic stretching mode at 6550 cm(-1) by infrared-pulsed microwave-Fourier transform microwave triple resonance spectroscopy. The average rotational constant (B) of the highly vibrationally mixed quantum states at 6550 cm(-1) is 2909.33 MHz, a value that is 40 MHz larger than the rotational constant expected for the unperturbed C-H stretch overtone (2869.39 MHz). The average rotational constant and rotational line shape of the molecular eigenstate rotational spectra are compared to the distribution of rotational constants expected for the ensemble of normal-mode vibrational states at 6550 cm(-1) that can interact by intramolecular vibrational energy redistribution (IVR). The normal-mode population distribution at 6550 cm(-1) can be described using a Boltzmann distribution with a microcanonical temperature of 1200 K. At this energy the rotational constant distribution in the normal-mode basis set is peaked at about 2910 MHz with a width of about 230 MHz. The distribution is slightly asymmetric with a tail to the high end. The experimentally measured dynamic rotational spectra are centered at the normal-mode distribution peak; however, the spectral width is significantly narrower (40 MHz) than normal-mode ensemble width (230 MHz). This reduction of the width, along with the Lorentzian shape of the eigenstate rotational spectra when compared to the Gaussian shape of the calculated ensemble distribution, illustrates the narrowing of the spectrum due to IVR exchange. The IVR exchange rate was determined to be 120 ps, about ten times faster than the rate at which energy is redistributed from the v=2 level of the acetylenic stretch.     

ac-Driven quantum decay

We study the enhancement of the quantum decay rate out of a metastable state, via tunneling, in presence of an external sinusoidal force. It is shown that the Floquet picture of quantum mechanics, together with the complex scaling method, provides an adequate methodology to describe the periodically driven decay process in a nonperturbative way. In the limiting cases of extremely slow and fast external forces the numerical results are compared with simple semiclassical estimates. The decay near the fundamental resonance assumes a Lorentzian line shape in agreement with recent experiments on Josephson junctions in the deep quantum regime. For small forces the enhancement grows proportional to the square of the forcing strength and saturates above a threshold value. Additionally our results also exhibit secondary resonances: at higher frequency corresponding roughly to a second harmonic induced by the nonlinear potential shape, and at lower frequency, exactly at the half of the first resonance, revealing a two-photon transition.     

Liquid stability in a model for ortho-terphenyl

We report an extensive study of the phase diagram of a simple model for ortho-terphenyl, focusing on the limits of stability of the liquid state. Reported data extend previous studies of the same model to both lower and higher densities and to higher temperatures. We estimate the location of the homogeneous liquid-gas nucleation line and of the spinodal locus. Within the potential energy landscape formalism, we calculate the distributions of depth, number, and shape of the potential energy minima and show that the statistical properties of the landscape are consistent with a Gaussian distribution of minima over a wide range of volumes. We report the volume dependence of the parameters entering in the Gaussian distribution (amplitude, average energy, variance). We finally evaluate the locus where the configurational entropy vanishes, the so-called Kauzmann line, and discuss the relative location of the spinodal and Kauzmann loci.     

Decay time distribution analysis of Yt-base in benzene-methanol mixtures

Frequency-domain fluorometry was used to measure intensity decays of synthetic Yt-base in mixtures of benzene-methanol at 20 degrees C. Multiexponential analysis shows that the decay of Yt-base fluorescence in benzene and methanol can be well fitted to a single-exponential model with tau = 9.67 ns and 6.25 ns respectively. In mixtures of benzene-methanol the decays became heterogeneous, and the maximum of heterogeneity observed was in a mixture containing 6% methanol. Since we expected a distribution of Yt-base solvation states in the solvent mixtures, and because the decay times of Yt-base are sensitive to solvent, we analyzed the data in terms of decay time distributions. The goodness-of-fit for the unimodal distribution model which has two floating parameters was equivalent to that found using the double exponential model with three floating parameters. The Lorentzian distribution model appears to provide a slightly superior fit relative to the Gaussian distribution model. These results suggest that the intensity decays of solvent-sensitive fluorophores in mixed solvents are described by a distribution of decay times.     

Solvent dependent analysis of isotropic Raman band shape of C=O stretching vibration

The isotropic Raman band shape corresponding to C=O stretching vibration of some molecules has been studied in neat liquids and as a function of solvent concentration using both polar and non-polar solvents. The Raman band shape was analyzed on the basis of correlation with the Lorentzian line shape by employinga simple method of linear curve fitting. In neat liquids and in low solvent concentration region, the band shape was found to be non-Lorentzian. With the gradual increase in solvent concentration the band shape approaches a Lorentzian function. The plot of the correlation coefficient for a Lorentzian shape shows a discontinuity in the intermediate range of solvent concentration. The influence of the structural characteristics of the solute and the solvent systems on the reference mode and various multipolar interactions together with the time varying spatial distribution of solvent molecules with respect to the reference molecule are expected to govern the microenvironmental fluctuations. This may be responsible for the discontinuity in the intermediate solvent concentration region.     

Quantum theory of time-resolved femtosecond stimulated Raman spectroscopy: direct versus cascade processes and application to CDCl3

We present a quantum mechanical wave packet treatment of time-resolved femtosecond stimulated Raman spectroscopy (FSRS), or two-dimensional (2D) FSRS, where a vibrational coherence is initiated with an impulsive Raman pump which is subsequently probed by FSRS. It complements the recent classical treatment by Mehlenbacher et al. [J. Chem. Phys. 131, 244512 (2009)]. In this 2D-FSRS, two processes can occur concurrently but with different intensities: a direct fifth-order process taking place on one molecule, and a cascade process comprising two third-order processes on two different molecules. The cascade process comprises a parallel and a sequential cascade. The theory is applied to the 2D-FSRS of CDCl(3) where calculations showed that: (a) the cascade process is stronger than the direct fifth-order process by one order of magnitude, (b) the sidebands assigned to C-Cl E and A(1) bends, observed on both sides of the Stokes C-D stretch frequency, are not due to anharmonic coupling between the C-D stretch and the C-Cl bends, but are instead due to the coherent anti-Stokes Raman spectroscopy (CARS) and coherent Stokes Raman spectroscopy (CSRS) fields produced in the first step of the cascade process, (c) for each delay time between the femtosecond impulsive pump and FSRS probe pulses, the line shape of the sidebands shows an inversion symmetry about the C-D stretch frequency, and this is due to the 180(°) phase difference between the CARS and CSRS fields that produced the left and right sidebands, and (d) for each sideband, the line shape changes from positive Lorentzian to dispersive to negative Lorentzian, then to negative dispersive and back to positive Lorentzian with the period of the bending vibration, and it is correlated with the momentum of the wave packet prepared on the ground-state surface by the impulsive pump along the sideband normal coordinate.     

Asymmetric line shape in the emission spectra of conjugated polymer thin films: an experimental signature of one-dimensional electronic states

The photoluminescence (PL) properties of thin films of the conjugated polymer [poly(2,5-bis(2(')-ethyl-hexyl)-1,4-phenylenevinylene] have been investigated. At low temperatures the PL spectra show a narrow peak for the electronic transition and a series of well defined vibronic sidebands, which clearly reveal the electron coupling with two different vibronic modes. The purely electronic transition peak is observed to be very asymmetric so that it cannot be adjusted by a single Lorentzian or Gaussian function. In order to understand and explain this asymmetry we have considered a model where the purely electronic transition line shape is partially generated by a broadened square-root singularity representing one-dimensional electron states, and partially by localized (zero-dimensional) states. The localized states are assumed to be those very close to the band edges and are represented in our model by a single Gaussian function. Numerical Franck-Condon analysis was performed, resulting in a very good agreement between the theoretical and the experimental emission spectra. This procedure has confirmed the one-dimensional character of the electron states as the basis for the understanding of the purely electronic line shape asymmetry in the PL spectra of conjugated polymers at low temperatures.     

Electronic relaxation of small molecules in a dense medium

In this paper we present a theoretical study of radiationless transitions in a small molecule embedded in a dense inert medium. Two extreme situations of the molecule-medium coupling were considered, involving the case of zero displacements of the medium modes between the two electronic states (i.e. the Shpolskii matrix) and the limit of strong molecule-medium coupling. The Fourier transform of the non radiative decay probability of a small molecule in a Shpolskii matrix involves exponential damping, while for the strong coupling situation Gaussian damping is involved. In the case of the Shpolskii matrix the decay rate of a small molecule can be expressed in terms of an infinite series where each term corresponds to a product of an (intramolecular) Poisson distribution and a (medium induced) Lorentzian distribution. The Lorentzian widths were explicitly expressed in terms of the vibrational relaxation widths. The Robinson-Frosch formula can be obtained for the extreme case of near degeneracy in a Shpolskii matrix. In the limit of strong molecule-medium coupling the decay rate of a small molecule can be recast in terms of an infinite sum where each term involves a superposition of a Poisson distribution and a Gaussian distribution. The medium induced Gaussian distribution is determined by intramolecular phonon broadening. We have elucidated some new features of the electronic relaxation of a small molecule in a dense medium pertaining to the problem of off-resonance intramolecular coupling which modifies the energy gap law and the deuterium isotope effect.

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Zusammenfassung Strahlungslose Übergänge in einem kleinen Molekül, das von einem dichten inerten Medium umgeben ist, werden untersucht, wobei zwei Grenzfälle bei der Kopplung Molekül/Medium zugrunde gelegt werden: keine Verschiebungen der Medium-Bewegungen beim Übergang (d.h. der Shpolskii-Matrix) einerseits und starke Kopplung Molekül/Medium andererseits. Die Fouriertransformierte für die Wahrscheinlichkeit des strahlungslosen Zerfalls eines kleinen Moleküls in Form einer Shpolskii-Matrix schließt exponentielle Dämpfung ein, wohingegen bei starker Kopplung die Dämpfung einer Gauss-Funktion entspricht. Im ersteren Fall läßt sich der Zerfall als unendliche Reihe von Produkten einer intramolekularen Poisson-Verteilung mit einer vom Medium induzierten Lorentz-Verteilung formulieren, wobei die Lorentz-Breite explizit mittels der Schwingungsrelaxationsbreiten angegeben wird. Die Robin-Frosch-Formel ergibt sich für den Grenzfall der Fastentartung der Shpolskii-Matrix. Bei starker Molekül-Medium-Kopplung laßt sich der Zerfallsverlauf als unendliche Summe von Überlagerungen von Poisson- und Gaussverteilungen angeben. Dabei wird die Medium-induzierte Gauss-Verteilung durch die intramolekulare Phononen-Verbreiterung bestimmt. In diesem Zusammenhang zeigten sich einige neue Gesichtspunkte für die elektronische Relaxation kleiner Moleküle in dichten Medien, wie z. B. das Problem von Nicht-Resonanz bei intramolekularer Kopplung, wo der Satz vom Energie-Sprung und der Deuterium-Isotopie-Effekt modifiziert werden müssen.

     

Fluorescence properties of perylyne aggregates in a polymer matrix (PMMA)

Fluorescene and fluorescence excitation spectra as well as fluorescence decay functions of solid solutions of up to 7×10⁻² M perylene in PMMA have been measured upon variable site-selective dopant excitation. Fluorescence spectra are the analogue to the Y emission of the -modification of crystalline perylene. Fluorescence decay is non-exponential, the average decay time being correlated with the appearance of the 1150 cm⁻¹ b_2u mode in the emission spectrum. It is concluded that the polymer matrix generates a distribution of ground state pair conformations. After excitation pairs relax to structures with statistically varying coordinates leading to a distribution of decay times. With increasing pair excitation energy the Stokes shift increases indicating greater stability of the excited pair. Spectral as well as decay time analysis suggest that in the parallel pair structure radiative decay is promoted by the non-totally symmetric 1150 cm⁻¹ molecular vibration.     

Spectral characteristics of zero-phonon transitions in crystal impurities: A diagrammatic approach

The zero-phonon line shape of a localized transition in a crystal is treated by use of a general interaction between the local transition and the lattice phonons with the harmonic approximation. The theory is carried out to infinite order perturbation by diagrammatic techniques and is thus valid for arbitrarily large phonon coupling. Within our model it is found that the spectral characteristics of the zero phonon line and their temperature dependence are due to resonant Raman-ike phonon scattering processes which cause a decay of the phase coherence of the excitation. The line shape due to this mechanism is found to be lorentzian, and its width increases with temperature, but is zero at 0 K. The line position is also a function of temperature.     

A model calculation on the transport of excitation energy in a molecular crystal

We report a model calculation of the transport of a local (site) excitation in a doped molecular crystal containing one impurity. We do not consider the impurity as a direct trap for electronic excitations (zero trap depth) but assume that exciton-phonon interaction is exclusively given by the coupling of excitons with the vibrational displacement of the impurity. The dynamical problem is solved by using a time-dependent effective potential consisting of equilibrium average exciton-phonon interaction and fluctuations around this average. Two correlation functions are computed using the slow phonon limit and assuming that the temperature of the system is 300 K. Transmission of the excitation energy over a distance of eight spacings takes place, electronically, within a few picoseconds. With the exciton-phonon interaction switched on, calculated correlation functions diminish very rapidly with increasing time, indicating that an irreversible transfer of excitonic energy to the thermal bath takes place. Thus transmission of the excitation energy over such a distance (and without a high rate of trapping) is not an efficient process.     

Electronic properties of the linear ladder polymer,poly[4-(3-pyridyl),8-methyl,2,3–6,7-quinolino] (PPMQ)

Electronic paramagnetic resonance (EPR) and conductivity of pristine and iodine-doped PPMQ were studied. The pristine polymer EPR signal exhibited a Lorentzian line shape. Unpaired spin density measurements indicated that the spin concentrations of the undoped polymer lie in the range of one spin per 150–190 repeat units at room temperature. The peak-to-peak width doubled, the line shape became asymmetric and the spin concentration in the polymer increased slightly after doping with iodine. EPR saturation experiments show that the spin lattice relaxation time T₁ is sensitive to trace impurity. Considerable reduction of T₁ after doping with iodine shows strong coupling between the spin system and N-iodonium nucleus. Conductivity increases up to 5 orders of magnitude by iodine doping; at room temperature, the best value found was 0.017 S/cm. The activation energy for conductance after doping is about half that of pristine polymer.     

Template copolymerization near a patterned surface: computer simulation

We perform a Monte Carlo simulation of irreversible template copolymerization near a chemically heterogeneous surface with a regular distribution of discrete adsorption sites that selectively adsorb from solution one of the two polymerizing monomers and the corresponding chain segments. In the polymerization model, the chain propagation process is simulated by adding individual monomers to the end of growing macroradical. We focus in this paper on the influence of polymerization rate, adsorption energy, and the distance between adsorption sites on the chain conformation and the primary sequence of the resulting two-letter (AB) copolymers and, specifically, on the coupling between polymerization and adsorption. The conditions for the realization of conformation-dependent copolymerization are formulated. For this regime, we observe the formation of a quasiregular copolymer with two types of alternating sections. One of them contains randomly distributed A and B segments. The second one consists mainly of strongly adsorbed A segments. It is found that the average length of the random sections is proportional to the distance between the nearest neighbor adsorption sites. The average length of the A-rich sections is determined by the "adsorption capacity" of adsorption site. By varying the strength of the effective monomer-substrate interaction and the distribution of adsorption sites on the substrate, the copolymers with different surface-induced primary sequences can be designed and synthesized in a controlled fashion.     

CW- and pulsed-EPR of carbonaceous matter in primitive meteorites: solving a lineshape paradox

Insoluble organic matter (IOM) of Orgueil and Tagish Lake meteorites are studied by CW-EPR and pulsed-EPR spectroscopies. The EPR line is due to polycyclic paramagnetic moieties concentrated in defect-rich regions of the IOM, with concentrations of the order of 4x10(19) spin/g. CW-EPR reveals two types of paramagnetic defects: centres with S=1/2, and centres with S=0 ground state and thermally accessible triple state S=1. In spite of the Lorentzian shape of the EPR and its narrowing upon increasing the spin concentration, the EPR line is not in the exchange narrowing regime as previously deduced from multi-frequency CW-EPR [L. Binet, D. Gourier, Appl. Magn. Reson. 30 (2006) 207-231]. It is inhomogeneously broadened as demonstrated by the presence of nuclear modulations in the spin-echo decay. The line narrowing, similar to an exchange narrowing effect, is the result of an increasing contribution of the narrow line of the triplet state centres in addition to the broader line of doublet states. Hyperfine sublevel correlation spectroscopy (HYSCORE) of hydrogen and (13)C nuclei indicates that IOM* centres are small polycyclic moieties that are moderately branched with aliphatic chains, as shown by the presence of aromatic hydrogen atoms. On the contrary the lack of such aromatic hydrogen in triplet states suggests that these radicals are most probably highly branched. Paramagnetic centres are considerably enriched in deuterium, with D/H approximately 1.5+/-0.5x10(-2) of the order of values existing in interstellar medium.     

Simultaneous photon absorption as a probe of molecular interaction and hydrogen-bond cooperativity in liquids

We have investigated the simultaneous absorption of near-infrared photons by pairs of neighboring molecules in liquid methanol. Simultaneous absorption by two OH-stretching modes is found to occur at an energy higher than the sum of the two absorbing modes. This frequency shift arises from interaction between the modes, and its value has been used to determine the average coupling between neighboring methanol molecules. We find a rms coupling strength of 46+/-1 cm(-1), larger than can be explained from a transition-dipole coupling mechanism, suggesting that hydrogen-bond mediated interactions also contribute to the coupling. The most important aspect of simultaneous vibrational absorption is that it allows for a quantitative investigation of hydrogen-bond cooperativity. We derive the extent to which the hydrogen-bond strengths of neighboring molecules are correlated by comparing the line shape of the absorption band caused by simultaneous absorption with that of the fundamental transition. Surprisingly, neighboring hydrogen bonds in methanol are found to be strongly correlated, and from the data we obtain an estimate for the hydrogen-bond correlation coefficient of 0.69+/-0.12.     

Temperature dependence of the Breit–Wigner–Fano Raman line in single-wall carbon nanotube bundles

The G band in Raman spectra of single-wall carbon nanotube (SWNT) bundles is studied between 3 and 500 K. The G band is best fit with five Lorentzian lines and one Breit–Wigner–Fano (BWF) line, indicating coupling of phonons to the electronic continuum of metallic SWNTs. It is found that the line width of the BWF line decreases with increasing temperature. This temperature-dependent behavior is contrary to that of the Lorentzian lines, where the line width increases with increasing temperature. The coupling constant 1/q of the BWF line is also found to decrease with increasing temperature. These temperature-dependent behaviors of BWF line provide evidence that it is the bundling effect of SWNTs that greatly enhances the BWF coupling.