Absorption Line Shape Function Research Articles

Cancellation between auto- and mutual correlation contributions of protein/water dynamics in terahertz time-domain spectra.

Terahertz time-domain spectra (THz-TDS) were investigated using the results of molecular dynamics (MD) simulations of Staphylococcal nuclease at two hydration states in the temperature range between 100 and 300 K. The temperature dependence of THz-TDS was found to differ significantly from that of the incoherent neutron scattering spectra (INSS) calculated from the same MD simulation results. We further examined contributions of the mutual and auto-correlations of the atomic fluctuations to THz-TDS and found that the negative value of the former contribution nearly canceled out the positive value of the latter, resulting in a monotonic increase of the reduced absorption cross section. Because of this cancellation, no distinct broad peak was observed in the absorption lineshape function of THz-TDS, whereas the protein boson peak was observed in INSS. The contribution of water molecules to THz-TDS was extremely large for the hydrated protein at temperatures above 200 K, in which large-amplitude motions of water were excited. The combination of THz-TDS, INSS and MD simulations has the potential to extract function-relevant protein dynamics occurring on the picosecond to nanosecond timescale.

Simulation of Near-Edge X-ray Absorption Fine Structure with Time-Dependent Equation-of-Motion Coupled-Cluster Theory.

An explicitly time-dependent (TD) approach to equation-of-motion (EOM) coupled-cluster theory with single and double excitations (CCSD) is implemented for simulating near-edge X-ray absorption fine structure in molecular systems. The TD-EOM-CCSD absorption line shape function is given by the Fourier transform of the CCSD dipole autocorrelation function. We represent this transform by its Padé approximant, which provides converged spectra in much shorter simulation times than are required by the Fourier form. The result is a powerful framework for the blackbox simulation of broadband absorption spectra. K-edge X-ray absorption spectra for carbon, nitrogen, and oxygen in several small molecules are obtained from the real part of the absorption line shape function and are compared with experiment. The computed and experimentally obtained spectra are in good agreement; the mean unsigned error in the predicted peak positions is only 1.2 eV. We also explore the spectral signatures of protonation in these molecules.

Calibration-free wavelength modulation spectroscopy: symmetry approach and residual amplitude modulation normalization

This paper offers a simple, practical strategy to implement wavelength modulation spectroscopy (WMS) with a tunable diode laser. It eliminates the need to pre-characterize the laser intensity parameters or make any design changes to a conventional WMS system. Consequently, sensitivity and signal strength remain the same as what can be obtained from a traditional WMS setup at low modulation amplitude. Like previously proposed calibration-free approaches, this new method also yields an absolute absorption line shape function. To recover residual amplitude modulation (RAM) contributions present in the first and second harmonic signals of WMS, we exploited their even or odd symmetric nature. We then used these isolated RAM signals to estimate the absolute line shape function, thus removing the impact of optical intensity fluctuations on measurement. We have also discussed uncertainties and noises associated with the estimated absolute line shape function and the applicability of this new method to detect several gases in the near infrared region. We used measurements of the 1650.96 nm absorption line for 1% and 8% methane concentration in the 60-100 kPa pressure range to validate the efficacy of this new RAM recovery technique and demonstrated a calibration-free system. Because this approach has minimal dependency on diode laser operating conditions, it is more robust and suitable for harsh industrial environments.

Wide absorption spectrum measuring methods by DFB-LDs in water vapor detection system

Two measuring methods of the wide absorption spectrum by distributed feedback laser diodes (DFB-LDs) are presented in detecting the water vapor absorption line. One is the subsection scanning method, and it takes advantage of the wide spectrum tuning range by the temperature modulation and fast spectrum tuning speed by current modulation. Specifically, this method is realized by dividing a target spectral region into several sections which correspond to the specific temperature of DFB-LD, scanning every section by current modulation for hundreds times, and averaging the data to raise the signal to noise ratio (SNR), then combining all sections to get the whole spectrum. An accuracy of 10 ppmv had been obtained in the measurement of water vapor with a 10-cm path length by this method. Another is data fitting method, based on the absorption line-shape function; the absorption line can be described by fitting with partial measured data. The fitting absorption line was fitted well with the measured data, and the square of correlation coefficient (R-square) was no less than 0.99.

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.

A new approach to electron-spin resonance absorption line shape function

We derive a new electron-spin resonance spectrum formula utilizing a quantum-statistical projection technique. The line shape factor appearing in the susceptibility tensor contains the many-body effects for electrons more realistically. It thus becomes possible to explain, in an organized way, all electron transitions including spin conserved processes and spin flipped processes.

Tunable Diode Laser Spectroscopy With Wavelength Modulation: A Phasor Decomposition Method for Calibration-Free Measurements of Gas Concentration and Pressure

The principles and implementation of a phasor decomposition method for analyzing signals in tunable diode laser spectroscopy with wavelength modulation are described. This new technique enables recovery of the isolated and normalized residual amplitude modulation (RAM) signal from measured first harmonic signals at any chosen fundamental modulation frequency. Like the previously reported RAM technique, this new approach is absolute, yielding gas absorption line shape functions, concentrations and pressures without the need for calibration, under certain defined operating conditions. It represents an advancement of the RAM technique in that it obviates the need to operate at a specific high frequency to achieve phase quadrature between the RAM and derivative signals: the signals may be recovered at their maximum levels at any frequency. Measurements of the 1650.96 nm and the 1666.2 nm rotation/vibration absorption line shape functions for 1% and 10% methane in nitrogen at various pressures are compared to theoretical predictions derived from HITRAN data. The excellent agreement confirms the validity of the new technique. Further measurements of concentration and pressure confirm the efficacy of the technique for determining concentration in industrial process environments where the pressure may be unknown and changing. With the above features this new method is particularly suited to stand alone instrumentation for on-line deployment in industrial processes where the calibration factors in the conventional approach would present significant difficulties.

Optical absorption by atomically doped carbon nanotubes under strong atom–field coupling

We analyze optical absorption by atomically doped carbon nanotubes with a special focus on the frequency range close to the atomic transition frequency. We derive the optical absorption line-shape function and, having analyzed particular achiral nanotubes of different diameters, predict the effect of absorption line splitting due to strong atom–vacuum–field coupling in small-diameter nanotubes.

Measurement of absorption line wing structure by wavelength modulation spectroscopy

The application of wavelength modulation absorption spectroscopy in the characterization of lineshape functions of molecular spectra is discussed theoretically, and experimental results for the weak spin-forbidden, magnetic dipole-driven transitions of the oxygen A band are provided. Factors affecting the accuracy of the method are discussed, and it is shown that the technique allows one to accurately probe absorption lineshape functions by using a simple, cost-effective apparatus. The advantages of using detection harmonics greater than the commonly used second are discussed, including an investigation of wing structures of absorption lines and the measurement of collision cross sections.

A theory of modulation spectroscopy with applications of higher harmonic detection

A theoretical treatment of modulation absorption spectroscopy, applicable when amplitude and frequency modulation are present simultaneously, is given. The effects of any relative phase difference between these two types of modulation are incorporated and the theory is applicable to an experiment involving detection at any harmonic order of the modulation frequency. The results obtained are given in terms of the derivatives of the absorption lineshape function and bring out the connection to Nth-order derivative spectroscopy naturally. General expressions for any gaseous molecular absorption line are given. It is shown that certain advantages are obtained when one performs higher harmonic detection, including an increase in the wavelength resolution. Experimental results are obtained and compared with the predictions of the theory developed.

Polaron Problem in Quantum Wells

The problem of the polaron ground state energy and of effective mass renormalization in quantum wells has been widely discussed in literature [1, 2]. Considerably less attention has been paid to the quantum well polaron lifetime [3], or more generally, to the spectral density function which is closely related to the excitonic absorption lineshape function. We employ the cumulant expansion method which has been proved to be very accurate in the case of three-dimensional po larons [4]. The main idea of this method is to expand the correction to the phase of the time dependent Green's function in powers of the coupling constant. Such an expansion is much faster convergent than a standard perturbation series for the Green's function. In practice, already the lowest order term provides a very reasonable approximation.

Effects of temperature on the absorption line-shape function for driven two-level atoms: A non-Markovian treatment.

The description of a non-Markovian process is presented and the asymptotic solution of the generalized master equation is obtained for a two-level atom pumped externally by a monochromatic time-dependent electric field. We give the explicit expression for the absorption line-shape function and discuss its features as a function of the temperature and the memory parameter. We verified the following interesting results: (a) At a critical temperature the line shape undergoes a phase transition, the single-bump profile splits into two bumps; (b) for small values of the memory parameter k the linewidths broaden, becoming larger than the ones calculated under the Markovian approximation, and after reaching some maximum value they narrow monotonically with increasing values of k, this behavior being standard for any finite temperature.

Inversion of time domain signals from a Balle–Flygare type microwave spectrometer

The method of sine and cosine Fourier transforms with a phase correction, well known in NMR and traveling wave Fourier transform microwave spectroscopy, is examined for the pulsed beam Fabry–Perot cavity. The validity of this approach is closely related to the result, noted previously elsewhere [J.-L. Le Gouët and P. R. Berman, Phys. Rev. A 20, 1105 (1979), and F. Rohart and B. Macke, J. Phys. 41, 837 (1980)] that only the polarization spatial harmonic that projects onto the driven fundamental mode of the cavity contributes appreciably to the free induction decay signal. When the full signal is recorded after a short polarization pulse, an absorption line shape function in the low power limit for a single nondegenerate transition can be recovered as an angular distribution weighted integral over the coordinate θ between the nozzle axis and a point on the cavity axis of Doppler-shifted Voight profiles. Passage of the beam through the transverse Gaussian profile of a TEM00q mode contributes an effective line broadening temperature. These results are a direct extension of a semiclassical derivation given earlier [E. J. Campbell, L. W. Buxton, T. J. Balle, and W. H. Flygare, J. Chem. Phys. 74, 813 (1981), and E. J. Campbell, L. W. Buxton, T. J. Balle, M. R. Keenan, and W. H. Flygare, J. Chem. Phys. 74, 829 (1981)]. Analytical results are derived using simplified cavity mode functional forms. Calculations using the exact mode expressions are reported. The relation between this approach and the direct absorption method is discussed.

Non-Markovian population and phase relaxation and absorption lineshape for a two-level system strongly coupled to a harmonic quantum bath

The study of the relaxation of open quantum systems is fundamental to both nonequilibrium statistical mechanics and spectroscopy. In this paper we study theoretically a model of two nondegenerate quantum levels coupled linearly and off-diagonally to a harmonic quantum-mechanical bath. In the weak-coupling limit it is well known for this model that after the system is perturbed from equilibrium the reduced density matrix elements relax exponentially to their equilibrium values, and that T2 = 2T1, where T1 and T2 are the population and phase relaxation times, respectively. In addition, the absorption lineshape is Lorentzian, with a FWHM in Hz of Δν = 12πT1. In this paper we go beyond lowest order in the system-bath interaction by using a time-convolutionless projection operator approach that allows us to avoid the usual “factorization assumption” for the initial density matrix and to include explicitly the effect of the initially prepared state, which we calculate by subjecting the system to a short intense pulse of radiation. We find that although when one is outside the weak-coupling regime the relaxation becomes non-Markovian, the relaxation times T1 and T2 are still well defined in an asymptotic sense. In some cases we find that T2>2T1. The absorption lineshape function becomes non-Lorentzian, and in some instances we find that Δν<12πT1. We find that the equilibrium population of the upper quantum level is nonzero at T = 0. We also investigate the infinite-temperature limit, making the connection to stochastic models of relaxation. Finally, we propose some possible experiments to verify some of our predictions.

Line shapes of saturated absorption spectra in hollow cathode discharges

The saturated absorption line shapes of sputtered uranium atoms in hollow cathode discharges have been investigated using a single axial mode tunable CW laser. The spectral profiles observed under specific experimental conditions exhibit a marked deviation from the usual saturated absorption line shape function. These new features appear under the low velocity changing collision rate, high quenching rate and in the regime of strong pump saturation. A generalized line shape function based on population dynamics along with quenching mechanisms is derived and used to discuss the observed spectra. Our results suggest that the additional features in the observed spectra may be attributed to coherent effects which are manifested under suitable experimental conditions.

Analytically soluble model for linear response of frequency-modulated oscillators with application to magnetic resonance.

The response of a quantum-mechanical multilevel system to external probe fields can often be formulated in terms of frequency-modulated oscillators. Experimental observation of the line shapes associated with a certain transition then gives information on the microscopic processes that are responsible for the frequency modulation. Model calculations have been very involved so far. We therefore present a model for the frequency modulation for which the response of the oscillator can be solved in closed form. The model is applied to the problem of microwave absorption of tumbling paramagnetic centra in liquid-crystalline systems. Explicit expressions for the absorption line-shape functions are derived, and their analytical structure in the frequency domain discussed

Theory of strongly saturated double-resonance line shapes in arbitrary angular momentum states of molecules

We calculate the steady-state probe absorption line-shape function for a strongly driven, Zeeman-degenerate molecular system. The probe laser is treated to lowest order while the pump laser is dealt with to all orders. We obtain the probe line shape for the cases of parallel and perpendicular linear polarization of the two lasers. As expected, the effects of M degeneracy, as well as differences due to the relative laser polarizations, are most pronounced when Doppler broadening is not important. However, even in the presence of large Doppler broadening we find a narrowing of the population hole by including the Zeeman degeneracy and a further narrowing if perpendicular laser polarizations are used.

Numerical investigation of the (s+p)(X)T1usystem: I. Vibronic eigenstates and absorption spectra

The eigenvalue problem of the ideal (s+p)(X)T1u pseudo-Jahn-Teller system is solved by numerical diagonalisation of the energy matrix. Low- and high-energy vibronic eigenstates, absorption lines and spectra at zero temperature are computed for representative values of the electronic 2s-2p spacing in all coupling regimes. In addition the semiclassical absorption lineshape function is calculated: best agreement with the absorption spectra is found for strong coupling. The computational results suggest especially for high energies a factorisation of the vibronic eigenstates for all coupling strengths. A reclassification of the vibronic states is then useful, which provides a link with the adiabatic energy surfaces, enabling a unified description of the absorption spectra. The system exhibits an optical resonance effect, and the calculations show under what conditions this effect can be neglected.

The origin of optical dephasing times and line shape functions for electronic transitions to localized and delocalized states in solids

A theory for optical dephasing times and the homogeneous component of the absorption line shape function to localized states and to the k=o levels of Frenkel exciton states is presented. The theory is based upon exchange between two or more optical transitions which are separated by a small frequency difference. Exchange averaging of the optical transition is brought about via phonon–exciton scattering which couples the optical transitions. This process causes both a temperature dependent line broadening and a temperature dependent frequency shift in the optical spectrum when quadratic phonon–exciton coupling terms are present. The optical dephasing time in such cases result from energy differences of the phonon branch in the ground and excited states and consequently it need not necessarily reflect the complete loss of coherence of the exciton wavepacket at k=o. A simple criterion is derived that allows one to determine whether the phonon–exciton interaction causes an optical transition line shape function to reflect random frequency modulation by the exchange of low frequency phonon or vibrational quanta. The theory allows the phonon–exciton scattering times for individual modes to be determined from an analysis of the frequency shift and line broadening relationships in favorable cases. This information coupled with knowledge of the exciton dispersion allows one to semiquantitatively determine the effect individual phonon and vibrational modes have on the exciton coherence time at a particular temperature.

A vibronic theory of the Raman effect and its application to antisymmetric resonance Raman scattering

A vibronic theory of the Raman effect is developed within a semiclassical framework which provides explicit expressions for the symmetric and antisymmetric components of both the real and imaginary parts of the vibrational Raman transition tensor. The antisymmetric component of the real part is shown to originate in vibronic coupling and to vanish completely at transparent frequencies. Dispersion and absorption lineshape functions are introduced, and by allowing for interference between the α and β electronic absorption bands in ferrocytochrome c, excitation profiles are derived for symmetric and antisymmetric resonance Raman scattering in this region which agree well with observation.