Absorption Line Shape Research Articles

Low-temperature vibronic spectroscopy of condensed chromophore exhibiting inhomogeneous distribution of vibrational frequencies in a mixed quantum-classical environment.

This work has been motivated by the recent paper by the author [M. Toutounji, Phys. Chem. Chem. Phys., 2021, 23, 21981] whereby a mixed quantum-classical Liouville equation was used to probe the spectroscopy and dynamics of a spin-boson system. A mixed quantum-classical Liouville equation treats the system of interest quantum mechanically, the bath classically, and the coupling term mixed quantum-classical mechanically. This paper offers a two-fold advantage: correcting the treatment of the electronic transition decay (width in frequency domain) and assessing the local heterogeneous vibrational structure. The homogeneous linear absorption spectrum of a chromophore embedded in a mixed quantum-classical environment at low temperature is composed of a sharp peak called a zero-phonon line (ZPL) and a broad phonon sideband (PSB), whereby the ZPL and the PSB are assimilated by a Lorentzian function and Voigt profiles, respectively. The PSB, in this case, is characterized by a local heterogeneous structure due to a dispersive medium of vibrations, modeled by vibrational Gaussian distributions to represent the arising inhomogeneous broadening and Lorentzians to model the homogeneous vibrations. This description seems to model proteins and amorphous solids exhibiting a local heterogeneous structure as both electronic and vibrational inhomogeneous broadening seems to be large in these media. This work provides a derivation of linear absorption lineshape and vibronic transition dipole moment time correlation functions, both of which account for pure electronic dephasing (ZPL width) the Voigt profile description of the phonon profiles (PSB) in dispersive media.

Modeling the vibrational spectroscopy of carbonmonoxymyoglobin using DFT and molecular dynamics

Ultrafast vibrational spectroscopy can be used as a tool to examine dynamics on the sub-picosecond timescale. These experiments have been performed probing carbonmonoxymyoglobin. Classical molecular dynamics simulations can aid in the interpretation of these experiments, but one must first develop a model by which the quantized vibrational frequency may be obtained from the classical simulation. In this paper, we use a classical simulation to provide a sampling of the atomic coordinates within the dynamic environment and using those coordinates we perform density functional theory calculations to obtain these frequencies. The frequency calculations are then mapped onto quantities that are readily available within the classical simulation allowing us to limit the number of the more expensive DFT calculations. Finally, we use these results to calculate the absorption lineshape which is in qualitative agreement with the experiment and examine how important the various contributions to the fluctuating frequency are to spectroscopic observables.

Microscopic theory of spin-spin and spin-lattice relaxation of bound protons in cellular and myelin membranes-A lateral diffusion model (LDM).

Deciphering salient features of biological tissue cellular microstructure in health and diseases is an ultimate goal of MRI. While most MRI approaches are based on studying MR properties of tissue "free" water indirectly affected by tissue microstructure, other approaches, such as magnetization transfer (MT), directly target signals from tissue-forming macromolecules. However, despite three-decades of successful applications, relationships between MT measurements and tissue microstructure remain elusive, hampering interpretation of experimental results. The goal of this paper is to develop microscopic theory connecting the structure of cellular and myelin membranes to their MR properties. Herein we introduce a lateral diffusion model (LDM) that explains the T2 (spin-spin) and T1 (spin-lattice) MRI relaxation properties of the macromolecular-bound protons by their dipole-dipole interaction modulated by the lateral diffusion of long lipid molecules forming cellular and myelin membranes. LDM predicts anisotropic T1 and T2 relaxation of membrane-bound protons. Moreover, their T2 relaxation cannot be described in terms of a standard R2 =1/T2 relaxation rate parameter, but rather by a relaxation rate function R2 (t) that depends on time t after RF excitation, having, in the main approximation, a logarithmic behavior: R2 (t) ∼ lnt. This anisotropic non-linear relaxation leads to an absorption lineshape that is different from Super-Lorentzian traditionally used in interpreting MT experiments. LDM-derived analytical equations connect the membrane-bound protons T1 and T2 relaxation with dynamic distances between protons in neighboring membrane-forming lipid molecules and their lateral diffusion. This sheds new light on relationships between MT parameters and microstructure of cellular and myelin membranes.

A comprehensive model for Doppler spectra in thermal atomic vapour

We theoretically and experimentally investigate the Doppler-broadened absorption spectrum of the D2-line (52 S 1/2 → 52 P 3/2) in thermal (room-temperature) Rb vapour over a wide range of probe intensity, probe diameter, and vapour cell temperature to understand the effect of hyperfine pumping and transit-relaxation on the absorption lineshape. We present a relatively simple but comprehensive five-level rate equation model which incorporates optical pumping of the atomic population into the other ‘dark’ ground hyperfine level (leading to absorption saturation), including contributions of the three closely spaced (within one Doppler linewidth) hyperfine levels in the excited state 52 P 3/2 (allowed by the dipole transition selection rules). D2-line transmission spectra predicted by our model show excellent agreement (rms error ) with the experimental data for a wide range of probe intensities (from all the way up to , where I sat0 is the usual two-level saturation intensity for the respective atomic transition), vapour cell temperatures (24.2°C–53.5 °C) and beam diameters (1/e 2 width mm). Our model also takes into account the finite transit time of atoms across the probe beam cross-section, and correctly predicts the dependence of effective saturation intensity on probe diameter (up to lower saturation intensity as compared to I sat0 for few-mm beam sizes). This ab initio five-level model can thus predict accurate Doppler lineshapes for any given experimental parameter set for a linearly polarized probe without any fitting parameters, and can be easily applied to any other atomic system by an appropriate change of the atomic constants in the rate equations.

Ultrafast Vibrational Response of Activated C–D Bonds in a Chloroform–Platinum(II) Complex

The vibrational response of the activated C–D bond in the chloroform complex [Pt(C6H5)2(btz-N,N′)·CDCl3, where btz = 2,2′-bi-5,6-dihydro-4H-1,3-thiazine] is studied by linear and nonlinear two-dimensional infrared (2D-IR) spectroscopy. The change of the C–D stretching vibration of metal-coordinated CDCl3 relative to the free solvent molecule serves as a measure of the non-classical Pt···D–C interaction strength. The stretching absorption band of the activated C–D bond displays a red shift of 119 cm–1 relative to uncoordinated CDCl3, a strong broadening, and an 8-fold enhancement of spectrally integrated absorption. The infrared (IR) absorption and 2D-IR line shapes are governed by spectral diffusion on 200 fs and 2 ps time scales, induced by the fluctuating solvent CDCl3. The enhanced vibrational absorption and coupling to solvent forces are assigned to the enhanced electric polarizability of the activated C–D bond. Density functional theory calculations show a significant increase of C–D bond polarizability of CDCl3 upon coordination to the 16 valence electron Pt(II) complex.

Direct manipulation of atomic excitation with intense extreme-ultraviolet laser fields

The coherent excitation and manipulation of a two-level system with ultrashort intense extreme-ultraviolet laser fields is investigated theoretically, based on numerically solving the time-dependent Schr\"odinger equation. We are particularly interested in the dynamical phase excursion of the energy states over the course of the interaction and the resulting spectral modifications. Fitting the absorption line shapes with the Fano profile quantifies the asymmetry parameter and the corresponding dipole phase offset, capturing the phase difference of the state coefficients after the interaction. Nonperturbative analytical calculations using rectangular driving pulses are employed, yielding physical insights into the dependence of the dipole phase shift on the external field. The validity of the formulas is validated by comparing their predictions with numerical results, which proves to be robust against the variation of laser parameters. The present investigation of strong-field dressing effects complements recent attosecond transient absorption studies assuming weak excitation, and marks a ubiquitous phenomenon that should be generally considered for the interaction of matter with intense laser fields.

A Fourier-domain-based line shape recovery method used in direct absorption spectroscopy

A novel absorption line shape recovery method with self-calibration function and ultra-easy implementation was introduced to direct absorption spectroscopy (DAS) in this study. The self-calibration function empowered the DAS system with the immunity to the laser power fluctuations. The ultra-easy implementation was achieved in that the DAS system was substantially simplified with a single-path DAS rather than the traditional dual-path differential optical absorption spectroscopy (DOAS), and the absorption profile can be directly recovered by an analog or digital filter instead of complex fitting algorithm or sophisticated balance detection circuits. The reliability and self-calibration characteristic of the new method were validated using CH4 transition at 1653.72 nm, where the line strength is 1.45×10-21cm/molec. The Voigt fitting residual and signal to noise ratio were optimized in detail and compared with the DOAS.

Collisional broadening and pressure shift of the potassium resonance doublets by nitrogen, helium, and hydrogen at high temperatures

This paper presents measurements of collisional broadening and pressure shift parameters for the potassium D1 and D2 transitions near 0.77 μm with the collisional partners of molecular nitrogen, helium, and molecular hydrogen. Experiments were conducted in a shock tube at temperatures from 1100 K up to 1900 K, using tunable diode laser absorption spectroscopy and KCl salts as precursors of atomic potassium. In many of the experiments, the target gas was blended with argon to increase the ratio of the driver to driven gas speed of sound. This approach was employed to generate strong incident and reflected shock waves with sufficient temperature rises to produce optimal potassium concentrations (1–10 ppb) in the test gas for high signal-to-noise ratio absorption line shape measurements. The well-resolved absorption line shapes were modeled as Voigt profiles and a least-squares fitting algorithm yielded multiple variables, including the potassium concentration, the collisional full half-widths, and the pressure-induced shifts. Any broadening and shift contributions from the argon dilution were subtracted from the measurements using previous correlations. The pressure-normalized results, i.e., collisional broadening coefficients and pressure shift coefficients, are presented as temperature-dependent power-law relations for the species of interest. The helium and hydrogen results show good agreement with lower-temperature experimental data within 15–20%, and high-temperature theoretical predictions within 10–30%. However, larger discrepancies are observed between the nitrogen results and existing low-temperature experimental data and simplified impact theory predictions. These results may suggest that a more detailed model for the nitrogen collisional broadening of potassium is warranted. The presented correlations may also be useful for the development of potassium-based sensing methods with application to combustion, hypersonics, and astrophysics.

Combined laser ablation-tuneable diode laser absorption spectroscopy and laser-induced breakdown spectroscopy for rapid isotopic analysis of uranium

Laser-induced breakdown spectroscopy (LIBS) can provide immediate in situ elemental characterisation of a sample from a stand-off distance with no sample preparation for bulk, minor and trace species. These attributes suggest the technique could be applied to many processes in the nuclear industry. However, at present, LIBS cannot quickly and easily be used to determine the isotopic composition of a sample, which limits its potential. We report the development of a system comprising laser ablation-tuneable diode laser absorption spectroscopy (LA-TDLAS) and LIBS which can maintain the benefits of traditional LIBS and enable isotopic analysis of certain elements, including lithium and uranium. In this feasibility study, we used this approach to analyse a uranium metal wire sample under ambient conditions of pressure and temperature. Simultaneously, from the same laser produced plasma, the 235U isotope fraction was determined with LA-TDLAS while the plasma emission was used to obtain the electron density of the plasma using Stark broadening of uranium and sodium emission lines. The accuracy of the isotopic analysis performed with LA-TDLAS was limited by the noise of the absorption spectra and low concentration of the minor 235U isotope (0.7%). The limit of detection was estimated to be 1.5 wt%. Using the Doppler broadening of absorption lineshapes, the plasma temperature was calculated to drop from 25,000 K to 2000 K during the plasma lifetime. The electron density rapidly decreased from 6 × 1016 cm−3 immediately after laser ablation to around 3 × 1016 cm−3 after a few μs. The combination of LIBS and LA-TDLAS opens the possibility of rapid elemental and isotopic analysis which would be useful across the nuclear fuel cycle. Furthermore, the LA-TDLAS technique could be further developed for a portable measuring instrument for nuclear forensics applications.

Theory of thin-vapor-layer linear-optical properties: The case of quenching of atomic polarization upon collisions of atoms with dielectric walls

Hot alkali metal vapors enclosed in submicron spectroscopic cells provide an ideal system for fundamental studies of the atom-wall and atom-light interactions at the nanoscale. Here, we propose an approach for calculating the eigenmodes of a thin vapor layer beyond the limitations of the first-order perturbation theory in optical density for the case of quenching of atomic polarization upon collisions of atoms with dielectric walls. We show that higher-order optical density corrections lead to a remarkable density-dependent blueshift and deformation of the spectral line shapes of reflection, transmission, and absorption. We also demonstrate that the eigenmodes of the thin vapor layer can be calculated independently of the choice of optical boundary conditions. This greatly extends the applicability of the constructed theory for the development of miniature atomic sensors.

Microwave-optical coupling via Rydberg excitons in cuprous oxide

We report exciton-mediated coupling between microwave and optical fields in cuprous oxide (Cu$_2$O) at low temperatures. Rydberg excitonic states with principal quantum number up to $n=12$ were observed at 4~K using both one-photon (absorption) and two-photon (second harmonic generation) spectroscopy. Near resonance with an excitonic state, the addition of a microwave field significantly changed the absorption lineshape, and added sidebands at the microwave frequency to the coherent second harmonic. Both effects showed a complex dependence on $n$ and angular momentum, $l$. All of these features are in semi-quantitative agreement with a model based on intraband electric dipole transitions between Rydberg exciton states. With a simple microwave antenna we already reach a regime where the microwave coupling (Rabi frequency) is comparable to the nonradiatively broadened linewidth of the Rydberg excitons. The results provide a new way to manipulate excitonic states, and open up the possibility of a cryogenic microwave to optical transducer based on Rydberg excitons.

Population Dynamics of Stretching Excitations of p-Azido-phenylalanine Incorporated in Calmodulin-Peptide Complexes.

We genetically incorporated the unnatural amino acid p-azido-phenylalanine (AzF) into the ubiquitous Ca2+ sensor protein calmodulin (CaM) in complex with different peptides to explore the response of the azido stretching line shape to varying binding motifs with femtosecond infrared spectroscopy. The dynamic response of the azido stretching mode varies in different CaM-peptide complexes. We model these dynamics as coherent excitations of Fermi resonances and extract a lifetime of the azido stretching vibration of about 1 ps. The resulting model parameters are commensurate with the linear infrared absorption lineshapes which suggests that the conformation-sensitive vibrational lineshape could be composed of Fermi resonances that differ between the protein-peptide complexes.

Simulation of Ab Initio Optical Absorption Spectrum of β-Carotene with Fully Resolved S0 and S2 Vibrational Normal Modes.

The electronic absorption spectrum of β-carotene (β-Car) is studied using quantum chemistry and quantum dynamics simulations. Vibrational normal modes were computed in optimized geometries of the electronic ground state S0 and the optically bright excited S2 state using the time-dependent density functional theory. By expressing the S2-state normal modes in terms of the ground-state modes, we find that no one-to-one correspondence between the ground- and excited-state vibrational modes exists. Using the ab initio results, we simulated the β-Car absorption spectrum with all 282 vibrational modes in a model solvent at 300 K using the time-dependent Dirac-Frenkel variational principle and are able to qualitatively reproduce the full absorption line shape. By comparing the 282-mode model with the prominent 2-mode model, widely used to interpret carotenoid experiments, we find that the full 282-mode model better describes the high-frequency progression of carotenoid absorption spectra; hence, vibrational modes become highly mixed during the S0 → S2 optical excitation. The obtained results suggest that electronic energy dissipation is mediated by numerous vibrational modes.

Theory of high-power excitation spectra of rf-SQUID

We discuss the theory of linear and non-linear spectroscopy of an rf-SQUID coupled to a Josephson spectrometer. Recent experimental measurements on this system have shown a strongly non-linear absorption lineshape, whose current peak maximum undergoes a forward-backward bending transition depending on the value of the rf-SQUID phase. We show that this transition can be qualitatively understood by mapping the dynamics of the driven rf-SQUID onto a generalized Duffing oscillator, with tunable drive and non-linearity, undergoing a bifurcation. Finally we show that in order to quantitatively reproduce the experimental data reported in arXiv:2106.02632, it is crucial to include the feedback from the load-line, leading to an additional source of non-linearity.

On the line shape of the total rovibronic absorption in laser‐dressed diatomic molecules

AbstractRecently, the rovibronic absorption and emission spectra of diatomic molecules dressed by medium‐intensity laser fields have been discussed. By computing the total absorption probability as a function of dressing wavelength an asymmetric line shape has been obtained strongly resembling to the well‐known Fano line shape. Applying two‐state analytical and three‐state numerical models the shape of the total absorption probability function is explained. Further confirmation of the model based results is provided by high resolution accurate numerical computations using large number of basis functions.

Theory of Nonradiative Energy Transfer between Two Optical Ions Using the Proper Adiabatic Approximation

Using adiabatic approximation of polyatomic molecules and methods of molecular quantum electrodynamics, we have derived the Förster-Dexter theory of energy transfer between two optical ions. Although we have assumed a single configurational coordinate, the theory can be easily formulated for multiple normal coordinate system. This approach leads smoothly to the energy transfer rates originally derived by Dexter1 for electric dipole-electric dipole interaction without any additional assumptions regarding the normalization of the wavefunctions in the energy space. Using the transfer rates thus derived, and the band shape functions, Wp , a new function F(T) has been proposed to study the temperature dependence of energy transfer rates due to the overlap of the emission and absorption line shapes of the donor and acceptor ions, respectively. This function has been studied for various scenarios of the relative alignment of the zero phonon lines of these ions in order to understand the participation of phonons in the energy transfer process. We have also compared this quantum mechanically derived F(T) function with that derived using semiclassical theory. The agreements are very good at high temperatures. D. L. Dexter, J. Chem. Phys. 21, 836(1953)

Influence of non-adiabatic effects on linear absorption spectra in the condensed phase: Methylene blue.

Modeling linear absorption spectra of solvated chromophores is highly challenging as contributions are present both from coupling of the electronic states to nuclear vibrations and from solute-solvent interactions. In systems where excited states intersect in the Condon region, significant non-adiabatic contributions to absorption line shapes can also be observed. Here, we introduce a robust approach to model linear absorption spectra accounting for both environmental and non-adiabatic effects from first principles. This model parameterizes a linear vibronic coupling (LVC) Hamiltonian directly from energy gap fluctuations calculated along molecular dynamics (MD) trajectories of the chromophore in solution, accounting for both anharmonicity in the potential and direct solute-solvent interactions. The resulting system dynamics described by the LVC Hamiltonian are solved exactly using the thermalized time-evolving density operator with orthogonal polynomials algorithm (T-TEDOPA). The approach is applied to the linear absorption spectrum of methylene blue in water. We show that the strong shoulder in the experimental spectrum is caused by vibrationally driven population transfer between the bright S1 and the dark S2 states. The treatment of the solvent environment is one of many factors that strongly influence the population transfer and line shape; accurate modeling can only be achieved through the use of explicit quantum mechanical solvation. The efficiency of T-TEDOPA, combined with LVC Hamiltonian parameterizations from MD, leads to an attractive method for describing a large variety of systems in complex environments from first principles.

Quantum-Classical Approach for Calculations of Absorption and Fluorescence: Principles and Applications.

Absorption and fluorescence spectroscopy techniques provide a wealth of information on molecular systems. The simulations of such experiments remain challenging, however, despite the efforts put into developing the underlying theory. An attractive method of simulating the behavior of molecular systems is provided by the quantum–classical theory—it enables one to keep track of the state of the bath explicitly, which is needed for accurate calculations of fluorescence spectra. Unfortunately, until now there have been relatively few works that apply quantum–classical methods for modeling spectroscopic data. In this work, we seek to provide a framework for the calculations of absorption and fluorescence lineshapes of molecular systems using the methods based on the quantum–classical Liouville equation, namely, the forward–backward trajectory solution (FBTS) and the non-Hamiltonian variant of the Poisson bracket mapping equation (PBME-nH). We perform calculations on a molecular dimer and the photosynthetic Fenna–Matthews–Olson complex. We find that in the case of absorption, the FBTS outperforms PBME-nH, consistently yielding highly accurate results. We next demonstrate that for fluorescence calculations, the method of choice is a hybrid approach, which we call PBME-nH-Jeff, that utilizes the effective coupling theory [GelzinisA.;J. Chem. Phys.2020, 152, 05110332035455] to estimate the excited state equilibrium density operator. Thus, we find that FBTS and PBME-nH-Jeff are excellent candidates for simulating, respectively, absorption and fluorescence spectra of real molecular systems.

Spectral lineshapes of collision-induced absorption (CIA) using isotropic intermolecular potential for N2-CH4

Quantum mechanical lineshapes of collision-induced absorption (CIA) at different temperatures are computed for gaseous mixtures of molecular nitrogen and methane using theoretical values for the induced dipole moments and intermolecular potential as input. Comparison with theoretical absorption spectra shows satisfactory agreement. An empirical model of the dipole moment which reproduces the experimental spectra and the first three spectral moments more closely than the fundamental theory, is also presented. Good agreement between computed and experimental absorption lineshapes is obtained when a potential model which is constructed from the thermophysical and transport properties is used.

Simultaneous determination of multiple coupling networks by high-resolution 2D J-edited NMR spectroscopy

J coupling constitutes an important NMR parameter for molecular-level composition analysis and conformation elucidation. Dozens of J-based approaches have been exploited for J coupling measurement and coupling network determination, however, they are generally imposed to insufficient spectral resolution to resolve crowded NMR resonances and low measurement efficiency that a single experiment records one J coupling network. Herein, we propose a general NMR method to collect high-resolution 2D J-edited NMR spectra, which are characterized with advantages of pure absorptive lineshapes, decoupled chemical shift dimension, as well as eliminated axial peaks, thus facilitating J coupling partner assignments and J coupling constant measurements. More meaningfully, this protocol allows simultaneous determination of multiple coupling networks for highly efficient multiplet analyses via addressing multiple protons within one single experiment. Additionally, another variant is proposed for high-resolution applications under adverse magnetic field conditions. Therefore, this study provides a useful NMR protocol for configurational and structural studies with extensive applications in chemistry, biology, and material science.