Vibrational Quantum States Research Articles

Vibration to Vibration: Product Energy Distribution of F + HD Crossed Molecular Beam Experiments.

We investigated the F + HD(v = 1, j = 0) → HF + D reaction using the crossed molecular beam technique combined with the D atom Rydberg tagging time-of-flight spectroscopy. By detecting the products at various scattering angles for different collision energies in the range of 0.8-1.2 kcal/mol, we observed the forward-scattering products of HF(v' = 4) and determined the threshold energy for the opening of this reaction channel. Similar experiments were conducted for the F + HD(v = 0, j = 0) → HF + D reaction within the range of 1.1-1.6 kcal/mol, where forward-scattering products of HF(v' = 3) were observed, and the threshold energy for this reaction channel was determined as well. Furthermore, we measured the differential cross-sections for the F + HD → HF + D reaction in both the vibrational ground state and the excited state of HD and analyzed the vibrational quantum-state distribution of the HF products. It was found that the population of vibrational quantum states of the HF products increases synchronously with the excitation of the reactant HD vibrationally.

Improved energy formula for highly excited vibrational states of Kratzer-Fues oscillator

A mixed supersymmetric-algebraic approach is employed to derive an improved Kratzer-Fues energy formula, which describes the highly excited states of vibrating diatomic systems up to the dissociation limit. The approach proposed has been used to reproduce the coherent anti-Stokes Raman spectra generated by the vibrational transitions of the nitrogen molecule 14\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{14}$$\\end{document}N2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document} in the ground electronic state X1Σg+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$X^1\\Sigma _g^+$$\\end{document} and the energy levels of dioxygen 16\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{16}$$\\end{document}O2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document} in the ground electronic state X3Σg-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$X^3\\Sigma _g^-$$\\end{document}. The model includes v-dependence of the potential depth D0→Dv\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D_0\\rightarrow D_v$$\\end{document} as well as interatomic equilibrium separation r0→rv\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r_0\\rightarrow r_v$$\\end{document} and can be used to describe vibrations of diatomic molecules in which nonadiabatic vibrational effects play a significant role. Exact analytical formulae relating the vibrational spectroscopic constants ωe\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega _e$$\\end{document}, ωexe\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega _ex_e$$\\end{document} and ωeye\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega _ey_e$$\\end{document} to the parameters defining the model proposed are derived. They enable calculation of the spectral parameters or determination of the model parameters from the experimental data using the inverse spectroscopic procedure. It has been proven that the improved Kratzer-Fues oscillator has a finite number of vibrational quantum states, which distinguishes it from the original model, endowed with infinite number of states.

Oxygen Molecule Formation and the Puzzle of Nitrogen Dioxide and Nitrogen Oxide during Lightning Flash.

Unlike the compounds of the natural air atmosphere, the lightning systems are primarily focused on NO(X2Π), NO2(12A'), and O(3P) concentrations that occurred newly and highly in the ground electronic structure. While the NO/NO2 concentrations ratio is about 2000 during the lightning flash, this ratio becomes about 0.8 right after the lightning flash. The reason for this decrease in the ratio is the disappearance of the high temperature that prevents the formation of NO2 (with the combination of NO and O) and of the photon energy that causes its dissociation (NO2 + hv → NO + O) right after the lightning flash. However, this study will focus on the reactions that contribute to the NO concentration, except for the combination of N and O atoms during lightning flash. To do this, it was focused on the reactive scattering states (especially the NO-exchange) of the NO + O collision and the photo-dissociation of NO2, which provide the formation of the NO molecule in the ground electronic state. This case raises important questions. To what extent do the NO-exchange reaction and the photo-dissociation of NO2 contribute to the atmospherically observed NO molecules? or how can the vibrational quantum states of the NO molecules formed by the photo-dissociation be effected on the NO + O1 collision to produce a NO1 molecule? These conditions may contribute to the concentrations of NO high during lightning flashes. Under low collision energy (between 0.1 and 0.3 eV), the NO (v = 0) population dissociated by a photon can act as reactants in the NO-exchange reactive scattering on the doublet electronic state. Since it is assumed that all of the NO2 molecules are due to NO in the lightning flash system, this is one of the reasons that makes the NO population so high during lightning flash. Therefore, in the light of considering that the lightning system supports the formation of highly vibrating molecular groups, it might also support the formation of O2 molecules. In particular, it was shown that the v = 4 quantum state of the NO molecule over the doublet state between collision energies of 0.9-1.5 eV and the v = 5 quantum state of the NO molecule over the quartet state between collision energies of 1.0-1.5 eV contribute to O2 formation.

Diatomic Molecules and Mass Spectrum of Heavy Quarkonium System with Kratzer- Screened Coulomb Potential (KSCP) through the Solutions of the Schrödinger Equation

In this work, we obtain solutions of the Schrödinger equation with Kratzer-screened Coulomb potential (KSCP) model using the series expansion method. Explicitly, we compute the bound state energy eigenvalues for selected diatomic molecules of N2, CO, NO, and CH, respectively, for the various vibrational and rotational quantum states and the numerical energy eigenvalues agree with the existing literature. Three special cases were considered. The energy eigenvalues are applied to obtain the mass spectra of heavy quarkonium system such as charmonium and bottomonium. The results agree with the experimental data and other recent theoretical studies.

Reactive collisions between electrons and BeT[formula omitted]: Complete set of thermal rate coefficients up to 5000 K

Rate coefficients for the dissociative recombination, vibrational excitation and vibrational de-excitation of the BeT+ ion for all vibrational levels of its ground electronic state (X1Σ+,vi+=0,…,27) are reported, including in the calculation the contribution of super-excited states of the BeT complex pertaining to three electronic symmetries - 2Π, 2Σ+, and 2Δ. These data are suitable for the kinetic modeling of beryllium and tritium containing plasma, as encountered in magnetic fusion devices with beryllium walls (JET, ITER). In the present study we restrict ourselves to incident electron energies from 10−3 up to 2.7eV, and to electron temperatures between 100 and 5000 K, respectively. Together with our earlier and closely related studies on the BeH+ and BeD+ systems, this present work completes the isotopic coverage for the beryllium monohydride ions. The vibrational energy (rather than the vibrational quantum state) is identified as a proper isotopic similarity parameter, e.g., for reduced but still isotopically correct plasma chemistry models.

Role of rotational coherence in femtosecond-pulse-driven nitrogen ion lasing

We experimentally investigated the rotationally resolved polarization characteristics of N$_2^+$ lasing at 391 and 428 nm using a pump-seed scheme. By varying the relative angle between the linear polarizations of the pump and seed, it is found that the polarizations of the P and R branches of 391-nm lasing are counter-rotated. By contrast, both branches of 428-nm lasing remain polarized along the pump. The origin of the puzzled abnormal polarization characteristics is found based on a complete physical model that simultaneously includes the transient photoionization and the subsequent coupling among the electronic, vibrational and rotational quantum states of ions.It suggests that the cascaded resonant Raman processes following ionization create negative coherence between the rotational states of $J$ and $J$+2 in the ionic ground state X$^2\Sigma_g^+(\nu=0)$, which leads to mirror-symmetrical polarization for the P and R branches of 391-nm lasing. Both the experiment and theory indicate that the demonstrated rotational coherence plays an extremely pivotal role in clarifying the gain mechanism of N$_2^+$ lasing and opens up the route toward quantum optics under ultrafast strong fields.

Hyperfine Magnetic Substate Resolved State-to-State Chemistry.

We extend state-to-state chemistry to a realm where besides vibrational, rotational, and hyperfine quantum states magnetic quantum numbers are also resolved. For this, we make use of the Zeeman effect, which energetically splits levels of different magnetic quantum numbers. The chemical reaction which we choose to study is three-body recombination in an ultracold quantum gas of ^{87}Rb atoms forming weakly bound Rb_{2} molecules. Here, we find the propensity rule that the total m_{F} quantum number of the two atoms forming the molecule is conserved. Our method can be employed for many other reactions and inelastic collisions and will allow for novel insights into few-body processes.

A Simple Method to Estimate Entropy and Free Energy of Atmospheric Gases from Their Action.

A convenient practical model for accurately estimating the total entropy (ΣSi) of atmospheric gases based on physical action is proposed. This realistic approach is fully consistent with statistical mechanics, but reinterprets its partition functions as measures of translational, rotational, and vibrational action or quantum states, to estimate the entropy. With all kinds of molecular action expressed as logarithmic functions, the total heat required for warming a chemical system from 0 K (ΣSiT) to a given temperature and pressure can be computed, yielding results identical with published experimental third law values of entropy. All thermodynamic properties of gases including entropy, enthalpy, Gibbs energy, and Helmholtz energy are directly estimated using simple algorithms based on simple molecular and physical properties, without resource to tables of standard values; both free energies are measures of quantum field states and of minimal statistical degeneracy, decreasing with temperature and declining density. We propose that this more realistic approach has heuristic value for thermodynamic computation of atmospheric profiles, based on steady state heat flows equilibrating with gravity. Potentially, this application of an action principle can provide better understanding of emergent properties of many natural or evolving complex systems, including modelling of predictions for global warming.

Simulating the vibrational quantum dynamics of molecules using photonics.

Advances in control techniques for vibrational quantum states in molecules present new challenges for modelling such systems, which could be amenable to quantum simulation methods. Here, by exploiting a natural mapping between vibrations in molecules and photons in waveguides, we demonstrate a reprogrammable photonic chip as a versatile simulation platform for a range of quantum dynamic behaviour in different molecules. We begin by simulating the time evolution of vibrational excitations in the harmonic approximation for several four-atom molecules, including H2CS, SO3, HNCO, HFHF, N4 and P4. We then simulate coherent and dephased energy transport in the simplest model of the peptide bond in proteins-N-methylacetamide-and simulate thermal relaxation and the effect of anharmonicities in H2O. Finally, we use multi-photon statistics with a feedback control algorithm to iteratively identify quantum states that increase a particular dissociation pathway of NH3. These methods point to powerful new simulation tools for molecular quantum dynamics and the field of femtochemistry.

Single-laser-induced quantum interference in photofragmentation reaction of D+2

ABSTRACTWe theoretically study quantum interference phenomena in the photofragmentation reaction of breaking up the diatomic molecular ion D+2 into an atom D and an ionic D+ by a single ultrashort laser pulse. The numerical results show that the occurrence of quantum interference in kinetic energy release spectra is sensitive to the angle between the molecular axis and the laser field polarisation direction. Such sensitivity is shown to be dependent on the initial vibrational quantum state of the system and the pulse intensity. The underlying mechanism for the single-pulse-induced quantum interference is analysed by using a light-induced potential and light-induced conical intersection concept.

Effect of reagent vibrational excitation on reaction of H+CH+C++H2

The effect of reagent vibrational excitation on the stereodynamical properties of H(2S)+CH+(X1+)C+(2P)+H2(X1g+)reaction is investigated by quasi-classical trajectory method on a globally smooth ab initio potential surface of the 2A' state at a collision energy of 500 meV. The reaction probability and the reaction cross-section are also studied. In the calculation, the vibrational levels of the reactant molecules are taken as v = 0, 1, 3, 5 and j = 0, respectively, where v is the vibrational quantum number and j is the rotational quantum number. The calculation results show that the reaction probability reaches a maximum when v = 1, and then decreases with the vibrational quantum number increasing. The integral cross-section decreases sharply with the increase of vibrational quantum number. The potential distribution P(r), the dihedral angle distribution P(r), and the polarization-dependent generalized differential cross sections are calculated. P(r) represents the relation between the reagent relative velocity k and the product rotational angular momentum j'. P(r) describes the correlation of k-k'-j', in which k' is the product reagent relative velocity. The peak of P(r) is at r = 90 and symmetric with respect to 90, which shows that the product rotational angular momentum vector is strongly aligned along the direction perpendicular to the relative velocity direction. The peak of P(r) distribution becomes increasingly obvious with the increase of the rotational quantum number. The dihedral angle distribution P(r) tends to be asymmetric with respect to the k-k' scattering plane (or about r= 180), directly reflecting the strong polarization of the product angular momentum for the title reaction. Each curve has two evident peaks at about r = 90 and r = 270, but the two peak intensities are obviously different, which suggests that j' is not only aligned, but also strongly orientated along the Y-axis of the center-of-mass frame. The peak at r= 90 is apparently stronger than that at r = 270, which indicates that j' tends to be oriented along the positive direction of Y-axis. In order to validate more information, we also plot the angular momentum polarization in the forms of polar plots r and r. The distribution of P(r; r) is well consistent with the distribution P(r) and also the distribution P(r) of the products at different vibrational quantum states. In addition, the polarization-dependent differential cross section is quite sensitive to the reagent vibrational excitation. Based on the obtained results, we find that the observed excess of the methylidyne cation CH+ is closely related to the reactant of vibrational excitation in interstellar chemistry.

Preparation of vibrational quantum states in nanomechanical graphene resonator

We study the quantum dynamics of a nanomechanical graphene resonator. Neglecting the nonlinearities in the graphene membrane and applying a back-gate voltage, the vibrational state of the graphene membrane can be manipulated. We show that in the specific regime coherent states can be generated in the membrane. Moreover, the interaction between the vibrating graphene membrane and a Rydberg atom is investigated. This interaction originates from the Casimir–Polder interaction. Consequently, squeezed states or nonlinear coherent states may be generated in the membrane. Depending on the initial state of the graphene membrane, the membrane state may exhibit quadrature squeezing.

Analytical chemistry, multidimensional spectral signatures, and the future of coherent multidimensional spectroscopy

Spectroscopy is a dominant measurement methodology because it resolves molecular level details over a wide concentration range. Its limitations, however, become challenged when applied to complex materials. Coherent multidimensional spectroscopy (CMDS) is the optical analogue of multidimensional NMR and like NMR, its multidimensionality promises to increase the spectral selectivity of vibrational and electronic spectroscopy. This article explores whether this promise can make CMDS a dominant spectroscopic method throughout the sciences. In order for CMDS to become a dominant methodology, it must create multidimensional spectral fingerprints that provide the selectivity required for probing complex samples. Pump-CMDS probe methods separate the pump’s measurement of dynamics from a multidimensional and selective probe. Fully coherent CMDS methods are ideal multidimensional probes because they avoid relaxation effects, spectrally isolate the output signals, and provide unique and invariant spectral signatures using any combination of vibrational and electronic quantum states.

Full-dimensional quantum molecular dynamics calculations of the rovibrationally mediated X 1A′ → 2 1A′′ transition of nitrous oxide

A full dimensional time-dependent quantum wavepacket approach is used to study the photodissociation dynamics of nitrous oxide for the X 1A′ → 2 1A′′ bound–bound transition based on new highly accurate potential energy and transition dipole moment surfaces. The computed 2 1A′′ absorption spectra at room temperature are characterized by sharp vibrational structures that contribute slightly to the diffuse vibrational structures around the maximum peak at 180 nm of the first ultraviolet absorption band (from the contribution of 2 1A′, 1 1A′′, and 2 1A′′ states) of N2O. Transitions from different initial rovibrational states reveal that the sharp structures arise mainly from N2O bending vibrations, whereas, at higher temperatures, the N2O and NNO stretching vibrations are responsible for enhancing the intensity of the structures. At absorption wavelengths 166 nm and 179 nm, vibrational quantum state distributions of N2 product fragments decrease monotonically with increasing vibrational quantum number v = 0, 1, 2. At 166 nm, rotational quantum state distributions of N2 at fixed v = 0 and v = 1 display multimodal profiles with maximum peaks at j = 77 and j = 75, respectively, whereas, the distributions at the 179 nm absorption wavelength display bimodal profiles with maximum peaks at j = 73 and j = 71, respectively. Accordingly, the presence of rotationally hot N2 from previous experimental and theoretical works in the first band strongly implies a significant influence of the 2 1A′′ state in determining the final dissociation pathway of N2 + O. © 2016 Wiley Periodicals, Inc.

One Million Quantum States of Benzene.

In this study, we compute all of the dynamically relevant vibrational quantum states of benzene, using an "exact" quantum dynamics (EQD) methodology. Benzene (C6H6), in addition to being a very large molecule for EQD (12 atoms, 30 vibrational modes), also has a very large number of vibrational states-around 10(6) in all, lying within 6500 cm(-1) of the ground state. The EQD methodology developed here uses a phase space picture to optimize the truncation of a harmonic oscillator basis-not only with respect to the molecular system of interest but also with respect to the targeted spectral range. By employing several such EQD calculations, targeted to different spectral ranges, a "hybridized" data set is constructed that provides the most accurate results everywhere. In particular, more than 500,000 states are converged to 15 cm(-1) or better.

Communication: Test of quantum chemistry in vibrationally hot hydrogen molecules.

Precision measurements are performed on highly excited vibrational quantum states of molecular hydrogen. The v = 12, J = 0 - 3 rovibrational levels of H2 (X(1)Σg (+)), lying only 2000 cm(-1) below the first dissociation limit, were populated by photodissociation of H2S and their level energies were accurately determined by two-photon Doppler-free spectroscopy. A comparison between the experimental results on v = 12 level energies with the best ab initio calculations shows a good agreement, where the present experimental accuracy of 3.5 × 10(-3) cm(-1) is more precise than theory, hence providing a gateway to further test theoretical advances in this benchmark quantum system.

Energy conversion in high enthalpy flows and non-equilibrium plasmas

Recent developments in the study of very high energy non-equilibrium fluid flows are reviewed. These are flows of molecular gases which exhibit substantial degrees of mode disequilibrium, specifically high energy in molecular vibrational and electronic modes, and high electron energies when the gases are weakly ionized. In contrast, the modes of molecular translation and rotation remain at lower energies. Attention is focused on high density, collision-dominated gases. Studies in two systems are presented: A small wind tunnel where an M=5 steady air flow over small models is produced, and a flowing carbon monoxide gas laser, exhibiting very high energy loading of the vibrational quantum states. The development of non-intrusive optical diagnostics to measure vibrational and electronic state populations and rotational/translational mode temperatures in the flows, with high spatial and temporal resolution, is presented. Kinetic modeling and experimental validation studies in these environments are also discussed.

Complete Quantum State Selectivity in Cold Molecular Beams Using Deflection-Resistant Dark States in a STIRAP Configuration.

One of the main goals of chemical dynamics is the creation of molecular beams composed of a single (vibrational, rotational, and magnetic) quantum state of choice. In this Letter, we propose a method to achieve complete quantum state selectivity by producing resistance to electromagnetically induced deflection (EID) and that the state to be selected can be "dialed in" at will. We illustrate the method by showing in detail how to purify thermal beams of the LiRb and IF molecules to yield molecular beams composed of a variety of prechosen single internal quantum states and/or superpositions of such states. We expect that this method will be implemented in all subsequent explorations of the fundamentals of chemical reactions and their control and the use of cold molecules as a vehicle for studying some of the most profound issues of quantum dynamics.

X-ray lasing in diatomic molecules

We predict high-gain x-ray lasing in diatomic molecules by ultrafast core ionization of the C K- and O K-edges in CO and the N K-edge in N2 with an x-ray free-electron laser source. We solve generalized Maxwell-Bloch equations, keeping track of the electronic and nuclear degrees of freedom. By controlling the molecular alignment and thereby the alignment of the transition dipole moment polarization control of the emitted x-ray radiation is achievable. Despite the broad fluorescence bandwidth, the amplified x-ray emission shows a narrow spectrum. Preparing the initial vibrational quantum state, the x-ray emission frequency can be tuned within the fluorescence band.

X-ray lasing in the CO molecule

We theoretically demonstrate the feasibility of x-ray lasing in the CO molecule by the core ionization of the C K- and O K-shell by x-ray free-electron laser sources. Our numerical simulations are based on the solution of generalized Maxwell–Bloch equations, accounting for the electronic and nuclear degrees of freedom. The amplified x-ray emission pulses have an extremely narrow linewidth of about 0.1 eV and a pulse duration shorter than 30 fs. We compare x-ray lasing transitions to the three lowest electronic states of singly ionized CO. The dependence of the lasing efficiency on the spectral width of the x-ray fluorescence band, value and orientation of the electronic transition dipole moment, lifetime of the core-excited state and the duration of the pump pulse is analysed. Using a pre-aligned molecular ensemble substantially increases the amplified emission. Moreover, by controlling the molecular alignment and thereby the alignment of the transition dipole moment polarization, the control of the emitted x-ray radiation is achievable. Preparing the initial vibrational quantum state, the x-ray emission frequency can be tuned within the fluorescence band. The present scheme is applicable to other diatomic systems, thereby extending the spectral range of coherent x-ray radiation sources based on stimulated x-ray emission on bound transitions.