Rotational-vibrational States Research Articles

Back-decay of the muonic molecular ion (αμt)012+ resonantly formed in (tμ)1s+4HeH+ collision

Abstract Resonant formation of the muonic molecular ion ( α μ t ) 01 2 + in the collision of the muonic tritium atom with the helium hydride ion, ( t μ ) 1 s + 4 HeH + → [ ( α μ t ) 01 2 + , p , e e ] + , is proposed. The ( α μ t ) 01 2 + ion is formed in the rotational-vibrational state (0,1) as one of the two nuclei of the final complex. Back-decay process [ ( α μ t ) 01 2 + , p , e e ] K n + → ( t μ ) 1 s + 4 HeH K ′ n ′ + , where K and n ( K ′ and n ′ ) is the rotational and vibrational quantum number, respectively, is considered in detail and the corresponding decay widths for all possible rotational-vibrational ( K , n ) → ( K ′ , n ′ ) transitions are calculated. Numerous inelastic decay channels of ( α μ t ) 01 2 + are also presented and discussed. The possible fast resonant formation of the ( α μ t ) 01 2 + ion may provide an interesting tool for experimental studies of t ( α , γ ) 7 Li nuclear fusion, which is one of the most important reactions in Big-Bang nucleosynthesis models. Studying this reaction may prove important for solving the lithium problem.

Merged-Beams Study of the Reaction of Cold HD+ with C Atoms Reveals a Pronounced Intramolecular Kinetic Isotope Effect

We present a merged-beams study of reactions between HD+ ions, stored in the Cryogenic Storage Ring (CSR), and laser-produced ground-term C atoms. The molecular ions are stored for up to 20 s in the extreme vacuum of the CSR, where they have time to relax radiatively until they reach their vibrational ground state (within 0.5 s of storage) and rotational states with J≤3 (after 5 s). We combine our experimental studies with quasiclassical trajectory calculations based on two reactive potential energy surfaces. In contrast to previous studies with internally excited H2+ and D2+ ions, our results reveal a pronounced isotope effect, favoring the production of CH+ over CD+ across all collision energies, and a significant increase in the absolute rate coefficient of the reaction. Our experimental results agree well with our theoretical calculations for vibrationally relaxed HD+ ions in their lowest rotational states. Published by the American Physical Society 2024

Quantum stereodynamics studies for the Li + HF (v = 0, j = 1) → H + LiF reaction

In reactive collisions, the colliding direction has an important effect on the reaction dynamics, and the study of reaction stereodynamics which controls the initial orientation or alignment of reactants is of great significance for controlling chemical reactions. In this work, the influence of different initial reactant orientations on the Li + HF (v0 = 0, j0 = 1) → LiF + H reaction dynamics are studied by using the quantum wave packet method. We found that the initial orientation of HF molecule has a great influence on the reactivity and scattering direction of product, but has little influence on the product rotational-vibrational state distribution.

Automated potential energy surface development and comprehensive dynamics for the F + CH3NH2 reaction.

This work is an extensive investigation of the F + CH3NH2 reaction dynamics using a newly-developed potential energy surface (PES). The full-dimensional spin-orbit (SO) corrected (MRCI+Q/aug-cc-pwCVDZ) PES is developed by the Robosurfer program package and the ManyHF method is used in order to fix the Hartree-Fock (HF) convergence issues in the entrance channel. On the surface, retrieved by the fitting of the iteratively extended set of the ManyHF-CCSD(T)-F12a/triple-zeta-quality and SO-corrected energy points, quasi-classical trajectory (QCT) simulations are run. By analyzing the opacity functions and integral cross sections (ICSs) of six reaction channels, the dynamics of the two most reactive hydrogen-abstraction reactions resulting in HF + CH2NH2/CH3NH products are selected for a thorough examination. Despite the statistically and thermodynamically expected results, the kinetically preferred amino hydrogen-abstraction is the dominant mechanism at low collision energies. The initial attack angle and scattering angle distributions are investigated as well. The post-reaction energy distributions show that the collision energy mostly converts into the translational energy of the products, while the reaction energy excites the vibration of the products. The computed vibrationally resolved rotational distributions and vibrational state distributions of the HF product are compared to experimental data, and the theory and experiment are found to be in good agreement.

Encapsulation of a Water Molecule inside C60 Fullerene: The Impact of Confinement on Quantum Features.

We introduce an efficient quantum fully coupled computational scheme within the multiconfiguration time-dependent Hartree (MCTDH) approach to handle the otherwise extremely costly computations of translational–rotational–vibrational states and energies of light-molecule endofullenes. Quantum calculations on energy levels are reported for a water molecule inside C60 fullerene by means of such a systematic approach that includes all nine degrees of freedom of H2O@C60 and does not consider restrictions above them. The potential energy operator is represented as a sum of natural potentials employing the n-mode expansion, along with the exact kinetic energy operator, by introducing a set of Radau internal coordinates for the H2O molecule. On the basis of the present rigorous computations, various aspects of the quantized intermolecular dynamics upon confinement of H2O@C60 are discussed, such as the rotational energy level splitting and the significant frequency shifts of the encapsulated water molecule vibrations. The impact of water encapsulation on quantum features is explored, and insights into the nature of the underlying forces are provided, highlighting the importance of a reliable first-principles description of the guest–host interactions.

SpectrumSDT: A program for parallel calculation of coupled rotational-vibrational energies and lifetimes of bound states and scattering resonances in triatomic systems

We present SpectrumSDT – a program for calculations of energies and lifetimes of bound rotational-vibrational states below and scattering resonances above the dissociation threshold on a global potential energy surface of a triatomic system, which may include stable molecules, weekly-bound van-der-Waals complexes, and unbound atom + diatom scattering systems. Large-amplitude vibrational motion is treated explicitly using hyper-spherical coordinates. Three options for the rotational-vibrational interaction are supported: uncoupled (symmetric top rotor), partially coupled (to include interaction between several nearest states only) and full-coupled (vibrating asymmetric-top rotor). In addition to energies and lifetimes, SpectrumSDT is able to integrate ro-vibrational wave functions over the user-defined regions of potential energy surface, which helps to classify these states. In this release of the code, SpectrumSDT is limited to ABA-type molecules with wave functions that do not extend into the regions near Eckart singularities. Program summaryProgram title: SpectrumSDTCPC Library link to program files:https://doi.org/10.17632/9gftxjs4yk.1Developer's repository link:https://github.com/IgorGayday/SpectrumSDTLicensing provisions: GNU General Public License 3 (GPL)Programming language: FortranNature of problem: Calculations of energies and lifetimes of bound rotational-vibrational states below and scattering resonances above the dissociation threshold on a global potential energy surface of a triatomic system, which may include stable molecules, weekly-bound van-der-Waals complexes, and unbound atom + diatom scattering systems.Solution method: A Hamiltonian matrix is built in APH coordinates using an optimal 2D basis set, adjusted for a given problem. A complex absorbing potential (CAP) is added to define a boundary condition for calculation of scattering resonances above the dissociation threshold. The eigenstates of the Hamiltonain matrix are found using a state-of-the-art iterative eigensolver.Restrictions: The present version is restricted to ABA-molecules and wave functions that do not extend into linear and equilateral triangle configurations.Additional comments including restriction and unusual features: Probabilities and lifetimes of the wave functions can be calculated in user-defined regions on the PES, which allows to analyze their localization properties (i.e. automatic isotopomer assignment) and obtain channel-specific lifetimes for scattering resonances.

Spectrum of beryllium dimer in ground [formula omitted] state

The calculations of the spectrum of vibrational-rotational bound states and new metastable states of the beryllium dimer in ground X1Σg+ state important for laser spectroscopy are presented. The problem is solved using the potential energy curves from [A.V. Mitin, Chem. Phys. Lett. 682, 30 (2017)] and [M. Lesiuk et al, Chem. Theory Comput. 15, 2470 (2019)], and the authors’ software package that implements the iteration Newton method and the high-accuracy finite element method. The efficiency of the proposed approach is demonstrated by the upper and lower estimates of the spectrum of vibrational-rotational bound states and, for the first time, rotational-vibrational metastable states with complex-valued energy eigenvalues (with negative imaginary parts of the order of (10−20÷6) cm−1) in the beryllium dimer. The existence of these metastable states is confirmed by calculating the corresponding scattering states with real-values resonance energies.

Reactive Rate Constants for the C+ + H2(v = 0, 1) Reaction: An Accurate State-to-state Quantum Dynamical Study

Abstract The accurately calculated thermal rate constants of the C+ + H2(v = 0, 1) reaction are important for estimating the CH+ emission spectra in different astronomical environments. In this study, reactive quantum dynamics of the C+ + H2(v = 0, 1) reaction have been investigated with the time-dependent wave packet method on the high-quality potential energy surface recently developed by Guo et al. The simulated total cross sections are compared in detail with previous experimental measurements and dynamical results. The calculated total rate constants are found to be in good agreement with previous quasi-classical results by Herráez-Aguilar et al., except for the v = 0 reaction at low temperatures. The ro-vibrational state-resolved rate constants show that the CH+ product, obtained from both the v = 0 and v = 1 reactions, is significantly populated in the vibrational ground but rotational excited states. In particular, for the v = 0 reaction, the CH+ product is preferably formed at j′ = 4, 5 rotational levels, while the CH+ product for the v = 1 reaction prefers rotational excitation j′ = 6–8. This finding varies with previous J-shifting calculations by Zanchet et al., owing to the different potential energy surface and methodology employed in the calculations.

Equation of Transport for Infrared Radiation in Dense Molecular Gas

Equation of transfer of infrared radiation propagating over a flat surface in a dense molecular gas with small temperature gradients is constructed. Interaction of the radiation field with a gas is manifested in radiative transitions between vibrational, rotational, or vibrational-rotational states of molecules. Therefore, the absorption spectrum of a molecular gas includes hundreds of transitions, and the absorption coefficient as a function of the photon frequency has an oscillatory structure with maxima in the centers of corresponding spectral lines and minima between the centers of neighboring lines. Analysis of the radiative transfer equation for specific problems requires knowledge a large number of parameters for the corresponding radiative transitions in molecules that are contained in the HITRAN data bank. Therefore this equation can be considered as addition to data of the HITRAN bank. The peculiarities of application of the infrared radiation transfer equation to certain cases are analyzed.

Very high-resolution synchrotron radiation far-infrared (FIR) spectrum of methanol‑D2 (CHD2OH) & millimeter-wave (MMW) measurements involving highly excited torsional vibrational rotational states, and identification of optically pumped FIR laser lines

Synchrotron radiation-based very high-resolution far-infrared (FIR) spectrum recorded at the Canadian Light Source (CSL) of doubly deuterated asymmetric methanol molecule (CHD2OH) have been analyzed for transitions associated with highly excited torsional-vibration–rotation levels. Complimentary millimeter-wave (MMW) transition frequencies have been measured using a backward wave oscillator based spectrometer at the Ohio State University. A new and simplified model has been proposed to treat the Hamiltonian Eigenvalues which do not require a large number of parameters with uncertain physical significance. A systematic approach has been laid out on how to proceed in order to obtain self-consistent and rigorously confirmed assignment of an extremely complicated spectrum arising due interaction with other states. New measurements in the MMW region should facilitate astrophysical determination of column densities of this abundant molecular species in cold interstellar clouds, especially in star-forming regions. The scarcity of MMW and the FIR laboratory database severely hindered the astrophysical work in the past. All the FIR assignments have been rigorously confirmed by closed combination relations (CR) using the MMW measurements and/or through ground state CRs from fundamental vibrational band analysis. These FIR transitions are presented in the form an atlas of about 900 lines. As a byproduct of the measurements, it was possible to put forward tentative assignments of optically pumped FIR laser lines.

State-resolved quantum mechanical study of the intramolecular isotope effect in the C+ + HD reaction

Accurate quantum scattering dynamics calculations for the C+ + HD reactions on the ground 12A′ potential energy surface have been performed in the collision energy range of 0.05–1.0 eV. The present integral cross sections and branching ratios are compared with previous experimental and theoretical results. Both the CH+ and CD+ products are distributed in vibrational cold but rotational hot states. Total differential cross sections for both channels exhibit forward–backward symmetry. The state - resolved differential cross sections and the opacity functions show that the product rotational quantum numbers correlate strongly with the total angular momentum J.

ExoMol line lists – XXXIX. Ro-vibrational molecular line list for CO2

ABSTRACT A new hot line list for the main isotopologue of CO2, 12C16O2 is presented. The line list consists of almost 2.5 billion transitions between 3.5 million rotation-vibration states of CO2 in its ground electronic state, covering the wavenumber range 0–20 000 cm−1 (λ > 0.5 µm) with the upper and lower energy thresholds of 36 000 cm−1 and 16 000 cm−1, respectively. The ro-vibrational energies and wavefunctions are computed variationally using the accurate empirical potential energy surface Ames-2. The ro-vibrational transition probabilities in the form of Einstein coefficients are computed using an accurate ab initio dipole moment surface with variational program TROVE. A new implementation of TROVE which uses an exact nuclear-motion kinetic energy operator is employed. Comparisons with the existing hot line lists are presented. The line list should be useful for atmospheric retrievals of exoplanets and cool stars. The UCL-4000 line list is available from the CDS and ExoMol data bases.

ExoMol line lists – XXXVIII. High-temperature molecular line list of silicon dioxide (SiO2)

ABSTRACT Silicon dioxide (SiO2) is expected to occur in the atmospheres of hot rocky super-Earth exoplanets but a lack of spectroscopic data is hampering its possible detection. Here, we present the first, comprehensive molecular line list for SiO2. The line list, named OYT3, covers the wavenumber range 0 – 6000 cm−1 (wavelengths λ > 1.67 μm) and is suitable for temperatures up to T = 3000 K. Almost 33 billion transitions involving 5.69 million rotation–vibration states with rotational excitation up to J = 255 have been computed using robust first-principles methodologies. The OYT3 line list is available from the ExoMol data base at www.exomol.com.

The role of rotation-vibration coupling in symmetric and asymmetric isotopomers of ozone.

A theoretical framework and a computer code (SpectrumSDT) are developed for accurate calculations of coupled rotational-vibrational states in triatomic molecules using hyper-spherical coordinates and taking into account the Coriolis coupling effect. Concise final formulas are derived for the construction of the Hamiltonian matrix using an efficient combination of the variational basis representation and discrete variable representation methods with locally optimized basis sets and grids. First, the new code is tested by comparing its results with those of the APH3D program of Kendrick et al. [Kendrick, Pack, Walker, and Hayes, J. Chem. Phys. 110, 6673 (1999)]. Then, accurate calculations of the rovibrational spectra are carried out for doubly substituted symmetric (18O16O18O) and asymmetric (18O18O16O) ozone isotopomers for the total angular momentum up to J = 5. Together with similar data recently reported for the singly substituted symmetric (16O18O16O) and asymmetric (16O16O18O) ozone isotopomers, these calculations quantify the role of the Coriolis coupling effect in the large mass-independent isotopic enrichment of ozone, observed in both laboratory experiments and the atmosphere of the Earth. It is found that the Coriolis effect in ozone is relatively small, as evidenced by deviations of its rotational constants from the symmetric-top-rotor behavior, magnitudes of parity splittings (Λ-doubling), and ratios of rovibrational partition functions for asymmetric vs symmetric ozone molecules. It is concluded that all of these characteristics are influenced by the isotopic masses as much as they are influenced by the overall symmetry of the molecule. It is therefore unlikely that the Coriolis coupling effect could be responsible for symmetry-driven mass-independent fractionation of oxygen isotopes in ozone.

Quantum dynamics studies of isotope effects in the Mg+(3p) + HD \u2192 MgH+/MgD+ + D/H insertion reaction

The time-dependent wave packet quantum dynamics studies for the Mg+(3p) + HD → MgH+/MgD+ + D/H diabatic reaction are carried out for the first time on recently developed diabatic YHWCH potential energy surfaces [Phys. Chem. Chem. Phys., 2018, 20, 6638–6647]. The results of reaction probabilities and total integral cross sections show a dramatic preference to the formation of MgD+ over MgH+ owing to the insertion reaction mechanism in the title reaction. The MgD+/MgH+ branching ratio witnesses a monotonic decrease from 10.58 to 3.88 at collision energy range of 0.01 to 0.20 eV, and at the collision energy of 0.114 eV, it is close to the experimental value of 5. The rovibrational state-resolved ICSs of the two channels show the products MgD+ have higher vibrational excitation and hotter rotational state distributions. The opacity function P(J) suggests that the MgH+ + D channel and MgD+ + H channel are dominated by high-b and low-b collisions, respectively. Both forward and backward scattering peaks are found in the differential cross section curves, whereas the angle distributions of products are not strictly forward-backward symmetric because of the short lifetime of the complex in the reaction.

Ultrafast selective excitation of surface-enhanced Raman scattering from a single molecule by shaping pump and Stokes pulses

Surface-enhanced Raman scattering (SERS) has attracted much attention as an important technique for studying and monitoring the behavior of molecules. Coherent control by shaping femtosecond pulses is an efficient method for controlling molecular vibration state, rotation state, ionization state, and other molecule dynamics. In this paper, we propose a theoretical scheme of selective excitation of SERS from a single porphycene molecule with two Raman peaks at 327[Formula: see text]cm[Formula: see text] and 367[Formula: see text]cm[Formula: see text] placed in the gap between silver dimer nanospheres. Based on the theory of quantum coherent control, selective excitation of the peak at 327[Formula: see text]cm[Formula: see text] and depression of another at 367[Formula: see text]cm[Formula: see text] are demonstrated by properly shaping femtosecond laser pulses with central frequency of 12500[Formula: see text]cm[Formula: see text] and a full width at half maximum (FWHM) of 300[Formula: see text]cm[Formula: see text]. Ultrafast dynamics of the response of dimer nanospheres to the shaped pump and Stokes pulses are simulated by finite difference time domain (FDTD) method followed by Fourier transform. The enhanced and selected single molecule SERS is realized simultaneously. The SERS probability is enhanced by more than six orders in magnitude compared with the case in air environment, and the FWHMs of the enhanced and the depressed Raman peaks are both larger than 17[Formula: see text]cm[Formula: see text] despite the narrow gap of only 40[Formula: see text]cm[Formula: see text] between the two Raman peaks.

Toward Automated Variational Computation of Rovibrational Resonances, Including a Case Study of the H2 Dimer.

A general and semi-automatic technique, based on the complex absorbing potential (CAP) method, is developed for the variational computation and identification of rotational-vibrational resonance states. This technique is an extension of a method introduced by Tremblay and Carrington ( J. Chem. Phys. 2005, 122, 244107 ), and it employs the damped eigenvectors of a CAP-modified Hamiltonian as a basis to describe resonance wave functions. The low-lying resonances of the weakly bound Ar·NO+ complex are computed with the new and the traditional CAP techniques to test the new algorithm. As an additional, more challenging test case, the bound and resonance rovibrational states of the H2 dimer, the latter with both negative and positive binding energies, are determined, corresponding to different rotational excitations of the H2 monomers. Resonances above the first few dissociation channels of (H2)2 are computed with the new and the traditional CAP methods, revealing some new, assigned resonance quantum states not reported in the literature.

Rovibrational quantum dynamics of the vinyl radical and its deuterated isotopologues.

Rotational-vibrational states up to 3200 cm-1, beyond the highest-lying stretching fundamental, are computed variationally for the vinyl radical (VR), H2Cβ[double bond, length as m-dash]CαH, and the following deuterated isotopologues of VR: CH2[double bond, length as m-dash]CD, CHD[double bond, length as m-dash]CH, and CD2[double bond, length as m-dash]CD. The height of the CαH tunneling rocking barrier of VR, partially responsible for the complex nuclear dynamics of VR and its isotopologues, is determined to be 1641 ± 25 cm-1 by the focal-point analysis approach. The definitive nuclear-motion computations performed utilize two previously published potential energy hypersurfaces and reveal interesting energy-level and tunneling patterns characterizing the internal motions of the four isotopologues. A full assignment, including symmetry labels, of the vibrational states computed for CH2[double bond, length as m-dash]CH is provided, whenever feasible, based on the analysis of wave functions and the related one- and two-mode reduced density matrices. The computed vibrational states of CH2[double bond, length as m-dash]CD and CD2[double bond, length as m-dash]CD are characterized up to slightly above the top of the barrier. Interestingly, it is the interplay of the ν6 (formally CH2 rock) and ν7 (formally CH rock) modes that determines the tunneling dynamics; thus, the description of tunneling in VR needs, as a minimum, the consideration of two in-plane bending motions at the two ends of the molecule. When feasible, the computed results are compared to their experimental counterparts as well as to previous computational results. Corrections to the placement of the ν4 and ν6 fundamentals of VR are proposed. Tunneling switching, a unique phenomenon characterizing tunneling in slightly asymmetric effective double-well potentials, is observed and discussed for CHD[double bond, length as m-dash]CH. Despite the extensive tunneling dynamics, the rotational energy-level structure of VR exhibits rigid-rotor-type behavior.

Excited states of neutral donor bound excitons in GaN

We investigate the excited states of a neutral donor bound exciton (D0X) in bulk GaN by means of high-resolution, polychromatic photoluminescence excitation (PLE) spectroscopy. The optically most prominent donor in our sample is silicon accompanied by only a minor contribution of oxygen—the key for an unambiguous assignment of excited states. Consequently, we can observe a multitude of Si0X-related excitation channels with linewidths down to 200 μeV. Two groups of excitation channels are identified, belonging either to rotational-vibrational or electronic excited states of the hole in the Si0X complex. Such identification is achieved by modeling the excited states based on the equations of motion for a Kratzer potential, taking into account the particularly large anisotropy of effective hole masses in GaN. Furthermore, several ground- and excited states of the exciton-polaritons and the dominant bound exciton are observed in the photoluminescence (PL) and PLE spectra, facilitating an estimate of the associated complex binding energies. Our data clearly show that great care must be taken if only PL spectra of D0X centers in GaN are analyzed. Every PL feature we observe at higher emission energies with regard to the Si0X ground state corresponds to an excited state. Hence, any unambiguous peak identification renders PLE spectra highly valuable, as important spectral features are obscured in common PL spectra. Here, GaN represents a particular case among the wide-bandgap, wurtzite semiconductors, as comparably low localization energies for common D0X centers are usually paired with large emission linewidths and the prominent optical signature of exciton-polaritons, making the sole analysis of PL spectra a challenging task.

Variational Approach to the General Problem Of Vibrational-Rotational States of Molecules

A new method is proposed to calculate energy levels and wave functions of vibrational-rotational molecular states without the necessity to separate the types of motion. The procedure is described to find the corresponding energy matrix which is diagonalized to obtain the final solution. The simplicity of computing matrix elements makes it possible to analyze very large molecules.