Vibration-rotation Spectra Research Articles

Quadrupole transitions in the bound rotational–vibrational spectrum of the tritium molecular ion

The nonrelativistic energies of the homonuclear ion are calculated for the ground state using the Lagrange-mesh method as was done for the isotopomers and (Olivares-Pilón and Baye 2012 J. Phys. B: At. Mol. Opt. Phys. 45 065101 and Olivares-Pilón 2013 J. Phys. B: At. Mol. Opt. Phys. 46 245101). Energies and eigenfunctions are obtained up to four of the lowest bound vibrational states () which support 62, 61, 60, and 58 bound rotational states, respectively. Some quasibound states are also presented until 68. From the obtained wave functions, electric quadrupole transitions per time unit are calculated between those states over the whole rotational bands. Extensive results are presented with six significant digits. The ground state energy of the symmetric systems , H−, Ps−, H−, D−, T−, , and is presented with high accuracy as a function of .

State-dependent molecular dynamics.

This paper proposes a new mixed quantum mechanics (QM)—molecular mechanics (MM) approach, where MM is replaced by quantum Hamilton mechanics (QHM), which inherits the modeling capability of MM, while preserving the state-dependent nature of QM. QHM, a single mechanics playing the roles of QM and MM simultaneously, will be employed here to derive the three-dimensional quantum dynamics of diatomic molecules. The resulting state-dependent molecular dynamics including vibration, rotation and spin are shown to completely agree with the QM description and well match the experimental vibration-rotation spectrum. QHM can be incorporated into the framework of a mixed quantum-classical Bohmian method to enable a trajectory interpretation of orbital-spin interaction and spin entanglement in molecular dynamics.

D-dimensional energies for cesium and sodium dimers

We solve the Schrödinger equation with the improved Rosen−Morse potential energy model in D spatial dimensions. The D-dimensional rotation-vibrational energy spectra have been obtained by using the supersymmetric shape invariance approach. The energies for the 33[Formula: see text]g+ state of the Cs2 molecule and the 51Δg state of the Na2 molecule increase as D increases in the presence of fixed vibrational quantum number and various rotational quantum numbers. We observe that the change in behavior of the vibrational energies in higher dimensions remains similar to that of the three-dimensional system.

Evidence for tetrahedral symmetry in (16)O.

We derive the rotation-vibration spectrum of a 4α configuration with tetrahedral symmetry Td and show evidence for the occurrence of this symmetry in the low-lying spectrum of (16)O. All vibrational states with A, E, and F symmetry appear to have been observed as well as the rotational bands with LP=0+, 3-, 4+, 6+ on the A states and part of the rotational bands built on the E, F states. We derive analytic expressions for the form factors and B(EL) values of the ground-state rotational band and show that the measured values support the tetrahedral symmetry of this band.

Diatomic molecule energies of the modified Rosen−Morse potential energy model

We solve the Schrödinger equation with the modified Rosen−Morse empirical potential model to obtain rotation-vibrational energy spectra and unnormalized radial wave functions. The vibrational energy levels calculated with the modified Rosen−Morse potential model for the 61Πu state of the 7Li2 molecule and the X3Π state of the SiC radical are in better agreement with the Rydberg−Klein−Rees data than the predictions of the Morse potential model.

IUPAC critical evaluation of the rotational–vibrational spectra of water vapor. Part IV. Energy levels and transition wavenumbers for D216O, D217O, and D218O

This paper is the fourth of a series of papers reporting critically evaluated rotational–vibrational line positions, transition intensities, pressure dependences, and energy levels, with associated critically reviewed assignments and uncertainties, for all the main isotopologues of water. This paper presents energy level and transition data for the following doubly and triply substituted isotopologues of water: D216O, D217O, and D218O. The MARVEL (Measured Active Rotational–Vibrational Energy Levels) procedure is used to determine the levels, the lines, and their self-consistent uncertainties for the spectral regions 0–14016, 0–7969, and 0–9108cm−1 for D216O, D217O, and D218O, respectively. For D216O, D217O, and D218O, 53534, 600, and 12167 lines are considered, respectively, from spectra recorded in absorption at room temperature and in emission at elevated temperatures. The number of validated energy levels is 12269, 338, and 3351 for D216O, D217O, and D218O, respectively. The energy levels have been checked against the ones determined, with an average accuracy of about 0.03cm−1, from variational rovibrational computations employing exact kinetic energy operators and an accurate potential energy surface. Furthermore, the rovibrational labels of the energy levels have been validated by an analysis of the computed wavefunctions using the rigid-rotor decomposition (RRD) scheme. The extensive list of MARVEL lines and levels obtained is deposited in the Supplementary Material of this paper, in a distributed information system applied to water, W@DIS, and on the official MARVEL website, where they can easily be retrieved.

Molecular energies of the improved Tietz potential energy model

We solve the Schrödinger equation with the improved Tietz empirical potential energy model. The rotation-vibrational energy spectra and the unnormalized radial wave functions have been obtained. The vibrational energy levels predicted by using the improved Tietz potential model for the 51Δgstate and C1Πustate of the Na2molecule are in good agreement with the experimental Rydberg−Klein−Rees data.

Nonrelativistic and relativistic bound state solutions of the molecular Tietz potential via the improved asymptotic iteration method

We have obtained the approximate analytical solutions of the relativistic and nonrelativistic molecular Tietz potential using the improved asymptotic iteration method. By approximating the centrifugal term through the Greene–Aldrich approximation scheme, we have obtained the energy eigenvalues and wave functions for all orbital quantum numbers [Formula: see text]. Where necessary, we made comparison with the result obtained previously in the literature. The relative closeness of the two results reveal the accuracy of the method presented in this study. We proceed further to obtain the rotational-vibrational energy spectrum for some diatomic molecules. These molecules are CO, HCl, H2, and LiH. We have also obtained the relativistic bound state solution of the Klein−Gordon equation with this potential. In the nonrelativistic limits, our result converges to that of the Schrödinger system.

D-dimensional energies for lithium dimer

We solve the Schrödinger equation with the improved Manning–Rosen potential energy model in D spatial dimensions. The bound state rotation-vibrational energy spectra have been obtained by using the supersymmetric shape invariance approach. For fixed vibrational quantum number and various rotational quantum numbers, the energies for the a3Σu+ states of 7Li2 molecule increase as D increases. We observe that the change behavior of the vibrational energies in higher dimensions remains similar to that of the three-dimensional system.

Molecular energies of the improved Rosen−Morse potential energy model

We solve the Schrödinger equation with the improved Rosen−Morse empirical potential energy model. The rotation-vibrational energy spectra and the unnormalized radial wave functions have been obtained. The interaction potential energy curves for the 33Σg+ state of the Cs2 molecule and the 51Δg state of the Na2 molecule are modeled by employing the improved Rosen−Morse potential and the Morse potential. Favourable agreement for the improved Rosen−Morse potential is found in comparing with the Rydberg−Klein−Rees potential. The vibrational energy levels predicted by using the improved Rosen−Morse potential for the 33Σg+ state of Cs2 and the 51Δg state of Na2 are in better agreement with the Rydberg−Klein−Rees data than the predictions of the Morse potential.

Theoretical rotation-vibration spectrum of thioformaldehyde

We present a variational calculation of the first comprehensive T = 300 K rovibrational line list for thioformaldehyde, H2CS. It covers 41,809 rovibrational levels for states up to J(max) = 30 with vibrational band origins up to 5000 cm(-1) and provides the energies and line intensities for 547,926 transitions from the ground vibrational state to these levels. It is based on our previously reported accurate ab initio potential energy surface and a newly calculated ab initio dipole moment surface. Minor empirical adjustments are made to the ab initio equilibrium geometry to reduce systematic errors in the predicted intra-band rotational energy levels. The rovibrational energy levels and transition intensities are computed variationally by using the methods implemented in the computer program TROVE. Transition wavelengths and intensities are found to be in excellent agreement with the available experimental data. The present calculations correctly reproduce the observed resonance effects, such as intensity borrowing, thus reflecting the high accuracy of the underlying ab initio surfaces. We report a detailed analysis of several vibrational bands, especially those complicated by strong Coriolis coupling, to facilitate future laboratory assignments.

CO2 phonon mode renormalization using phonon-assisted energy up-conversion

Molecular dissociation under incident light whose energy is lower than the bond dissociation energy has been achieved through multi step excitation using a coupled state of a photon, electron, and multimode-coherent phonon as known as the dressed photon phonon (DPP). Here, we have investigated the effects of the DPP on CO2, a very stable molecule with high absorption and dissociation energies, by introducing ZnO nanorods to generate the DPP. Then, the changes in CO2 absorption bands were evaluated using light with a wavelength longer than the absorption wavelength, which confirmed the DPP-assisted energy up-conversion. To evaluate the specific CO2 modes related to this process, we measured the CO2 vibration-rotation spectra in the near-infrared region. Detailed analysis of the 3ν3 vibrational band when a DPP source is present showed that DPP causes a significant increase in the intensity of certain absorption bands, especially those that require higher energies to activate.

Fourier transform far-infrared spectroscopy of HN2+ on the AILES beamline of synchrotron SOLEIL

We report the pure rotation spectrum of HN2+ as measured by Fourier transform (FT) absorption spectroscopy in the 20–40 cm−1 spectral range. The cations are produced in a liquid nitrogen cooled hollow cathode discharge cell developed on the AILES beamline of synchrotron SOLEIL. The setup was optimized by recording rotation–vibration spectra of H3+ (with the ν2 band centered at about 2521 cm−1), HN2+ (with the ν1 band centered at about 3234 cm−1), and HCO+ (with the ν1 band centered at about 3089 cm−1). Many rotation–vibration lines have been assigned for each ion and five pure rotational transitions have been detected for HN2+. These results demonstrate the feasibility of recording far-infrared spectra of cationic species using FT broad band spectroscopy associated with the bright synchrotron radiation continuum as an alternative to laser-based frequency tunable techniques.

Rotational-vibrational coupling in the BPS Skyrme model of baryons

We calculate the rotational-vibrational spectrum in the BPS Skyrme model for the hedgehog skyrmion with baryon number one. The resulting excitation energies for the nucleon and delta Roper resonances are slightly above their experimental values. Together with the fact that in the standard Skyrme model these excitation energies are significantly lower than the experimental ones, this provides strong evidence for the conjecture that the inclusion of the BPS Skyrme model is required for a successful quantitative description of physical properties of baryons and nuclei.

The structure of the Hoyle state via a measurement of the 'Hoyle Rotational Band' in 12C

We have measured the 12C(γ, 3α) reaction with an Optical Time Projection Chamber (O-TPC) detector operating with the CO2(80%) + N2(20%) gas mixture and gamma-ray beams from the HIγS facility of the TUNL at Duke. We measured complete angular distributions (between 9.1 – 10.7 MeV) from which we determine the cross section yield curve and E1-E2 relative phases leading to an unambiguous identification of the second 2+ state in 12C at 10.03(11) MeV. The observed spectrum of 12C below 12 MeV including the 2+2 observed in this work resembles the rotation-vibration spectrum predicted for a triangular shape oblate spinning top in which the Hoyle state is the first vibrational breathing mode of the triangular three alpha particle system. The predicted rotation-vibration spectrum of a triangular shape oblate spinning top (with a D3h symmetry) allows us to compare the moment of inertia of the predicted Hoyle rotational band to the ground state rotational band and in this way extract the model radius parameter of the Hoyle state of 3.22(8) fm ( time the r.m.s. radius of the ground state) which is close to the radius extracted from 12C(x,x') data.

LABORATORY CHARACTERIZATION AND ASTROPHYSICAL DETECTION OF VIBRATIONALLY EXCITED STATES OF ETHYL CYANIDE

Ethyl cyanide, CH3CH2CN, is an important interstellar molecule with a very dense rotational-vibrational spectrum. On the basis of new laboratory data in the range of 17-605 GHz and ab initio calculations, two new vibrational states, ν12 and ν20, have been detected in molecular clouds of Orion. Laboratory data consist of Stark spectroscopy (17-110 GHz) and frequency-modulated spectrometers (GEM laboratory in Valladolid: 17-170, 270-360 GHz; Toyama: 26-200 GHz; Emory: 200-240 GHz; Ohio State: 258-368 GHz; and JPL: 270-318, 395-605 GHz). More than 700 distinct lines of each species were measured in J up to 71 and in Ka up to 25. The states were fitted with Watson's S-reduction Hamiltonian. The two new states have been identified in the interstellar medium toward the Orion Nebula (Orion KL). The ground state, the isotopologues of CH3CH2CN, and the vibrationally excited states have been fitted to obtain column densities and to derive vibrational temperatures. All together, ethyl cyanide is responsible for more than 2000 lines in the observed frequency range of 80-280 GHz.

Calculation of the interaction potential energy curve and vibrational levels for the state of molecule

Abstract We solve the Schrodinger equation with the improved expression of the Manning–Rosen empirical potential energy model. The rotation-vibrational energy spectra and the unnormalized radial wave functions have been obtained. The interaction potential energy curve for the a 3 Σ u + state of Li 2 7 molecule is modeled by employing Manning–Rosen potential model. Favorable agreement for the Manning–Rosen potential is found in comparing with ab initio data. The vibrational energy levels predicted by using the Manning–Rosen potential for the a 3 Σ u + state of Li 2 7 are in good agreement with the RKR data and ab initio determinations.

Rotation and Rotation–Vibration Spectroscopy of the 0+–0– Inversion Doublet in Deuterated Cyanamide

The pure rotation spectrum of deuterated cyanamide was recorded at frequencies from 118 to 649 GHz, which was complemented by measurement of its high-resolution rotation-vibration spectrum at 8-350 cm(-1). For D2NCN the analysis revealed considerable perturbations between the lowest Ka rotational energy levels in the 0(+) and 0(-) substates of the lowest inversion doublet. The final data set for D2NCN exceeded 3000 measured transitions and was successfully fitted with a Hamiltonian accounting for the 0(+) ↔ 0(-) coupling. A smaller data set, consisting only of pure rotation and rotation-vibration lines observed with microwave techniques was obtained for HDNCN, and additional transitions of this type were also measured for H2NCN. The spectroscopic data for all three isotopic species were fitted with a unified, robust Hamiltonian allowing confident prediction of spectra well into the terahertz frequency region, which is of interest to contemporary radioastronomy. The isotopic dependence of the determined inversion splitting, ΔE = 16.4964789(8), 32.089173(3), and 49.567770(6) cm(-1), for D2NCN, HDNCN, and H2NCN, respectively, is found to be in good agreement with estimates from a simple reduced quartic-quadratic double minimum potential.

Infrared Spectroscopy of Chloromethyl Radical in Solid Parahydrogen and Its Nuclear Spin Conversion

We present high-resolution infrared absorption spectra of chloromethyl radical produced by in situ UV photolysis of chloroiodomethane isolated in solid parahydrogen. The radicals were stable over a few days in solid parahydrogen kept at 3.6 K. Analysis of the rotation-vibration spectra revealed that the radical exhibited quantized one-dimensional rotational motion about the C-Cl bond, while the ortho and para nuclear spin species were still clearly distinguishable in the spectra. Temporal change of the spectra indicated that the nuclear spin conversion between the ortho and para nuclear spin species of the radical in solid parahydrogen occurred in a time scale of a few hours at 3.6 K. It was also found that the nuclear spin conversion became significantly slower in a higher concentration of chloroiodomethane.

Nonclassical rotations of single molecules in small helium and hydrogen clusters: Manifestation of “microscopic superfluidity”

The studies of small helium clusters (up to 100 atoms) and molecular-hydrogen clusters (up to 20 molecules) that are formed in a supersonic gas jet and are coupled by the weak van der Waals interaction with a linear chromophore molecule are reviewed The shift of the frequency of the fundamental vibration of the chromophore, as well as a change in the moment of inertia of a cluster with its growth, has been detected by their rotational and vibrational-rotational spectra. A nonclassical behavior of the moment of inertia manifested in its decrease beginning with a certain number of attached He atoms (H2 molecules) has been revealed. This behavior indicates that a part of a cluster is decoupled from the rotational motion of a molecule. The key question of these studies is whether such behavior of the moment of inertia is the manifestation of the super-fluidity of helium and hydrogen at microscopic level. The results are compared to the spectroscopy of molecules and hydrogen clusters in liquid-helium nanodroplets.