Rovibrational Energy Research Articles

Solutions of the Dirac and Schrödinger equations with shifted Tietz-Wei potential

We solved the Dirac equation using the modified factorization method with the shifted Tietz-Wei potential model. Relativistic and non-relativistic ro-vibrational energy spectra were obtained as well as numerical solutions for different diatomic molecules ( ${\rm H}_2(X^{1}\sum_{g}^{+})$ , ${\rm N}_{2}(X^{1}\sum_{g}^{+})$ , and ${\rm O}_{2}(X^{3}\sum_{g}^{-})$ ). The eigenfunction for this potential has been obtained in terms of hypergeometric function. The energy variations were discussed graphically for different parameters of the shifted Tietz-Wei potential. Our results are in good agreement with the ones available in the literature.

Predicted infrared spectra in the HF stretching band of the H2-HF complex.

The infrared spectra with hydrogen fluoride (HF) and deuterium fluoride (DF) (v2 = 1 ← 0) for eight isotropic species of H2-HF complex are predicted, based on our newly constructed high-accuracy ab initio potential energy surface [D. Yang et al., J. Chem. Phys. 148, 184301 (2018)]. The radial discrete variable representation/angular finite basis representation method and Lanczos algorithm were used to determine the ro-vibrational energy levels and wave functions for eight species of H2-HF complex (para-H2-HF, ortho-H2-HF, para-D2-HF, ortho-D2-HF, para-H2-DF, ortho-H2-DF, para-D2-DF, and ortho-D2-DF) with separating the inter- and intra-molecular vibrations. Bound states properties including their dissociation energies and rotational constants were presented. The calculated band origins are all red shifted to the isolated HF molecule and in good agreement with available experimental values. The frequencies and line intensities of ro-vibrational transitions in the HF stretching band were further calculated, and the predicted infrared spectra are consistent with available observed spectra. Among them, the spectra for three isotopic species of H2-HF (para-H2-DF, para-D2-DF, and ortho-D2-DF) were predicted for the first time.

Extended high-resolution analysis of the ν10 band of C2D4

The high–resolution Fourier–transform spectrum of C2D4 was recorded at the optical resolution of up to 0.00096 cm−1 and analyzed in the region of 460–710 cm−1, where the whole ν10 band was considered including P, Q and R branches. The experimentally recorded line positions (5040 experimental lines with Jmax.=47 and Kamax.=27) are theoretically analyzed, and effective spectroscopic parameters are derived from the corresponding fit procedures. The 1247 ro–vibrational energies of the (v10=1) vibrational state are reproduced by a set of 47 fitted spectroscopic parameters with the drms=2.2×10−4 cm−1. Line list of the ro–vibrational transitions of the ν10 band is presented in the Supplementary material.

Ro-vibrational excitation of H2 by H extended to high temperatures

Collisions between H2 and H are crucial to the thermal balance of astrophysical media, especially that of the early Universe. We report Quasi-Classical Trajectory (QCT) calculations of rate coefficients for the collisional (de-)excitation of H2 by H – including the three-body collisional dissociation – on a highly accurate H3 potential energy surface (PES). Translational temperatures ranging from 100 to 15 000 K, and ro-vibrational energy levels of H2 up to ≈50 000 K are considered. Our QCT rate coefficients agree well with those obtained from previous quantum calculations on the same PES. This good agreement supports our claim that, in order to study the 5000 to 15 000 K temperature range, typical of the early Universe, inexpensive QCT calculations should be preferred to extrapolation of costly quantum calculations run at lower temperatures. The new collisional rate coefficients should enhance our ability to model the cooling and heating budget of the primordial gas.

Improved potential energy surface and spectral assignments for ammonia in the near-infrared region

A new ‘spectroscopic’ potential energy surface (PES) for 14NH3 has been generated by refinement of a high accuracy ab initio PES to experimental data. The quality of the PES is reflected in the excellent agreement between calculated rovibrational energy levels and the empirical values of MARVEL. The PES is used in conjunction with two different DMSs to generate room temperature line lists up to 12 000 and 20 000 cm−1, including all transitions from lower states up to 4000 cm−1, with total angular momentum up to J=20. Several strong bands are found to be missing from HITRAN 2016 in the 5700–6200 cm−1 region. Using the line lists, 769 transitions in the 7400–8000 cm−1 are assigned by ground state combination difference (GSCDs), along with empirical upper state energies and full quantum labels for 284 levels. 53 of our assignments were found to disagree with those given in HITRAN 2016.

Analysis of Rotational–Vibrational Transition Frequencies of the HCl Molecule and Its RKR Potentials in the Ground Electronic State

The consistency of all data that have been published to date on the rovibrational line centers of the hydrogen chloride molecule HCl is analyzed. It was revealed that a number of corrections are needed because of systematic inaccuracies in the line center determination. A simultaneous fit of rovibrational transition frequencies was performed in the region from 7.4 to 18075 cm–1. The isotopically independent spectroscopic parameters for calculating rovibrational energy levels in the ground electronic state are determined. The calculated line centers are compared with the HITRAN data. The obtained spectroscopic parameters are used to calculate the turning points (rmin and rmax) of RKR-potentials of HCl isotopologues. The use of experimental data, including the highest vibrational state with Vmax = 8 that lies approximately at half the potential well depth allowed the pointwise potentials to be calculated up to Vmax = 20.

Accurate rovibrational energies of ozone isotopologues up to J = 10 utilizing artificial neural networks.

In recent years, ozone and its isotopologues have been a topic of interest in many fields of research, due to its importance in atmospheric chemistry and its anomalous isotopic enrichment-or the so-called "mass-independent fractionation." In the field of potential energy surface (PES) creation, debate over the existence of a potential barrier just under the dissociation threshold (referred to as a "potential reef") has plagued research for some years. Recently, Dawes and co-workers [Dawes, Lolur, Li, Jiang, and Guo (DLLJG) J. Chem. Phys. 139, 201103 (2013)] created a highly accurate global PES, for which the reef is found to be replaced with a (monotonic) "plateau." Subsequent dynamical calculations on this "DLLJG" PES have shown improved agreement with experiment, particularly the vibrational spectrum. However, it is well known that reaction dynamics is also highly influenced by the rovibrational states, especially in cases like ozone that assume a Lindemann-type mechanism. Accordingly, we present the first significant step toward a complete characterization of the rovibrational spectrum for various isotopologues of ozone, computed using the DLLJG PES together with the ScalIT suite of parallel codes. Additionally, artificial neural networks are used in an innovative fashion-not to construct the PES function per se but rather to greatly speed up its evaluation.

First high resolution ro–vibrational analysis of C2HD3 in the region of the ν12 band

The high-resolution infrared spectra of C2HD3 ethylene was analyzed for the first time in the region of 1230–1340 cm−1, where the strong ν12 band is located. The 1748 transitions with the maximum values of the upper quantum numbers Jmax.=43 and Kamax.=14 were assigned to the ν12 band. The 14 transitions have been assigned to the 2ν10 band whose appearance is caused by the strong resonance interaction with the ν12 one. For description of the assigned transitions (upper ro-vibrational energy levels), the effective Hamiltonian was used which takes resonance interactions between the vibrational state (v12=1) and three other closely located states, (v10=2),(v7=v10=1) and (v4=v10=1) into account. A set of 70 spectroscopic parameters obtained from a weighted least square fit reproduces the initial experimental data (593 upper energy values, 1762 transitions) with the drms= 1.3 ×10−3 cm−1. Finally, the strengths of 106 ro–vibrational lines of the ν12 band were roughly estimated.

Collision-induced rovibrational energy transfer in small polyatomic molecules: the role of intramolecular perturbations

ABSTRACTVarious forms of time-resolved optical double-resonance spectroscopy facilitate rotationally resolved measurements of collision-induced intramolecular vibration-to-vibration (V–V) energy-transfer processes, which take a gas-phase polyatomic molecule from one distinct rovibrational energy level to another. Of longstanding mechanistic interest are questions concerning the extent to which such V–V energy transfer (ET) may be influenced by intramolecular perturbations – notably Fermi resonance (and other anharmonic mixing effects) and Coriolis coupling – within polyatomic molecular rovibrational manifolds of interest. It is evident that quantum-mechanical interference effects can arise, either inhibiting or enhancing the probability of collision-induced ET in perturbed rovibrational manifolds of certain small gas-phase polyatomic molecules, notably CO2, D2CO and C2H2. This article focuses on a blend of high-resolution rovibrational spectroscopy (characterising initial and final molecular levels and their intramolecular perturbations) and collision dynamics (with colliding molecules defined in terms of isolated-molecule spectroscopic basis states). It aims to offer fresh insights and to consider some apparent mechanistic anomalies (e.g. collision-induced quasi-continuous background effects in the 4νCH rovibrational manifold of C2H2). Various reported experiments and related theoretical treatments are critically re-examined, in order to pose and address mechanistic questions some of which still challenge detailed understanding.

Analyses of infrared FT spectra of asymmetric ozone isotopologue 16O16O18O in the range 950–3850 cm−1

Fifteen bands of the most abundant asymmetric ozone isotopomer 16O16O18O were observed in new spectra generated from various 18O2/16O2 mixtures in the 950–3850 cm−1 range. These bands were fully analyzed, leading to the assignment of a total of 9976 transitions, corresponding to 7030 upper state rovibrational energy levels. The analyses include also six “dark” vibrational states perturbing upper states of the observed bands through anharmonic and Coriolis resonance coupling. The modeling of very congested spectra simultaneously containing lines of six isotopic species resulted to the root mean squares deviations that vary from 0.001 to 0.003 cm−1 in line positions, not exceeding the experimental accuracy. To this end, two different approaches both guided by the ab initio theory were employed. Below 2500 cm−1, all the interacting vibrational states involved in the usual polyad scheme corresponding to the same total stretching excitation were observed. In these cases all symmetry allowed Coriolis and anharmonic coupling terms were initially predicted from ab initio potential energy surface (PES) using the contact transformation method. The major coupling terms were then held fixed to theoretical values during the least-square fits of the observed transitions in order to avoid correlations among adjusted parameters. Above 2500 cm−1, some bands were too weak to be observed. In these cases, the observations did not permit including complete stretching polyads and we used truncated effective models, for which the theory helped to predict initial values of the band centers, their assignments and vibrational dependence of Av, Bv, Cv rotational constants. The final comparison of fifteen experimentally detected and ab initio band centers of 16O16O18O gave the rms deviation of 0.59 cm−1. This drops down to 0.09 cm−1 when using the PES that had been empirically optimized to 16O3 data. The (observed-predicted) rms deviation for Av and Bv is very small - about 0.1%. Average deviations for Cv are somewhat larger ∼0.8% as they are affected by Coriolis resonances. Effective dipole transition moment parameters were either fitted or estimated from a qualitative comparison of observed and simulated spectra involving overlapping contributions of various isotopic species. The line lists built from data reduction models containing about 51,100 transitions are provided in Supplementary Materials.

Treating linear molecule HCCH in calculations of rotation-vibration spectra.

Special treatment is required for ro-vibrational calculations involving polyatomic molecules of linear geometry in order to avoid singularities in the kinetic energy operator. Here we present a variational approach which allows calculations involving such configurations, with a set of 3N-5 linearized coordinates used to represent the vibrations. This approach has been implemented as part of the variational nuclear motion program TROVE (Theoretical ROVibrational Energies). A symmetry adapted basis set based on the Dnh symmetry point group is used. As an illustration of the 3N-5 model presented, TROVE has been used to compute an ab initio room temperature line list for C212H2 using symmetry-adapted ab initio potential energy (CCSD(T)-F12c/cc-pVQZ-F12) and dipole moment surfaces for the ground electronic state. Line positions and intensities (J ≤ 58, l < 8, covering the wavenumbers up to 10 000 cm-1) are compared against HITRAN-2016 and ASD-1000. Alternative methods for treating linear molecules and future work are discussed.

Direct Computation of the Quantum Partition Function by Path-Integral Nested Sampling.

In the present work we introduce a computational approach to the absolute rovibrational quantum partition function using the path-integral formalism of quantum mechanics in combination with the nested sampling technique. The numerical applicability of path-integral nested sampling is demonstrated for small molecules of spectroscopic interest. The computational cost of the method is determined by the evaluation time of a point on the potential energy surface (PES). For efficient PES implementations, the path-integral nested sampling method can be a viable alternative to the direct-Boltzmann-summation technique of variationally computed rovibrational energies, especially for medium-sized molecules and at elevated temperatures.

Extended analysis of the high resolution FTIR spectra of H2MS ([formula omitted]) in the region of the bending fundamental band: The ν2 and [formula omitted] bands: Line positions, strengths, and pressure broadening widths

The high resolution infrared spectra of hydrogen sulfide, H2MS (M=32,33,34,36) in the natural abundance (95.041% of H232S, 0.748% of H233S, 4.196% of H234S and 0.015% of H236S), were recorded with a Bruker IFS 125HR Fourier transform infrared spectrometer (Zürich prototype ZP2001) and analyzed in the ν2 fundamental band region (700 – 1800 cm−1). In the experimental spectra 1564, 1019, and 685 transitions were assigned to the ν2 bands of H232S, H234S and H233S (the maximum values of the quantum numbers are Jmax./Kamax. = 24/17, 20/14, 17/14). The subsequent weighted fits of experimentally assigned transitions were made with the Watson Hamiltonian and a set of parameters which reproduces the initial 333/249/216 infrared ro-vibrational energy values has been obtained from the assigned experimental line positions with the root mean square deviations of drms=2.2×10−4 cm−1,1.7×10−4 cm−1 and 1.5×10−4 cm−1 for the H232S, H234S and H233S isotopologues. Additionally, 703, 182 and 23 transitions with the values of quantum numbers Jmax./Kamax. = 18/14, 14/8 and 9/6 belonging to the 2ν2−ν2 hot bands of H232S, H234S and H233S (for the first time for the hot bands of the H234S and H233S species) were assigned in the experimental spectra. Rotational parameters of the ground vibrational state of H236S were re-determined, and, for the first time, 103 transitions (Jmax.=11,Kamax.=8) of the ν2 band of H236S were assigned in the experimental spectra. An analysis of ro-vibrational line strengths of 61 experimental isolated unsaturated and not too weak lines of the ν2 band of H232S was made (Jmax.=9,Kamax.=8), and five effective dipole moment parameters were obtained from the fit which reproduce the initial experimental line intensities with the drms = 1.4 %. An analogous analysis was performed for the H234S and H233S isotopologues. The half-widths analysis was made on the basis of the multi-spectrum fit with the Hartmann-Tran line profile, and self-pressure broadening coefficients were estimated for a few tens of lines for the three most abundant isotopologues.

A full-dimensional potential energy surface and quantum dynamics of inelastic collision process for H2-HF.

A full-dimensional ab initio potential energy surface for the H2-HF van der Waals complex was constructed by employing the coupled-cluster singles and doubles with noniterative inclusion of connected triples with augmented correlation-consistent polarised valence quadruple-zeta basis set plus bond functions. Using the improved coupled-states approximation including the nearest neighbor Coriolis couplings, we calculated the state-to-state scattering dynamics for pure rotational and ro-vibrational energy transfer processes. For pure rotational energy transfer, our results showed a different dynamical behavior for para-H2 and ortho-H2 in collision with hydrogen fluoride (HF), which is consistent with the previous study. Interestingly, some strong resonant peaks were presented in the cross sections for ro-vibrational energy transfer. In addition, the calculated vibrational-resolved rate constant is in agreement with the experimental results reported by Bott et al. These dynamics data can be further applied to the numerical simulation of HF chemical lasers.

Symmetry Adaptation of the Rotation-Vibration Theory for Linear Molecules

A numerical application of linear-molecule symmetry properties, described by the D ∞ h point group, is formulated in terms of lower-order symmetry groups D n h with finite n. Character tables and irreducible representation transformation matrices are presented for D n h groups with arbitrary n-values. These groups can subsequently be used in the construction of symmetry-adapted ro-vibrational basis functions for solving the Schrödinger equations of linear molecules. Their implementation into the symmetrisation procedure based on a set of “reduced” vibrational eigenvalue problems with simplified Hamiltonians is used as a practical example. It is shown how the solutions of these eigenvalue problems can also be extended to include the classification of basis-set functions using ℓ, the eigenvalue (in units of ℏ) of the vibrational angular momentum operator L ^ z . This facilitates the symmetry adaptation of the basis set functions in terms of the irreducible representations of D n h . 12 C 2 H 2 is used as an example of a linear molecule of D ∞ h point group symmetry to illustrate the symmetrisation procedure of the variational nuclear motion program Theoretical ROVibrational Energies (TROVE).

Benchmark Linelists and Radiative Cooling Functions for LiH Isotopologues

Linelists and radiative cooling functions in the local thermodynamic equilibrium limit have been computed for the six most important isotopologues of lithium hydride, 7LiH, 6LiH, 7LiD, 6LiD, 7LiT, and 6LiT. The data are based on the most accurate dipole moment and potential energy curves presently available, the latter including adiabatic and leading relativistic corrections. Distance-dependent reduced vibrational masses are used to account for non-adiabatic corrections of the rovibrational energy levels. Even for 7LiH, for which linelists have been reported previously, the present linelist is more accurate. Among all isotopologues, 7LiH and 6LiH are the best coolants, as shown by the radiative cooling functions.

Symmetry analysis of trimers rovibrational spectra: the case of Ne3

An approximate method to assign the symmetry to the rovibrational spectrum of homonuclear trimers based on the solution of the rotational Hamiltonian by means of a purely vibrational basis combined with standard rotational functions is applied on Ne3. The neon trimer constitutes an ideal test between heavier systems such as Ar3 for which the method proves to be an extremely useful technique and some other previously investigated cases such as H3+ where some limitations were observed. Comparisons of the calculated rovibrational energy levels are established with results from different calculations reported in the literature.

High resolution FTIR spectroscopy of fluoroform 12CHF3 and critical analysis of the infrared spectrum from 25 to 1500 cm−1

ABSTRACTWe report high-resolution ( 0.001 cm−1) Fourier Transform Infrared spectra of fluoroform (CHF3) including the pure rotational (far infrared or THz) range (28–65 cm−1), the ν3 fundamental ( = 700.099 cm−1), as well as the associated “hot’ band 2ν3 − ν3 ( = 699.295 cm−1) and the ‘atmospheric window’ range 1100–1250 cm−1 containing the strongly coupled polyad of the levels ν2, ν5 and ν3 + ν6, at room temperature and at 120 K using the collisional cooling cell coupled to our Bruker IFS 125 HR prototype (ZP2001) spectrometer and Bruker IFS 125 HR ETH-SLS prototype at the Swiss Light Source providing intense synchrotron radiation. The pure rotational spectra provide new information about the vibrational ground state of CHF3, which is useful for further analysis of excited vibrational states. The ν3 fundamental band is re-investigated together with the corresponding ‘hot’ band 2ν3 − ν3 leading to an extension of the existing line lists up to 4430 transitions with = 66 for ν3 and 1040 transitions with = 43 for 2ν3 − ν3. About 6000 transitions were assigned to rovibrational levels in the polyad ν2/ν5/ν3 + ν6 with = 63 for ν2 ( = 1141.457 cm−1), = 63 for ν5 ( = 1157.335 cm−1) and = 59 for ν3 + ν6 ( = 1208.771 cm−1)( = in each case). The resonance interactions between the ν2, ν5 and ν3 + ν6 states have been taken into account providing an accurate set of effective hamiltonian parameters, which reproduce the experimental results with an accuracy close to the experimental uncertainties (with a root mean square deviation drms = 0.00025 cm−1). The analysis is further extended to the ν4 fundamental ( = 1377.847 cm−1) interacting with 2ν3 ( = 1399.394 cm−1). The results are discussed in relation to the importance of understanding the spectra of CHF3 as a greenhouse gas and as part of our large effort to measure and understand the complete spectrum of CHF3 from the far-infrared to the near-infrared as a prototype for intramolecular quantum dynamics and rovibrational energy redistribution.

Theoretical Study of Infrared Spectra of OCS-( pH2)2, OCS-( oD2)2, OCS-(HD)2, and Mixed OCS- pH2-He Trimers.

The calculated rovibrational energy levels and infrared spectra for OCS-( pH2)2, OCS-( oD2)2, OCS-(HD)2 and mixed OCS- pH2-He trimers are obtained by performing the exact basis-set calculations for the first time based on the newly developed potential energy surfaces ( J. Chem. Phys. 2017, 147, 044313). The "adiabatic-hindered-rotor" (AHR) method is used for reduced-dimension treatment of the hydrogen rotation. The predicted band origin shifts and the infrared spectra are in good agreement with the available experimental values: for the band origin shifts and infrared transitions, the root-mean-square(rms) deviations are smaller than 0.044 and 0.002 cm-1, respectively. We extend the assignments to the unrecorded infrared transitions for OCS-( pH2)2 and OCS-(HD)2 complexes and identify the infrared spectra for OCS-( oD2)2 and OCS- pH2-He for the first time. Three-dimensional density distributions for the ground states of OCS-( pH2)2, OCS- pH2-He, and OCS-(He)2 show that the pH2 molecules are localized in their corresponding global minimum regions, while the pronounced locations of the He atoms are missing in OCS- pH2-He and OCS-(He)2 with forming incomplete circles around the OCS axis. A clear tunneling splitting is observed for the torsional motion of the two hydrogen molecules ( pH2, HD, or oD2) on a ring about the OCS molecular axis, whereas no tunneling splitting is found in OCS- pH2-He or OCS-(He)2 due to a much lower torsional barrier.

Line Lists for LiF and LiCl in the X1Σ+ Ground State

Abstract Vibration–rotation line lists for 6LiF, 7LiF, 6Li35Cl, 6Li37Cl, 7Li35Cl, and 7Li37Cl in the X 1Σ+ ground states have been prepared. The rovibrational energy levels have been calculated using potential energy surfaces determined by direct potential-fitting employing the rotational and rovibrational transition frequencies of all isotopologues, and required the inclusion of Born–Oppenheimer breakdown terms. Dipole moment functions calculated ab initio at the MRCI/aug-cc-pwCV5Z level have been used for line strength calculations. Partition functions for temperatures up to 5000 K have been calculated. LiF and LiCl are predicted to be present in the atmospheres of hot rocky exoplanets, brown dwarfs, and cool stars.