Vibrational-rotational Levels Research Articles

A Reduced Method of Coupled Vibrational Channels: Analysis of Regular Perturbations in the $${{c}^{3}}{\mathbf{\Sigma }}_{{\mathbf{\Omega }}}^{ + }$$ -State of a KRb Molecule

To reduce the dimension of a vibrational problem to be solved by the coupled channel method in the case of interacting electronic states of diatomic molecules, we propose to use the contact van Vleck transformations, which make it possible to take into account the nonadiabatic intramolecular interactions with distant states by modifying the initial potential energy matrix. The efficiency of the reduced coupled vibrational channel method (RCVCM) has been demonstrated by an example of analyzing the regular spin–orbital, electron–rotational, and spin–rotational perturbations discovered in the fine structure of vibrational–rotational levels of the $${{c}^{3}}{\Sigma\text{}}_{{\Omega\text{}}}^{ + }$$ -state of a KRb molecule by methods of high-precision laser-emission spectroscopy. The adiabatic potentials and nonadiabatic electron matrix elements, as functions of the internuclear distance necessary for application of the RCVCM, were obtained in the framework of the nonempirical high-level calculation. It has been demonstrated that the RCVCM has broad extrapolation possibilities and makes it possible to describe the position of the regularly perturbed energy levels of Ω-components of the triplet $${{c}^{3}}{\Sigma\text{}}_{{\Omega\text{}}}^{ + }$$ ‑state at the spectroscopic accuracy level.

Vibration-rotation energy levels and corresponding eigenfunctions of 12CH4 up to the tetradecad

In this paper, we report the vibration-rotation energy levels of methane (12CH4) calculated using the latest version of the global effective Hamiltonian developed in Dijon [B. AMYAY et al.. J. Chem. Phys., 148, 134–306 (2018)]. 238,429 vibration-rotation energy levels are calculated rotationally up to J= 50 and vibrationally up to the Tetradecad ( ≈ 6200 cm−1). The corresponding wavefunctions mixings are also investigated in this work. The knowledge of both energy levels and wavefunctions mixings are essential for simulating high-resolution spectra of methane of astrophysical and atmospheric interests. An evidence of distinct regular and oscillatory contributions, is observed in the number of vibration-rotation levels of methane. This can be fully understood using the generating functions presented by Sadovskií and Zhilinskií [J. Chem. Phys. 103, 10–520 (1995)].

High Accuracy ab Initio Calculations of Rotational-Vibrational Levels of the HCN/HNC System.

Highly accurate ab initio calculations of vibrational and rotational-vibrational energy levels of the HCN/HNC (hydrogen cyanide/hydrogen isocyanide) isomerising system are presented for several isotopologues. All-electron multireference configuration interaction (MRCI) electronic structure calculations were performed using basis sets up to aug-cc-pCV6Z on a grid of 1541 geometries. The ab initio energies were used to produce an analytical potential energy surface (PES) describing the two minima simultaneously. An adiabatic Born-Oppenheimer diagonal correction (BODC) correction surface as well as a relativistic correction surface were also calculated. These surfaces were used to compute vibrational and rotational-vibrational energy levels up to 25 000 cm-1 which reproduce the extensive set of experimentally known HCN/HNC levels with a root-mean-square deviation σ = 1.5 cm-1. We studied the effect of nonadiabatic effects by introducing opportune radial and angular corrections to the nuclear kinetic energy operator. Empirical determination of two nonadiabatic parameters results in observed energies up to 7000 cm-1 for four HCN isotopologues (HCN, DCN, H13CN, and HC15N) being reproduced with σ = 0.37 cm-1. The height of the isomerization barrier, the isomerization energy and the dissociation energy were computed using a number of models; our best results are 16 809.4, 5312.8, and 43 729 cm-1, respectively.

Experimental studies of the NaCs 12(0+) [71Σ+] state: Spin-orbit and non-adiabatic interactions and quantum interference in the 12(0+) [71Σ+] and 11(0+) [53Π0] emission spectra.

We present results from experimental studies of the 11(0+) and 12(0+) electronic states of the NaCs molecule. An optical-optical double resonance method is used to obtain Doppler-free excitation spectra. Selected data from the 11(0+) and 12(0+) high-lying electronic states are used to obtain Rydberg-Klein-Rees and Inverse Perturbation Approach potential energy curves. Interactions between these two electronic states are evident in the patterns observed in the bound-bound and bound-free fluorescence spectra. A model, based on two separate interaction mechanisms, is presented to describe how the wavefunctions of the two states mix. The electronic parts of the wavefunctions interact via spin-orbit coupling, while the individual rotation-vibration levels interact via a second mechanism, which is likely to be non-adiabatic coupling. A modified version of the BCONT program was used to simulate resolved fluorescence from both upper states. Parameters of the model that describe the two interaction mechanisms were varied until simulations were able to adequately reproduce experimental spectra.

Investigations of the Rg-BrCl (Rg = He, Ne, Ar, Kr, Xe) binary van der Waals complexes: ab initio intermolecular potential energy surfaces, vibrational states and predicted pure rotational transition frequencies

The intermolecular potential energy surfaces (PESs) of the ground electronic state for the Rg-BrCl (Rg=He, Ne, Ar, Kr, Xe) van der Waals complexes have been constructed by using the coupled-cluster method in combination with the augmented quadruple-zeta correlation-consistent basis sets supplemented with an additional set of bond functions. The features of the anisotropic PESs for these complexes are remarkably similar, which are characterized by three minima and two saddle points between them. The global minimum corresponds to a collinear Rg-Br-Cl configuration. Two local minima, correlate with an anti-linear Rg-Cl-Br geometry and a nearly T-shaped structure, can also be located on each PES. The quantum bound state calculations enable us to investigate intermolecular vibrational states and rotational energy levels of the complexes. The transition frequencies are predicted and are fitted to obtain their corresponding spectroscopic constants. In general, the periodic trends are observed for this complex family. Comparisons with available experimental data for the collinear isomer of Ar-BrCl demonstrate reliability of our theoretical predictions, and our results for the other two isomers of Ar-BrCl as well as for other members of the complex family are also anticipated to be trustable. Except for the collinear isomer of Ar-BrCl, the data presented in this paper would be beneficial to improve our knowledge for these experimentally unknown species.

Preparation of a selected high vibrational energy level of isolated molecules.

Stark induced adiabatic Raman passage (SARP) allows us to prepare an appreciable concentration of isolated molecules in a specific, high-lying vibrational level. The process has general applicability, and, as a demonstration, we transfer nearly 100 percent of the HD (v = 0, J = 0) in a supersonically expanded molecular beam of HD molecules to HD (v = 4, J = 0). This is achieved with a sequence of partially overlapping nanosecond pump (355 nm) and Stokes (680 nm) single-mode laser pulses of unequal intensities. By comparing our experimental data with our theoretical calculations, we are able to draw two important conclusions: (1) using SARP a large population (>1010 molecules per laser pulse) is prepared in the (v = 4, J = 0) level of HD and (2) the polarizability α00,40 (≅0.6 × 10-41 C m2 V-1) for the (v = 0, J = 0) to (v = 4, J = 0) Raman overtone transition is only about five times smaller than α00,10 for the (v = 0, J = 0) to (v = 1, J = 0) fundamental Raman transition. Moreover, the SARP process selects a specific rotational level in the vibrational manifold and can prepare one or a phased linear combination of magnetic sublevels (M states) within the selected vibrational-rotational level. This capability of preparing selected, highly excited vibrational levels of molecules under collision-free conditions opens new opportunities for fundamental scattering experiments.

Perspective: Accurate ro-vibrational calculations on small molecules.

In what has been described as the fourth age of quantum chemistry, variational nuclear motion programs are now routinely being used to obtain the vibration-rotation levels and corresponding wavefunctions of small molecules to the sort of high accuracy demanded by comparison with spectroscopy. In this perspective, I will discuss the current state-of-the-art which, for example, shows that these calculations are increasingly competitive with measurements or, indeed, replacing them and thus becoming the primary source of data on key processes. To achieve this accuracy ab initio requires consideration of small effects, routinely ignored in standard calculations, such as those due to quantum electrodynamics. Variational calculations are being used to generate huge lists of transitions which provide the input for models of radiative transport through hot atmospheres and to fill in or even replace measured transition intensities. Future prospects such as the study of molecular states near dissociation, which can provide a link with low-energy chemical reactions, are discussed.

Uncertainty of the potential curve minimum for diatomic molecules extrapolated from Dunham type coefficients

In the traditional description of electronic states of diatomic molecules by means of molecular constants or Dunham coefficients, one of the important fitting parameters is the value of the zero point energy – the minimum of the potential curve or the energy of the lowest vibrational-rotational level – E00. Their values are almost always the result of an extrapolation and it may be difficult to estimate their uncertainties, because they are connected not only with the uncertainty of the experimental data, but also with the distribution of experimentally observed energy levels and the particular realization of set of Dunham coefficients. This paper presents a comprehensive analysis based on Monte Carlo simulations, which aims to demonstrate the influence of all these factors on the uncertainty of the extrapolated minimum of the potential energy curve U(Re) and the value of E00. The very good extrapolation properties of the Dunham coefficients are quantitatively confirmed and it is shown that for a proper estimate of the uncertainties, the ambiguity in the composition of the Dunham coefficients should be taken into account.

Determination of the Ground Vibrational State Parameters of the C2D4 Molecule

The object of the study is the C2D4 molecule, as it is important to know its properties to address numerous problems of molecular physics. The analysis of high-resolution spectra of the deuterated ethylene molecule was made in the range of 600–1200 cm–1, specifically bands ν7 and ν12. The results obtained were used to determine high-accurate values of the vibrational-rotational levels of the ground vibrational state of the C2D4 molecule.

Theoretical investigation of potential energy surface and bound states for the van der Waals complex Ar–BrCl dimer

The intermolecular potential energy surface (PES) of the ground electronic state for the Ar–BrCl dimer is constructed at the CCSD(T) level with the aug-cc-pVQZ basis set and mid-bond functions. The PES is characterized by three minima and two saddle points. The global minimum corresponding to a collinear Ar–BrCl configuration, which has been observed experimentally, is located at R=4.10Å and θ=2.5° with a well depth of −285.207cm−1. A nearly T-shaped structure and an anti-linear Ar–ClBr geometry is also predicted. The bound state calculations are preformed to study intermolecular vibrational modes, rotational levels and average structures for the complex. Our transition frequencies, spectroscopic constants and average structures for all isotopomers of the collinear isomer agree well with experimental data. We have also provided pure rotational transitional frequencies for both nearly T-shaped and anti-linear isomers. These results are significant for further experimental investigations of the Ar–BrCl dimer.

Determination and Study the Energy Characteristics of Vibrational-Rotational Levels and Spectral Lines of GaF, GaCl, GaBr and GaI for Ground State

A theoretical study of four gallium monohalides molecules (GaF, GaCl, GaBr and GaI) of ground state 1∑+ by using computer model is presented to study the energy characteristics of vibrational-rotational levels as a function of the vibrational and rotational quantum number , respectively. The calculations has been performed to examine the vibrational-rotational characteristics of some gallium halides molecules. These calculations appeared that all energies (Gv, Ev,J, and Fv,J) increase with increasing vibrational and rotational quantum number and by increasing the vibrational quantum number, and by increasing the vibrational quantum number, the vibrational constant will decrease. Also theoretical study of spectra of these molecules for ground state 1∑+ has been carried out. The values of spectral lines R(J) and P(J) were calculated and the relationship between the spectral lines and the rotational quantum number was established. The results appeared the spectra line values R(J) increases when the values of rotational quantum number decrease but the spectra line values P(J) decrease when the values of rotational quantum number increase, also the spectra line values P(J) decrease when the values of (m) increase, while the values of R(J) increase at first, then decrease showing Fortrar parabola.

Determination and Study the Energy Characteristics of Vibrational-Rotational Levels and Spectral Lines of GaF, GaCl, GaBr and GaI for Ground State

A theoretical study of four gallium monohalides molecules (GaF, GaCl, GaBr and GaI) of ground state 1∑+ by using computer model is presented to study the energy characteristics of vibrational-rotational levels as a function of the vibrational and rotational quantum number , respectively. The calculations has been performed to examine the vibrational-rotational characteristics of some gallium halides molecules. These calculations appeared that all energies (Gv, Ev,J, and Fv,J) increase with increasing vibrational and rotational quantum number and by increasing the vibrational quantum number, and by increasing the vibrational quantum number, the vibrational constant will decrease. Also theoretical study of spectra of these molecules for ground state 1∑+ has been carried out. The values of spectral lines R(J) and P(J) were calculated and the relationship between the spectral lines and the rotational quantum number was established. The results appeared the spectra line values R(J) increases when the values of rotational quantum number decrease but the spectra line values P(J) decrease when the values of rotational quantum number increase, also the spectra line values P(J) decrease when the values of (m) increase, while the values of R(J) increase at first, then decrease showing Fortrar parabola.

LED-based Fourier transform spectroscopy of H218O in the 15,000–16,000 cm−1 range

The spectrum of Н218О has been recorded between 15,000 and 16,000cm−1 by a Fourier transform spectrometer with spectral resolutions of 0.03cm−1 and 0.05cm−1 using high luminance LED light sources and a 60-cm multipath cell with a path length of 1920 and 3480cm. A high signal-to-noise ratio (S/N=10,000) enabled us to register more than 1500 water vapor lines with intensities 1.0×10–27 to 2.2×10−24cm/molecule at 296K. 426 rotational-vibrational levels of the H218O molecule were assigned to eleven vibrational states: (014), (033), (052), (113), (132), (151), (212), (231), (311), (330) and (410). 72 Rotational-vibrational levels of the H217O molecule were assigned to six vibrational states: (014), (033), (113), (212), (311) and (410). An extended set of H218O transitions in the 15,000–16,000cm−1 range was generated using the obtained energy level list and the results of a variational intensity calculation.

Towards the computations of accurate spectroscopic parameters and vibrational spectra for organic compounds

We present multi-component computations for rotational constants, vibrational and torsional levels of medium-sized molecules. Through the treatment of two organic sulphur molecules, ethyl mercaptan and dimethyl sulphide, which are relevant for atmospheric and astrophysical media, we point out the outstanding capabilities of explicitly correlated coupled clusters (CCSD(T)-F12) method in conjunction with the cc-pVTZ-F12 basis set for the accurate predictions of such quantities. Indeed, we show that the CCSD(T)-F12/cc-pVTZ-F12 equilibrium rotational constants are in good agreement with those obtained by means of a composite scheme based on CCSD(T) calculations that accounts for the extrapolation to the complete basis set (CBS) limit and core-correlation effects [CCSD(T)/CBS+CV], thus leading to values of ground-state rotational constants rather close to the corresponding experimental data. For vibrational and torsional levels, our analysis reveals that the anharmonic frequencies derived from CCSD(T)-F12/cc-pVTZ-F12 harmonic frequencies and anharmonic corrections (Δν = ω − ν) at the CCSD/cc-pVTZ level closely agree with experimental results. The pattern of the torsional transitions and the shape of the potential energy surfaces along the torsional modes are also well reproduced using the CCSD(T)-F12/cc-pVTZ-F12 energies. Interestingly, this good accuracy is accompanied with a strong reduction of the computational costs. This makes the procedures proposed here as schemes of choice for effective and accurate prediction of spectroscopic properties of organic compounds. Finally, popular density functional approaches are compared with the coupled cluster (CC) methodologies in torsional studies. The long-range CAM-B3LYP functional of Handy and co-workers is recommended for large systems.

Hessian facilitated analysis of optimally controlled quantum dynamics of systems with coupled primary and secondary states.

The efficacy of optimal control of quantum dynamics depends on the topology and associated local structure of the underlying control landscape defined as the objective as a function of the control field. A commonly studied control objective involves maximization of the transition probability for steering the quantum system from one state to another state. This paper invokes landscape Hessian analysis performed at an optimal solution to gain insight into the controlled dynamics, where the Hessian is the second-order functional derivative of the control objective with respect to the control field. Specifically, we consider a quantum system composed of coupled primary and secondary subspaces of energy levels with the initial and target states lying in the primary subspace. The primary and secondary subspaces may arise in various scenarios, for example, respectively, as sub-manifolds of ground and excited electronic states of a poly-atomic molecule, with each possessing a set of rotational-vibrational levels. The control field may engage the system through electric dipole transitions that occur either (I) only in the primary subspace, (II) between the two subspaces, or (III) only in the secondary subspace. Important insights about the resultant dynamics in each case are revealed in the structural patterns of the corresponding Hessian. The Fourier spectrum of the Hessian is shown to often be complementary to mechanistic insights provided by the optimal control field and population dynamics.

H2O maser pumping: The effect of quasi-resonance energy transfer in collisions between H2 and H2O molecules

The effect of quasi-resonance energy transfer in collisions between H2 and H2O molecules in H2O maser sources is investigated. New data on the state-to-state rate coefficients for collisional transitions for H2O and H2 molecules are used in the calculations. The results of ortho-H2O level population inversion calculations for the 22.2-, 380-, 439-, and 621-GHz transitions are presented. The ortho-H2O level population inversion is shown to depend significantly on the population distribution of the para-H2 J = 0 and 2 rotational levels. The possibility of quasi-resonance energy transfer in collisions between H2 molecules at highly excited rotational-vibrational levels and H2O molecules is considered. The quasi-resonance energy transfer effect can play a significant role in pumping H2O masers in the central regions of active galactic nuclei and in star-forming regions.

LED-based Fourier-transform spectroscopy of H2 18O in the range 15000–15700 cm−1

The spectrum of H218O in the range 15000–15700 cm−1 has been recorded for the first time on a Fourier-transform spectrometer using a high-brightness light-emitting diode as a radiation source. The measurements have been conducted at room temperature with a resolution of 0.05 cm−1. A threshold sensitivity in absorption of 2 × 10−7 cm−1 has been achieved due to both the use of a light-emitting diode and optimization of the multipass cell with a base length of 60 cm, which ensured a 19.2-m length of the absorbing layer. A high signal-to-noise ratio (S/N = 2000–10000) made it possible to record about 670 water-vapor lines with intensities of 1.0 × 10−26–2.2 × 10–24 cm/mol at 296 K. The energies of 265 vibrational-rotational levels of the H218O molecule are determined and attributed to seven vibrational states, namely, (033), (113), (212), (231), (311), (330), and (410).

Studies of the distribution functions of molecular nitrogen and its ion over the vibrational and rotational levels in the dc glow discharge and the microwave discharge in a nitrogen-hydrogen mixture by the emission spectroscopy technique

The positive column and the electrode zones of the DC glow discharge and the microwave discharge in nitrogen with the hydrogen additions are investigated. The spectral composition of the emission is determined, and the distribution functions over the vibrational-rotational levels of the electron-excited states of the nitrogen molecule and the nitrogen molecule ion are recovered.

Rovibrational Energies of the Hydrocarboxyl Radical from a RCCSD(T) Study

A RCCSD(T)/cc-pVQZ potential energy surface is constructed for the HOCO radical in the ground electronic state and used to compute rotation-vibration levels of HOCO and DOCO. Two numerical strategies are employed to study in detail the wave function properties. The importance of stretch-bend coupling, such as ν4/ν5 and ν3/ν4, for the internal dynamics is demonstrated. The rotational constants computed for the vibrational ground state of trans and cis conformers are in good agreement with experimental values.

Infrared spectroscopy of 15ND3: The ν2 and ν4 bending fundamental bands

The infrared spectrum of the ammonia isotopologue 15ND3 has been investigated by high resolution Fourier transform spectroscopy in the region from 450 to 1600cm−1. In total, 2217 transitions involving the (s) and (a) inversion–rotation–vibration levels have been identified and assigned to the ν2 and ν4 bending fundamentals. The assigned transitions have been fitted simultaneously using an inversion–rotation–vibration effective Hamiltonian which includes all symmetry allowed interactions between and within the excited state levels. The adopted model has been successful in rationalizing the complicated energy level pattern. Accurate values for the vibration and rotation spectroscopic constants, including 11 interaction coefficients, have been obtained for both inversion levels of the v2=1 and v4=1 states. The standard deviation of the fit, 0.00071cm−1, is about two times the estimated measurement precision.