Rotational Energy Levels Research Articles

Investigating the spectroscopic characteristics of twelve isotopologues for the Ar–CO2 complex

In this paper, we perform a theoretical study of isotope effects for the Ar–CO2 complex. Based on the two-dimensional potential energy surfaces (PESs) for the ground and vibrational excited state, the rotational energy levels are obtained for twelve isotopologues of the Ar–CO2 complex via bound state calculations. Our predicted vibrational shifts and rotational constants display two interesting characteristics for these twelve isotopologues. Firstly, the vibrational shifts and rotational constants for these isotopologues are determined to be a linear relationship, which is in good agreement with the available experimental results. Furthermore, the linear relationship for the vibrational shifts and rotational constants can be classified into two types according to the 12C and 13C in the CO2 monomer. Then the vibrational shifts of the remaining nine isotopologues unobserved experimentally are deduced based on our theoretical predictions and available experimental data. Finally, the infrared spectra of ten isotopologues for the Ar–CO2 complex are accurately predicted.

Theoretical study on the low-lying electronic excited states and laser cooling feasibility of AuH molecule

To evaluate characteristics of the low-lying electronic states and the feasibility of the laser cooling of the AuH molecule, we investigate the potential energy curves (PECs), the vibrational and rotational characteristics of the ground and low-lying excited electronic states based on ab initio calculations. The PECs of the X1Σ+, A1Σ+, B1Σ+, a3Σ+, b3Σ+, e3Σ+, C1П, D1П, c3П and d3П states and the transition dipole moments among these states are calculated with the multi-reference configuration interaction method with Davidson correction and all-electron basis sets. Based on the obtained PECs, the Schrödinger equations of nuclear movement are solved to obtain the rotational and vibrational energy levels of the electronic states. The spectroscopic parameters are obtained by fitting the obtained rotational and vibrational levels with Dunham series expansion. The matrices of the Franck-Condon factors (FCFs) dependent on the vibrational quantum numbers are obtained. The feasibility of laser cooling is explored. The FCF of the D1П (v′ = 0) ↔ X1Σ+ (v″ = 0) transition is 0.9862, which implies that the AuH molecule is feasible but not the much better ones for laser cooling and more pumping lasers are needed. The optical laser cooling scheme is suggested and the Einstein coefficient and the recoil temperature are calculated to evaluate the effect of the cooling scheme.

The spectroscopic properties of the low-lying excited states and laser cooling scheme of SrBr molecule.

The potential energy curves and the transition dipole moments for seven electronic states of SrBr molecule are obtained via the multi-reference configuration interaction method and the all-electron basis sets. The Davidson and relativistic corrections are also included. Based on the obtained potential energy curves, the rotational and vibrational energy levels of each electronic state are determined by solving the nuclear motion equation of the molecule. The spectroscopic parameters are fitted from the obtained energy levels by using Dunham expression. Moreover, the spin-orbit coupling splits of the A2Π state are considered to construct the optical laser cooling scheme. The Frank-Condon factors, radiation lifetimes, radiation widths between the ground electronic state and 2Π1/2, 3/2/B2Σ+ states are calculated. Then, the feasibility of laser cooling is explored and the optical scheme is proposed. The results demonstrate that the SrBr molecule is a promising candidate for laser cooling.

The excitation of NH2 in the interstellar medium

ABSTRACT Accurate estimation of the abundance of the NH2 radical in the interstellar medium requires accurate radiative and collisional rate coefficients. The calculation of hyperfine-resolved rate coefficients for the collisional (de-)excitation of NH2 by both ortho- and para-H2 is presented in this work. Hyperfine-resolved rate coefficients are calculated from pure rotational close-coupling rate coefficients using the Mj randomizing approximation. Rate coefficients for temperatures ranging from 5 to 150 K were computed for all hyperfine transitions among the first 15 rotational energy levels of both ortho- and para-NH2 in collisions with ortho- and para-H2. The new data were then employed in radiative transfer calculations to simulate the excitation of NH2 in typical star-forming regions such as W31C, where NH2 is seen in emission. We compared the excitation and brightness temperatures for different NH2 transitions obtained using the new and the previously available collisional data. It is found that the new rate coefficients increase the simulated line intensities by a factor ∼10–30. As a consequence, NH2 abundance derived from the observations will be significantly reduced by the use of the present rate coefficients.

The [formula omitted] and [formula omitted] interacting bands of C2D4 by high-resolution FTIR spectroscopy

The Fourier transform infrared (FTIR) spectrum of C2D4 in the 1443–1550 cm−1 region was recorded at an unapodized resolution of 0.0063 cm−1 to analyze its A-type ν7+ν8 band. Rovibrational constants of the (ν7=ν8=1) state of C2D4 up to five quartic terms were derived for the first time from a fit 1405 assigned infrared (IR) transitions using the Watson’s A-reduced Hamiltonian in the Ir representation with a root-mean-square (rms) deviation of 0.00068 cm−1. Majority of the rotational energy levels of the (ν7=ν8=1) state of C2D4 were perturbed by the nearby (ν4=ν8=1) state by a c-type Coriolis interaction. Rovibrational analysis of the IR transitions (both perturbed and unperturbed) of the ν7+ν8 band allows for the c-type Coriolis resonance parameters, Z7,4c and w7,4c, for the ν7+ν8 and ν4+ν8 interacting bands to be determined for the first time. In addition, the band center and three rotational constants (A, B and C) of the unobserved ν4+ν8 band were also derived from the perturbed analysis of this work. The rotational constants of the ν7+ν8 and ν4+ν8 bands derived from this study were found to agree within 2.6% to the calculated values using MP2/cc-pVQZ and B3LYP/cc-pVQZ levels of theory. The band centers of the ν7+ν8 and ν4+ν8 bands were determined to be 1495.894487(40) cm−1 and 1504.5065(37) cm−1 respectively. Furthermore, the band center and rotational constants of the infrared inactive ν8 band of C2D4 were derived from the present analysis of the ν7+ν8 band and that of the previously reported ν7 band of C2D4.

Strong-field coherence breaking as a tool for identifying methyl rotor states in microwave spectra: 2-hexanone.

The rotational spectrum of 2-hexanone was recorded over the 8-18 GHz region using a chirped pulse Fourier transform microwave spectrometer. Strong field coherence breaking (SFCB) was utilized to selectively modulate the intensities of rotational transitions belonging to the two lowest energy conformers of 2-hexanone, aiding the assignment. In addition, the SFCB method was applied for the first time to selectively identify rotational transitions built off the two lowest energy hindered methyl rotor states of each conformer, 0a1 and 1e. Since these two states have rotational energy levels with different nuclear spin symmetries, their intensities could be selectively modulated by the resonant monochromatic pulses used in the SFCB method. The difference spectra, final fit, and structural parameters are discussed for the three assigned conformers of 2-hexanone.

High-resolution Fourier transform infrared spectrum of the [formula omitted] band of formamide-d1 (DCONH2)

The high-resolution rovibrational spectrum of the ν6 band of formamide-d1 (DCONH2) was recorded using the Fourier transform infrared (FTIR) spectrometer at the Australian Synchrotron with an unapodized resolution of 0.00142 cm−1 in the mid-infrared region of 910–990 cm−1 region. From the rovibrational analysis of this A-type band, the v6 = 1 state rovibrational constants up to one sextic term were derived for the first time from a total of 1450 infrared transitions. These transitions were fitted using the Watson's A-reduced Hamiltonian in the Ir representation with a root-mean-square (rms) deviation of 0.00078 cm−1. The center of the ν6 band of DCONH2 was accurately determined to be 954.857070(41) cm−1. This v6 = 1 state was found to be perturbed by the nearby (v10=1,v12 = 1) state, just around 16 cm−1 higher. Two c-Coriolis parameters were obtained from the perturbation analysis of the interaction between the rotational energy levels of the v6 = 1 and (v10=1,v12 = 1) states. Additionally, the center of the ν10+ν12 band was found at 970.671(41) cm−1 and rotational constant C was fitted accurately. Ground state rotational constants and centrifugal distortion constants up to two sextic terms were obtained by fitting of 1432 ground state combination differences (GSCDs) derived from the infrared (IR) transitions of both the ν6 band of the present work and ν12 band of previous work of DCONH2, together with 6 previously reported microwave frequencies. The root-mean-square (rms) deviation value of this fit was 0.000183 cm−1. The ground state constants in this study provide a better representation for the DCONH2 isotopologue as the values were derived from a larger pool of GSCDs. In addition, ground state rovibrational constants up to five quartic terms and rotational constants of the v6 = 1 state were computed from theoretical anharmonic calculations at two different levels of theory, B3LYP and MP2 with the cc-pVTZ basis set, for comparison with the experimental results.

Revisiting Separation of Vibrations and Rotations in the Theory of Molecular Spectra

A new method is proposed for solving the problem of separation of vibrational and rotational motions in a molecule, as well as a formula for the rotational energy levels. A kinetic energy operator in general form is used for arbitrary generalized coordinates. It is shown that for a triatomic nonlinear molecule, the motions are separated exactly. The problem of a polyatomic molecule is reduced to a "triatomic" molecule.

LVG analysis of amidogen radical (NH2) found in interstellar medium and in cometary material

Amidogen (NH2), a b-type asymmetric top molecule with electric dipole moment 1.82 ± 0.05 Debye, is detected in Sgr B2, in high-mass star-forming regions W31C (G10.6−0.4), W49N (G43.2−0.1), W51 (G49.5−0.4), G34.3+0.1, and in several comets. Because of two hydrogen atoms, each with nuclear spin 1/2, its rotational energy levels can be classified into ortho and para groups. We have not considered for fine structure splitting and hyper-fine structure splitting of rotational levels. For 15 rotational levels in the ground vibrational state, having energy up to 400 cm−1, for each specie, the energies of rotational levels, and Einstein A and B coefficients for radiative transitions between the levels are calculated, using accurate values of spectroscopic data. These radiative transition probabilities along with the collisional rate coefficients (obtained from a scaling law) are employed as input parameters for solving a set of statistical equilibrium equations coupled with the equations of radiative transfer for each group. Several emission lines produced by amidogen are found. For each species of NH2, we have considered some strongest emission lines along with the observed one, which may help for identification of NH2 in the interstellar medium (ISM) and in the cometary material.

Rotational Motion and Nuclear Spin Interconversion of H2O Encapsulated in C60 Appearing in the Low-Temperature Heat Capacity

The heat capacity of H2O encapsulated in fullerene C60 is determined for the first time at temperatures between 0.6 and 200 K. The water molecule in H2O@C60 undergoes quantum rotation at low temperature, and the ortho-H2O and para-H2O isomers are identified by labeling the rotational energy levels with the nuclear spin states. A rounded heat capacity maximum is observed at ∼2 K after rapid cooling due to splitting of the rotational J KaKc = 101 ground state of ortho-H2O. This anomalous feature decreases in magnitude over time, reflecting the conversion of ortho-H2O to para-H2O. Time-dependent heat capacity measurements at constant temperature reveal three nuclear spin conversion processes: a thermally activated transition with Ea ≈ 3.2 meV and two temperature-independent tunneling processes with time constants of τ1 ≈ 1.5 h and τ2 ≈ 11 h.

Theoretical study on the low-lying excited electronic states and laser cooling feasibility of CuH molecule.

To evaluate the feasibility of the laser cooling of CuH molecule, we investigate the electronic properties, the vibrational and rotational characteristics of the molecule based on the multi-reference configuration interaction method with all-electron basis sets. The potential energy curves (PECs) of X1Σ+, A1Σ+, B1Σ+, a3Σ+, b3Σ+, e3Σ+, C1П, D1П, c3П and d3П states and the transition dipole moments between these states are calculated. The Schrödinger equation of nuclear movement is solved for each electronic state to obtain the rotational and vibration energy levels. The spectroscopic parameters are calculated based on the fitted analytical function from the PECs. The present results are in good agreement with the theoretical and experimental values available in the literature. The optical scheme of the laser cooling for CuH molecule is constructed with A1Σ+ ↔ X1Σ+ as the close-loop transition. Three lasers are necessary in each direction to maintain enough scattering photons because of the limited Franck-Condon factor of 0.78. The wavelengths of the pumping lasers are determined. The recoil temperature is 1.72 μk, which is the expected temperature to be reached through the method of the cooling below the doppler limit.

Laser cooling of molecules

ABSTRACTRecently, laser cooling methods have been extended from atoms to molecules. The complex rotational and vibrational energy level structure of molecules makes laser cooling difficult, but these difficulties have been overcome and molecules have now been cooled to a few microkelvin and trapped for several seconds. This opens many possibilities for applications in quantum science and technology, controlled chemistry, and tests of fundamental physics. This article explains how molecules can be decelerated, cooled and trapped using laser light, reviews the progress made in recent years, and outlines some future applications.

High-resolution FTIR spectroscopy of H13COOD: The ground state and v2 = 1 state rovibrational constants

The Fourier transform infrared (FTIR) rovibrational spectrum of the ν2 band of the formic acid isotopologue H13COOD was recorded in the 2550–2710 cm−1 region at an unapodized resolution of 0.0063 cm−1. Rovibrational constants up to three quartic terms were derived for the first time with high precision for the v2=1 state through the fitting of 626 infrared transitions using the Watson’s A-reduced Hamiltonian in the Ir representation with a root-mean-square (rms) deviation of 0.0023 cm−1. The rotational energy levels of the ν2 band was found to be perturbed by a nearby 3ν7 + ν8 band. From the analysis, a- and b-Coriolis resonance parameters from the interactions of the ν2 band with 3ν7 + ν8 band were obtained for the first time. The rotational constants A and B along with the band center of the 3ν7 + ν8 band were also derived for the first time in this work. The band centers of the ν2 and 3ν7 + ν8 bands of H13COOD were determined as 2631.13155(34) cm−1 and 2596.31(19) cm−1 respectively. The ground state constants of H13COOD were determined with higher precision than previously by fitting 301 ground state combination-differences (GSCDs) from the present work and 24 previous microwave measurements with rms deviation of 0.00073 cm−1. The equilibrium state rovibrational constants up to five quartic terms were derived from theoretical anharmonic calculations at four levels of theory: MP2/cc-pVTZ, B3LYP/cc-pVTZ, MP2/cc-pVQZ and B3LYP/cc-pVQZ using the principal axis coordinate system. These calculated constants agree with the ground state constants of H13COOD derived from the current experimental GSCD combined with microwave transitions fit. In addition, all three rotational constants (A, B and C) of the ground state of H13COOD were obtained from anharmonic calculations using B3LYP and MP2 levels with the cc-pVTZ and cc-pVQZ basis sets. These rotational constants were found to agree with those derived experimentally with percentage deviations within 1.0%.

Theoretical studies of Ar–AgX (X = F, Cl, Br, I) complexes: Potential energy surfaces, intermolecualr vibrations and microwave spectra

Theoretical studies of the potential energy surfaces (PESs) and bound state calculations were performed for Ar–AgX (X = F, Cl, Br, and I) complexes. A two-dimensional intermolecular PES was constructed at the level of single and double excitation coupled-cluster method with a non-iterative perturbation treatment of triple excitations [CCSD(T)] plus aug-cc-pVQZ basis set supplemented with bond functions for each complex. The global minimum was assigned as the collinear structure of Ar–Ag–X, while the local minimum was assigned as the anti-linear structure of Ar–X–Ag. Both Ar–Ag and Ar–X distances display us an increasing trend from Ar–AgF to Ar–AgI complexes. Based on the bound state results, the intermolecular vibrational modes of collinear and anti-linear isomers were studied in detail via the wavefunction analysis. Due to the very low well depth for the anti-linear structure, an obvious delocalization effect was observed for each complex, except for Ar–AgI. Furthermore, our calculated results suggest that the anti-linear isomer of Ar–AgBr and Ar–AgI could be observed in experiment. The rotational energy levels were also determined based on the ab initio PESs via the bound state calculations. The microwave spectrum for the collinear isomer of each complex was predicted with the maximal percentage error of 1.55% for the complex Ar–AgF. A simple method of coordinate translation was used to re-interpolate the PES for each isotopomer to determine the isotope effects for Ar–AgX complexes and the deduced results are in good agreement with those of experimental observation. The microwave spectrum can be much better reproduced with an equivalent percentage error of 0.07% cm−1 for each isotopomer based on a scaled PES. Finally, we checked the effects of the basis set superposition error (BSSE) correction and core correlation, and found that the BSSE correction has great influence on the intermolecular interactions for the Ar–AgX complexes.

Investigation of the ν8 and ν21 bands of propane CH3CH2CH3 at 11.5 and 10.9 µm: evidence of large amplitude tunnelling effects

ABSTRACTWe present the first investigation of the ν8 band (C–C symmetric stretch at 870.3137 cm−1), together with an extended analysis of the neighbouring ν21 band (CH3 rock at 921.3756 cm−1) of propane (C3H8). Our previous investigation of the ν21 A-type band [A.Perrin, F. Kwabia-Tchana, J.M.Flaud, L.Manceron, P.Groner, W.J.Lafferty. J. Mol. Spectrosc. 315, 55 (2015)] revealed that the rotational energy levels of 211 are split because of interactions with the internal rotations of the methyl groups, leading to the identification of AA, EE, AE and EA torsional components. In this work, a similar behaviour was observed for the B-type ν8 band and the analysis of the ν21 band was greatly extended. One of the results of the present study is to show that these torsional splittings are due to the existence of anharmonic and Coriolis resonances, coupling the 211 and 81 rotational levels to nearby highly excited levels of the two internal rotations of the methyl groups. Accordingly, an effective ‘vibration – torsion- rotation’ Hamiltonian model was built in the G36 symmetry group which accounts for both types of resonances. In parallel, a code computing the line intensities was developed to allow unambiguous torsional component assignments. The line assignments were performed using a high resolution (0.0015 cm−1) infrared spectrum of propane, recorded with synchrotron radiation at the SOLEIL French light source facility coupled to a Bruker IFS-125 Fourier transform spectrometer. Finally, a linelist of positions and intensities which can be used for the detection of propane in the Earth and outer planets atmospheres was produced.

ANALOG COMPUTER FOR STUDYING DIATOMIC MOLECULAR SPECTRA IN TERAHERTZ FREQUENCY

This paper introduces a harmonic oscillator model for rovibronic terahertz spectrum of a model of a rigid diatomic rotor with some control parameters. The model shows a study of rotationally-resolved terahertz band spectra of the vibrational transition in diatomic molecules. THz radiation absorption is used as a closed-form system known as the analog computer dynamics mode. The optical terahertz region spectrum of the diatomic molecule consists of a series of lines. Their separations are not exactly constant. A diatomic molecule is not truly a rigid rotator, because it simultaneously vibrates with a small amplitude. Due to quantized vibrational and rotational energy levels and the selection rules, allowed transitions result in a highly ordered spectrum consisting of a P branch separated by a central gap. Adjacent spectral lines are separated by a spacing of 2B, and since line intensities depend on Boltzmann factor for thermal population and quantum number J, each branch monotonically increases and decreases. As temperature increases, more lines are observed, and line intensities decrease due to the population being spread over more rotational levels. Interactivity research also involves on effects of the fundamental vibrational frequency, rotational constant B and temperature included line width on the observed spectrum.

A theoretical study on the laser cooling scheme for the three-energy-level system of the CN molecule

The X2Σ+ and B2Σ+ states of the CN molecule are suitable for the closed-loop transition of the optical laser cooling scheme because of the high diagonal Franck-Condon factor. However, the low-lying state of A2Π between X2Σ+ and B2Σ+ states makes the laser cooling scheme for the CN molecule become a three-energy-level system. The treatment of the intervening state is a key issue for laser cooling. To explore the feasibility of the scheme, we calculate the potential energy curves and transition dipole moments of X2Σ+, B2Σ+ and A2Π states of the CN molecule using the multi-reference configuration interaction method and large all-electron basis sets. Based on the obtained potential energy curves, the rotational and vibrational energy levels of the states are obtained by solving the Schrödinger equation of nuclear movement. The calculated spectroscopic parameters for the CN molecule are in good agreement with available theoretical and experimental results. The feasibility of laser cooling for the three-energy-level system of the molecule is examined using the results of the molecular electronic and spectroscopic properties. Based on the examination of the transition dipole moment, Franck-Condon factor, the spectroscopic term and the vibration energy levels, we find that the intervening state A2Π proves to be a significant influence on the closed-loop transition, but a large number of scattering photons are still available. Therefore, the optical schemes for the laser cooling of the three-energy-level system can be designed with a two-energy-level model according to the characteristic of X2Σ+ and B2Σ+ states. Finally, the optical scheme for cooling the CN molecule is constructed with three lasers.

Theoretical studies for the infrared spectra of Ar–CO2 complex: Fundamental and combination bands

Two potential energy surfaces (PESs) were constructed for the ground and excited states of Ar–CO2 complex at the rigid rotor approximation. Besides the notable T-shape structure, two equivalent linear structures were also found on the PES for the first time. Based on the PESs of ground and excited states, the bound state calculations were performed to determine the rotational energy levels for the ground and excited states. In combination of the experimental spectroscopic parameters of ground state and the differences of rotational energy levels, we give a theoretical prediction of infrared spectra including one fundamental band and two combination bands for two isotopomers Ar–12C16O2 and Ar–12C18O2 in the ν3 region of CO2 monomer. The predicted transition frequencies and spectroscopic parameters of excited states are in excellent agreement with the available experimental data, and these results can also be used as a guide to perform the further investigation for the infrared spectra of combination bands experimentally.

Quantum Dynamics of H_{2} Trapped within Organic Clathrate Cages.

The rotational and translational dynamics of molecular hydrogen trapped within β-hydroquinone clathrate (H_{2}@β-HQ)-a practical example of a quantum particle trapped within an anisotropic confining potential-were investigated using inelastic neutron scattering and Raman spectroscopy. High-resolution vibrational spectra, including those collected from the VISION spectrometer at Oak Ridge National Laboratory, indicate relatively strong attractive interaction between guest and host with a strikingly large splitting of rotational energy levels compared with similar guest-host systems. Unlike related molecular systems in which confined H_{2} exhibits nearly free rotation, the behavior of H_{2}@β-HQ is explained using a two-dimensional (2D) hindered rotor model with barrier height more than 2 times the rotational constant (-16.2 meV).

On the Relaxation of Molecules’ Rotational Energy in the Direct Simulation Monte Carlo Method

Rotational-translational energy exchange simulation in the direct simulation Monte Carlo method is considered for the problem of the entry of hypersonic space vehicles in the atmosphere of the Earth, Mars, Venus, Titan, and gas giants. The diatomic and polyatomic molecules’ discrete quantum energy levels are systematized. The energy exchange Larsen-Borgnakke algorithm is described for the molecules with discrete rotational energy levels. The parameters of the model of hard spheres of variable diameters (VHS) are derived for molecules present in the atmospheres from the experimental data on the viscosity of gases and calculation of cross sections of clashing molecules elastic. Analogously, the parameters in Parker’s formula, describing the rotational-translational relaxation, are chosen from the experimental data on the times of relaxation of the rotational energy of the molecules. Close agreement between The calculated and experimental data are in close agreement for moving away and the width of the shock wave before the sphere in nitrogen gas. This means that the used models and their parameters are adequate.