Rovibrational States Research Articles

Collision-Induced C60 Rovibrational Relaxation Probed by State-Resolved Nonlinear Spectroscopy

Quantum state-resolved spectroscopy was recently achieved for C60 molecules when cooled by buffer gas collisions and probed with a midinfrared frequency comb. This rovibrational quantum state resolution for the largest molecule on record is facilitated by the remarkable symmetry and rigidity of C60, which also present new opportunities and challenges to explore energy transfer between quantum states in this many-atom system. Here we combine state-specific optical pumping, buffer gas collisions, and ultrasensitive intracavity nonlinear spectroscopy to initiate and probe the rotation-vibration energy transfer and relaxation. This approach provides the first detailed characterization of C60 collisional energy transfer for a variety of collision partners, and determines the rotational and vibrational inelastic collision cross sections. These results compare well with our theoretical modeling of the collisions, and establish a route towards quantum state control of a new class of unprecedentedly large molecules.

Magic wavelength for a rovibrational transition in molecular hydrogen

Molecular hydrogen, among other simple calculable atomic and molecular systems, possesses a huge advantage of having a set of ultralong living rovibrational states that make it well suited for studying fundamental physics. Further experimental progress will require trapping cold H2 samples. However, due to the large energy of the first electronic excitation, the conventional approach to finding a magic wavelength does not work for H2. We find a rovibrational transition for which the AC Stark shift is largely compensated by the interplay between the isotropic and anisotropic components of polarizability. The residual AC Stark shift can be completely eliminated by tuning the trapping laser to a specific “magic wavelength” at which the weak quadrupole polarizability cancels the residual dipole polarizability.

Application of quantum supersymmetry to rovibrational states of diatomic molecules with an energy dependent Morse potential

Application of quantum supersymmetry to rovibrational states of diatomic molecules with an energy dependent Morse potential

State-to-state dynamical studies of the C+ + H2(v = 0, j = 0) → CH+ + H reaction using time-dependent wave packet method

The quantum state-resolved dynamics studies of the C+ + H2(v = 0, j = 0) → CH+ + H reaction were carried out using time-dependent wave packet method based on the potential energy surface (PES) reported by Li et al. The dynamics properties such as reaction probability, integral cross section, differential cross section, the rovibrational state distribution of product and rate constant were calculated and compared with available theoretical and experimental values. The results indicated that present values are in general good agreement with the experimental data. The forward–backward symmetry scattering signals shows that the “complex-forming” reaction mechanism dominates the title reaction. The rate constants of the initial state (v = 0, j = 0) were studied in the temperature range from 10 to 5000 K. The results indicated that the rate constant sharply increases with the increase of temperature.

HF, DF, TF: approximating potential curves, calculating rovibrational states

A simple analytical expression for the potential energy curve for the ground state X 1Σ+ of the hydrogen fluoride molecule HF obtained in the framework of the Born–Oppenheimer approximation is proposed. This analytical expression for the potential energy curve is based in the two point Padé approximation, which correctly reproduces the asymptotic behavior at small R → 0 and large R → ∞ internuclear distances, and position and depth of potential well, leading to the accuracy of 4–5 decimal digits when compared with experimental data. The rovibrational spectra of the diatomic molecule HF is calculated by solving the Schrödinger equation for nuclear motion using the Lagrange-mesh method. The ground state X 1Σ+ contains 21 vibrational states (ν, 0) and 724 rovibrational states (ν, L) with maximal angular momentum equal to 55. The change of reduced mass in the Schrödinger equation for nuclear motion allows us to obtain the rovibrational spectrum of the ground state potential curve of the deuterium fluoride DF (contains 29 vibrational states (ν, 0) and 1377 rovibrational states (ν, L)) and tritium fluoride TF (contains 35 vibrational states (ν, 0) and 1967 rovibrational states (ν, L)) with maximal angular momenta 76 and 92, respectively. Entire rovibrational spectra is presented for the HF molecule and its two isotopologues DF and TF.

Two-photon Raman transition channels of NaCs predicted from ab initio calculations

Obtaining effective spontaneous radiative transition channels is a fundamental topic in the preparation of ultracold rovibrational ground states of molecules. Herein, the ranges of prospective transition channels in the NaCs dimer are predicted via exploring the complex energy level structure and transition properties. The potential energy curves of \ensuremath{\Lambda}-$S$ states and \ensuremath{\Omega} states, spectroscopy constants, absolute energies of bound states, and transition information (Frank-Condon factors, lifetimes, transition dipole moments) have been researched. With this purpose, the results of our experiment on binding energies of the ${b}^{3}{\mathrm{\ensuremath{\Pi}}}_{0}{}^{+}$ rovibrational states are analyzed; the transition from the higher (photoassociated) ${}^{1}\mathrm{\ensuremath{\Pi}}$ state to the ground ${X}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+}$ state is discussed. The wavelengths of the two lasers are predicted as 622.8-656.7 nm and 896.3-969.8 nm with the ${B}^{1}{\mathrm{\ensuremath{\Pi}}}_{1}$ and ${c}^{3}{\mathrm{\ensuremath{\Sigma}}}_{1}^{+}$ states, respectively, for the stimulated raman adiabatic passage method.

Absorption Spectra of Electrified Hydrogen Molecules

Molecular hydrogen normally has only weak, quadrupole transitions between its rovibrational states, but in a static electric field it acquires a dipole moment and a set of allowed transitions. Here we use published ab initio calculations of the static electrical response tensors of the H2 molecule to construct the perturbed rovibrational eigensystem and its ground state absorptions. We restrict attention to two simple field configurations that are relevant to condensed hydrogen molecules in the interstellar medium (ISM): a uniform electric field and the field of a pointlike charge. The energy eigenstates are mixtures of vibrational and angular momentum eigenstates so there are many transitions that satisfy the dipole selection rules. We find that mixing is strongest among the states with high vibrational excitation, leading to hundreds of absorption lines across the optical and near-infrared. These spectra are very different from that of the field-free molecule, so if they appeared in astronomical data they would be difficult to assign. Furthermore, in a condensed environment the excited states likely have short lifetimes to internal conversion, giving the absorption lines a diffuse appearance. We therefore suggest electrified H2 as a possible carrier of the diffuse interstellar bands (DIBs). We further argue that in principle it may be possible to account for all of the DIBs with this one carrier. However, despite electrification, the transitions are not very strong and a large column of condensed H2 would be required, making it difficult to reconcile this possibility with our current understanding of the ISM.

Dissociation Dynamics of Anionic Carbon Dioxide in the Shape Resonant State 2Πu.

Dissociative electron attachments via the lowest shape resonant state 2Πu of CO2-, e- + CO2 → O- + CO, are investigated with our high-resolution anion velocity map imaging apparatus. The production efficiency curve of O- obtained in this work is consistent with those reported previously. The forward-backward asymmetric distribution superimposed on the isotopic background is observed in the time-sliced velocity image of O- yield, implying that the dissociation of CO2-(2Πu) proceeds through a combinational motion of bond stretching and bending. Thereby, the coproduct CO is proposed to be in the rovibrational states. The long-standing arguments about the dissociation dynamics of CO2-(2Πu) are settled.

The nuclear-spin-forbidden rovibrational transitions of water from first principles.

The water molecule occurs in two nuclear-spin isomers that differ by the value of the total nuclear spin of the hydrogen atoms, i.e., I = 0 for para-H2O and I = 1 for ortho-H2O. Spectroscopic transitions between rovibrational states of ortho and para water are extremely weak due to the tiny hyperfine nuclear-spin-rotation interaction of only ∼30 kHz and, so far, have not been observed. We report the first comprehensive theoretical investigation of the hyperfine effects and ortho-para transitions in H2 16O due to nuclear-spin-rotation and spin-spin interactions. We also present the details of our newly developed general variational approach to the simulation of hyperfine effects in polyatomic molecules. Our results for water suggest that the strongest ortho-para transitions with room-temperature intensities on the order of 10-31 cm/molecule are about an order of magnitude larger than previously predicted values and should be detectable in the mid-infrared ν2 and near-infrared 2ν1 + ν2 and ν1 + ν2 + ν3 bands by current spectroscopy experiments.

Rovibrational-Specific QCT and Master Equation Study on N2(X1Σg+) + O(3P) and NO(X2Π) + N(4S) Systems in High-Energy Collisions.

This work presents a detailed investigation of the energy-transfer and dissociation mechanisms in N2(X1Σg+) + O(3P) and NO(X2Π) + N(4S) systems using rovibrational-specific quasiclassical trajectory (QCT) and master equation analyses. The complete set of state-to-state kinetic data, obtained via QCT, allows for an in-depth investigation of the Zel'dovich mechanism leading to the formation of NO molecules at microscopic and macroscopic scales. The master equation analysis demonstrates that the low-lying vibrational states of N2 and NO have dominant contributions to the NO formation and the corresponding extinction of N2 through the exchange process. For the considered temperature range, it is found that nearly 50% of the dissociation processes for N2 and NO molecules occur in the quasi-steady-state (QSS) regime, while for the Zel'dovich reaction, the distribution of the reactants does not reach the QSS conditions. Furthermore, using the QSS approximation to model the Zel'dovich mechanism leads to overestimating NO production by more than a factor of 4 in the high-temperature range. The breakdown of this well-known approximation has profound consequences for the approaches that heavily rely on the validity of QSS assumption in hypersonic applications. Finally, the investigation of the rovibrational state population dynamics reveals substantial similarities among different chemical systems for the energy-transfer and the dissociation processes, providing promising physical foundations for the use of reduced-order strategies in other chemical systems without significant loss of accuracy.

Coherent multichannel optical theorem: Quantum control of the total scattering cross section

The optical theorem is a fundamental aspect of quantum scattering theory. Here, we generalize this theorem to the case where the incident scattering state is a superposition of internal states of the collision partners, introducing additional interference contributions and, e.g., providing a route to control the total integral cross section. As in its standard form, forward scattering plays an essential role in the multichannel optical theorem, but with interference terms being related to the inelastic forward scattering amplitudes between states in the initial superposition. Using the resultant control index, we show that extensive control is possible over ultracold collisions of oxygen molecules in their rovibrational ground states, and of $^{85}\mathrm{Rb}\text{\ensuremath{-}}^{85}\mathrm{Rb}$ collisions, promising systems for the experimental demonstration of the quantum interference control of the total scattering cross section.

The thermodynamics of the van der Waals dimer and trimer formation in gaseous carbon dioxide and methane and their heterodimers with dinitrogen

The equilibrium thermochemical properties of the dimers and trimers of the greenhouse gases carbon dioxide and methane, as well as their heterodimers with dinitrogen, have been calculated from the CO2 and CH4 equations of state (EOSs) and statistical mechanics. The standard dimer and trimer equilibrium constants, along with the respective ΔHoandΔSo values are reported for CO2 and CH4 between 220 and 260, and 95 and 135 K, respectively, and for the heterodimers between 100 and 250 K. Statistical mechanical calculations based on experimental and computational data of the dimers provide qualitative agreement with the EOS results. The equilibrium thermochemical properties of the CH4 dimer and the CO2–N2 and CH4–N2 heterodimers are calculated using a Morse potential to represent pairwise interactions in an “atom–diatom” model that accounts for both bound and metastable rovibrational states.

Wave Packet Approach to Adiabatic and Nonadiabatic Dynamics of Cold Inelastic Scatterings.

Due to the extremely large de Broglie wavelength of cold molecules, cold inelastic scattering is always characterized by the time-independent close-coupling (TICC) method. However, the TICC method is difficult to apply to collisions of large molecular systems. Here, we present a new strategy for characterizing cold inelastic scattering using wave packet (WP) method. In order to deal with the long de Broglie wavelength of cold molecules, the total wave function is divided into interaction, asymptotic and long-range regions (IALR). The three regions use different numbers of ro-vibrational basis functions, especially the long-range region, which uses only one function corresponding to the initial ro-vibrational state. Thus, a very large grid range can be used to characterize long de Broglie wavelengths in scattering coordinates. Due to its better numerical scaling law, the IALR-WP method has great potential in studying the inelastic scatterings of larger collision systems at cold and ultracold regimes.

ClF diatomic molecule: Rovibrational spectra

Following the first principles the analytic Born–Oppenheimer (BO) potential curve for the ground state X1Σ+ of the molecule ClF is proposed for whole range of internuclear distances R∈[0,∞). It is based on matching the perturbation theory at small internuclear distances R and multipole expansion at large distances R, it has the form of two-point Pade approximant and provides 3–4 figures in rovibrational energies. It supports 5719 rovibrational states with maximal vibrational number νmax=47 and maximal angular momentum Lmax=210 including 36 weakly-bound states close to threshold (to dissociation limit) with the energies ≲10-4hartree. The van der Waals constant C6(ClF)∼29.3a.u. is predicted.

Towards the analytic theory of potential energy curves for diatomic molecules: studying He2 + and LiH diatomics as illustration

Following the first principles, the elements of the analytic theory of potential curves for diatomic molecules (diatomics) are presented. It is based on matching the perturbation theory at small internuclear distances R and multipole expansion at large distances, modified by exponentially small terms for homonuclear case, with the addition of the phenomenologically described equilibrium configuration, if it exists. It leads to a new class of (generalised) rational potentials (modified by exponentially small terms) with a difference in degrees of polynomials in numerator and denominator equal to 4 (6) for positively charged (neutral) diatomics. For example, the He and LiH diatomics in Born–Oppenheimer approximation are considered. For He (He) diatomics it is found the approximate analytic expression for the potential energy curves (analytic PEC) for the ground state and the first excited state . It provides 3–4 s.d. correctly for distances a.u. with some irregularities for PEC at small distances (much are smaller than equilibrium distances) probably related to level (quasi)-crossings that may occur there. The analytic PEC for the ground state supports 829 (626) rovibrational states with 3–4 s.d. of accuracy in energy, which is only by 1 state less (more) than 830 (625) reported in the literature. The analytic PEC for the excited state supports all 9 reported weakly-bound rovibrational states. For LiH it is found the analytic expression for the ground state PEC in the form of a rational function, which supports 906 rovibrational states with 3–4 s.d. accuracy in energy, it is only of 5 states more than reported in the literature (901). For both diatomics, the difference in a number of rovibrational states is related to the non-existence/existence of weakly-bound states close to the threshold (to dissociation limit). Entire rovibrational spectra are found in a single calculation using the code based on the Lagrange mesh method.

Collisional excitation of HD by H

ABSTRACT The HD molecule plays an important role in many astrophysical environments. Accurate modelling of the gas cooling induced by HD and its abundance in such media requires a proper modelling of its excitation by both radiative and collisional processes. Reliable state-to-state collisional rate coefficients in extended temperature regimes are then essential to allow for the description of different astrophysical environments where deviations from local thermodynamic equilibrium regime can occur. Here, we report exact quantum time-independent reactive scattering calculations for the rovibrational excitation of HD by H. Rate coefficients are computed for temperatures up to 5000 K and transitions between all rovibrational states with internal energies up to 14 000 cm−1. Previous results neglecting reactive and exchange channels of the colliding system are compared to the new ones and significant differences are found. The present work represent a big step in the complete description of the HD–H collisional system, in terms of rovibrational states considered, temperature range explored and accuracy. Hence, we recommend the use of the new HD–H collisional data presented here to accurately model the astrophysical environments where HD plays a role.

Rotating and vibrating symmetric-top molecule RaOCH3 in fundamental P, T -violation searches

We study the influence of the rotations and vibrations of the symmetric-top ${\mathrm{RaOCH}}_{3}$ molecule on its effectiveness as a probe for the $\mathcal{P}, \mathcal{T}$-violating effects, such as the electron electric dipole moment and the scalar-pseudoscalar electron-nucleon interaction. The corresponding enhancement parameters ${E}_{\mathrm{eff}}$ and ${E}_{\mathrm{s}}$ are computed for the ground and first excited rovibrational states with different values of the angular momentum component $K$. For the lowest $K$ doublet with ${v}_{\ensuremath{\perp}}=0$ and $K=1$ the values are ${E}_{\mathrm{eff}}=47.647\phantom{\rule{0.28em}{0ex}}\mathrm{GV}/\mathrm{cm}$ and ${E}_{\mathrm{s}}=62.109\phantom{\rule{0.16em}{0ex}}\mathrm{kHz}$. The results show larger deviation from the equilibrium values than in triatomic molecules.

Ultraprecise relative energies in the (2 0 0) vibrational band of H2 16O

The technique of Noise-Immune Cavity Enhanced Optical Heterodyne Molecular Spectroscopy (NICE-OHMS) is employed to detect rovibrational transitions of at wavelengths of 1.4 m. This intracavity-saturation approach narrows down the typical Doppler-broadened linewidths of about 600 MHz to the sub-MHz domain. The locking of the spectroscopy laser to a frequency-comb laser and the assessment of collisional and further line broadening effects result in transition frequencies with an absolute uncertainty below 10 kHz. The lines targeted for measurement are selected by the spectroscopic-network-assisted precision spectroscopy (SNAPS) approach. The principal aim is to derive precise and accurate relative energies from a limited set of Doppler-free transitions. The 71 newly observed lines, combined with further highly accurate literature transitions, allow the determination of the relative energies for all of the 59 rovibrational states up to J = 6 within the vibrational parent of , where J is the overall rotational quantum number and , , and are quantum numbers associated with the symmetric stretch, bend, and antisymmetric stretch normal modes, respectively. An experimental curiosity of this study is that for strong transitions an apparent signal inversion in the Lamb-dip spectra is observed; a novelty reserved to the NICE-OHMS technique.

Variational rovibrational calculations for tetra atomic linear molecules using Watson’s isomorphic Hamiltonian, I: The C8v4 approach

The implementation of an algorithm for the variational determination of rovibrational state energies and wave functions for linear tetra atomic molecules is presented. The approach, termed C8v4, is based on Watson’s isomorphic Hamiltonian formulated in normal coordinates. Products of harmonic oscillator and rigid-rotor functions are used to expand the rovibrational wave function. Intricacies related to the coupling of the bending–rotation basis and the vibrational angular momentum in linear molecules require a careful study of symmetry properties to set up a symmetry adapted basis set. Kinetic energy matrix elements can be evaluated in a fast mixed numerical/analytical fashion. The main computational bottlenecks are the integration of the potential energy matrix and the diagonalization of the Hamiltonian. These can be overcome by exploiting the block structure of the Hamiltonian which is discussed in some detail. Test calculations on acetylene (HCCH) and boranimine (HBNH) are presented and the C8v4 results reproduce previous variational calculations based on a Hamiltonian formulated in internal coordinates.

Laser control of a dark vibrational state of acetylene in the gas phase-Fourier transform pulse shaping constraints and effects of decoherence.

We propose a methodology to tackle the laser control of a non-stationary dark ro-vibrational state of acetylene (C2H2), given realistic experimental limitations in the 7.7 μm (1300cm-1) region. Simulations are performed using the Lindblad master equation, where the so-called Lindblad parameters are used to describe the effect of the environment in the dilute gas phase. A phenomenological representation of the parameters is used, and they are extracted from high-resolution spectroscopy line broadening data. An effective Hamiltonian is used for the description of the system down to the rotational level close to experimental accuracy. The quality of both the Hamiltonian and Lindblad parameters is assessed by a comparison of a calculated infrared spectrum with the available experimental data. A single shaped laser pulse is used to perform the control, where elements of optics and pulse shaping using masks are introduced with emphasis on experimental limitations. The optimization procedure, based on gradients, explicitly takes into account the experimental constraints. Control performances are reported for shaping masks of increasing complexity. Although modest performances are obtained, mainly due to the strong pulse shaping constraints, we gain insights into the control mechanism. This work is the first step toward the conception of a realistic experiment that will allow for population characterization and manipulation of a non-stationary vibrational "dark" state. Effects of the collisions on the laser control in the dilute gas phase, leading to decoherence in the molecular system, are clearly shown.