Low-lying Rovibrational States Research Articles

Magic conditions for multiple rotational states of bialkali molecules in optical lattices

We investigate magic-wavelength trapping of ultracold bialkali molecules in the vicinity of weak optical transitions from the vibrational ground state of the X$^1\Sigma^+$ potential to low-lying rovibrational states of the b$^3\Pi_0$ potential, focussing our discussion on the $^{87}$Rb$^{133}$Cs molecule in a magnetic field of $B=181\,$G. We show that a frequency window exists between two nearest neighbor vibrational poles in the dynamic polarizability where the trapping potential is "near magic" for multiple rotational states simultaneously. We show that the addition of a modest DC electric field of $E=0.13\,\text{kV}/\text{cm}$ leads to an exact magic-wavelength trap for the lowest three rotational states at a angular-frequency detuning of $\Delta_{v'=0} = 2\pi\times 218.22$\,GHz from the X$^1\Sigma^+ (v=0, J=0)\rightarrow$ b$^3\Pi_0 (v'=0, J=1)$ transition. We derive a set of analytical criteria that must be fulfilled to ensure the existence of such magic frequency windows and present an analytic expression for the position of the frequency window in terms of a set of experimentally measurable parameters. These results should inform future experiments requiring long coherence times on multiple rotational transitions in ultracold polar molecules.

Inelastic cross sections and rate coefficients for collisions between CO and H2

A five-dimensional coupled states (5D-CS) approximation is used to compute cross sections and rate coefficients for CO+H2 collisions. The 5D-CS calculations are benchmarked against accurate six-dimensional close-coupling (6D-CC) calculations for transitions between low-lying rovibrational states. Good agreement between the two formulations is found for collision energies greater than 10cm−1. The 5D-CS approximation is then used to compute two separate databases which include highly excited states of CO that are beyond the practical limitations of the 6D-CC method. The first database assumes an internally frozen H2 molecule and allows rovibrational transitions for v ≤ 5 and j ≤ 30, where v and j are the vibrational and rotational quantum numbers of the initial state of the CO molecule. The second database allows H2 rotational transitions for initial CO states with v ≤ 5 and j ≤ 10. The two databases are in good agreement with each other for transitions that are common to both basis sets. Together they provide data for astrophysical models which were previously unavailable.

Quasi-Classical Trajectory Study of Atom-Diatomic Molecule Collisions in Symmetric Hyperspherical Coordinates: The F + HCl Reaction as a Test Case.

We investigate the reactive dynamics of the triatomic system F + HCl → HF + Cl for total angular momentum equal zero and for different low-lying rovibrational states of the diatomic molecule. For each of the initial vibrational quantum numbers, the time evolution of the atom-diatom collision process is investigated for a wide range of impact angles and collision energies. To this purpose, the Quasi-Classical Trajectories (QCT) method was implemented in a hyperspherical configuration space. The Hamilton equations of motion are solved numerically in an intermediate effective Cartesian space to exploit the relative simplicity of this intermediate representation. Interatomic interactions are described by a London-Eyring-Polanyi-Sato potential energy surface, specifically developed for the title reaction, and the results of the QCT simulations are discussed in terms of the time-evolution of the hyperangles. The analysis of the collision dynamics using symmetric hyperspherical coordinates provides, in addition to the description in terms of a natural reaction coordinate (the hyperradius), a more striking representation of the exchange dynamics, in terms of the time-dependent probability distribution along the kinematic rotation hyperangle, and a precise distinction between direct and indirect mechanisms of the reaction.

Static Dipole Polarizabilities for Low-Lying Rovibrational States of HD+**Supported by the National Natural Science Foundation of China under Grant Nos 11474319 and 11274348, the National Basic Research Program of China under Grant No 2012CB821305, the Natural Sciences and Engineering Research Council of Canada, and the CAS/SAFEA International Partnership Program for Creative Research Teams.

Accurate calculations are performed for the static dipole polarizabilities of HD+ in the rovibrational states with both of the vibrational and angular momentum quantum numbers v and L from 0 to 5, by using variationally generated wavefunctions in Hylleraas coordinates. Comparison is made with recently published results. Significant improvements are achieved for the angular momentum quantum number L > 0 excited states by including another independent block to optimize meticulously the intermediate states of unnatural parity.

Low-lying quasibound rovibrational states of H2 16O**

A complex coordinate scaling (CCS) method is described allowing the quantum chemical computation of quasibound (also called resonance or metastable) rovibrational states of strongly bound triatomic molecules. The molecule chosen to test the method is H2 16O, for which an accurate global potential energy surface, a previous computation of a few resonance states via the complex absorbing potential (CAP) method, and some Feshbach (J = 0, where J is the quantum number characterising overall rotations of the molecule) and shape (J ≠ 0) resonances measured via a state-selective, triple-resonance technique are all available. Characterisation of the computed resonance states is performed via probability density plots based on CCS rovibrational wavefunctions. Such plots provide useful details about the physical nature of the resonance states. Based on the computations and the resonance plots, the following useful facts about the resonance states investigated are obtained: (a) Feshbach resonances are formed by accumulation of a large amount of energy in either the non-dissociative bending or symmetric streching modes, excitations by more than five quanta are not uncommon; (b) there are several resonance states with low and medium bending excitation, the latter are different from the states observed somewhat below dissociation by the same triple-resonance technique; (c) several types of dissociation bahavior can be identified, varying greatly among the states; (d) several pairs of J = 0 and J = 1 Feshbach resonance states can be identified which differ by rigid-rotor type energies; and (e) the lifetimes of the assigned J = 1 rovibrational Feshbach resonances are considerably longer than the lifetimes of their J = 0 vibrational counterparts.

Oscillator strengths between low-lying ro-vibrational states of hydrogen molecular ions

It is important for experimental design to know the transition oscillator strengths in hydrogen molecular ions. In this work, for HD(+), HT(+), and DT(+), we calculate the ro-vibrational energies and oscillator strengths of dipole transitions between two ro-vibrational states with the vibrational quantum number ν = 0-5 and the total angular momentum L = 0-5. The oscillator strengths of HT(+) and DT(+) are presented as supplementary material.

Lowest quartet states of heteronuclear alkali-metal trimers

We analyze three-body nonadditive interactions and characterize critical points on potential energy surfaces of the lowest A{sub 2}B (A,B=Li,Na,K,Rb,Cs) quartet states using high-level ab initio calculations. Our calculations indicate that near equilibrium geometries, large nonadditive effects are stabilizing the systems. We also show that trimer formation reactions are always energetically allowed even for low-lying rovibrational states of heteronuclear triplet-{Sigma} dimers.

Non-Born−Oppenheimer State-to-State Dynamics of the N(2D) + H2 → NH(X̃3Σ−) + H Reaction: Influence of the Renner−Teller Coupling

This publication examines the influence of electronically nonadiabatic Renner-Teller coupling between the two lowest-lying electronic states of NH(2) on state-to-state reaction dynamics. The fully Coriolis coupled quantum mechanical calculations were carried out on the recently developed NH(2) potential energy surfaces of both the X̃(2)A″ and Ã(2)A' states. It is shown that the Renner-Teller coupling has a dramatic effect on the low-lying ro-vibrational states on the excited Ã(2)A' potential, but its impact on the differential and integral cross sections of the N((2)D) + H(2) → NH(X(3)Sigma(-)) + H reaction is relatively minor.

Accurate computations of the rovibrational spectrum of the He–HF van der Waals complex

The rovibrational spectrum of the He–HF van der Waals complex is calculated from an accurate intermolecular potential energy surface. This is obtained by fitting a considerable number of interaction energies evaluated at the Coupled Cluster Singles and Doubles level including connected triple corrections and with an augmented correlation consistent polarized valence quintuple zeta basis set extended with a set of 3s3p2d1f1g mid-bond functions. The basis set was selected after a systematic study carried out at four intermolecular geometries. The potential is characterized by two linear minima, i.e., He–HF and He–FH, with distances from the He atom to the HF centre of mass of 3.1662 Å and 2.9989 Å and binding energies of −43.844 and −26.169 cm−1, respectively. These results are compared to data available in the literature. An analytic fit to this potential energy surface is presented and used to compute several low-lying rovibrational energy states using coupled channel methods. These results are compared with fixed-frame diffusion Monte-Carlo calculations using a method developed specifically for linear molecules.

Ab initio vibration and ro-vibrational spectrum of the 1A 1 state of He 2Si 2+

The low-lying ro-vibrational states for the ground electronic state ( 1A 1) of HeSi 2+ have been calculated using an ab initio variational solution of the nuclear Schrödinger equation. A 96 point CCSD(T)/cc-pCVQZ potential energy surface (PES) has been calculated and a Ogilvie-Padé (3,6) potential energy function has been generated. This force field was embedded in the Eckart–Watson Hamiltonian from which the vibrational and ro-vibrational eigenfunctions and eigenenergies have been variationally calculated. A 70 point QCISD/aug-cc-pCVTZ discrete dipole moment surface (DMS) was calculated and a 5th order power series expansion (in terms of the two bond lengths and the included bond angle) has been generated. Absolute line intensities have been calculated and are presented for some of the most intense transitions between the vibrational ground state and the low-lying ro-vibrational states of this ion.

Ab initio calculations of the rovibrational states of He 2C 2 + 1

The low-lying rovibrational states of the dihelium carbene dication, He 2C 2+, have been calculated using ab initio techniques. A 75-point potential energy surface was constructed using an all-electron coupled cluster single, double and triple excitation (CCSD (T)) method together with a correlation-consistent polarised core valence triple-zeta basis set. The CCSD(T) optimised geometry was of C 2v symmetry with an R C- He bondlength of 1.570 Å and a bond angle of 84.1 °. The discrete potential energy surface was fitted using a Padé (4, 5) power series expansion yielding a ( x 2) 1 2 of 8.2 × 1 −6 a.u. The potential function was embedded in the Eckart-Watson Hamiltonian, which was solved variationally. The anharmonic fundamental frequencies for the breathe, bend and asymmetric stretch vibrations were calculated to be 683.1, 329.5, 623.8 cm −1 respectively. The low-lying rovibrational states were calculated variationally using a 560-configuration basis involving products of the vibrational eigenfunctions and plus and minus combinations of regular symmetric-top rotor functions.

Ab initio calculations of the rovibrational states of He 2O 2+

All-electron CCSD(T)/cc-pCVTZ theory was used to calculate the equilibrium geometry and a 68 point discrete potential energy hypersurface for the dihelium oxene dication He 2O 2+. The CCSD(T) optimised geometry was of C 2v symmetry with an R OHe bond length of 1.168 Å and an included bond angle of 92.6 °. An analytical potential function was obtained from this surface using an Ogilvie Padé (4,5) power series expansion, which yielded a (χ 2) 1 2 value of 2.810 × 10 −5 a.u. The analytical function was then embedded in the Eckart-Watson Hamiltonian, which was solved variationally. Within the anharmonic approximation, the fundamental frequencies for the breathe, bend and asymmetric stretch vibrations were calculated to be 1247.3 cm −1, 816.8 −1 and 1275.6 cm −1, respectively. Using a 560 configuration basis involving products of vibrational eigenfunctions and plus/minus combinations of regular symmetric-top rotor functions, the low-lying rovibrational states of the 1A 1 electronic state of He 2O 2+ were determined.

Ab initio calculations of the rovibrational states of He2N2+

Abstract The low-lying rovibrational states of the 2 B 1 ground electronic state of He 2 N 2+ were calculated using ab initio techniques. A 74 point potential energy surface was constructed using the CCSD(T) method coupled with a cc-pCVTZ basis set. The CCSD(T) optimised equilibrium geometry was of C 2v symmetry with an R NHe bond length of 1.329 A and a θ HeNHe bond angle of 88.6°. The discrete potential energy surface was fitted using a Pade (4,5) power series expansion, yielding a (χ 2 ) 1 2 of 9.98 × 10 −5 au. The potential function was embedded in the nuclear Schrodinger equation and solved variationally to yield the low-lying rovibrational states.

Variational calculations for the rovibrational states of Si 212C and Si 213C

Rovibrational states of the ground electronic state of Si 2 12C and Si 2 13C isotopomers have been calculated variationally. The potential energy surface used in the calculations was obtained from an MP2/TZ2Pf ab initio surface of Barone et al. (V. Barone, P. Jensen and C. Minichino, J. Mol. Spectrosc., 154 (1992) 252) by applying the restrictions of 100° ⩽ α < 150°. The ab initio surface was refitted to a fourth-order polynomial with an Ogilvie-Tipping variable using a multi-dimensional least-squares procedure. The force field was then embedded in an Eckart-Watson vibration-rotation Hamiltonian, from which low-lying vibrational states and rovibrational states of Si 2 12C and Si 2 13C were obtained. The calculated vibrational states (100) and (001) of Si 2 12C and the 13C isotopic shifts agree well with a recent experiment (J.D. Presilla-Marquez and W.R.M. Graham, J. Chem. Phys., 95 (1991) 5612). Also, the calculations support the vibrational transition at 658.2 cm −1 found by Kafafi et al. (Z.H. Kafafi, R.H. Hauge, L. Fredin and J.L. Margrave, J. Chem. Phys., 87 (1983) 797). The rotational energies of these isotopomers for the lowest six vibrational states are given as are the rotational constants for Si 2 12C and Si 2 13C.

Variational calculations of the rovibrational energy levels of K 2Na +

Ab initio variational calculations of the low-lying rovibrational states of K 2Na + were performed. A sixth order power series expansion using an exponential Dunham variable was embedded in the Eckart-Watson Hamiltonian, which was solved variationally. The anharmonic fundamental frequencies for the breathe, bend and asymmetric stretch vibrations were calculated to be 188.2 (A 1), 78.2 (A 1) and 94.9 (B 2) cm −1 respectively. The low-lying rovibrational states were calculated using a 560 configuration basis involving products of the vibrational eigenfunctions and plus and minus combinations of regular symmetric-top rotor functions.

Variational calculations of rovibrational states of Li 2K +

The low-lying rovibrational states for the ground electronic state of Li 2K + were calculated using an ab initio variational solution of the nuclear Schrödinger equation. A discrete configuration interaction potential energy surface was generated and an analytical representation was obtained using a power series expansion. This force filed was embedded in the Eckart-Watson Hamiltonian from which rovibrational wavefunctions and eigenenergies were variationally calculated. An SCF dipole moment surface was generated and used to calculate absolute line intensities and square dipole moment matrix elements for some of the most intense transitions within the P, Q and R branches, between the vibrational ground state and the low-lying rovibrational states.

Variational calculation of the ro-vibrational states of Na3+

An ab initio variational ro-vibration calculation has been performed for the ground electronic state of Na3 +. A discrete potential energy surface was generated using the configuration interaction ansatz, within the frozen-core approximation. An analytical surface was generated from a Pade approximate expansion, which utilized a Dunham expansion variable. The force field was embedded in the Eckart-Watson Hamiltonian from which ro-vibrational wavefunctions and eigenenergies were variationally calculated for the low-lying ro-vibrational states.

Electric dipole moment function of ammonia

A full-dimensional electric dipole moment function of NH 3 is determined by fitting to experimental data (Stark splittings, absorption intensities) and to ab initio calculated dipole moment values using the nonrigid inverter Hamiltonian approximation. The dipole moment function is used to calculate transition moments of some low-lying rovibrational states of symmetric isotopomers of NH 3. A close reproduction of the available experimental data is achieved which indicates that the predicted values are reliable.

The use of supercomputers for the variational calculation of ro-vibrationally excited states of floppy molecules

The advent of supercomputers has led to great advances in electronic structure calculations and to the ab initio calculation of molecular spectra. Recent theoretical developments have allowed us to develop a two-step variational algorithm for the calculation of rotationally highly excited states of floppy molecules. This algorithm allows highly accurate nuclear motion calculations to be performed on low-lying ro-vibrational states and greatly extends the range of states that can practicably be considered. The algorithm has been adapted to run efficiently on the Cray supercomputers. Analysis of the timings suggest that construction of the secular matrix is highly vectorised and that the special structure of secular matrix can be used to give rapid diagonalisation. The limiting factor on these calculations is the available fast storage, but analysis suggests that this bottleneck could be removed by use of a Solid State Device (SSD). Sample results are given for calculations involving a range of rotational excitation. An adaptation of the algorithm to a loop of parallel processors is also suggested.

The infrared spectrum of H + 3 and its isotopomers. A challenge to theory and experiment

H+3 and its isotopomers are seen as a benchmark for the comparison of theory and experiment. The stages of an ab initio calculation (electronic structure, potential fitting and nuclear motion) are discussed and the sources of error highlighted by consideration of recent results. Fitting of the electronic structure data is seen to be an area needing more development. New results are presented for the low-lying rovibrational states of D+3. While rovibrational properties can be calculated in the low-energy region to within ca. 0.1 % accuracy, the high-energy region is still largely unexplored. New developments in the calculation of excited rotational states (J⩽ 20) are outlined and the possibility of quantum-mechanical calculations of vibrational levels in the near-dissociation region is discussed in the light of illustrative calculations.