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Journal of Physics B Atomic Molecular and Optical Physics

Accurate calculations of the ground state and low-lying excited states of the (RbBa)+molecular ion: a proposed system for ultracold reactive collisions

Stefan Knecht, Lasse Kragh Sørensen, Hans Jørgen Aa. Jensen, Timo Fleig, Christel M. Marian

Published Feb 16, 2010• 17 citations
Publisher

Abstract

Collisions of ultracold Ba + ions on a Rb Bose–Einstein condensate have been suggested as a possible benchmark system for ultracold ion-neutral collision experiments. However, a priori knowledge of the possible processes is desirable. For this purpose, we here present high-level four-component coupled cluster and multi-reference configuration interaction calculations of potential energy curves, dipole moments and spectroscopic constants of the experimentally interesting low-lying electronic states of the (RbBa) + molecule. Our results show significant avoided crossings between the Rb + Ba + entrance channels and low-lying charge transfer states of the Rb + and Ba ( 3 D) atomic channels, indicating that a fast non-radiative charge transfer is possible. Population analysis shows that a partially covalent polar bond is formed in the ground state, which thus deviates significantly from a pure Rb + + Ba interaction. This finding is corroborated by the electric dipole moment which is found only to be 4.5 D at the equilibrium bond distance, compared with the 14 D for a pure Rb + + Ba interaction, thereby supporting the view of a partial charge transfer between the two atoms.

DOI
10.1088/0953-4075/43/5/055101

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Collisions of ultracold Ba + ions on a Rb Bose–Einstein condensate have been suggested as a possible benchmark system for ultracold ion-neutral collision experiments. However, a priori knowledge of the possible processes is desirable. For this purpose, we here present high-level four-component coupled cluster and multi-reference configuration interaction calculations of potential energy curves, dipole moments and spectroscopic constants of the experimentally interesting low-lying electronic states of the (RbBa) + molecule. Our results show significant avoided crossings between the Rb + Ba + entrance channels and low-lying charge transfer states of the Rb + and Ba ( 3 D) atomic channels, indicating that a fast non-radiative charge transfer is possible. Population analysis shows that a partially covalent polar bond is formed in the ground state, which thus deviates significantly from a pure Rb + + Ba interaction. This finding is corroborated by the electric dipole moment which is found only to be 4.5 D at the equilibrium bond distance, compared with the 14 D for a pure Rb + + Ba interaction, thereby supporting the view of a partial charge transfer between the two atoms.
State-of-the-art ab initio techniques have been applied to compute the potential energy curves of the (BaRb)+{}^{+}+ molecular ion in the Born-Oppenheimer approximation for the singlet and triplet states dissociating into the ground-state 1{}^{1}1SSS Rb+{}^{+}+ ion and the Ba atom in the ground 1{}^{1}1SSS state or the lowest singlet or triplet ddd excited states, and for the singlet and triplet states dissociating into the ground-state 2{}^{2}2SSS Rb atom and the ground-state 2{}^{2}2SSS Ba+{}^{+}+ ion. The ground-state potential energy was obtained with the coupled-cluster method restricted to single, double, and nonperturbative triple excitations. The first triplet states in the $\ensuremath{\Sigma}$, $\ensuremath{\Pi}$, and $\ensuremath{\Delta}$ symmetries were computed with the restricted open-shell coupled-cluster method restricted to single, double, and nonperturbative triple excitations. All other excited-state potential energy curves were computed using the equation of motion approach within the coupled-cluster singles, doubles, and linear triples framework. The long-range coefficients describing the electrostatic, induction, and dispersion interactions at large interatomic distances are also reported. The electric transition dipole moments governing the xxx ${}^{1}\ensuremath{\Sigma}\ensuremath{\rightarrow}{}^{1}\ensuremath{\Sigma},{}^{1}\ensuremath{\Pi}$ transitions have been obtained as the first residue of the polarization propagator computed with the linear response coupled-cluster method restricted to single and double excitations. Nonadiabatic radial and angular coupling matrix elements as well as the spin-orbit coupling matrix elements have been evaluated using the multireference configuration-interaction method restricted to single and double excitations with a large active space. With these couplings, the spin-orbit-coupled (relativistic) potential energy curves for the 0+{}^{+}+ and 1 states relevant for the running experiments have been obtained. Finally, relativistic transition moments and nonadiabatic coupling matrix elements were obtained from the nonrelativistic results and spin-orbit eigenvectors. The electronic structure input has been employed in the single-channel scattering calculations of the collisional cross sections between the Ba+{}^{+}+ ion and Rb atom. Both nonrelativistic and relativistic potentials were used in these calculations. Our results show that the inelastic cross section corresponding to the charge transfer from the Rb atom to the Ba+{}^{+}+ ion is much smaller than the elastic one over a wide range of energies up to 1 mK. This suggests that sympathetic cooling of the Ba+{}^{+}+ ion by collisions with ultracold Rb atoms should be possible.
Cold ion-neutral reactive processes were studied in an hybrid trap down to average collision energies <E_coll>/k_B > 20 mK. The atomic ion-neutral systems Ca^+ + Rb and Ba^+ + Rb were studied, and the results interpreted with high-level quantum chemical and quantum scattering calculations. Three reactive processes were found to be in competition, namely non-radiative charge transfer induced by non-adiabatic couplings between potential energy surfaces, radiative charge transfer, and radiative association of molecular ions, which were observed using mass spectrometry. The role of light in these processes was investigated. Enhancement of reaction rate constants from electronically excited entrance channels was observed and rationalised using computed potential energy curves. The collision-energy dependence of the reaction rate constants was investigated, and was found to be in line with predictions of both classical and quantum models uncovering general effects in cold ion-neutral systems. Cold reactions in the molecular ion-neutral system N_2^+ + Rb were also investigated with average collision energies two orders of magnitude lower than previously realised. The reaction rate constant in this system was found to depend strongly on the Rb ^2P_3/2 population, with the rate constant from the corresponding excited entrance channel being significantly faster than the collision rate predicted by Langevin theory. A classical capture model was developed taking into account the charge permanent-quadrupole intermolecular force and was found to reproduce the observed rate. The implied near unit reaction probability was rationalised by a near electronic resonance of entrance and product channels. A detailed description of the implementation of the ion-neutral hybrid trap is given. A thorough comparison of the results from state-of-the-art experiments and theory reveals general features of light assisted cold ion-neutral reactions. \n
In this work, a comprehensive theoretical investigation is carried out to explore the electronic and spectroscopic properties of selected diatomic molecular ions MgRb+ and SrRb+. Using high-level ab initio calculations based on a pseudopotential approach, along with large Gaussian basis sets and full valence configuration interaction (FCI), we accurately determine adiabatic potential energy curves, spectroscopic constants, transition dipole moments (TDMs), and permanent electric dipole moments (PDMs). To deepen our understanding of these systems, we calculate radiative lifetimes for vibrational levels in both ground and low-lying excited electronic states. This includes evaluating spontaneous and stimulated emission rates, as well as the effects of blackbody radiation. We also compute Franck–Condon factors and analyze photoassociation processes for both ions. Furthermore, to explore low-energy collisional dynamics, we investigate elastic scattering in the first excited states (21Σ+) describing the collision between the Ra atom and Mg+ or Sr+ ions. Our findings provide detailed insights into the theoretical electronic structure of these molecular ions, paving the way for future experimental studies in the field of cold and ultracold molecular ion physics.
Charge-transfer cold Yb+{}^{+}++++ Rb collision dynamics is investigated theoretically using high-level ab initio potential energy curves, dipole moment functions, and nonadiabatic coupling matrix elements. Within the scalar-relativistic approximation, the radiative transitions from the entrance $A{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+}$ to the ground $X{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+}$ state are found to be the only efficient charge-transfer pathway. The spin-orbit coupling does not open other efficient pathways, but alters the potential energy curves and the transition dipole moment for the $A\ensuremath{-}X$ pair of states. The radiative, as well as the nonradiative, charge-transfer cross sections calculated within the ${10}^{\ensuremath{-}3}--10$ cm${}^{\ensuremath{-}1}$ collision energy range exhibit all features of the Langevin ion-atom collision regime, including a rich structure associated with centrifugal barrier tunneling (orbiting) resonances. Theoretical rate coefficients for two Yb isotopes agree well with those measured by immersing Yb+{}^{+}+ ions in an ultracold Rb ensemble in a hybrid trap. Possible origins of discrepancy in the product distributions and relations to previously studied similar processes are discussed.
Abstract The electronic structure and the spectroscopic properties for low‐lying electronic states of the LiRb+ molecular ion, dissociating into Li (2s, 2p, 3s, 3p, 3d, 4s, and 4p) + Rb+ and Li+ + Rb (5s, 5p, 4d, 6s, 6p, 5d, and 7s), have been investigated using an ab initio approach based on non‐empirical pseudo potentials for the Li and Rb cores and parametrized l‐dependent polarization potential. We have determined the adiabatic potential energy curves and their spectroscopic constants for many electronic states of 2Σ+, 2Π, and 2Δ symmetries. A satisfying agreement, for the spectroscopic constants, has been obtained for the ground and the first excited states with the available theoretical works. Potential energy curves were presented, for the first time, for the higher excited states. In addition, we have localised and analysed the avoided crossings between electronic states of 2Σ+ and 2Π symmetries. Their existences can be related to the interaction between the potential energy curves and to the charge transfer process between the two ionic systems Li+Rb and LiRb+. Moreover, we have determined the transition dipole moments from X2Σ+ and 22Σ+ states to higher excited states of 2Σ+ and 2Π symmetries. For our best knowledge, no experimental data on the LiRb+ molecular ion is available. These theoretical data can help experimentalists to optimize photoassociative formation of ultracold LiRb+ molecular ion and their longevity in a trap or in an optical lattice. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012
Radiative emission during cold collisions between trapped laser-cooled Rb atoms and alkaline-earth ions (Ca+^++, Sr+^++, Ba+^++) and Yb+^++, and between Li and Yb+^++, are studied theoretically, using accurate effective-core-potential based quantum chemistry calculations of potential energy curves and transition dipole moments of the related molecular ions. Radiative association of molecular ions is predicted to occur for all systems with a cross section two to ten times larger than the radiative charge transfer one. Partial and total rate constants are also calculated and compared to available experiments. Narrow shape resonances are expected, which could be detectable at low temperature with an experimental resolution at the limit of the present standards. Vibrational distributions are also calculated, showing that the final molecular ions are not created in their ground state level.