The electronic structure, including the spin–orbit coupling effect of the HfH molecule, has been studied to determine if it can be cooled through Doppler and Sysphus laser cooling techniques. The multi-reference configuration interaction plus Davidson correction (MRCI + Q) method has been used to calculate its potential energy curves (P.E.C.s) in the Ω(±) and 2s+1Ʌ(+/-) representation. The spectroscopic constants Te, Re, ωe, Be, αe, the dipole moment µe, and the dissociation energies De agree very well with previously published work. In addition, we present in this work twenty new doublet and quartet states in the Ω(±) representation. The electronic transition dipole moment curves (TDMCs) between the lowest-lying electronic states have been investigated for the Δ -Π, Π - ∑+ and Δ - Φ transitions among specific Ω(±) states. The Franck-Condon factors (FCFs), the Einstein coefficient of spontaneous emission Aν′ν, and the radiative lifetime τ have been computed for the investigated transitions. In addition, properties of the molecules' electronic and vibrational states, such as the static dipole moment curves (D.M.C.s), the ionic character fionic, and the rovibrational constants are calculated. We deduce from our results that the HfH molecule is indeed a laser-cooling candidate that can reach a temperature as low as the nK regime. We present a complementary scheme with suitable experimental parameters. These results can be of great interest to experimental spectroscopists interested in ultracold diatomic molecules and their applications.
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
1S Rb
+ ion and the Ba atom in the ground
1S state or the lowest singlet or triplet
d excited states, and for the singlet and triplet states dissociating into the ground-state
2S Rb atom and the ground-state
2S 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
x ${}^{1}\ensuremath{\Sigma}\ensuremath{\rightarrow}{}^{1}\ensuremath{\Sigma},{}^{1}\ensuremath{\Pi}$ 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.
Polar radioactive molecules have been suggested to be exceptionally sensitive systems in the search for signatures of symmetry-violating effects in their structure. Radium monofluoride (RaF) possesses an especially attractive electronic structure for such searches, as the diagonality of its Franck-Condon matrix enables the implementation of direct laser cooling for precision experiments. To maximize the sensitivity of experiments with short-lived RaF isotopologues, the molecular beam needs to be cooled to the rovibrational ground state. Due to the high kinetic energies and internal temperature of extracted beams at radioactive ion beam (RIB) facilities, in-flight rovibrational cooling would be restricted by a limited interaction timescale. Instead, cooling techniques implemented on ions trapped within a radiofrequency quadrupole cooler-buncher can be highly efficient due to the much longer interaction times (up to seconds). In this work, the feasibility of rovibrationally cooling trapped RaF+ and RaH+ cations with repeated laser excitation is investigated. Due to the highly diagonal nature between the ionic ground state and states in the neutral system, any reduction of the internal temperature of the molecular ions would largely persist through charge-exchange without requiring the use of cryogenic buffer gas cooling. Quasirelativistic X2C and scalar-relativistic ECP calculations were performed to calculate the transition energies to excited electronic states and to study the nature of chemical bonding for both RaF+ and RaH+. The results indicate that optical manipulation of the rovibrational distribution of trapped RaF+ and RaH+ is unfeasible due to the high electronic transition energies, which lie beyond the capabilities of modern laser technology. However, more detailed calculations of the structure of RaH+ might reveal possible laser-cooling pathways.
Ultracold polar and magnetic
23Na6Li molecules in the rovibrational ground state of the lowest triplet ${a}^{3}{\mathrm{\ensuremath{\Sigma}}}^{+}$ electronic state have been recently produced. Here, we calculate the electronic and rovibrational structure of these 14-electron molecules with spectroscopic accuracy ($<0.5\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$) using state-of-the-art ab initio methods of quantum chemistry. We employ the hierarchy of the coupled-cluster wave functions and Gaussian basis sets extrapolated to the complete basis set limit. We show that the inclusion of higher-level excitations, core-electron correlation, relativistic, QED, and adiabatic corrections is necessary to accurately reproduce scattering and spectroscopic properties of alkali-metal systems. We obtain the well depth, ${D}_{e}=229.9(5)\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$, the dissociation energy, ${D}_{0}=208.2(5)\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$, and the scattering length, ${a}_{s}=\ensuremath{-}{84}_{\ensuremath{-}41}^{+25}\phantom{\rule{4pt}{0ex}}\mathrm{bohr}$, in good agreement with recent experimental measurements. We predict the permanent electric dipole moment in the rovibrational ground state,
d0=0.167(1) D. These values are obtained without any adjustment to experimental data, showing that quantum chemistry methods are capable of predicting scattering properties of many-electron systems, provided relatively weak interaction and small reduced mass of the system.
We present high-level four-component coupled cluster and multireference configuration interaction calculations of potential energy curves, dipole moment, Franck-Condon factors and spectroscopic constants of the newly formed RbYb molecule. From finite-field calculations we obtain an electric dipole moment for RbYb of almost 1 D. In combination with its magnetic dipole moment this makes RbYb an excellent candidate for trapping and for studying dipolar interaction in the ultracold regime. Significant Franck-Condon factors are found between the rovibronic ground state and the lowest rovibrational levels of the first excited 2Sigma1/2+ state but also between a broad range of rovibrational levels of the 2Pi1/2 and 2Pi3/2 states. This allows for several two-step approaches to reach the rovibronic ground state after initial photoassociation.
Rovibrational energies, wave functions, and Raman transition moments are reported for the lowest-energy states of the H_{3}^{+} molecular ion including the magnetic couplings of the proton spins and molecular rotation in the presence of a weak external magnetic field. The rovibrational-hyperfine-Zeeman Hamiltonian matrix is constructed and diagonalized using the rovibrational eigenstates and the proton spin functions. The developed methodology can be used to compute hyperfine-Zeeman effects also for higher-energy rovibrational excitations of H_{3}^{+} and other closed-shell polyatomic molecules. These developments will guide future experiments extending quantum logic spectroscopy to polyatomic systems.