Abstract Systematic quantum chemical calculations were performed for the ground and a number of low-lying electronically excited doublet and quartet states of the rubidium trimer molecule. The obtained potential energy surfaces (PES), spin-orbit couplings (SOC) and electronic transition dipole moments (ETDM) can be useful for optimizing paths for laser synthesis, cooling and manipulation of stable ensembles of Rb3 molecules at ultralow temperatures. Ab initio calculations of the electronic structure of the homonuclear Rb3 molecule, in linear, isosceles triangle and equilateral triangle geometries, were performed using the multi-reference configuration interaction method, taking into account single and double excitations (M-R‑CISD) and with explicit dynamic correlation of only the three valence electrons. The structure of each atom was approximated using a nine-electron effective core potential (ECP28MDF), and molecular orbitals (MOs) were optimized using the spin averaged (over doublet and quartet states) multi-configuration self-consistent field (SA-CASSCF) method. Core–valence correlations between twenty-four subvalence electrons located on doubly occupied MOs and three valence electrons were implicitly taken into account using a one-electron angular momentum-independent Müller–Mayer core polarization potential (CPP). As a result of topological investigations at over 35 000 points, two dimensional PES, SOC, and ETDM functions were obtained and the geometric parameters Rb3 were found at which the most intense vertical transitions and the maximum influence of the SOC are expected.
Abstract Systematic quantum chemical calculations were performed for the ground and a number of low-lying electronically excited doublet and quartet states of the rubidium trimer molecule. The obtained potential energy surfaces (PES), spin-orbit couplings (SOC) and electronic transition dipole moments (ETDM) can be useful for optimizing paths for laser synthesis, cooling and manipulation of stable ensembles of Rb3 molecules at ultralow temperatures. Ab initio calculations of the electronic structure of the homonuclear Rb3 molecule, in linear, isosceles triangle and equilateral triangle geometries, were performed using the multi-reference configuration interaction method, taking into account single and double excitations (M-R‑CISD) and with explicit dynamic correlation of only the three valence electrons. The structure of each atom was approximated using a nine-electron effective core potential (ECP28MDF), and molecular orbitals (MOs) were optimized using the spin averaged (over doublet and quartet states) multi-configuration self-consistent field (SA-CASSCF) method. Core–valence correlations between twenty-four subvalence electrons located on doubly occupied MOs and three valence electrons were implicitly taken into account using a one-electron angular momentum-independent Müller–Mayer core polarization potential (CPP). As a result of topological investigations at over 35 000 points, two dimensional PES, SOC, and ETDM functions were obtained and the geometric parameters Rb3 were found at which the most intense vertical transitions and the maximum influence of the SOC are expected.
This paper deals with the electronic structure of RbSr, a molecule possessing both a magnetic dipole moment and an electric dipole moment in its own frame, allowing its manipulation with external fields. Two complementary ab initio approaches are used for the ground and lowest excited states: first, an approach relying on optimized effective core potentials with core polarization potentials based on a full configuration interaction involving three valence electrons and second, an approach using a small-size effective core potential with 19 correlated electrons in the framework of coupled-cluster theory. We have found excellent agreement between these two approaches for the ground-state properties including the permanent dipole moment. We have focused on studies of excited states correlated to the two lowest asymptotes Rb(5p2P)+Sr(5s21S) and Rb(5s2S)+Sr(5s5p3P) relevant for ongoing experiments on ultracold quantum degenerate gases. We also present approximate potential curves including spin-orbit interaction based on atomic spin-orbit constants. These potential curves are an excellent starting point for experimental studies of molecular structure of RbSr using high-resolution spectroscopy.
Ab initio techniques have been applied to investigate the electronic structure of the LiYb molecule. The potential energy curves have been computed in the Born-Oppenheimer approximation for the ground and 29 low-lying doublet and quartet excited electronic states. Complete active space self-consistent field, multi-reference configuration interaction, and Rayleigh Schrödinger perturbation theory to second order calculations have been utilized to investigate these states. The spectroscopic constants, ωe, Re, Be, …, and the static dipole moment, μ, have been investigated by using the two different techniques of calculation with five different types of basis. The eigenvalues, Ev, the rotational constant, Bv, the centrifugal distortion constant, Dv, and the abscissas of the turning points, Rmin and Rmax, have been calculated by using the canonical functions approach. The comparison between the values of the present work, calculated by different techniques, and those available in the literature for several electronic states shows a very good agreement. Twenty-one new electronic states have been studied here for the first time.
Electronic structure of the molecule SrCl has been investigated by employing the ab initio methods CASSCF/MRCI+Q with Davidson correction in the representation 2s+1 Λ ± , neglecting spin-orbit effects, and using the computational program Molpro. The potential energy curves of the low-lying doublet and quartet electronic states have been investigated. The harmonic vibrational wave number ω e , the relative electronic energy T e , referred to the ground state, the rotational constant B e and the equilibrium internuclear distance R e , have been calculated for the investigated electronic states. Moreover, the static dipolar moments have been determined in term of the internuclear distance R e .
In this work, we present a thorough theoretical structure and spectroscopic study of the ground and low lying excited states of RbBa molecule. High-level ab-initio calculations are performed, using MCSCF/MRCI+Q level of method, based on the effective core potential (ECP) and core-polarization potential (CPP) approach. The potential energy curves, spectroscopic parameters, vibrationnel energy levels of the 16( 2,4 Σ + , 2,4 Π, 2,4 Δ) first electronic states, with respect to the lowest five dissociation limits were calculated. The comparison of the spectroscopic constants of the ground state X 2 Σ + with the available theoretical work, are in good agreement. The study of all the excited states is performed in this work for the first time. Afterwards, the spin-orbit operator is incorporated in valence MRCI calculation using optimized relativistic spin-orbit pseudo-potentials and 33 Ω states are generated and split into Λ-S states. In addition, both relativistic and non relativistic calculations of permanent and transition dipole moments are presented and discussed. Stimulated black body ( T = 300 K) and spontaneous transition rates of vibrational states of X 2 Σ + state were evaluated. The related vibrational lifetimes for RbBa are found to be in order of 10 3 s which is sufficiently large for ultracold experiments. Moreover, the vibrational life-time for the A 2 Σ + ( v’ ) and A 2 П ( v” ) states are measured and the possibility of Laser Cooling for the RbBa molecule is discussed based on Franck–Condon factors calculation of A 2 Σ + ( v’ )→ X 2 Σ + ( v ) and A 2 П( v” ) → X 2 Σ + ( v ) transition. This work represents a significant contribution for experimentalists as it provides efficient information in order to form cold alkali and alkaline-earth RbBa molecules.
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.