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Physical Review A

Approximate relativistic coupled-cluster calculations on heavy alkali-metal diatomics: Application to the spin-orbit-coupled A1Σ+ and b3Π states of RbCs and Cs2

Andrei V. Zaitsevskii, N. S. Mosyagin, A. V. Stolyarov, Ephraim Eliav

Published Aug 29, 2017• 34 citations
Publisher

Abstract

A simple approximate version of the Fock-space relativistic coupled-cluster method is developed and applied for modeling the spin-orbit-coupling effect in the ${A}^{1}{\mathrm{\ensuremath{\Sigma}}}_{(u)}^{+}$ and ${b}^{3}{\mathrm{\ensuremath{\Pi}}}_{(u)}$ states of the heavy alkali diatomics RbCs and ${\mathrm{Cs}}_{2}$. Numerical stability in a wide range of molecular geometries is achieved at the cost of a very moderate loss of accuracy for low-lying states and negligibly small deviations of the computational scheme from strict size consistency. The adiabatic potential energy curves computed for the $(2,3){0}^{+}$ (RbCs) and $(1,2){0}_{u}^{+}$ (${\mathrm{Cs}}_{2}$) states are converted into ``quasidiabatic'' potentials and effective spin-orbit-coupling functions via projection of the scalar relativistic states onto the subsets of fully relativistic states. A detailed comparison of the present ab initio results with their experimental and preceding theoretical counterparts is performed.

DOI
10.1103/physreva.96.022516

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A simple approximate version of the Fock-space relativistic coupled-cluster method is developed and applied for modeling the spin-orbit-coupling effect in the A1\ensuremathΣ(u)+{A}^{1}{\mathrm{\ensuremath{\Sigma}}}_{(u)}^{+}A1\ensuremathΣ(u)+​ and b3\ensuremathΠ(u){b}^{3}{\mathrm{\ensuremath{\Pi}}}_{(u)}b3\ensuremathΠ(u)​ states of the heavy alkali diatomics RbCs and Cs2{\mathrm{Cs}}_{2}Cs2​. Numerical stability in a wide range of molecular geometries is achieved at the cost of a very moderate loss of accuracy for low-lying states and negligibly small deviations of the computational scheme from strict size consistency. The adiabatic potential energy curves computed for the (2,3)0+(2,3){0}^{+}(2,3)0+ (RbCs) and (1,2)0u+(1,2){0}_{u}^{+}(1,2)0u+​ (Cs2{\mathrm{Cs}}_{2}Cs2​) states are converted into ``quasidiabatic'' potentials and effective spin-orbit-coupling functions via projection of the scalar relativistic states onto the subsets of fully relativistic states. A detailed comparison of the present ab initio results with their experimental and preceding theoretical counterparts is performed.
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We apply the relativistic configuration-interaction valence-bond method to calculate various characteristics of the alkali-metal RbCs dimer. These include the electronic potentials and transition dipole moments between the ground and first excited states and permanent dipole moments of the X 1sigma+ and a 3sigma+ states of the ground configuration. In addition, we estimate the lifetime of the rovibrational levels of the X state due to blackbody radiation. These data can help experimentalists to optimize photoassociative formation of ultracold RbCs molecules and their longevity in a trap or in an optical lattice. Extended basis sets, constructed from Dirac-Fock and Sturm's orbitals, have been used to ensure convergence of our calculations. We compare our data with other theoretical and experimental results when they were available.
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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.
The properties of the electronic ground state of the polar and paramagnetic europium--S-state-atomS\text{-state-atom}S-state-atom molecules have been investigated. Ab initio techniques have been applied to compute the potential energy curves for the europium--alkali-metal-atom, EuX(X=Li,Na,K,Rb,Cs)\mathrm{Eu}X(X=\mathrm{Li},\mathrm{Na},\mathrm{K},\mathrm{Rb},\mathrm{Cs})EuX(X=Li,Na,K,Rb,Cs), europium--alkaline-earth-metal-atom, EuY(Y=Be,Mg,Ca,Sr,Ba)\mathrm{Eu}Y(Y=\mathrm{Be},\mathrm{Mg},\mathrm{Ca},\mathrm{Sr},\mathrm{Ba})EuY(Y=Be,Mg,Ca,Sr,Ba), and europium-ytterbium, EuYb, molecules in the Born-Oppenheimer approximation for the high-spin electronic ground state. The spin restricted open-shell coupled cluster method restricted to single, double, and noniterative triple excitations, RCCSD(T), was employed and the scalar relativistic effects within the small-core energy-consistent pseudopotentials were included. The permanent electric dipole moments and static electric dipole polarizabilities were computed. The leading long-range coefficients describing the dispersion interaction between atoms at large internuclear distances C6{C}_{6}C6​ are also reported. The EuK, EuRb, and EuCs molecules are examples of species possessing both large electric and magnetic dipole moments making them potentially interesting candidates for ultracold many-body quantum simulations when confined in an optical lattice in combined electric and magnetic fields.