Physical Review A

Changing the paradigm in f -containing cold molecules: The impact of spin-orbit coupling and f − d transitions

Marta Gałyńska, Matheus Morato F. de Moraes, Paweł Tecmer, Katharina Bogusławski

Published Jan 8, 2025• 0 citations

Abstract

Present-day state-of-the-art ab initio many-body calculations on $f$-block-containing cold molecules rely heavily on perturbative approaches for spin-orbit coupling and exclude a substantial part of the atomic transitions in the $f$ and $d$ shells. Here, we demonstrate the importance of proper relativistic treatment of the $f$ and $d$ shells in Yb-containing diatomics and the inclusion of the $f\ensuremath{\rightarrow}d$ transition to obtain accurate spectra of ${\mathrm{YbLi}}^{+}$. We focus on state-of-the-art relativistic many-body calculations for the Yb atom's ground and excited states and the ${\mathrm{YbLi}}^{+}$ potential energy surface. For that purpose, we exploit various quantum many-body methods, namely, a spin-free and four-component implementation of the coupled-cluster singles and doubles (CCSD) model and its equation-of-motion (EOM) extensions, spin-free complete-active-space self-consistent field, and internally contracted multireference (MR) configuration interaction approaches. We oppose scalar relativistic calculations to four-component variants to support the reliability of our EOM-CCSD study and shed new light on the interplay between these systems' spin-orbit coupling and the proper treatment of relativistic effects. Finally, we provide new reference potential-energy curves for ground and excited states. Additionally, we compute spectroscopic constants and analyze the Einstein coefficients.

DOI: 10.1103/physreva.111.012803

Related papers

Sympathetic cooling of the Ba + ion by collisions with ultracold Rb atoms: Theoretical prospects

Michał Krych, Wojciech Skomorowski, Filip Pawłowski +2 more

arXiv:1008.0840Physical Review AMar 31, 201160 citations

Relativistic calculations of ground and excited states of LiYb molecule for ultracold photoassociation spectroscopy studies

Geetha Gopakumar, Minori Abe, Bhanu Pratap Das +2 more

The Journal of Chemical PhysicsSep 28, 201039 citations

Prospects for ultracold polar and magnetic chromium–closed-shell-atom molecules

Michał Tomza

arXiv:1306.5450Physical Review AJul 25, 201319 citations

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 +1 more

Physical Review AAug 29, 201734 citations

Ab initioBogoliubov coupled cluster theory for open-shell nuclei

A. Signoracci, T. Duguet, G. Hagen +1 more

arXiv:1412.2696Physical Review CJun 29, 201596 citations

Reexamination of the ground-state Born-Oppenheimer Yb 2 potential

Giorgio Visentin, Alexei A. Buchachenko, Paweł Tecmer

arXiv:2107.10353Physical Review ANov 10, 20214 citations

Physical Review A

Changing the paradigm in f -containing cold molecules: The impact of spin-orbit coupling and f − d transitions

Marta Gałyńska, Matheus Morato F. de Moraes, Paweł Tecmer, Katharina Bogusławski

Published Jan 8, 2025• 0 citations

Publisher

Abstract

Present-day state-of-the-art ab initio many-body calculations on

f

-block-containing cold molecules rely heavily on perturbative approaches for spin-orbit coupling and exclude a substantial part of the atomic transitions in the

f

and

d

shells. Here, we demonstrate the importance of proper relativistic treatment of the

f

and

d

shells in Yb-containing diatomics and the inclusion of the

f\ensuremath{\rightarrow}d

transition to obtain accurate spectra of

{\mathrm{YbLi}}^{+}

. We focus on state-of-the-art relativistic many-body calculations for the Yb atom's ground and excited states and the

{\mathrm{YbLi}}^{+}

potential energy surface. For that purpose, we exploit various quantum many-body methods, namely, a spin-free and four-component implementation of the coupled-cluster singles and doubles (CCSD) model and its equation-of-motion (EOM) extensions, spin-free complete-active-space self-consistent field, and internally contracted multireference (MR) configuration interaction approaches. We oppose scalar relativistic calculations to four-component variants to support the reliability of our EOM-CCSD study and shed new light on the interplay between these systems' spin-orbit coupling and the proper treatment of relativistic effects. Finally, we provide new reference potential-energy curves for ground and excited states. Additionally, we compute spectroscopic constants and analyze the Einstein coefficients.

DOI: 10.1103/physreva.111.012803

Related papers

Sympathetic cooling of the Ba + ion by collisions with ultracold Rb atoms: Theoretical prospects

Michał Krych, Wojciech Skomorowski, Filip Pawłowski +2 more

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 ${}^{1}$ $S$ Rb ${}^{+}$ ion and the Ba atom in the ground ${}^{1}$ $S$ state or the lowest singlet or triplet $d$ excited states, and for the singlet and triplet states dissociating into the ground-state ${}^{2}$ $S$ Rb atom and the ground-state ${}^{2}$ $S$ 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.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}$$S$ Rb${}^{+}$ ion and the Ba atom in the ground ${}^{1}$$S$ state or the lowest singlet or triplet $d$ excited states, and for the singlet and triplet states dissociating into the ground-state ${}^{2}$$S$ Rb atom and the ground-state ${}^{2}$$S$ 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.

arXiv:1008.0840Physical Review AMar 31, 201160 citations

Relativistic calculations of ground and excited states of LiYb molecule for ultracold photoassociation spectroscopy studies

Geetha Gopakumar, Minori Abe, Bhanu Pratap Das +2 more

We report a series of quantum-chemical calculations for the ground and some of the low-lying excited states of an isolated LiYb molecule by the spin-orbit multistate complete active space second-order perturbation theory (SO-MS-CASPT2). Potential energy curves, spectroscopic constants, and transition dipole moments (TDMs) at both spin-free and spin-orbit levels are obtained. Large spin-orbit effects especially in the TDMs of the molecular states dissociating to Yb((3)P(0,1,2)) excited states are found. To ensure the reliability of our calculations, we test five types of incremental basis sets and study their effect on the equilibrium distance and dissociation energy of the ground state. We also compare CASPT2 and CCSD(T) results for the ground state spectroscopic constants at the spin-free relativistic level. The discrepancies between the CASPT2 and CCSD(T) results are only 0.01 Å in equilibrium bond distance (R(e)) and 200 cm(-1) in dissociation energy (D(e)). Our CASPT2 calculation in the supermolecular state (R=100 a.u.) with the largest basis set reproduces experimental atomic excitation energies within 3% error. Transition dipole moments of the super molecular state (R=100 a.u.) dissociating to Li((2)P) excited states are quite close to experimental atomic TDMs as compared to the Yb((3)P) and Yb((1)P) excited states. The information obtained from this work would be useful for ultracold photoassociation experiments on LiYb.We report a series of quantum-chemical calculations for the ground and some of the low-lying excited states of an isolated LiYb molecule by the spin-orbit multistate complete active space second-order perturbation theory (SO-MS-CASPT2). Potential energy curves, spectroscopic constants, and transition dipole moments (TDMs) at both spin-free and spin-orbit levels are obtained. Large spin-orbit effects especially in the TDMs of the molecular states dissociating to Yb((3)P(0,1,2)) excited states are found. To ensure the reliability of our calculations, we test five types of incremental basis sets and study their effect on the equilibrium distance and dissociation energy of the ground state. We also compare CASPT2 and CCSD(T) results for the ground state spectroscopic constants at the spin-free relativistic level. The discrepancies between the CASPT2 and CCSD(T) results are only 0.01 Å in equilibrium bond distance (R(e)) and 200 cm(-1) in dissociation energy (D(e)). Our CASPT2 calculation in the supermolecular state (R=100 a.u.) with the largest basis set reproduces experimental atomic excitation energies within 3% error. Transition dipole moments of the super molecular state (R=100 a.u.) dissociating to Li((2)P) excited states are quite close to experimental atomic TDMs as compared to the Yb((3)P) and Yb((1)P) excited states. The information obtained from this work would be useful for ultracold photoassociation experiments on LiYb.

The Journal of Chemical PhysicsSep 28, 201039 citations

Prospects for ultracold polar and magnetic chromium–closed-shell-atom molecules

Michał Tomza

The properties of the electronic ground state of the polar and paramagnetic chromium--closed-shell-atom molecules have been investigated. State-of-the-art ab initio techniques have been applied to compute the potential energy curves for the chromium--alkaline-earth-metal-atom, Cr $X$ ( $X=\mathrm{Be}$ , Mg, Ca, Sr, Ba), and chromium--ytterbium, CrYb, molecules in the Born-Oppenheimer approximation for the high-spin ${X}^{7}{\ensuremath{\Sigma}}^{+}$ 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 Douglas-Kroll-Hess Hamiltonian or 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 the atoms at large interatomic distances ${C}_{6}$ are also reported. The molecules under investigation are examples of species possessing both large magnetic and electric dipole moments making them potentially interesting candidates for ultracold many-body physics studies.The properties of the electronic ground state of the polar and paramagnetic chromium--closed-shell-atom molecules have been investigated. State-of-the-art ab initio techniques have been applied to compute the potential energy curves for the chromium--alkaline-earth-metal-atom, Cr$X$ ($X=\mathrm{Be}$, Mg, Ca, Sr, Ba), and chromium--ytterbium, CrYb, molecules in the Born-Oppenheimer approximation for the high-spin ${X}^{7}{\ensuremath{\Sigma}}^{+}$ 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 Douglas-Kroll-Hess Hamiltonian or 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 the atoms at large interatomic distances ${C}_{6}$ are also reported. The molecules under investigation are examples of species possessing both large magnetic and electric dipole moments making them potentially interesting candidates for ultracold many-body physics studies.

arXiv:1306.5450Physical Review AJul 25, 201319 citations

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 +1 more

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.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.

Physical Review AAug 29, 201734 citations

Ab initioBogoliubov coupled cluster theory for open-shell nuclei

A. Signoracci, T. Duguet, G. Hagen +1 more

Background: Ab initio many-body methods have been developed over the past 10 yr to address closed-shell nuclei up to mass $A\ensuremath{\approx}130$ on the basis of realistic two- and three-nucleon interactions. A current frontier relates to the extension of those many-body methods to the description of open-shell nuclei. Several routes to address open-shell nuclei are currently under investigation, including ideas that exploit spontaneous symmetry breaking.Purpose: Singly open-shell nuclei can be efficiently described via the sole breaking of U(1) gauge symmetry associated with particle-number conservation as a way to account for their superfluid character. While this route was recently followed within the framework of self-consistent Green's function theory, the goal of the present work is to formulate a similar extension within the framework of coupled cluster theory.Methods: We formulate and apply Bogoliubov coupled cluster (BCC) theory, which consists of representing the exact ground-state wave function of the system as the exponential of a quasiparticle excitation cluster operator acting on a Bogoliubov reference state. Equations for the ground-state energy and the cluster amplitudes are derived at the singles and doubles level (BCCSD) both algebraically and diagrammatically. The formalism includes three-nucleon forces at the normal-ordered two-body level. The first BCC code is implemented in $m$ scheme, which will permit the treatment of doubly open-shell nuclei via the further breaking of SU(2) symmetry associated with angular momentum conservation.Results: Proof-of-principle calculations in an ${N}_{\text{max}}=6$ spherical harmonic oscillator basis for $^{16,18}\mathrm{O}$ and $^{18}\mathrm{Ne}$ in the BCCD approximation are in good agreement with standard coupled cluster results with the same chiral two-nucleon interaction, while $^{20}\mathrm{O}$ and $^{20}\mathrm{Mg}$ display underbinding relative to experiment. The breaking of U(1) symmetry, monitored by computing the variance associated with the particle-number operator, is relatively constant for all five nuclei, in both the Hartree-Fock-Bogoliubov and BCCD approximations.Conclusions: The newly developed many-body formalism increases the potential span of ab initio calculations based on single-reference coupled cluster techniques tremendously, i.e., potentially to reach several hundred additional midmass nuclei. The new formalism offers a wealth of potential applications and further extensions dedicated to the description of ground and excited states of open-shell nuclei. Short-term goals include the implementation of three-nucleon forces at the normal-ordered two-body level. Midterm extensions include the approximate treatment of triples corrections and the development of the equation-of-motion methodology to treat both excited states and odd nuclei. Long-term extensions include exact restoration of U(1) and SU(2) symmetries.Background: Ab initio many-body methods have been developed over the past 10 yr to address closed-shell nuclei up to mass $A\ensuremath{\approx}130$ on the basis of realistic two- and three-nucleon interactions. A current frontier relates to the extension of those many-body methods to the description of open-shell nuclei. Several routes to address open-shell nuclei are currently under investigation, including ideas that exploit spontaneous symmetry breaking.Purpose: Singly open-shell nuclei can be efficiently described via the sole breaking of U(1) gauge symmetry associated with particle-number conservation as a way to account for their superfluid character. While this route was recently followed within the framework of self-consistent Green's function theory, the goal of the present work is to formulate a similar extension within the framework of coupled cluster theory.Methods: We formulate and apply Bogoliubov coupled cluster (BCC) theory, which consists of representing the exact ground-state wave function of the system as the exponential of a quasiparticle excitation cluster operator acting on a Bogoliubov reference state. Equations for the ground-state energy and the cluster amplitudes are derived at the singles and doubles level (BCCSD) both algebraically and diagrammatically. The formalism includes three-nucleon forces at the normal-ordered two-body level. The first BCC code is implemented in $m$ scheme, which will permit the treatment of doubly open-shell nuclei via the further breaking of SU(2) symmetry associated with angular momentum conservation.Results: Proof-of-principle calculations in an ${N}_{\text{max}}=6$ spherical harmonic oscillator basis for $^{16,18}\mathrm{O}$ and $^{18}\mathrm{Ne}$ in the BCCD approximation are in good agreement with standard coupled cluster results with the same chiral two-nucleon interaction, while $^{20}\mathrm{O}$ and $^{20}\mathrm{Mg}$ display underbinding relative to experiment. The breaking of U(1) symmetry, monitored by computing the variance associated with the particle-number operator, is relatively constant for all five nuclei, in both the Hartree-Fock-Bogoliubov and BCCD approximations.Conclusions: The newly developed many-body formalism increases the potential span of ab initio calculations based on single-reference coupled cluster techniques tremendously, i.e., potentially to reach several hundred additional midmass nuclei. The new formalism offers a wealth of potential applications and further extensions dedicated to the description of ground and excited states of open-shell nuclei. Short-term goals include the implementation of three-nucleon forces at the normal-ordered two-body level. Midterm extensions include the approximate treatment of triples corrections and the development of the equation-of-motion methodology to treat both excited states and odd nuclei. Long-term extensions include exact restoration of U(1) and SU(2) symmetries.

arXiv:1412.2696Physical Review CJun 29, 201596 citations

Reexamination of the ground-state Born-Oppenheimer Yb 2 potential

Giorgio Visentin, Alexei A. Buchachenko, Paweł Tecmer

The precision of the photoassociation spectroscopy of the Yb dimer in degenerate gases is enough to improve the constraints on short-range gravitylike forces if the theoretical knowledge of the Born-Oppenheimer interatomic potential and non-Born-Oppenheimer interactions is refined [Borkowski et al., Sci. Rep. 9, 14807 (2019)]. The ground-state interaction potential of the ytterbium dimer is investigated at the exact two-component core-correlated coupled-cluster method with singles, doubles, and noniterative triples [CCSD(T)] level of ab initio theory in the complete-basis-set limit with extensive augmentation by diffuse functions. For the small basis set the comparison is made with the four-component relativistic finite-nuclei CCSD(T) calculations to identify the contraction of the dimer bond length as the main unrecoverable consequence of the scalar-relativistic approximation. The empirical constraint on the number of bound vibrational energy levels of the $^{174}\mathrm{Yb}_{2}$ dimer is accounted for by representing the global ab initio--based Born-Oppenheimer potential with the model semianalytical function containing the scale and shift parameters. The results support the previous evaluation of the Yb dimer potentials from the photoassociation spectroscopy data and provide an accurate and flexible reference for future refinement of the constraints on short-range gravitylike forces by ultracold atomic spectroscopy.The precision of the photoassociation spectroscopy of the Yb dimer in degenerate gases is enough to improve the constraints on short-range gravitylike forces if the theoretical knowledge of the Born-Oppenheimer interatomic potential and non-Born-Oppenheimer interactions is refined [Borkowski et al., Sci. Rep. 9, 14807 (2019)]. The ground-state interaction potential of the ytterbium dimer is investigated at the exact two-component core-correlated coupled-cluster method with singles, doubles, and noniterative triples [CCSD(T)] level of ab initio theory in the complete-basis-set limit with extensive augmentation by diffuse functions. For the small basis set the comparison is made with the four-component relativistic finite-nuclei CCSD(T) calculations to identify the contraction of the dimer bond length as the main unrecoverable consequence of the scalar-relativistic approximation. The empirical constraint on the number of bound vibrational energy levels of the $^{174}\mathrm{Yb}_{2}$ dimer is accounted for by representing the global ab initio--based Born-Oppenheimer potential with the model semianalytical function containing the scale and shift parameters. The results support the previous evaluation of the Yb dimer potentials from the photoassociation spectroscopy data and provide an accurate and flexible reference for future refinement of the constraints on short-range gravitylike forces by ultracold atomic spectroscopy.

arXiv:2107.10353Physical Review ANov 10, 20214 citations

Present-day state-of-the-art ab initio many-body calculations on

f

-block-containing cold molecules rely heavily on perturbative approaches for spin-orbit coupling and exclude a substantial part of the atomic transitions in the

f

and

d

shells. Here, we demonstrate the importance of proper relativistic treatment of the

f

and

d

shells in Yb-containing diatomics and the inclusion of the

f\ensuremath{\rightarrow}d

transition to obtain accurate spectra of

{\mathrm{YbLi}}^{+}

. We focus on state-of-the-art relativistic many-body calculations for the Yb atom's ground and excited states and the

{\mathrm{YbLi}}^{+}

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}

S

{}^{+}

ion and the Ba atom in the ground

{}^{1}

S

state or the lowest singlet or triplet

d

excited states, and for the singlet and triplet states dissociating into the ground-state

{}^{2}

S

Rb atom and the ground-state

{}^{2}

S

{}^{+}

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.

X

(

X=\mathrm{Be}

, Mg, Ca, Sr, Ba), and chromium--ytterbium, CrYb, molecules in the Born-Oppenheimer approximation for the high-spin ${X}^{7}{\ensuremath{\Sigma}}^{+}$ 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 Douglas-Kroll-Hess Hamiltonian or 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 the atoms at large interatomic distances

{C}_{6}

are also reported. The molecules under investigation are examples of species possessing both large magnetic and electric dipole moments making them potentially interesting candidates for ultracold many-body physics studies.

{\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.

m

scheme, which will permit the treatment of doubly open-shell nuclei via the further breaking of SU(2) symmetry associated with angular momentum conservation.Results: Proof-of-principle calculations in an

{N}_{\text{max}}=6

spherical harmonic oscillator basis for

^{16,18}\mathrm{O}

and

^{18}\mathrm{Ne}

in the BCCD approximation are in good agreement with standard coupled cluster results with the same chiral two-nucleon interaction, while

^{20}\mathrm{O}

and

^{20}\mathrm{Mg}

display underbinding relative to experiment. The breaking of U(1) symmetry, monitored by computing the variance associated with the particle-number operator, is relatively constant for all five nuclei, in both the Hartree-Fock-Bogoliubov and BCCD approximations.Conclusions: The newly developed many-body formalism increases the potential span of ab initio calculations based on single-reference coupled cluster techniques tremendously, i.e., potentially to reach several hundred additional midmass nuclei. The new formalism offers a wealth of potential applications and further extensions dedicated to the description of ground and excited states of open-shell nuclei. Short-term goals include the implementation of three-nucleon forces at the normal-ordered two-body level. Midterm extensions include the approximate treatment of triples corrections and the development of the equation-of-motion methodology to treat both excited states and odd nuclei. Long-term extensions include exact restoration of U(1) and SU(2) symmetries.

^{174}\mathrm{Yb}_{2}

dimer is accounted for by representing the global ab initio--based Born-Oppenheimer potential with the model semianalytical function containing the scale and shift parameters. The results support the previous evaluation of the Yb dimer potentials from the photoassociation spectroscopy data and provide an accurate and flexible reference for future refinement of the constraints on short-range gravitylike forces by ultracold atomic spectroscopy.