Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2506.16897 · Physical Review A

CaF + CaF interactions in the ground and excited electronic states: Implications for collisional losses

Dibyendu Sardar, Marcin Gronowski, Michał Tomza, John L. Bohn

Published Sep 22, 2025• 1 citation
arXivHTMLPDF

Abstract

Accurate ab initio potential energy surfaces are essential to understand and predict collisional outcomes in ultracold molecular systems. In this study, we explore the intermolecular interactions between two laser-cooled CaF molecules, in both their ground and excited electronic states, aiming to understand the mechanisms behind the observed collisional losses on the nonreactive, spin-polarized surface of the $\mathrm{CaF}+\mathrm{CaF}$ system. Using state-of-the-art ab initio methods, we compute 12 electronic states of the ${\mathrm{Ca}}_{2}{\mathrm{F}}_{2}$ complex within the rigid rotor approximation applied to CaF. Calculating the potential energy surfaces for the excited electronic states of ${\mathrm{Ca}}_{2}{\mathrm{F}}_{2}$ is challenging and computationally expensive. Our approach employs the multireference configuration interaction method, restricted to single and double excitations, along with a reasonably large active space to ensure the convergence in the excited states. We also compute the spin-orbit coupling between the ground state and the lowest spin-polarized triplet state, as well as the spin-spin coupling within the lowest triplet state (1) $^{3}{\mathrm{A}}^{\ensuremath{'}}$. Additionally, we determine the electric transition dipole moments for the (1) $^{3}{\mathrm{A}}^{\ensuremath{'}}$--(2) $^{3}{\mathrm{A}}^{\ensuremath{'}}$ and (1) $^{3}{\mathrm{A}}^{\ensuremath{'}}$--(1) $^{3}{\mathrm{A}}^{\ensuremath{''}}$ transitions. Notably, we find that the lowest spin-polarized state (1) $^{3}{\mathrm{A}}^{\ensuremath{'}}$, shifted by 1064 nm of laser light from the optical dipole trap, intersects several electronically excited states. Finally, by analyzing the potential energy surfaces, we discuss two plausible pathways that may account for the observed collisional losses on the spin-polarized surface of the $\mathrm{CaF}+\mathrm{CaF}$ system.

DOI
10.1103/f2gg-mdgy

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.

arXiv:1008.0840•Physical Review A•Mar 31, 2011•60 citations

Ab Initio Study of Chemical Reactions of Cold SrF and CaF Molecules with Alkali-Metal and Alkaline-Earth-Metal Atoms: The Implications for Sympathetic Cooling

Maciej B. Kosicki, Dariusz Kędziera, Piotr Szymon Żuchowski

We investigate the energetics of the atom exchange reaction in the SrF + alkali-metal atom and CaF + alkali-metal atom systems. Such reactions are possible only for collisions of SrF and CaF with the lithium atoms, while they are energetically forbidden for other alkali-metal atoms. Specifically, we focus on SrF interacting with Li, Rb, and Sr atoms and use ab initio methods to demonstrate that the SrF + Li and SrF + Sr reactions are barrierless. We present potential energy surfaces for the interaction of the SrF molecule with the Li, Rb, and Sr atoms in their energetically lowest-lying electronic spin states. The obtained potential energy surfaces are deep and exhibit profound interaction anisotropies. We predict that the collisions of SrF molecules in the rotational or Zeeman excited states most likely have a strong inelastic character. We discuss the prospects for the sympathetic cooling of SrF and CaF molecules using ultracold alkali-metal atoms.

arXiv:1703.07192•The Journal of Physical Chemistry A•May 1, 2017•17 citations

Cold collisions of ground-state calcium atoms in a laser field: A theoretical study

Béatrice Bussery‐Honvault, Jean–Michel Launay, Robert Moszyński

State-of-the-art ab initio techniques have been applied to compute the potential-energy curves for the ground $X{}^{1}{\ensuremath{\Sigma}}_{g}^{+}$ and excited ${}^{1}{\ensuremath{\Pi}}_{g}(4s3d)$ states of the calcium dimer in the Born-Oppenheimer approximation. The weakly bound ground state was calculated by symmetry-adapted perturbation theory, while the strongly bound excited state was computed using a combination of the linear-response theory within the coupled-cluster singles and doubles framework for the core-valence electronic correlation and of the full configuration interaction for the valence-valence correlation. The ground-state potential has been corrected by considering the relativistic terms resulting from the first-order many-electron Breit theory, and the retardation corrections. The magnetic electronic transition dipole moment governing the ${}^{1}{\ensuremath{\Pi}}_{g}{\ensuremath{\leftarrow}}^{1}{\ensuremath{\Sigma}}_{g}^{+}$ transitions has been obtained as the first residue of the polarization propagator computed with the coupled-cluster method restricted to single and double excitations. The computed energies and transition moments have been analytically fitted and used in the dynamical calculations of the rovibrational energy levels, ground-state scattering length, photoassociation intensities at ultralow temperatures, and spontaneous emission coefficients from the ${}^{1}{\ensuremath{\Pi}}_{g}(4s3d)$ to the $X{}^{1}{\ensuremath{\Sigma}}_{g}^{+}$ state. The spectroscopic constants of the theoretical ground-state potential are in a good agreement with the experimental values derived from the Fourier-transform spectra [O. Allard et al., Eur. Phys. J. D (to be published)]. The theoretical s-wave scattering length for the ground state is $a=44\mathrm{bohrs},$ suggesting that it should be possible to obtain a stable Bose-Einstein condensate of calcium atoms. Finally, the computed photoassociation intensities and spontaneous emission coefficients suggest that it should be possible to obtain cold calcium molecules by photoassociation of cold atoms to the first ${}^{1}{\ensuremath{\Pi}}_{g}$ state followed by a spontaneous emission to the ground state.

Physical Review A•Sep 23, 2003•51 citations

Collisions of ultracold molecules in bright and dark optical dipole traps

Roman Bause, Andreas Schindewolf, Renhao Tao +7 more

Understanding collisions between ultracold molecules is crucial for making stable molecular quantum gases and harnessing their rich internal degrees of freedom for quantum engineering. Transient complexes can strongly influence collisional physics, but in the ultracold regime, key aspects of their behavior have remained unknown. To explain experimentally observed loss of ground-state molecules from optical dipole traps, it was recently proposed that molecular complexes can be lost due to photoexcitation. By trapping molecules in a repulsive box potential using laser light near a narrow molecular transition, we are able to test this hypothesis with light intensities three orders of magnitude lower than what is typical in red-detuned dipole traps. This allows us to investigate light-induced collisional loss in a gas of nonreactive fermionic $^{23}\mathrm{Na}^{40}\mathrm{K}$ molecules. Even for the lowest intensities available in our experiment, our results are consistent with universal loss, meaning unit loss probability inside the short-range interaction potential. Our findings disagree by at least two orders of magnitude with latest theoretical predictions, showing that crucial aspects of molecular collisions are not yet understood and provide a benchmark for the development of new theories.

arXiv:2103.00889•Physical Review Research•Jul 2, 2021•89 citations

Formation of ultracold SrYb molecules in an optical lattice by photoassociation spectroscopy: theoretical prospects

Michał Tomza, Filip Pawłowski, Małgorzata Jeziorska +2 more

State-of-the-art ab initio techniques have been applied to compute the potential energy curves for the SrYb molecule in the Born-Oppenheimer approximation for the electronic ground state and the first fifteen excited singlet and triplet states. All the excited state potential energy curves were computed using the equation of motion approach within the coupled-cluster singles and doubles framework and large basis-sets, while the ground state potential was computed using the coupled cluster method with single, double, and noniterative triple excitations. The leading long-range coefficients describing the dispersion interactions at large interatomic distances are also reported. The electric transition dipole moments 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. 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. The electronic structure data were employed to investigate the possibility of forming deeply bound ultracold SrYb molecules in an optical lattice in a photoassociation experiment using continuous-wave lasers. Photoassociation near the intercombination line transition of atomic strontium into the vibrational levels of the strongly spin-orbit mixed b(3)Σ(+), a(3)Π, A(1)Π, and C(1)Π states with subsequent efficient stabilization into the v'' = 1 vibrational level of the electronic ground state is proposed. Ground state SrYb molecules can be accumulated by making use of collisional decay from v'' = 1 to v'' = 0. Alternatively, photoassociation and stabilization to v'' = 0 can proceed via stimulated Raman adiabatic passage provided that the trapping frequency of the optical lattice is large enough and phase coherence between the pulses can be maintained over at least tens of microseconds.

arXiv:1104.3015•Physical Chemistry Chemical Physics•Jan 1, 2011•41 citations

Interactions and Cold Collisions of AlF in the Ground and Excited Electronic States with He

Sangami Ganesan-Santhi, Matthew D. Frye, Marcin Gronowski +1 more

High Resolution Image Download MS PowerPoint Slide Aluminum monofluoride (AlF) is a promising candidate for laser cooling and the production of dense ultracold molecular gases, thanks to its relatively high chemical stability and diagonal Franck–Condon factors. In this study, we examine the interactions and collisions of AlF in its X 1 Σ +, a 3 Π, and A 1 Π electronic states with ground-state He using state-of-the-art ab initio quantum chemistry techniques. We construct accurate potential energy surfaces (PESs) employing either the explicitly correlated coupled-cluster CCSD(T)-F12 method augmented by the CCSDT correction or the multireference configuration-interaction method for higher-excited electronic states. Subsequently, we employ these PESs in coupled-channel calculations to determine the scattering cross sections for AlF + He collisions and bound states of the complex. We estimate the uncertainty of the calculated PESs and apply it to assess the uncertainty of the scattering results. We find a relatively low sensitivity of the cross sections to the variation of the PESs, but the positions of shape resonances remain uncertain. The present results are relevant for further improvements and optimizations of buffer-gas cooling of AlF molecules.

arXiv:2405.03276•The Journal of Physical Chemistry A•Sep 2, 2025•1 citation
Accurate ab initio potential energy surfaces are essential to understand and predict collisional outcomes in ultracold molecular systems. In this study, we explore the intermolecular interactions between two laser-cooled CaF molecules, in both their ground and excited electronic states, aiming to understand the mechanisms behind the observed collisional losses on the nonreactive, spin-polarized surface of the CaF+CaF\mathrm{CaF}+\mathrm{CaF}CaF+CaF system. Using state-of-the-art ab initio methods, we compute 12 electronic states of the Ca2F2{\mathrm{Ca}}_{2}{\mathrm{F}}_{2}Ca2​F2​ complex within the rigid rotor approximation applied to CaF. Calculating the potential energy surfaces for the excited electronic states of Ca2F2{\mathrm{Ca}}_{2}{\mathrm{F}}_{2}Ca2​F2​ is challenging and computationally expensive. Our approach employs the multireference configuration interaction method, restricted to single and double excitations, along with a reasonably large active space to ensure the convergence in the excited states. We also compute the spin-orbit coupling between the ground state and the lowest spin-polarized triplet state, as well as the spin-spin coupling within the lowest triplet state (1) 3A\ensuremath′^{3}{\mathrm{A}}^{\ensuremath{'}}3A\ensuremath′. Additionally, we determine the electric transition dipole moments for the (1) 3A\ensuremath′^{3}{\mathrm{A}}^{\ensuremath{'}}3A\ensuremath′--(2) 3A\ensuremath′^{3}{\mathrm{A}}^{\ensuremath{'}}3A\ensuremath′ and (1) 3A\ensuremath′^{3}{\mathrm{A}}^{\ensuremath{'}}3A\ensuremath′--(1) 3A\ensuremath′′^{3}{\mathrm{A}}^{\ensuremath{''}}3A\ensuremath′′ transitions. Notably, we find that the lowest spin-polarized state (1) 3A\ensuremath′^{3}{\mathrm{A}}^{\ensuremath{'}}3A\ensuremath′, shifted by 1064 nm of laser light from the optical dipole trap, intersects several electronically excited states. Finally, by analyzing the potential energy surfaces, we discuss two plausible pathways that may account for the observed collisional losses on the spin-polarized surface of the CaF+CaF\mathrm{CaF}+\mathrm{CaF}CaF+CaF system.
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.
We investigate the energetics of the atom exchange reaction in the SrF + alkali-metal atom and CaF + alkali-metal atom systems. Such reactions are possible only for collisions of SrF and CaF with the lithium atoms, while they are energetically forbidden for other alkali-metal atoms. Specifically, we focus on SrF interacting with Li, Rb, and Sr atoms and use ab initio methods to demonstrate that the SrF + Li and SrF + Sr reactions are barrierless. We present potential energy surfaces for the interaction of the SrF molecule with the Li, Rb, and Sr atoms in their energetically lowest-lying electronic spin states. The obtained potential energy surfaces are deep and exhibit profound interaction anisotropies. We predict that the collisions of SrF molecules in the rotational or Zeeman excited states most likely have a strong inelastic character. We discuss the prospects for the sympathetic cooling of SrF and CaF molecules using ultracold alkali-metal atoms.
State-of-the-art ab initio techniques have been applied to compute the potential-energy curves for the ground $X{}^{1}{\ensuremath{\Sigma}}_{g}^{+}$ and excited ${}^{1}{\ensuremath{\Pi}}_{g}(4s3d)$ states of the calcium dimer in the Born-Oppenheimer approximation. The weakly bound ground state was calculated by symmetry-adapted perturbation theory, while the strongly bound excited state was computed using a combination of the linear-response theory within the coupled-cluster singles and doubles framework for the core-valence electronic correlation and of the full configuration interaction for the valence-valence correlation. The ground-state potential has been corrected by considering the relativistic terms resulting from the first-order many-electron Breit theory, and the retardation corrections. The magnetic electronic transition dipole moment governing the ${}^{1}{\ensuremath{\Pi}}_{g}{\ensuremath{\leftarrow}}^{1}{\ensuremath{\Sigma}}_{g}^{+}$ transitions has been obtained as the first residue of the polarization propagator computed with the coupled-cluster method restricted to single and double excitations. The computed energies and transition moments have been analytically fitted and used in the dynamical calculations of the rovibrational energy levels, ground-state scattering length, photoassociation intensities at ultralow temperatures, and spontaneous emission coefficients from the ${}^{1}{\ensuremath{\Pi}}_{g}(4s3d)$ to the $X{}^{1}{\ensuremath{\Sigma}}_{g}^{+}$ state. The spectroscopic constants of the theoretical ground-state potential are in a good agreement with the experimental values derived from the Fourier-transform spectra [O. Allard et al., Eur. Phys. J. D (to be published)]. The theoretical s-wave scattering length for the ground state is a=44bohrs,a=44\mathrm{bohrs},a=44bohrs, suggesting that it should be possible to obtain a stable Bose-Einstein condensate of calcium atoms. Finally, the computed photoassociation intensities and spontaneous emission coefficients suggest that it should be possible to obtain cold calcium molecules by photoassociation of cold atoms to the first ${}^{1}{\ensuremath{\Pi}}_{g}$ state followed by a spontaneous emission to the ground state.
Understanding collisions between ultracold molecules is crucial for making stable molecular quantum gases and harnessing their rich internal degrees of freedom for quantum engineering. Transient complexes can strongly influence collisional physics, but in the ultracold regime, key aspects of their behavior have remained unknown. To explain experimentally observed loss of ground-state molecules from optical dipole traps, it was recently proposed that molecular complexes can be lost due to photoexcitation. By trapping molecules in a repulsive box potential using laser light near a narrow molecular transition, we are able to test this hypothesis with light intensities three orders of magnitude lower than what is typical in red-detuned dipole traps. This allows us to investigate light-induced collisional loss in a gas of nonreactive fermionic 23Na40K^{23}\mathrm{Na}^{40}\mathrm{K}23Na40K molecules. Even for the lowest intensities available in our experiment, our results are consistent with universal loss, meaning unit loss probability inside the short-range interaction potential. Our findings disagree by at least two orders of magnitude with latest theoretical predictions, showing that crucial aspects of molecular collisions are not yet understood and provide a benchmark for the development of new theories.
State-of-the-art ab initio techniques have been applied to compute the potential energy curves for the SrYb molecule in the Born-Oppenheimer approximation for the electronic ground state and the first fifteen excited singlet and triplet states. All the excited state potential energy curves were computed using the equation of motion approach within the coupled-cluster singles and doubles framework and large basis-sets, while the ground state potential was computed using the coupled cluster method with single, double, and noniterative triple excitations. The leading long-range coefficients describing the dispersion interactions at large interatomic distances are also reported. The electric transition dipole moments 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. 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. The electronic structure data were employed to investigate the possibility of forming deeply bound ultracold SrYb molecules in an optical lattice in a photoassociation experiment using continuous-wave lasers. Photoassociation near the intercombination line transition of atomic strontium into the vibrational levels of the strongly spin-orbit mixed b(3)Σ(+), a(3)Π, A(1)Π, and C(1)Π states with subsequent efficient stabilization into the v'' = 1 vibrational level of the electronic ground state is proposed. Ground state SrYb molecules can be accumulated by making use of collisional decay from v'' = 1 to v'' = 0. Alternatively, photoassociation and stabilization to v'' = 0 can proceed via stimulated Raman adiabatic passage provided that the trapping frequency of the optical lattice is large enough and phase coherence between the pulses can be maintained over at least tens of microseconds.
High Resolution Image Download MS PowerPoint Slide Aluminum monofluoride (AlF) is a promising candidate for laser cooling and the production of dense ultracold molecular gases, thanks to its relatively high chemical stability and diagonal Franck–Condon factors. In this study, we examine the interactions and collisions of AlF in its X 1 Σ +, a 3 Π, and A 1 Π electronic states with ground-state He using state-of-the-art ab initio quantum chemistry techniques. We construct accurate potential energy surfaces (PESs) employing either the explicitly correlated coupled-cluster CCSD(T)-F12 method augmented by the CCSDT correction or the multireference configuration-interaction method for higher-excited electronic states. Subsequently, we employ these PESs in coupled-channel calculations to determine the scattering cross sections for AlF + He collisions and bound states of the complex. We estimate the uncertainty of the calculated PESs and apply it to assess the uncertainty of the scattering results. We find a relatively low sensitivity of the cross sections to the variation of the PESs, but the positions of shape resonances remain uncertain. The present results are relevant for further improvements and optimizations of buffer-gas cooling of AlF molecules.