A six-dimensional potential energy surface is constructed for the spin-polarized triplet state of CaF–CaF by ab initio calculations at the CCSD(T) level of theory, followed by Gaussian process interpolation. The potential is utilized to calculate the density of states for this bialkaline-earth-halogen system where we find the value 0.038 μK –1, implying a mean resonance spacing of 26 μK in the collision complex. This value implies an associated Rice–Ramsperger–Kassel–Marcus lifetime of 1.8 μs, thus predicting long-lived complexes in collisions at ultracold temperatures.
A six-dimensional potential energy surface is constructed for the spin-polarized triplet state of CaF–CaF by ab initio calculations at the CCSD(T) level of theory, followed by Gaussian process interpolation. The potential is utilized to calculate the density of states for this bialkaline-earth-halogen system where we find the value 0.038 μK –1, implying a mean resonance spacing of 26 μK in the collision complex. This value implies an associated Rice–Ramsperger–Kassel–Marcus lifetime of 1.8 μs, thus predicting long-lived complexes in collisions at ultracold temperatures.
We report on the sticking time of the AlF dimer in the ultracold regime. We employ a full-dimensional potential energy surface for AlF-AlF, constructed using a machine learning approach [X. Liu et al., J. Chem. Phys. 159, 144103 (2023)], to compute the density of states using a semiclassical counting method. Next, using the Rice-Ramsperger-Kassel-Marcus (RRKM) theory, we determine an RRKM sticking time of 216.0 $\ifmmode\pm\else\textpm\fi{}$ 4.8 ns, which is shorter than that of other previously reported nonreactive dimers. Then, based on the available potential energy surfaces and RRKM sticking time data for a few dimers, we observe that the RRKM sticking time correlates with the ratio of the dimer dissociation energy to the dissociation energy of its parent molecule. Thus, we propose this ratio as a parameter to estimate RRKM sticking times. Furthermore, using ab initio methods, we optimize and calculate the energies of the equilibrium geometries of AlCl-AlCl, CaH-CaH, and MgF-MgF, thereby determining the ratio of the dimer dissociation energy to the parent molecule dissociation energy. Based on this ratio, we propose a hierarchy to order the sticking lifetimes of those dimers in the ultracold regime.
We derive a quasiclassical expression for the density of states (DOS) of an arbitrary, ultracold, N-atom collision complex, for a general potential energy surface (PES). We establish the accuracy of our quasiclassical method by comparing to exact quantum results for the ${\mathrm{K}}_{2}\text{\ensuremath{-}}\mathrm{Rb}$ and NaK-NaK systems, with isotropic model PESs. Next, we calculate the DOS for an accurate NaK-NaK PES to be 0.124 $\ensuremath{\mu}{\mathrm{K}}^{\ensuremath{-}1}$, with an associated Rice-Ramsperger-Kassel-Marcus sticking time of 6.0 $\ensuremath{\mu}\mathrm{s}$. We extrapolate the DOS and sticking times to all other polar bialkali-bialkali collision complexes by scaling with atomic masses, equilibrium bond lengths, dissociation energies, and dispersion coefficients. The sticking times calculated here are two to three orders of magnitude shorter than those reported by Mayle et al. [Phys. Rev. A 85, 062712 (2012)]. We estimate dispersion coefficients and collision rates between molecules and complexes. We find that the sticking-amplified three-body loss mechanism is not likely the cause of the losses observed in the experiments.
The puzzle of "sticky collisions," in which molecular collision complexes exhibit unexpectedly long lifetimes, remains an unresolved mystery. A central challenge to solving this mystery is that traditional close-coupling calculations remain limited by the vast computational cost needed to take into account all the degrees of freedom involved in the collision. In this work, we propose a statistical model designed to simulate the result of full close-coupling calculations, with the goal of collecting statistics about reasonable lifetimes of collision complexes. To do so, we numerically sample resonances using random matrix theory and utilize results from quantum defect theory to calculate scattering properties and lifetimes. We find that in the limit of dense resonances, our theory agrees well with the Rice-Ramsperger-Kassel-Markus (RRKM) prediction, whereas in the limit of sparse resonances, the physics is governed by threshold behavior rather than resonant effects. By comparing these predictions to experimental results in two limits, we argue that close-coupling calculations alone may be insufficient to resolve the issue of long lifetimes.
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 system. Using state-of-the-art ab initio methods, we compute 12 electronic states of the Ca2F2 complex within the rigid rotor approximation applied to CaF. Calculating the potential energy surfaces for the excited electronic states of Ca2F2 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 CaF+CaF system.
A full six-dimensional Born-Oppenheimer singlet potential-energy surface is constructed for the reaction CaF + CaF $\ensuremath{\rightarrow}\phantom{\rule{4pt}{0ex}}{\mathrm{CaF}}_{2} +$ Ca using a multireference configuration-interaction electronic structure calculation. The ab initio data thus calculated are interpolated by Gaussian process regression. The four-body potential-energy surface features one D2h global minimum and one Cs local minimum, connected by a barrierless transition state that lends insight to the reaction mechanism. This surface is intended to be of use in understanding ultracold chemistry of CaF molecules.
We calculate permanent electric dipole moments (PDMs), as well as spontaneous and black body lifetimes, of alkaline-earth-metal--Li (AEM-Li) ultracold polar molecules to study anisotropic long-range dipole-dipole interactions in a single quantum state. We obtain potential energy curves for the ${}^{2}\phantom{\rule{-0.16em}{0ex}}\ensuremath{\Sigma}$ ground state of MgLi, CaLi, SrLi, and BaLi molecules at the coupled cluster singles and doubles with partial triples [CCSD(T)] level of electron correlation. Calculated spectroscopic constants for the isotopes: 24Mg7Li, 40Ca7Li, 88Sr7Li, and 138Ba7Li, show good agreement with available theoretical and experimental results. We obtain PDM curves using finite field perturbation theory at the CCSD(T) level. We find that AEM-Li molecules have moderate values of PDM at the equilibrium bond distance (MgLi: 0.90 D, CaLi: 1.15 D, SrLi: 0.33 D, and BaLi: --0.42 D) and hence might be suitable candidates for the proposed study in a single quantum state. Radiative lifetime calculations of the $\ensuremath{\nu}$ = 0 state (24Mg6Li: 22 s, 40Ca6Li: 39 s, 88Sr6Li: 380 s, and 138Ba6Li: 988 s) are found to be longer than the typical time scale associated with ultracold experiments with these molecules. The uncertainty in the lifetime calculations are estimated to be less than 10.