High Resolution Image Download MS PowerPoint Slide Long-range intermolecular interaction plays an essential role in (ultra)cold collisions. For monomers with degenerate electronic states, an accurate description of the long-range interaction can be challenging due to the potential breakdown of the Born–Oppenheimer approximation. In this work, we developed a general method to construct long-range interaction potential energy surfaces (IPESs) between arbitrary molecules using the degenerate perturbation theory of Schrödinger. To further simplify the application of this method, a group-theoretical method is introduced to identify nonzero components of electrostatic properties of monomers, especially for the nonlinear molecules. To demonstrate this approach, we report the long-range IPESs of the O( 3 P)–OH( 2 Π) and OH( 2 Π)–OH( 2 Π) systems. The excellent agreement with ab initio calculations in large separations, even near electronic degeneracies, confirms the accuracy of our approach. The method is expected to lay the groundwork for the accurate investigation of (ultra)cold collisional dynamics involving open-shell species.
High Resolution Image Download MS PowerPoint Slide Long-range intermolecular interaction plays an essential role in (ultra)cold collisions. For monomers with degenerate electronic states, an accurate description of the long-range interaction can be challenging due to the potential breakdown of the Born–Oppenheimer approximation. In this work, we developed a general method to construct long-range interaction potential energy surfaces (IPESs) between arbitrary molecules using the degenerate perturbation theory of Schrödinger. To further simplify the application of this method, a group-theoretical method is introduced to identify nonzero components of electrostatic properties of monomers, especially for the nonlinear molecules. To demonstrate this approach, we report the long-range IPESs of the O( 3 P)–OH( 2 Π) and OH( 2 Π)–OH( 2 Π) systems. The excellent agreement with ab initio calculations in large separations, even near electronic degeneracies, confirms the accuracy of our approach. The method is expected to lay the groundwork for the accurate investigation of (ultra)cold collisional dynamics involving open-shell species.
We present the basic ideas about the broad topic of molecular interactions in the context of low-energy collisions. We start by introducing the concept of the interaction energy and the crucial approximation behind it—the Born–Oppenheimer approximation. Next, we focus on understanding of molecular interactions within the framework of the perturbation theory. We discuss the essentials of symmetry-adapted perturbation theory (SAPT) which provides partitioning of the interaction energy into physically meaningful components, such as electrostatic, dispersion, induction, and exchange interactions. We examine the role of these components and how they can be calculated. We also discuss the supermolecular approach to calculation of the interaction energy with various quantum chemistry methods. We indicate potential pitfalls of the latter approach and give recommendations on how to alleviate them. To illustrate the theory presented in this chapter, we provide a detailed discussion of interactions within several systems of relevance in cold chemistry and cold collisions: He-NH(3Σ−), N-NH, He-OH(2Π), NH-NH, O2(3Σ−g)-O2. The calculations of collision rates and scattering cross-sections impose stringent requirements on the accuracy of the potential energy surfaces. To address the issue, we present the analysis of the scattering length dependence upon the potential scaling. Finally, we indicate trends in calculations of intermolecular forces stimulated by the state-of-the-art cold chemistry experiments.
Theory of long-range interactions between an atom in its ground S state and a linear molecule in a degenerate state with a nonzero projection of the electronic orbital angular momentum is presented. It is shown how the long-range coefficients can be related to the first and second-order molecular properties. The expressions for the long-range coefficients are written in terms of all components of the static and dynamic multipole polarizability tensor, including the nondiagonal terms connecting states with the opposite projection of the electronic orbital angular momentum. It is also shown that for the interactions of molecules in excited states that are connected to the ground state by multipolar transition moments additional terms in the long-range induction energy appear. All these theoretical developments are illustrated with the numerical results for systems of interest for the sympathetic cooling experiments: interactions of the ground state Rb((2)S) atom with CO((3)Π), OH((2)Π), NH((1)Δ), and CH((2)Π) and of the ground state Li((2)S) atom with CH((2)Π).
The interaction of a Rydberg electron with a ground-state atom is modeled using the Fermi approximation to obtain long-range potentials for various excited diatomic molecules. Particular attention is paid to cases of degenerate and near-degenerate atomic Rydberg levels. Extensive comparisons are performed with recent ab initio calculations for ${}^{1}{\ensuremath{\Sigma}}^{+}$ and ${}^{3}{\ensuremath{\Sigma}}^{+}$ states of LiH and H2, also ${}^{2}{\ensuremath{\Sigma}}^{+}$ states of LiHe, for up to the ninth state of a specified symmetry. Results for LiNe are also discussed. Overall, good qualitative and in some cases quantitative agreement is found. For isolated states, the undulations in the potentials clearly reflect the nodal pattern of the Rydberg state involved and the magnitude is fixed in the Fermi approach by the electron-ground-state atom scattering length. When several states are close in energy, in the Fermi model because of the factorizable nature of the interaction, only a single nonzero potential emerges from the remaining flat manifold. Such behavior explains, for example, the presence of high barriers at large distances seen in ab initio calculations for the ${}^{1,3}{\ensuremath{\Sigma}}_{g,u}^{+}$ n=3 states of molecular hydrogen. For the systems involving H the Fermi results are generally better for the weaker, triplet, interactions than the singlets. In the case of near-degenerate levels the weaker interactions are normally described better than the stronger interaction, where avoided crossings (not included in this simple model) may be important. In LiHe, where the interactions are weaker, generally for separations larger than about 10a0 the Fermi model obtains barrier positions within 1a0 and maxima within 10 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$. For LiNe, because of the very small scattering length for electrons in neon, largely qualitative results are obtained. The Fermi model is also shown to yield a physically sound diabatic approach for excited states of diatomic molecules, allowing for a deeper understanding of the unusual shapes of the adiabatic curves. Limitations of the Fermi model are also discussed.
High Resolution Image Download MS PowerPoint Slide High-quality potential energy surfaces (PESs) are prerequisites for quantitative atomistic simulations with both quantum and classical dynamics approaches. The ultimate test for the validity of a PES entails comparisons with judiciously chosen experimental observables. Here we ask whether cold collision measurements are sufficiently informative to validate and distinguish between high-level, state-of-the art PESs for the strongly interacting Ne–H 2 + system. We show that measurement of the final state distributions for a process that involves several metastable intermediate states is sufficient to identify the PES that captures the long-range interactions properly. Furthermore, we show that a modest increase in the experimental energy resolution will allow for resolving individual Feshbach resonances and enable a quantitative probe of the interactions in the short and intermediate ranges.
The term long-range interactions refers to electrostatic and magnetostatic potential energies between atoms and molecules with mutual distances ranging from a few tens to a few hundreds of Bohr radii. The energies involved are much smaller than the usual chemical bond energies. However, they are comparable with the typical kinetic energies of particles in an ultracold gas (T ≪ 1 K), so that the long-range interactions play a central role in its dynamics. The progress of research devoted to ultracold gases sheds a new light on the well-established topic of long-range interactions, because (i) the interacting atoms and molecules can be prepared in a well-defined quantum (electronic, vibrational, rotational, fine or hyperfine), ground or excited level; and (ii) long-range interactions can be tailored at will using external electromagnetic fields. In this chapter, we present the essential concepts and mathematical relations to calculate long-range potential energies. We start by deriving the multipolar expansion of the electrostatic interaction energy between classical charge distributions, both in Cartesian coordinates for pedagogical purpose, and in spherical coordinates for practical use. Then we combine multipolar expansion and quantum perturbation theory, to obtain the general first- and second-order energy corrections, including the well-known van der Waals energy. We consider two central examples in the current context of ultracold gases: (i) a pair of alkali metal atoms and (ii) a pair of alkali metal heteronuclear diatomic molecules in the presence of an electric field. We highlight the key role of the total angular momenta of the interacting particles and of the complex, irrespective of their electronic or nuclear, orbital or spin nature.
Divalent atoms have emerged as powerful alternatives to alkalis in ultracold atom platforms, offering unique advantages arising from their two-electron structure. Among these species, ytterbium (Yb) is especially promising, yet its anionic properties and its Rydberg spectrum remain comparatively unexplored. In this work, we perform a first and comprehensive experimental and theoretical investigation of ultralong-range Rydberg molecules (ULRMs) of 174Yb in 6sns1S0 Rydberg states across nearly two decades in principal quantum number n and three orders of magnitude in molecular binding energy. Using the Coulomb Green's function formalism, we compute Born-Oppenheimer molecular potentials describing the Rydberg atom in the presence of a ground-state perturber and achieve quantitative agreement with high-resolution molecular spectra. This enables the extraction of low-energy electron-Yb scattering phase shifts, including the zero-energy s-wave scattering length and the positions of two spin-orbit split p-wave shape resonances. Our results provide strong evidence that the Yb− anion exists only as a metastable resonance.% We additionally show the sensitivity of ULRM spectra to the atomic quantum defects, using this to determine the quantum defect of the 6s23f1F3 state. Together, these findings establish Yb ULRMs as a powerful probe of electron-Yb interactions and lay essential groundwork for future Rydberg experiments with divalent atoms.