Figure 2 - State-to-state reaction rate coefficients of the LiYb+Li reaction to form Yb and a Li dimer in vibrational state v.

Figure 1. Ab-initio three-body interaction potential surface of LiYbLi.

We explore the reactivity of small alkali-metal and alkaline-earth molecules at cold and ultracold temperatures, where the molecules are assumed to be in their lowest ro-vibrational state.

Computations involve the determination and analytic fitting of the three-dimen-sional potential energy surface (PES) for the ground-state system. We compute multi-dimensional potential surfaces by solving the Schrodinger equation for the electronic motion with the nuclei held in fixed positions. Such calculations are computationally expensive as the energies of many molecular geometries are needed. We use the ab initio coupled-cluster method with single, double, and perturbative triple excitations (CCSD(T)) of the chemistry package CFOUR. As an example, a cut through our three-dimensional PES for Li-Yb-Li as a function of the LiYb and Li2 bond lengths with the atoms restricted to a linear geometry is shown in Figure 1.

We have also performed quantum dynamics calculations using the PES. They were done at three levels of complexity. These are an exact quantum mechanics calculation (EQM) within a close-coupling scheme, a statistical quantum method (SQM), and an ``universal'' QDT model. We showed that the two simplified SQM and QDT models yield zero-temperature reaction rate coefficients that are in reasonable agreement with the full EQM close-coupling calculations. Moreover, the effect of the three-body term in the PES was explored by comparing quantum dynamics results using a pairwise potential that neglects the three-body term to that derived from the full interaction potential. Inclusion of the three-body term reduced the zero-temperature rate coefficients by a factor of two.

## Ultracold Chemical Reactions and Conical Intersections

The exact quantum dynamics method allowed us to study state-to-state reaction rates and, in particular, the distribution over the vibrational and rotational levels of the product molecule. Figure 2 plots the total three-atomic angular momentum J=0 rate coefficients to form Li2 vibrational states (summed over all open rotational states) as a function of collision energy. Vibrational levels as high as v=19 of the product molecule can be produced in the limit of zero collision energy between ground-state LiYb and Li. This product vibrational distribution is sensitive to the inclusion of three-body forces in the interaction potential.

Read more: Phys. Rev. A 91, 012708 (2015).

Conical intersections between molecular electronic potential surfaces can greatly affect molecular dyna-mics and chemical properties. The different condi-tions under which they occur have been extensively reviewed in the literature. These studies, however, were mostly restricted to temperatures above 1 K, where typically many angular momenta or partial waves contribute to the overall reaction outcome.

Recently has it become possible to investigate che-mical reactions between small molecules at tem-peratures well below 1 mK, where quantum effects and threshold phenomena begin to dominate col-lisions.

Figure 3. Effect of conical intersection on the ultra cold reaction dynamics.

The goal of our study is to develop theoretical models of and practical applications for conical intersections with their geometric pha-ses to ultracold chemical reactions with molecules confined in optical potentials. We focus on heteronuclear polar molecules that are laser cooled to mK or nK temperatures. These are primarily ground-state alkali-metal molecules that can collide with each other or with their constituent atoms and undergo chemical reactions. Earlier it was proven that symmetry-required conical intersections exist in electronic states of all alkali-metal trimers and tetramers. We investigate non-adiabatic nuclear reaction dynamics of intermediate trimer and tetramer complexes in collisions between ultracold, laser-cooled and trapped heteronuclear molecules.