Geometric Phase and Interference Effects
in Ultracold Chemical Reactions
N. Balakrishnan and B. K. Kendrick
Abstract Electronically non-adiabatic effects play an important role in many chemical reactions and light induced processes. Non-adiabatic effects are important, when
there is an electronic degeneracy for certain nuclear geometries leading to a conical intersection between two adiabatic Born-Oppenheimer electronic states. The
geometric phase effect arises from the sign change of the adiabatic electronic wave
function as it encircles the conical intersection between two electronic states (e.g.,
a ground state and an excited electronic state). This sign change requires a corresponding sign change on the nuclear motion wave function to keep the overall wave
function single-valued. Its effect on bimolecular chemical reaction dynamics remains
a topic of active experimental and theoretical interrogations. However, most prior
studies have focused on high collision energies where many angular momentum partial waves contribute and the effect vanishes under partial wave summation. Here,
we examine the geometric phase effect in cold and ultracold collisions where a single partial wave, usually the s-wave, dominates. It is shown that unique properties of
ultracold collisions, including isotropic scattering and an effective quantization of the
scattering phase shift, lead to large geometric phase effects in state-to-state reaction
rate coefficients. Illustrative results are presented for the hydrogen exchange reaction
in the fundamental H+H 2 system and its isotopic counterparts.
Keywords Geometric phase ⋅ Ultracold molecules ⋅ Ultracold chemistry
Ultracold collisions
N. Balakrishnan ( ✉ )
Department of Chemistry, University of Nevada, Las Vegas, NV 89154, USA
e-mail: naduvala@unlv.nevada.edu
B. K. Kendrick
Los Alamos National Laboratory, Theoretical Division (T-1, MS B221),
Los Alamos, NM 87545, USA
© Springer International Publishing AG, part of Springer Nature 2018
Y. A. Wang et al. (eds.), Concepts, Methods and Applications of Quantum Systems
in Chemistry and Physics, Progress in Theoretical Chemistry and Physics 31,
https://doi.org/10.1007/978-3-319-74582-4_15
265
in Ultracold Chemical Reactions
N. Balakrishnan and B. K. Kendrick
Abstract Electronically non-adiabatic effects play an important role in many chemical reactions and light induced processes. Non-adiabatic effects are important, when
there is an electronic degeneracy for certain nuclear geometries leading to a conical intersection between two adiabatic Born-Oppenheimer electronic states. The
geometric phase effect arises from the sign change of the adiabatic electronic wave
function as it encircles the conical intersection between two electronic states (e.g.,
a ground state and an excited electronic state). This sign change requires a corresponding sign change on the nuclear motion wave function to keep the overall wave
function single-valued. Its effect on bimolecular chemical reaction dynamics remains
a topic of active experimental and theoretical interrogations. However, most prior
studies have focused on high collision energies where many angular momentum partial waves contribute and the effect vanishes under partial wave summation. Here,
we examine the geometric phase effect in cold and ultracold collisions where a single partial wave, usually the s-wave, dominates. It is shown that unique properties of
ultracold collisions, including isotropic scattering and an effective quantization of the
scattering phase shift, lead to large geometric phase effects in state-to-state reaction
rate coefficients. Illustrative results are presented for the hydrogen exchange reaction
in the fundamental H+H 2 system and its isotopic counterparts.
Keywords Geometric phase ⋅ Ultracold molecules ⋅ Ultracold chemistry
Ultracold collisions
N. Balakrishnan ( ✉ )
Department of Chemistry, University of Nevada, Las Vegas, NV 89154, USA
e-mail: naduvala@unlv.nevada.edu
B. K. Kendrick
Los Alamos National Laboratory, Theoretical Division (T-1, MS B221),
Los Alamos, NM 87545, USA
© Springer International Publishing AG, part of Springer Nature 2018
Y. A. Wang et al. (eds.), Concepts, Methods and Applications of Quantum Systems
in Chemistry and Physics, Progress in Theoretical Chemistry and Physics 31,
https://doi.org/10.1007/978-3-319-74582-4_15
265