# Geometric Phase Effects in Ultracold Chemical Reactions

## Abstract

The role of the geometric phase effect in chemical reaction dynamics has long been a topic of active experimental and theoretical investigations. The topic has received renewed interest in recent years in cold and ultracold chemistry where it was shown to play a decisive role in state-to-state chemical dynamics. We provide a brief review of these developments focusing on recent studies of O + OH and hydrogen exchange in the H + H 2 and D + HD reactions at cold and ultracold temperatures. Non-adiabatic effects in ultracold chemical dynamics arising from the conical intersection between two electronic potential energy surfaces are also briefly discussed. By taking the hydrogen exchange reaction as an illustrative example it is shown that the inclusion of the geometric phase effect captures the essential features of non-adiabatic dynamics at collision energies below the conical intersection.

- Authors:

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA); USDOE Laboratory Directed Research and Development (LDRD) Program

- OSTI Identifier:
- 1530916

- Alternate Identifier(s):
- OSTI ID: 1570645

- Report Number(s):
- LA-UR-19-23245

Journal ID: ISSN 2218-2004; ATOMC5; PII: atoms7030065

- Grant/Contract Number:
- 20170221ER; 89233218CNA000001

- Resource Type:
- Published Article

- Journal Name:
- Atoms

- Additional Journal Information:
- Journal Name: Atoms Journal Volume: 7 Journal Issue: 3; Journal ID: ISSN 2218-2004

- Publisher:
- MDPI

- Country of Publication:
- Switzerland

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; ultracold molecules; ultracold chemistry; ultracold reactions; geometric phase effect; controlled chemistry

### Citation Formats

```
Kendrick, Brian K., and Balakrishnan, N. Geometric Phase Effects in Ultracold Chemical Reactions. Switzerland: N. p., 2019.
Web. doi:10.3390/atoms7030065.
```

```
Kendrick, Brian K., & Balakrishnan, N. Geometric Phase Effects in Ultracold Chemical Reactions. Switzerland. doi:10.3390/atoms7030065.
```

```
Kendrick, Brian K., and Balakrishnan, N. Wed .
"Geometric Phase Effects in Ultracold Chemical Reactions". Switzerland. doi:10.3390/atoms7030065.
```

```
@article{osti_1530916,
```

title = {Geometric Phase Effects in Ultracold Chemical Reactions},

author = {Kendrick, Brian K. and Balakrishnan, N.},

abstractNote = {The role of the geometric phase effect in chemical reaction dynamics has long been a topic of active experimental and theoretical investigations. The topic has received renewed interest in recent years in cold and ultracold chemistry where it was shown to play a decisive role in state-to-state chemical dynamics. We provide a brief review of these developments focusing on recent studies of O + OH and hydrogen exchange in the H + H 2 and D + HD reactions at cold and ultracold temperatures. Non-adiabatic effects in ultracold chemical dynamics arising from the conical intersection between two electronic potential energy surfaces are also briefly discussed. By taking the hydrogen exchange reaction as an illustrative example it is shown that the inclusion of the geometric phase effect captures the essential features of non-adiabatic dynamics at collision energies below the conical intersection.},

doi = {10.3390/atoms7030065},

journal = {Atoms},

number = 3,

volume = 7,

place = {Switzerland},

year = {2019},

month = {7}

}

DOI: 10.3390/atoms7030065

#### Figures / Tables:

Works referenced in this record:

##
Is the simplest chemical reaction really so simple?

journal, December 2013

- Jankunas, J.; Sneha, M.; Zare, R. N.
- Proceedings of the National Academy of Sciences, Vol. 111, Issue 1

##
Geometric phase effects in ultracold hydrogen exchange reaction

journal, September 2016

- Hazra, Jisha; Kendrick, Brian K.; Balakrishnan, N.
- Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 49, Issue 19

##
Multiple scattering mechanisms causing interference effects in the differential cross sections of H + D _{2} → HD( *v* ′ = 4, *j* ′) + D at 3.26 eV collision energy

journal, July 2016

- Sneha, Mahima; Gao, Hong; Zare, Richard N.
- The Journal of Chemical Physics, Vol. 145, Issue 2

##
Diabatic Definition of Geometric Phase Effects

journal, October 2016

- Izmaylov, Artur F.; Li, Jiaru; Joubert-Doriol, Loïc
- Journal of Chemical Theory and Computation, Vol. 12, Issue 11

##
Quantum reactive scattering calculations for the D+H2→HD+H reaction

journal, June 2003

- Kendrick, Brian K.
- The Journal of Chemical Physics, Vol. 118, Issue 23

##
Symmetry and the geometric phase in ultracold hydrogen-exchange reactions

journal, August 2017

- Croft, J. F. E.; Hazra, J.; Balakrishnan, N.
- The Journal of Chemical Physics, Vol. 147, Issue 7

##
Superposition of reactive and nonreactive scattering amplitudes in the presence of a conical intersection

journal, March 1980

- Mead, C. Alden
- The Journal of Chemical Physics, Vol. 72, Issue 6

##
The quantitative prediction and lifetime of a pronounced reactive scattering resonance

journal, July 1995

- Kuppermann, Aron; Wu, Yi-Shuen Mark
- Chemical Physics Letters, Vol. 241, Issue 3

##
Geometric phase effects in the H+D2→HD+D reaction

journal, April 2000

- Kendrick, Brian K.
- The Journal of Chemical Physics, Vol. 112, Issue 13

##
Geometric phase effects in the resonance spectrum, state-to-state transition probabilities and bound state spectrum of HO _{2}

journal, March 1997

- Kendrick, Brian; Pack, Russell T.
- The Journal of Chemical Physics, Vol. 106, Issue 9

##
The importance of the geometric phase effect for the H + D2 → HD + D reaction

journal, March 1995

- Wu, Yi-Shuen Mark; Kuppermann, Aron
- Chemical Physics Letters, Vol. 235, Issue 1-2

##
Complex scattering lengths in multi-channel atom–molecule collisions

journal, November 1997

- Balakrishnan, N.; Kharchenko, V.; Forrey, R. C.
- Chemical Physics Letters, Vol. 280, Issue 1-2

##
Reaction Product Imaging: The H + D2 Reaction

journal, June 1993

- Kitsopoulos, T. N.; Buntine, M. A.; Baldwin, D. P.
- Science, Vol. 260, Issue 5114

##
Geometric phase effects in H+O _{2} scattering. I. Surface function solutions in the presence of a conical intersection

journal, May 1996

- Kendrick, Brian; Pack, Russell T.
- The Journal of Chemical Physics, Vol. 104, Issue 19

##
Geometric phase effects in H+O _{2} scattering. II. Recombination resonances and state‐to‐state transition probabilities at thermal energies

journal, May 1996

- Kendrick, Brian; Pack, Russell T.
- The Journal of Chemical Physics, Vol. 104, Issue 19

##
Constructive and Destructive Interference in Nonadiabatic Tunneling via Conical Intersections

journal, April 2017

- Xie, Changjian; Kendrick, Brian K.; Yarkony, David R.
- Journal of Chemical Theory and Computation, Vol. 13, Issue 5

##
Geometric phase effects in excited state dynamics through a conical intersection in large molecules: N-dimensional linear vibronic coupling model study

journal, August 2017

- Li, Jiaru; Joubert-Doriol, Loïc; Izmaylov, Artur F.
- The Journal of Chemical Physics, Vol. 147, Issue 6

##
Hyperspherical surface functions for nonzero total angular momentum. I. Eckart singularities

journal, April 1999

- Kendrick, Brian K.; Pack, Russell T.; Walker, Robert B.
- The Journal of Chemical Physics, Vol. 110, Issue 14

##
Importance of Geometric Phase Effects in Ultracold Chemistry

journal, September 2015

- Hazra, Jisha; Kendrick, Brian K.; Balakrishnan, Naduvalath
- The Journal of Physical Chemistry A, Vol. 119, Issue 50

##
On the determination of Born–Oppenheimer nuclear motion wave functions including complications due to conical intersections and identical nuclei

journal, March 1979

- Mead, C. Alden; Truhlar, Donald G.
- The Journal of Chemical Physics, Vol. 70, Issue 5

##
Measurement of relative state‐to‐state rate constants for the reaction D+H _{2} ( *v* , *j* )→HD( *v* ’, *j* ’)+H

journal, November 1992

- Adelman, David E.; Shafer, Neil E.; Kliner, Dahv A. V.
- The Journal of Chemical Physics, Vol. 97, Issue 10

##
Quantum reactive scattering calculations for the H+D2→HD+D reaction

journal, May 2001

- Kendrick, Brian K.
- The Journal of Chemical Physics, Vol. 114, Issue 20

##
The effects of pseudomagnetic fields in molecular spectra and scattering

journal, January 1997

- Kendrick, Brian
- International Journal of Quantum Chemistry, Vol. 64, Issue 5

##
Unambiguous Proof for Berry's Phase in the Sodium Trimer: Analysis of the Transition ${\mathit{A}}^{2}{\mathit{E}}^{\prime \prime}\leftarrow {\mathit{X}}^{2}{\mathit{E}}^{\prime}$

journal, November 1998

- von Busch, H.; Dev, Vas; Eckel, H. -A.
- Physical Review Letters, Vol. 81, Issue 21

##
Hunt for geometric phase effects in H + HD → HD( *v* ′, *j′* ) + H

journal, October 2013

- Jankunas, Justin; Sneha, Mahima; Zare, Richard N.
- The Journal of Chemical Physics, Vol. 139, Issue 14

##
The geometric phase effect shows up in chemical reactions

journal, April 1993

- Kuppermann, Aron; Wu, Yi-Shuen Mark
- Chemical Physics Letters, Vol. 205, Issue 6

##
The geometric phase controls ultracold chemistry

journal, July 2015

- Kendrick, B. K.; Hazra, Jisha; Balakrishnan, N.
- Nature Communications, Vol. 6, Issue 1

##
Non-adiabatic quantum reactive scattering in hyperspherical coordinates

journal, January 2018

- Kendrick, Brian K.
- The Journal of Chemical Physics, Vol. 148, Issue 4

##
Laser-excited fluorescence spectroscopy of the jet-cooled copper trimer

journal, May 1986

- Rohlfing, Eric A.; Valentini, James J.
- Chemical Physics Letters, Vol. 126, Issue 2

##
Geometric phase effects in the H+H2 reaction: Quantum wave-packet calculations of integral and differential cross sections

journal, May 2005

- Juanes-Marcos, Juan Carlos; Althorpe, Stuart C.
- The Journal of Chemical Physics, Vol. 122, Issue 20

##
Geometric Phase Effects in Nonadiabatic Dynamics near Conical Intersections

journal, June 2017

- Ryabinkin, Ilya G.; Joubert-Doriol, Loïc; Izmaylov, Artur F.
- Accounts of Chemical Research, Vol. 50, Issue 7

##
Theoretical Study of Geometric Phase Effects in the Hydrogen-Exchange Reaction

journal, August 2005

- Juanes-Marcos, J. C.
- Science, Vol. 309, Issue 5738

##
Geometric phase effects in the ultracold H + H _{2} reaction

journal, October 2016

- Kendrick, B. K.; Hazra, Jisha; Balakrishnan, N.
- The Journal of Chemical Physics, Vol. 145, Issue 16

##
The infrared spectrum of cyclic-N3: Theoretical prediction

journal, November 2010

- Babikov, Dmitri; Kendrick, Brian K.
- The Journal of Chemical Physics, Vol. 133, Issue 17

##
Quantal Phase Factors Accompanying Adiabatic Changes

journal, March 1984

- Berry, M. V.
- Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 392, Issue 1802

##
Geometric phase effects in the ultracold D + HD $ \rightarrow $ D + HD and D + HD $\leftrightarrow $ H + D _{2} reactions

journal, December 2016

- Kendrick, B. K.; Hazra, Jisha; Balakrishnan, N.
- New Journal of Physics, Vol. 18, Issue 12

##
Geometric Phase Effects in Chemical Reaction Dynamics and Molecular Spectra

journal, September 2003

- Kendrick, Brian K.
- The Journal of Physical Chemistry A, Vol. 107, Issue 35

##
Effect of the geometric phase on nuclear dynamics at a conical intersection: Extension of a recent topological approach from one to two coupled surfaces

journal, December 2008

- Althorpe, Stuart C.; Stecher, Thomas; Bouakline, Foudhil
- The Journal of Chemical Physics, Vol. 129, Issue 21

##
Comparison of experimental and theoretical integral cross sections for D+H _{2} ( *v* =1, *j* =1)→HD( *v* ’=1, *j* ’)+H

journal, August 1991

- Kliner, Dahv A. V.; Adelman, David E.; Zare, Richard N.
- The Journal of Chemical Physics, Vol. 95, Issue 3

##
Observation of the geometric phase effect in the H + HD → H _{2} + D reaction

journal, December 2018

- Yuan, Daofu; Guan, Yafu; Chen, Wentao
- Science, Vol. 362, Issue 6420

##
Rovibrational structures of the pseudorotating lithium trimer 21Li3: Rotationally resolved spectroscopy and *ab initio* calculations of the A 2E″←X 2E′ system

journal, November 2000

- Keil, M.; Krämer, H. -G.; Kudell, A.
- The Journal of Chemical Physics, Vol. 113, Issue 17

##
Non-adiabatic quantum reactive scattering calculations for the ultracold hydrogen exchange reaction: H + H2( $v=4-8,\phantom{\rule{0.25em}{0ex}}j=0$ ) $\to $ H + H2( ${v}^{\prime},\phantom{\rule{0.25em}{0ex}}{j}^{\prime}$ )

journal, November 2018

- Kendrick, Brian K.
- Chemical Physics, Vol. 515

##
Dynamic mapping of conical intersection seams: A general method for incorporating the geometric phase in adiabatic dynamics in polyatomic systems

journal, July 2017

- Xie, Changjian; Malbon, Christopher L.; Yarkony, David R.
- The Journal of Chemical Physics, Vol. 147, Issue 4

##
Geometric Phase Appears in the Ultracold Hydrogen Exchange Reaction

journal, October 2015

- Kendrick, B. K.; Hazra, Jisha; Balakrishnan, N.
- Physical Review Letters, Vol. 115, Issue 15

##
Quantum reactive scattering in three dimensions using hyperspherical (APH) coordinates. Theory

journal, October 1987

- Pack, Russell T.; Parker, Gregory A.
- The Journal of Chemical Physics, Vol. 87, Issue 7

##
General explanation of geometric phase effects in reactive systems: Unwinding the nuclear wave function using simple topology

journal, February 2006

- Althorpe, Stuart C.
- The Journal of Chemical Physics, Vol. 124, Issue 8

##
Shape resonances in ground-state diatomic molecules: General trends and the example of RbCs

journal, July 2010

- Londoño, B. E.; Mahecha, J. E.; Luc-Koenig, E.
- Physical Review A, Vol. 82, Issue 1

##
Cyclic-N3. II. Significant geometric phase effects in the vibrational spectra

journal, January 2005

- Babikov, Dmitri; Kendrick, Brian K.; Zhang, Peng
- The Journal of Chemical Physics, Vol. 122, Issue 4

##
Intersection of potential energy surfaces in polyatomic molecules

journal, January 1963

- Herzberg, G.; Longuet-Higgins, H. C.
- Discussions of the Faraday Society, Vol. 35

Figures / Tables found in this record:

*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*