skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Non-adiabatic quantum reactive scattering in hyperspherical coordinates

Abstract

A new electronically non-adiabatic quantum reactive scattering methodology is presented based on a time-independent coupled channel formalism and the adiabatically adjusting principal axis hyperspherical coordinates of Pack and Parker [J. Chem. Phys. 87, 3888 (1987)]. The methodology computes the full state-to-state scattering matrix for A + B2(v, j) ↔ AB(v', j') + B and A + AB(v, j) → A + AB(v', j') reactions that involve two coupled electronic states which exhibit a conical intersection. The methodology accurately treats all six degrees of freedom relative to the center-of-mass which includes non-zero total angular momentum J and identical particle exchange symmetry. The new methodology is applied to the ultracold hydrogen exchange reaction for which large geometric phase effects have been recently reported [B. K. Kendrick et al., Phys. Rev. Lett. 115, 153201 (2015)]. Rate coefficients for the H/D + HD(v = 4, j = 0) → H/D + HD(v', j') reactions are reported for collision energies between 1 μK and 100 K (total energy ≈1.9 eV). A new diabatic potential energy matrix is developed based on the Boothroyd, Keogh, Martin, and Peterson (BKMP2) and double many body expansion plus single-polynomial (DSP) adiabatic potential energy surfaces for the ground and first excitedmore » electronic states of H3, respectively. The rate coefficients computed using the new non-adiabatic methodology and diabatic potential matrix reproduce the recently reported rates that include the geometric phase and are computed using a single adiabatic ground electronic state potential energy surface (BKMP2). The dramatic enhancement and suppression of the ultracold rates due to the geometric phase are confirmed as well as its effects on several shape resonances near 1 K. In conclusion, the results reported here represent the first fully non-adiabatic quantum reactive scattering calculation for an ultracold reaction and validate the importance of the geometric phase on the Wigner threshold behavior.« less

Authors:
ORCiD logo [1]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1431067
Alternate Identifier(s):
OSTI ID: 1418724
Report Number(s):
LA-UR-17-30356
Journal ID: ISSN 0021-9606; TRN: US1802641
Grant/Contract Number:  
AC52-06NA25396
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 148; Journal Issue: 4; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Inorganic and Physical Chemistry; non-adiabatic dynamics; ultracold chemistry; quantum reactive scattering

Citation Formats

Kendrick, Brian K. Non-adiabatic quantum reactive scattering in hyperspherical coordinates. United States: N. p., 2018. Web. doi:10.1063/1.5014989.
Kendrick, Brian K. Non-adiabatic quantum reactive scattering in hyperspherical coordinates. United States. doi:10.1063/1.5014989.
Kendrick, Brian K. Sun . "Non-adiabatic quantum reactive scattering in hyperspherical coordinates". United States. doi:10.1063/1.5014989. https://www.osti.gov/servlets/purl/1431067.
@article{osti_1431067,
title = {Non-adiabatic quantum reactive scattering in hyperspherical coordinates},
author = {Kendrick, Brian K.},
abstractNote = {A new electronically non-adiabatic quantum reactive scattering methodology is presented based on a time-independent coupled channel formalism and the adiabatically adjusting principal axis hyperspherical coordinates of Pack and Parker [J. Chem. Phys. 87, 3888 (1987)]. The methodology computes the full state-to-state scattering matrix for A + B2(v, j) ↔ AB(v', j') + B and A + AB(v, j) → A + AB(v', j') reactions that involve two coupled electronic states which exhibit a conical intersection. The methodology accurately treats all six degrees of freedom relative to the center-of-mass which includes non-zero total angular momentum J and identical particle exchange symmetry. The new methodology is applied to the ultracold hydrogen exchange reaction for which large geometric phase effects have been recently reported [B. K. Kendrick et al., Phys. Rev. Lett. 115, 153201 (2015)]. Rate coefficients for the H/D + HD(v = 4, j = 0) → H/D + HD(v', j') reactions are reported for collision energies between 1 μK and 100 K (total energy ≈1.9 eV). A new diabatic potential energy matrix is developed based on the Boothroyd, Keogh, Martin, and Peterson (BKMP2) and double many body expansion plus single-polynomial (DSP) adiabatic potential energy surfaces for the ground and first excited electronic states of H3, respectively. The rate coefficients computed using the new non-adiabatic methodology and diabatic potential matrix reproduce the recently reported rates that include the geometric phase and are computed using a single adiabatic ground electronic state potential energy surface (BKMP2). The dramatic enhancement and suppression of the ultracold rates due to the geometric phase are confirmed as well as its effects on several shape resonances near 1 K. In conclusion, the results reported here represent the first fully non-adiabatic quantum reactive scattering calculation for an ultracold reaction and validate the importance of the geometric phase on the Wigner threshold behavior.},
doi = {10.1063/1.5014989},
journal = {Journal of Chemical Physics},
number = 4,
volume = 148,
place = {United States},
year = {2018},
month = {1}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 4 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Accurate nonadiabatic dynamics
journal, January 2016

  • Guo, Hua; Yarkony, David R.
  • Physical Chemistry Chemical Physics, Vol. 18, Issue 38
  • DOI: 10.1039/c6cp05553b

Approximately diabatic states from block diagonalization of the electronic Hamiltonian
journal, December 1988

  • Pacher, T.; Cederbaum, L. S.; Köppel, H.
  • The Journal of Chemical Physics, Vol. 89, Issue 12
  • DOI: 10.1063/1.455268

Diabatic-At-Construction Method for Diabatic and Adiabatic Ground and Excited States Based on Multistate Density Functional Theory
journal, February 2017

  • Grofe, Adam; Qu, Zexing; Truhlar, Donald G.
  • Journal of Chemical Theory and Computation, Vol. 13, Issue 3
  • DOI: 10.1021/acs.jctc.6b01176

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
  • DOI: 10.1088/0953-4075/49/19/194004

Diabolical conical intersections
journal, October 1996


Tertiary and general-order collisions (II)
journal, October 1960


Role of Conical Intersections in Molecular Spectroscopy and Photoinduced Chemical Dynamics
journal, May 2012


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
  • DOI: 10.1021/acs.jctc.6b00760

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
  • DOI: 10.1063/1.1573183

An optimal adiabatic-to-diabatic transformation of the 1 2A′ and 2 2A′ states of H3
journal, January 2002

  • Abrol, Ravinder; Kuppermann, Aron
  • The Journal of Chemical Physics, Vol. 116, Issue 3
  • DOI: 10.1063/1.1419257

Ultracold collisions and reactions of vibrationally excited OH radicals with oxygen atoms
journal, January 2011

  • Juanes-Marcos, Juan Carlos; Quéméner, Goulven; Kendrick, Brian K.
  • Physical Chemistry Chemical Physics, Vol. 13, Issue 42
  • DOI: 10.1039/c1cp21141b

Perspective: Nonadiabatic dynamics theory
journal, December 2012

  • Tully, John C.
  • The Journal of Chemical Physics, Vol. 137, Issue 22
  • DOI: 10.1063/1.4757762

Perspective: Ultracold molecules and the dawn of cold controlled chemistry
journal, October 2016

  • Balakrishnan, N.
  • The Journal of Chemical Physics, Vol. 145, Issue 15
  • DOI: 10.1063/1.4964096

Generalized Angular Momentum in Many-Body Collisions
journal, November 1960


Nonadiabatic quantum wave packet dynamics of H+H2 (HD) reactions
journal, March 2007


Generalized discrete variable approximation in quantum mechanics
journal, February 1985

  • Light, J. C.; Hamilton, I. P.; Lill, J. V.
  • The Journal of Chemical Physics, Vol. 82, Issue 3
  • DOI: 10.1063/1.448462

Nonadiabatic photodynamics and UV absorption spectrum of all-trans-octatetraene
journal, January 2017

  • Lyskov, Igor; Köppel, Horst; Marian, Christel M.
  • Physical Chemistry Chemical Physics, Vol. 19, Issue 5
  • DOI: 10.1039/c6cp07640h

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
  • DOI: 10.1063/1.481143

On the Jahn–Teller effect in the X 2 E electronic ground state of CH3F+
journal, January 2017


Conditions for the definition of a strictly diabatic electronic basis for molecular systems
journal, December 1982

  • Mead, C. Alden; Truhlar, Donald G.
  • The Journal of Chemical Physics, Vol. 77, Issue 12
  • DOI: 10.1063/1.443853

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
  • DOI: 10.1063/1.471460

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
  • DOI: 10.1063/1.471461

Reactive Scattering Dynamics on Conically Intersecting Potential Energy Surfaces: The H + H 2 Exchange Reaction
journal, March 2001

  • Mahapatra, Susanta; Köppel, Horst; Cederbaum, Lorenz S.
  • The Journal of Physical Chemistry A, Vol. 105, Issue 11
  • DOI: 10.1021/jp003784b

Scalable Algorithms for Three-Dimensional Reactive Scattering: Evaluation of a New Algorithm for Obtaining Surface Functions
journal, August 1994

  • Pendergast, Phil; Darakjian, Zareh; Hayes, Edward F.
  • Journal of Computational Physics, Vol. 113, Issue 2
  • DOI: 10.1006/jcph.1994.1130

The Kinetic Energy of Polyatomic Molecules
journal, September 1934


The molecular Aharonov—Bohm effect in bound states
journal, June 1980


Geometric Phase Effects in the Vibrational Spectrum of Na 3 ( X )
journal, September 1997


Coupled 3D Time-Dependent Wave-Packet Approach in Hyperspherical Coordinates: The D + +H 2 Reaction on the Triple-Sheeted DMBE Potential Energy Surface
journal, October 2015

  • Ghosh, Sandip; Sahoo, Tapas; Adhikari, Satrajit
  • The Journal of Physical Chemistry A, Vol. 119, Issue 50
  • DOI: 10.1021/acs.jpca.5b07718

Some Studies Concerning Rotating Axes and Polyatomic Molecules
journal, April 1935


Cold and ultracold molecules: science, technology and applications
journal, May 2009


Few-femtosecond passage of conical intersections in the benzene cation
journal, October 2017


The geometric phase controls ultracold chemistry
journal, July 2015

  • Kendrick, B. K.; Hazra, Jisha; Balakrishnan, N.
  • Nature Communications, Vol. 6, Issue 1
  • DOI: 10.1038/ncomms8918

Nonadiabatic tunneling via conical intersections and the role of the geometric phase
journal, February 2017


Preparation of a selected high vibrational energy level of isolated molecules
journal, October 2016

  • Perreault, William E.; Mukherjee, Nandini; Zare, Richard N.
  • The Journal of Chemical Physics, Vol. 145, Issue 15
  • DOI: 10.1063/1.4964938

Geometric Phase Effects in Dynamics Near Conical Intersections: Symmetry Breaking and Spatial Localization
journal, November 2013


Nonadiabatic effects in the H+H2 exchange reaction: Accurate quantum dynamics calculations at a state-to-state level
journal, April 2009

  • Chu, Tian-Shu; Han, Ke-Li; Hankel, Marlies
  • The Journal of Chemical Physics, Vol. 130, Issue 14
  • DOI: 10.1063/1.3089724

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
  • DOI: 10.1063/1.4966037

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
  • DOI: 10.1098/rspa.1984.0023

Quantum dynamics of the O+OH→H+O2 reaction at low temperatures
journal, December 2008

  • Quéméner, Goulven; Balakrishnan, Naduvalath; Kendrick, Brian K.
  • The Journal of Chemical Physics, Vol. 129, Issue 22
  • DOI: 10.1063/1.3035904

Ultracold chemistry with alkali-metal–rare-earth molecules
journal, January 2015


Formation of molecular oxygen in ultracold O + O H collisions
journal, February 2009

  • Quéméner, Goulven; Balakrishnan, Naduvalath; Kendrick, Brian K.
  • Physical Review A, Vol. 79, Issue 2
  • DOI: 10.1103/physreva.79.022703

Strong geometric-phase effects in the hydrogen-exchange reaction at high collision energies
journal, March 2008

  • Bouakline, Foudhil; Althorpe, Stuart C.; Peláez Ruiz, Daniel
  • The Journal of Chemical Physics, Vol. 128, Issue 12
  • DOI: 10.1063/1.2897920

Controlled state-to-state atom-exchange reaction in an ultracold atom–dimer mixture
journal, April 2017

  • Rui, Jun; Yang, Huan; Liu, Lan
  • Nature Physics, Vol. 13, Issue 7
  • DOI: 10.1038/nphys4095

Quantum-State Controlled Chemical Reactions of Ultracold Potassium-Rubidium Molecules
journal, February 2010


A double many‐body expansion of the two lowest‐energy potential surfaces and nonadiabatic coupling for H 3
journal, June 1987

  • Varandas, Antonio J. C.; Brown, Franklin B.; Mead, C. Alden
  • The Journal of Chemical Physics, Vol. 86, Issue 11
  • DOI: 10.1063/1.452463

Erratum: “Geometric phase effects in the H+D2→HD+D reaction” [J. Chem. Phys. 112 , 5679 (2000)]
journal, March 2001

  • Kendrick, Brian K.
  • The Journal of Chemical Physics, Vol. 114, Issue 9
  • DOI: 10.1063/1.1346648

Nonadiabatic quantum wave packet dynamics of the H + H2 reaction including the coriolis coupling
journal, September 2009


Ultracold molecules and ultracold chemistry
journal, January 2009


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
  • DOI: 10.1063/1.4990002

Ultracold Molecules under Control!
journal, April 2012

  • Quéméner, Goulven; Julienne, Paul S.
  • Chemical Reviews, Vol. 112, Issue 9
  • DOI: 10.1021/cr300092g

The geometric phase in molecular systems
journal, January 1992


Anomalous symmetries of the rovibrational states of HO 2 : Consequences of a conical intersection
journal, September 1995

  • Barclay, V. J.; Dateo, Christopher E.; Hamilton, I. P.
  • The Journal of Chemical Physics, Vol. 103, Issue 9
  • DOI: 10.1063/1.470039

Generalization of Levinson's Theorem to Three-Body Systems
journal, July 1965


Derivation of the geometrical phase
journal, February 1991


Intersection of potential energy surfaces in polyatomic molecules
journal, January 1963

  • Herzberg, G.; Longuet-Higgins, H. C.
  • Discussions of the Faraday Society, Vol. 35
  • DOI: 10.1039/df9633500077

Quantum control of molecular collisions at 1 kelvin
journal, October 2017

  • Perreault, William E.; Mukherjee, Nandini; Zare, Richard N.
  • Science, Vol. 358, Issue 6361
  • DOI: 10.1126/science.aao3116

Extension of the Pack–Parker quantum reactive scattering method to include direct calculation of time delays
journal, December 1990

  • Darakjian, Zareh; Hayes, Edward F.
  • The Journal of Chemical Physics, Vol. 93, Issue 12
  • DOI: 10.1063/1.459268

The renormalized Numerov method applied to calculating bound states of the coupled‐channel Schroedinger equation
journal, November 1978

  • Johnson, B. R.
  • The Journal of Chemical Physics, Vol. 69, Issue 10
  • DOI: 10.1063/1.436421

Cold controlled chemistry
journal, January 2008

  • Krems, R. V.
  • Physical Chemistry Chemical Physics, Vol. 10, Issue 28
  • DOI: 10.1039/b802322k

Implicit Application of Polynomial Filters in a k -Step Arnoldi Method
journal, January 1992

  • Sorensen, D. C.
  • SIAM Journal on Matrix Analysis and Applications, Vol. 13, Issue 1
  • DOI: 10.1137/0613025

The effects of pseudomagnetic fields in molecular spectra and scattering
journal, January 1997


On the uniqueness of the Berry connection
journal, July 1992

  • Bohm, Arno; Boya, Luis J.; Kendrick, Brian
  • Journal of Mathematical Physics, Vol. 33, Issue 7
  • DOI: 10.1063/1.529571

Existence of Universal Connections
journal, July 1961

  • Narasimhan, M. S.; Ramanan, S.
  • American Journal of Mathematics, Vol. 83, Issue 3
  • DOI: 10.2307/2372896

A refined H3 potential energy surface
journal, May 1996

  • Boothroyd, Arnold I.; Keogh, William J.; Martin, Peter G.
  • The Journal of Chemical Physics, Vol. 104, Issue 18
  • DOI: 10.1063/1.471430

The molecular Aharonov–Bohm effect redux
journal, December 2016


The Berry phase in molecular physics
journal, January 1992

  • Bohm, A.; Kendrick, B.; Loewe, Mark E.
  • International Journal of Quantum Chemistry, Vol. 41, Issue 1
  • DOI: 10.1002/qua.560410108

Optical preparation of H 2 rovibrational levels with almost complete population transfer
journal, August 2013

  • Dong, Wenrui; Mukherjee, Nandini; Zare, Richard N.
  • The Journal of Chemical Physics, Vol. 139, Issue 7
  • DOI: 10.1063/1.4818526

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
  • DOI: 10.1063/1.4998226

Tertiary and general-order collisions
journal, January 1958


The multichannel log-derivative method for scattering calculations
journal, November 1973


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
  • DOI: 10.1063/1.473449

Photodissociation dynamics of the pyridinyl radical: Time-dependent quantum wave-packet calculations
journal, March 2017

  • Ehrmaier, Johannes; Picconi, David; Karsili, Tolga N. V.
  • The Journal of Chemical Physics, Vol. 146, Issue 12
  • DOI: 10.1063/1.4978283

Full-dimensional potentials and state couplings and multidimensional tunneling calculations for the photodissociation of phenol
journal, January 2014

  • Yang, Ke R.; Xu, Xuefei; Zheng, Jingjing
  • Chem. Sci., Vol. 5, Issue 12
  • DOI: 10.1039/c4sc01967a

Universality and chaoticity in ultracold K+KRb chemical reactions
journal, July 2017

  • Croft, J. F. E.; Makrides, C.; Li, M.
  • Nature Communications, Vol. 8, Issue 1
  • DOI: 10.1038/ncomms15897

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
  • DOI: 10.1021/acs.jctc.7b00124

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
  • DOI: 10.1063/1.4985925

Existence of Universal Connections II
journal, April 1963

  • Narasimhan, M. S.; Ramanan, S.
  • American Journal of Mathematics, Vol. 85, Issue 2
  • DOI: 10.2307/2373211

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
  • DOI: 10.1063/1.478574

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
  • DOI: 10.1021/acs.jpca.5b06410

A Symmetric Representation for Three‐Body Problems. I. Motion in a Plane
journal, July 1962

  • Smith, Felix T.
  • Journal of Mathematical Physics, Vol. 3, Issue 4
  • DOI: 10.1063/1.1724275

Localized representations for large amplitude molecular vibrations
journal, September 1988


The Jahn-Teller plus pseudo-Jahn-Teller vibronic problem in the C 3 radical and its topological implications
journal, February 2016

  • Rocha, C. M. R.; Varandas, A. J. C.
  • The Journal of Chemical Physics, Vol. 144, Issue 6
  • DOI: 10.1063/1.4941382

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
  • DOI: 10.1063/1.437734

Minimizing development and maintenance costs in supporting persistently optimized BLAS
journal, January 2005

  • Whaley, R. Clint; Petitet, Antoine
  • Software: Practice and Experience, Vol. 35, Issue 2
  • DOI: 10.1002/spe.626

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
  • DOI: 10.1063/1.1367377

Appearance of gauge potentials in atomic collision physics
journal, December 1987


Nonadiabatic effects in the H+D2 reaction
journal, October 2006

  • Lu, Rui-Feng; Chu, Tian-Shu; Zhang, Yan
  • The Journal of Chemical Physics, Vol. 125, Issue 13
  • DOI: 10.1063/1.2202826

Non-Abelian geometric phase and long-range atomic forces
journal, January 1990


Quantum nonadiabatic dynamics of hydrogen exchange reactions
journal, November 2009


Participation of Vibration in Exchange Reactions
journal, November 1959

  • Smith, Felix T.
  • The Journal of Chemical Physics, Vol. 31, Issue 5
  • DOI: 10.1063/1.1730598

Geometric phase effects in low-energy dynamics near conical intersections: A study of the multidimensional linear vibronic coupling model
journal, December 2013

  • Joubert-Doriol, Loïc; Ryabinkin, Ilya G.; Izmaylov, Artur F.
  • The Journal of Chemical Physics, Vol. 139, Issue 23
  • DOI: 10.1063/1.4844095

Properties of nonadiabatic couplings and the generalized Born–Oppenheimer approximation
journal, March 2002


The Berry connection and Born–Oppenheimer method
journal, March 1992

  • Bohm, A.; Kendrick, B.; Loewe, Mark E.
  • Journal of Mathematical Physics, Vol. 33, Issue 3
  • DOI: 10.1063/1.529751

Zur Quantentheorie der Molekeln
journal, January 1927


When do we need to account for the geometric phase in excited state dynamics?
journal, June 2014

  • Ryabinkin, Ilya G.; Joubert-Doriol, Loïc; Izmaylov, Artur F.
  • The Journal of Chemical Physics, Vol. 140, Issue 21
  • DOI: 10.1063/1.4881147

Chemical reaction versus vibrational quenching in low energy collisions of vibrationally excited OH with O
journal, November 2013

  • Pradhan, G. B.; Juanes-Marcos, J. C.; Balakrishnan, N.
  • The Journal of Chemical Physics, Vol. 139, Issue 19
  • DOI: 10.1063/1.4830398

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
  • DOI: 10.1088/1367-2630/aa4fd2

Accurate quantum calculations on three-body collisions in recombination and collision-induced dissociation. I. Converged probabilities for the H+Ne2 system
journal, October 2002

  • Parker, Gregory A.; Walker, Robert B.; Kendrick, Brian K.
  • The Journal of Chemical Physics, Vol. 117, Issue 13
  • DOI: 10.1063/1.1503313

Accurate first-derivative nonadiabatic couplings for the H3 system
journal, September 2001

  • Abrol, Ravinder; Shaw, Amy; Kuppermann, Aron
  • The Journal of Chemical Physics, Vol. 115, Issue 10
  • DOI: 10.1063/1.1390510

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
  • DOI: 10.1021/jp021865x

The classical dynamics of three particles in hyperspherical coordinates
journal, August 1983

  • Johnson, B. R.
  • The Journal of Chemical Physics, Vol. 79, Issue 4
  • DOI: 10.1063/1.445969

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
  • DOI: 10.1063/1.3031215

Full-dimensional multi-state simulation of the photodissociation of thioanisole
journal, July 2017

  • Li, Shaohong L.; Truhlar, Donald G.
  • The Journal of Chemical Physics, Vol. 147, Issue 4
  • DOI: 10.1063/1.4994923

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
  • DOI: 10.1063/1.452944

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
  • DOI: 10.1063/1.2161220

Resonant femtosecond stimulated Raman spectroscopy with an intense actinic pump pulse: Application to conical intersections
journal, February 2017

  • Rao, B. Jayachander; Gelin, Maxim F.; Domcke, Wolfgang
  • The Journal of Chemical Physics, Vol. 146, Issue 8
  • DOI: 10.1063/1.4976317

Magnetically Controlled Exchange Process in an Ultracold Atom-Dimer Mixture
journal, February 2010


The quantum dynamics of three particles in hyperspherical coordinates
journal, August 1983

  • Johnson, B. R.
  • The Journal of Chemical Physics, Vol. 79, Issue 4
  • DOI: 10.1063/1.445970

New numerical methods applied to solving the one-dimensional eigenvalue problem
journal, January 1999

  • Johnson, B. R.
  • The Journal of Chemical Physics, Vol. 67, Issue 9
  • DOI: 10.1063/1.435384

On hyperspherical coordinates and mapping the internal configurations of a three body system
journal, November 1980

  • Johnson, B. R.
  • The Journal of Chemical Physics, Vol. 73, Issue 10
  • DOI: 10.1063/1.439983

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
  • DOI: 10.1063/1.1824905

Gravitation, gauge theories and differential geometry
journal, December 1980