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Title: Permutation invariant polynomial neural network approach to fitting potential energy surfaces. IV. Coupled diabatic potential energy matrices

Abstract

A machine learning method is proposed for representing the elements of diabatic potential energy matrices (PEMs) with high fidelity. This is an extension of the so-called permutation invariant polynomial-neural network (PIP-NN) method for representing adiabatic potential energy surfaces. While for one-dimensional irreducible representations the diagonal elements of a diabatic PEM are invariant under exchange of identical nuclei in a molecular system, the off-diagonal elements require special symmetry consideration, particularly in the presence of a conical intersection. A multiplicative factor is introduced to take into consideration the particular symmetry properties while maintaining the PIP-NN framework. Here, we demonstrate here that the extended PIP-NN approach is accurate in representing diabatic PEMs, as evidenced by small fitting errors and by the reproduction of absorption spectra and product branching ratios in both H2O$$(\tilde{X} / \tilde{B})$$ and NH3$$(\tilde{X} $$/Ã) non-adiabatic photodissociation.

Authors:
 [1]; ORCiD logo [2]; ORCiD logo [3]; ORCiD logo [1]
+ Show Author Affiliations
  1. Univ. of New Mexico, Albuquerque, NM (United States)
  2. Johns Hopkins Univ., Baltimore, MD (United States); Stanford Univ., CA (United States)
  3. Johns Hopkins Univ., Baltimore, MD (United States)
Publication Date:
Research Org.:
Univ. of New Mexico, Albuquerque, NM (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1612363
Alternate Identifier(s):
OSTI ID: 1476847
Grant/Contract Number:  
SC0015997
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 149; Journal Issue: 14; 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; Chemistry; Physics; Quantum chemical dynamics; Artificial neural networks; Diabatization; Machine learning; Potential energy surfaces; Photodissociation; Absorption spectroscopy

Citation Formats

Xie, Changjian, Zhu, Xiaolei, Yarkony, David R., and Guo, Hua. Permutation invariant polynomial neural network approach to fitting potential energy surfaces. IV. Coupled diabatic potential energy matrices. United States: N. p., 2018. Web. doi:10.1063/1.5054310.
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Xie, Changjian, Zhu, Xiaolei, Yarkony, David R., & Guo, Hua. Permutation invariant polynomial neural network approach to fitting potential energy surfaces. IV. Coupled diabatic potential energy matrices. United States. https://doi.org/10.1063/1.5054310
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Xie, Changjian, Zhu, Xiaolei, Yarkony, David R., and Guo, Hua. Tue . "Permutation invariant polynomial neural network approach to fitting potential energy surfaces. IV. Coupled diabatic potential energy matrices". United States. https://doi.org/10.1063/1.5054310. https://www.osti.gov/servlets/purl/1612363.
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@article{osti_1612363,
title = {Permutation invariant polynomial neural network approach to fitting potential energy surfaces. IV. Coupled diabatic potential energy matrices},
author = {Xie, Changjian and Zhu, Xiaolei and Yarkony, David R. and Guo, Hua},
abstractNote = {A machine learning method is proposed for representing the elements of diabatic potential energy matrices (PEMs) with high fidelity. This is an extension of the so-called permutation invariant polynomial-neural network (PIP-NN) method for representing adiabatic potential energy surfaces. While for one-dimensional irreducible representations the diagonal elements of a diabatic PEM are invariant under exchange of identical nuclei in a molecular system, the off-diagonal elements require special symmetry consideration, particularly in the presence of a conical intersection. A multiplicative factor is introduced to take into consideration the particular symmetry properties while maintaining the PIP-NN framework. Here, we demonstrate here that the extended PIP-NN approach is accurate in representing diabatic PEMs, as evidenced by small fitting errors and by the reproduction of absorption spectra and product branching ratios in both H2O$(\tilde{X} / \tilde{B})$ and NH3$(\tilde{X} $/Ã) non-adiabatic photodissociation.},
doi = {10.1063/1.5054310},
journal = {Journal of Chemical Physics},
number = 14,
volume = 149,
place = {United States},
year = {Tue Oct 09 00:00:00 EDT 2018},
month = {Tue Oct 09 00:00:00 EDT 2018}
}
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https://doi.org/10.1063/1.5054310
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Works referenced in this record:

Interpolation of diabatic potential energy surfaces
journal, January 2004

  • Evenhuis, Christian R.; Collins, Michael A.
  • The Journal of Chemical Physics, Vol. 121, Issue 6
  • DOI: 10.1063/1.1770756

Accurate nonadiabatic dynamics
journal, January 2016

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

Automated construction of potential energy surfaces
journal, September 2015

Non-adiabaticity: the importance of conical intersections
journal, May 2016

Ab Initio Nonadiabatic Quantum Molecular Dynamics
journal, February 2018

Neural Networks in Chemical Reaction Dynamics
January 2012

Diabolical conical intersections
journal, October 1996

Conical Intersections: Electronic Structure, Dynamics and Spectroscopy
book, July 2004

  • Domcke, Wolfgang; Yarkony, David R.; Köppel, Horst
  • Advanced Series in Physical Chemistry, Vol. 15
  • DOI: 10.1142/5406

Permutationally invariant potential energy surfaces in high dimensionality
journal, October 2009

  • Braams, Bastiaan J.; Bowman, Joel M.
  • International Reviews in Physical Chemistry, Vol. 28, Issue 4
  • DOI: 10.1080/01442350903234923

Extremely short-lived reaction resonances in Cl + HD ( v = 1) → DCl + H due to chemical bond softening
journal, January 2015

MCSCF study of the avoided curve crossing of the two lowest 1 Σ + states of LiF
journal, May 1981

  • Werner, Hans‐Joachim; Meyer, Wilfried
  • The Journal of Chemical Physics, Vol. 74, Issue 10
  • DOI: 10.1063/1.440893

Feshbach resonances in the exit channel of the F + CH3OH → HF + CH3O reaction observed using transition-state spectroscopy
journal, July 2017

  • Weichman, Marissa L.; DeVine, Jessalyn A.; Babin, Mark C.
  • Nature Chemistry, Vol. 9, Issue 10
  • DOI: 10.1038/nchem.2804

Permutation invariant polynomial neural network approach to fitting potential energy surfaces. III. Molecule-surface interactions
journal, July 2014

  • Jiang, Bin; Guo, Hua
  • The Journal of Chemical Physics, Vol. 141, Issue 3
  • DOI: 10.1063/1.4887363

Neural network-based approaches for building high dimensional and quantum dynamics-friendly potential energy surfaces
journal, October 2014

  • Manzhos, Sergei; Dawes, Richard; Carrington, Tucker
  • International Journal of Quantum Chemistry, Vol. 115, Issue 16
  • DOI: 10.1002/qua.24795

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

Interpolation of multidimensional diabatic potential energy matrices
journal, September 2006

  • Godsi, Oded; Evenhuis, Christian R.; Collins, Michael A.
  • The Journal of Chemical Physics, Vol. 125, Issue 10
  • DOI: 10.1063/1.2338912

Implications of rotation–inversion–permutation invariance for analytic molecular potential energy surfaces
journal, November 1993

  • Collins, Michael A.; Parsons, Drew F.
  • The Journal of Chemical Physics, Vol. 99, Issue 9
  • DOI: 10.1063/1.465819

Potential energy surfaces near intersections
journal, August 1991

  • Atchity, Gregory J.; Xantheas, Sotirios S.; Ruedenberg, Klaus
  • The Journal of Chemical Physics, Vol. 95, Issue 3
  • DOI: 10.1063/1.461036

Improved direct diabatization and coupled potential energy surfaces for the photodissociation of ammonia
journal, March 2007

  • Li, Zhen Hua; Valero, Rosendo; Truhlar, Donald G.
  • Theoretical Chemistry Accounts, Vol. 118, Issue 1
  • DOI: 10.1007/s00214-006-0237-7

Permutationally Invariant Polynomial Basis for Molecular Energy Surface Fitting via Monomial Symmetrization
journal, November 2009

  • Xie, Zhen; Bowman, Joel M.
  • Journal of Chemical Theory and Computation, Vol. 6, Issue 1
  • DOI: 10.1021/ct9004917

Perspective: Machine learning potentials for atomistic simulations
journal, November 2016

  • Behler, Jörg
  • The Journal of Chemical Physics, Vol. 145, Issue 17
  • DOI: 10.1063/1.4966192

Recent advances in quantum scattering calculations on polyatomic bimolecular reactions
journal, January 2017

  • Fu, Bina; Shan, Xiao; Zhang, Dong H.
  • Chemical Society Reviews, Vol. 46, Issue 24
  • DOI: 10.1039/c7cs00526a

On the incorporation of the geometric phase in general single potential energy surface dynamics: A removable approximation to ab initio data
journal, December 2016

  • Malbon, Christopher L.; Zhu, Xiaolei; Guo, Hua
  • The Journal of Chemical Physics, Vol. 145, Issue 23
  • DOI: 10.1063/1.4971369

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

Beyond Born-Oppenheimer
journal, January 2008

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

Communication: Fitting potential energy surfaces with fundamental invariant neural network
journal, August 2016

  • Shao, Kejie; Chen, Jun; Zhao, Zhiqiang
  • The Journal of Chemical Physics, Vol. 145, Issue 7
  • DOI: 10.1063/1.4961454

Atom-centered symmetry functions for constructing high-dimensional neural network potentials
journal, February 2011

  • Behler, Jörg
  • The Journal of Chemical Physics, Vol. 134, Issue 7
  • DOI: 10.1063/1.3553717

Training feedforward networks with the Marquardt algorithm
journal, January 1994

  • Hagan, M. T.; Menhaj, M. B.
  • IEEE Transactions on Neural Networks, Vol. 5, Issue 6
  • DOI: 10.1109/72.329697

C ONSTRUCTING M ULTIDIMENSIONAL M OLECULAR P OTENTIAL E NERGY S URFACES FROM A B I NITIO D ATA
journal, October 1999

Communication: State-to-state differential cross sections for H 2 O(B̃) photodissociation
journal, June 2011

  • Jiang, Bin; Xie, Daiqian; Guo, Hua
  • The Journal of Chemical Physics, Vol. 134, Issue 23
  • DOI: 10.1063/1.3604567

Recent Progress in Surface Hopping: 2011–2015
journal, May 2016

  • Wang, Linjun; Akimov, Alexey; Prezhdo, Oleg V.
  • The Journal of Physical Chemistry Letters, Vol. 7, Issue 11
  • DOI: 10.1021/acs.jpclett.6b00710

Studies of the Jahn-Teller effect .II. The dynamical problem
journal, February 1958

  • Longuet-Higgins, Hugh Christopher; Öpik, U.; Lecorney Pryce, Maurice Henry
  • Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 244, Issue 1236, p. 1-16
  • DOI: 10.1098/rspa.1958.0022

Permutation invariant polynomial neural network approach to fitting potential energy surfaces
journal, August 2013

  • Jiang, Bin; Guo, Hua
  • The Journal of Chemical Physics, Vol. 139, Issue 5
  • DOI: 10.1063/1.4817187

A new method to generate spin-orbit coupled potential energy surfaces: Effective relativistic coupling by asymptotic representation
journal, January 2012

  • Ndome, Hameth; Welsch, Ralph; Eisfeld, Wolfgang
  • The Journal of Chemical Physics, Vol. 136, Issue 3
  • DOI: 10.1063/1.3675846

Molecular potential-energy surfaces for chemical reaction dynamics
journal, December 2002

  • Collins, Michael A.
  • Theoretical Chemistry Accounts: Theory, Computation, and Modeling (Theoretica Chimica Acta), Vol. 108, Issue 6
  • DOI: 10.1007/s00214-002-0383-5

Ab Initio Potential Energy Surfaces and Quantum Dynamics for Polyatomic Bimolecular Reactions
journal, March 2018

Nonadiabatic Quantum Chemistry—Past, Present, and Future
journal, November 2011

Dissociation of NH 3 to NH 2 +H
journal, June 1987

  • McCarthy, M. I.; Rosmus, P.; Werner, H. ‐J.
  • The Journal of Chemical Physics, Vol. 86, Issue 12
  • DOI: 10.1063/1.452417

Interpolation of multi-sheeted multi-dimensional potential-energy surfaces via a linear optimization procedure
journal, June 2013

  • Opalka, Daniel; Domcke, Wolfgang
  • The Journal of Chemical Physics, Vol. 138, Issue 22
  • DOI: 10.1063/1.4808358

Construction of Diabatic Hamiltonian Matrix from ab Initio Calculated Molecular Symmetry Adapted Nonadiabatic Coupling Terms and Nuclear Dynamics for the Excited States of Na 3 Cluster
journal, April 2013

  • Mukherjee, Saikat; Bandyopadhyay, Sudip; Paul, Amit Kumar
  • The Journal of Physical Chemistry A, Vol. 117, Issue 16
  • DOI: 10.1021/jp311597c

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
  • DOI: 10.1021/acs.accounts.7b00220

Constructing diabatic states from adiabatic states: Extending generalized Mulliken–Hush to multiple charge centers with Boys localization
journal, December 2008

  • Subotnik, Joseph E.; Yeganeh, Sina; Cave, Robert J.
  • The Journal of Chemical Physics, Vol. 129, Issue 24
  • DOI: 10.1063/1.3042233

Encoding of vinylidene isomerization in its anion photoelectron spectrum
journal, October 2017

  • DeVine, Jessalyn A.; Weichman, Marissa L.; Laws, Benjamin
  • Science, Vol. 358, Issue 6361
  • DOI: 10.1126/science.aao1905

Full-Dimensional Quantum State-to-State Nonadiabatic Dynamics for Photodissociation of Ammonia in its A -Band
journal, March 2014

  • Xie, Changjian; Ma, Jianyi; Zhu, Xiaolei
  • The Journal of Physical Chemistry Letters, Vol. 5, Issue 7
  • DOI: 10.1021/jz500227d

Permutationally Invariant Potential Energy Surfaces
journal, April 2018

Permutation invariant polynomial neural network approach to fitting potential energy surfaces. II. Four-atom systems
journal, November 2013

  • Li, Jun; Jiang, Bin; Guo, Hua
  • The Journal of Chemical Physics, Vol. 139, Issue 20
  • DOI: 10.1063/1.4832697

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

HN 2 ( 2 A ‘) Electronic Manifold. II. Ab Initio Based Double-Sheeted DMBE Potential Energy Surface via a Global Diabatization Angle
journal, April 2008

  • Mota, Vinícius C.; Varandas, António J. C.
  • The Journal of Physical Chemistry A, Vol. 112, Issue 16
  • DOI: 10.1021/jp710610d

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

Neural network based coupled diabatic potential energy surfaces for reactive scattering
journal, August 2017

  • Lenzen, Tim; Manthe, Uwe
  • The Journal of Chemical Physics, Vol. 147, Issue 8
  • DOI: 10.1063/1.4997995

Nonadiabatic Tunneling in Photodissociation of Phenol
journal, June 2016

  • Xie, Changjian; Ma, Jianyi; Zhu, Xiaolei
  • Journal of the American Chemical Society, Vol. 138, Issue 25
  • DOI: 10.1021/jacs.6b03288

Direct observation of forward-scattering oscillations in the H+HD→H2+D reaction
journal, April 2018

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

The geometric phase in molecular systems
journal, January 1992

Diabatization based on the dipole and quadrupole: The DQ method
journal, September 2014

  • Hoyer, Chad E.; Xu, Xuefei; Ma, Dongxia
  • The Journal of Chemical Physics, Vol. 141, Issue 11
  • DOI: 10.1063/1.4894472

State-to-state photodissociation dynamics of triatomic molecules: H 2 O in the B band
journal, January 2012

  • Jiang, Bin; Xie, Daiqian; Guo, Hua
  • The Journal of Chemical Physics, Vol. 136, Issue 3
  • DOI: 10.1063/1.3676725

Construction of diabatic energy surfaces for LiFH with artificial neural networks
journal, December 2017

  • Guan, Yafu; Fu, Bina; Zhang, Dong H.
  • The Journal of Chemical Physics, Vol. 147, Issue 22
  • DOI: 10.1063/1.5007031

Assigning signs to the electronic nonadiabatic coupling terms:  The {H2,O} system as a case study
journal, April 2005

  • Vibók, Ágnes; Halász, Gábor J.; Suhai, Sándor
  • The Journal of Chemical Physics, Vol. 122, Issue 13
  • DOI: 10.1063/1.1867438

Effects of higher order Jahn-Teller coupling on the nuclear dynamics
journal, March 2004

  • Viel, Alexandra; Eisfeld, Wolfgang
  • The Journal of Chemical Physics, Vol. 120, Issue 10
  • DOI: 10.1063/1.1646371

From ab Initio Potential Energy Surfaces to State-Resolved Reactivities: X + H 2 O ↔ HX + OH [X = F, Cl, and O( 3 P)] Reactions
journal, May 2015

  • Li, Jun; Jiang, Bin; Song, Hongwei
  • The Journal of Physical Chemistry A, Vol. 119, Issue 20
  • DOI: 10.1021/acs.jpca.5b02510

Beyond Born-Oppenheimer
book, January 2006

On the representation of coupled adiabatic potential energy surfaces using quasi-diabatic Hamiltonians: A distributed origins expansion approach
journal, May 2012

  • Zhu, Xiaolei; Yarkony, David R.
  • The Journal of Chemical Physics, Vol. 136, Issue 17
  • DOI: 10.1063/1.4704789

A new approach for the development of diabatic potential energy surfaces: Hybrid block-diagonalization and diabatization by ansatz
journal, November 2016

  • Wittenbrink, Nils; Venghaus, Florian; Williams, David
  • The Journal of Chemical Physics, Vol. 145, Issue 18
  • DOI: 10.1063/1.4967258

Recent Advances in Quantum Dynamics of Bimolecular Reactions
journal, May 2016

Signatures of a Conical Intersection in Adiabatic Dissociation on the Ground Electronic State
journal, February 2018

  • Xie, Changjian; Malbon, Christopher L.; Yarkony, David R.
  • Journal of the American Chemical Society, Vol. 140, Issue 6
  • DOI: 10.1021/jacs.7b11489

Interpolation of diabatic potential-energy surfaces: Quantum dynamics on ab initio surfaces
journal, October 2005

  • Evenhuis, Christian R.; Lin, Xin; Zhang, Dong H.
  • The Journal of Chemical Physics, Vol. 123, Issue 13
  • DOI: 10.1063/1.2047569

The direct calculation of diabatic states based on configurational uniformity
journal, January 2001

  • Nakamura, Hisao; Truhlar, Donald G.
  • The Journal of Chemical Physics, Vol. 115, Issue 22
  • DOI: 10.1063/1.1412879
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