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Title: A Robust and Unified Solution for Choosing the Phases of Adiabatic States as a Function of Geometry: Extending Parallel Transport Concepts to the Cases of Trivial and Near-Trivial Crossings

Abstract

We investigate a simple and robust scheme for choosing the phases of adiabatic electronic states smoothly (as a function of geometry) so as to maximize the performance of ab initio non-adiabatic dynamics methods. Our approach is based upon consideration of the overlap matrix (U) between basis functions at successive points in time and selecting the phases so as to minimize the matrix norm of log(U). In so doing, one can extend the concept of parallel transport to cases with sharp curve crossings. We demonstrate that this algorithm performs well under extreme situations where dozens of states cross each other either through trivial crossings (where there is zero effective diabatic coupling), or through non-trivial crossings (when there is a non-zero diabatic coupling), or through a combination of both. In all cases, we compute the time-derivative coupling matrix elements (or equivalently non-adiabatic derivative coupling matrix elements) that are as smooth as possible. Finally, our results should be of interest to all who are interested in either non-adiabatic dynamics, or more generally, parallel transport in large systems.

Authors:
ORCiD logo [1];  [1]; ORCiD logo [1]; ORCiD logo [1];  [1]
  1. Univ. of Pennsylvania, Philadelphia, PA (United States)
Publication Date:
Research Org.:
Univ. of Pennsylvania, Philadelphia, PA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES); US Air Force Office of Scientific Research (AFOSR)
OSTI Identifier:
1656843
Grant/Contract Number:  
SC0019281; FA9550-18-1-0497; FA9550-18-1-0420
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Theory and Computation
Additional Journal Information:
Journal Volume: 16; Journal Issue: 2; Journal ID: ISSN 1549-9618
Publisher:
American Chemical Society
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; non-adiabatic dynamics; algorithms; phases of matter; mathematical methods; phase transitions; Hamiltonians

Citation Formats

Zhou, Zeyu, Jin, Zuxin, Qiu, Tian, Rappe, Andrew M., and Subotnik, Joseph Eli. A Robust and Unified Solution for Choosing the Phases of Adiabatic States as a Function of Geometry: Extending Parallel Transport Concepts to the Cases of Trivial and Near-Trivial Crossings. United States: N. p., 2019. Web. https://doi.org/10.1021/acs.jctc.9b00952.
Zhou, Zeyu, Jin, Zuxin, Qiu, Tian, Rappe, Andrew M., & Subotnik, Joseph Eli. A Robust and Unified Solution for Choosing the Phases of Adiabatic States as a Function of Geometry: Extending Parallel Transport Concepts to the Cases of Trivial and Near-Trivial Crossings. United States. https://doi.org/10.1021/acs.jctc.9b00952
Zhou, Zeyu, Jin, Zuxin, Qiu, Tian, Rappe, Andrew M., and Subotnik, Joseph Eli. Mon . "A Robust and Unified Solution for Choosing the Phases of Adiabatic States as a Function of Geometry: Extending Parallel Transport Concepts to the Cases of Trivial and Near-Trivial Crossings". United States. https://doi.org/10.1021/acs.jctc.9b00952. https://www.osti.gov/servlets/purl/1656843.
@article{osti_1656843,
title = {A Robust and Unified Solution for Choosing the Phases of Adiabatic States as a Function of Geometry: Extending Parallel Transport Concepts to the Cases of Trivial and Near-Trivial Crossings},
author = {Zhou, Zeyu and Jin, Zuxin and Qiu, Tian and Rappe, Andrew M. and Subotnik, Joseph Eli},
abstractNote = {We investigate a simple and robust scheme for choosing the phases of adiabatic electronic states smoothly (as a function of geometry) so as to maximize the performance of ab initio non-adiabatic dynamics methods. Our approach is based upon consideration of the overlap matrix (U) between basis functions at successive points in time and selecting the phases so as to minimize the matrix norm of log(U). In so doing, one can extend the concept of parallel transport to cases with sharp curve crossings. We demonstrate that this algorithm performs well under extreme situations where dozens of states cross each other either through trivial crossings (where there is zero effective diabatic coupling), or through non-trivial crossings (when there is a non-zero diabatic coupling), or through a combination of both. In all cases, we compute the time-derivative coupling matrix elements (or equivalently non-adiabatic derivative coupling matrix elements) that are as smooth as possible. Finally, our results should be of interest to all who are interested in either non-adiabatic dynamics, or more generally, parallel transport in large systems.},
doi = {10.1021/acs.jctc.9b00952},
journal = {Journal of Chemical Theory and Computation},
number = 2,
volume = 16,
place = {United States},
year = {2019},
month = {12}
}

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