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 NearTrivial 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 nonadiabatic 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 nontrivial crossings (when there is a nonzero diabatic coupling), or through a combination of both. In all cases, we compute the timederivative coupling matrix elements (or equivalently nonadiabatic derivative coupling matrix elements) that are as smooth as possible. Finally, our results should be of interest to all who are interested in either nonadiabatic dynamics, or more generally, parallel transport in large systems.
 Authors:

 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; FA95501810497; FA95501810420
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Chemical Theory and Computation
 Additional Journal Information:
 Journal Volume: 16; Journal Issue: 2; Journal ID: ISSN 15499618
 Publisher:
 American Chemical Society
 Country of Publication:
 United States
 Language:
 English
 Subject:
 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; nonadiabatic 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 NearTrivial 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 NearTrivial 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 NearTrivial 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 NearTrivial 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 nonadiabatic 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 nontrivial crossings (when there is a nonzero diabatic coupling), or through a combination of both. In all cases, we compute the timederivative coupling matrix elements (or equivalently nonadiabatic derivative coupling matrix elements) that are as smooth as possible. Finally, our results should be of interest to all who are interested in either nonadiabatic 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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