We present a molecular geometry optimization algorithm based on the gradient-enhanced universal kriging (GEUK) formalism with ab initio prior mean functions, which incorporates prior physical knowledge to surrogate-based optimization. In this formalism, we have demonstrated the advantage of allowing the prior mean functions to be adaptive during geometry optimization over a pre-fixed choice of prior functions. Our implementation is general and flexible in two senses. First, the optimizations on the surrogate surface can be in both Cartesian coordinates and curvilinear coordinates. We explore four representative curvilinear coordinates in this work, including the redundant Coulombic coordinates, the redundant internal coordinates, the non-redundant delocalized internal coordinates, and the non-redundant hybrid delocalized internal Z-matrix coordinates. We show that our GEUK optimizer accelerates geometry optimization as compared to conventional non-surrogate-based optimizers in internal coordinates. We further showcase the power of the GEUK with on-the-fly adaptive priors for efficient optimizations of challenging molecules (Criegee intermediates) with a high-accuracy electronic structure method (the coupled-cluster method). Second, we present the usage of internal coordinates under the complete curvilinear scheme. A complete curvilinear scheme performs both surrogate potential-energy surface (PES) fitting and structure optimization entirely in the curvilinear coordinates. Our benchmark indicates that the complete curvilinear scheme significantly reduces the cost of structure minimization on the surrogate compared to the incomplete curvilinear scheme, which fits the surrogate PES in curvilinear coordinates partially and optimizes a structure in Cartesian coordinates through curvilinear coordinates via the chain rule.
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14 January 2023
Research Article|
January 12 2023
A spur to molecular geometry optimization: Gradient-enhanced universal kriging with on-the-fly adaptive ab initio prior mean functions in curvilinear coordinates
Special Collection:
2022 JCP Emerging Investigators Special Collection
Chong Teng
;
Chong Teng
(Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Supervision, Validation, Writing – original draft, Writing – review & editing)
1
Department of Chemistry, Boston College
, Chestnut Hill, Massachusetts 02467, USA
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Daniel Huang
;
Daniel Huang
(Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Writing – original draft, Writing – review & editing)
2
Department of Computer Science, San Francisco State University
, San Francisco, California 94132, USA
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Junwei Lucas Bao
Junwei Lucas Bao
a)
(Conceptualization, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Supervision, Validation, Writing – original draft, Writing – review & editing)
1
Department of Chemistry, Boston College
, Chestnut Hill, Massachusetts 02467, USA
a)Author to whom correspondence should be addressed: lucas.bao@bc.edu
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a)Author to whom correspondence should be addressed: lucas.bao@bc.edu
Note: This paper is part of the 2022 JCP Emerging Investigators Special Collection.
J. Chem. Phys. 158, 024112 (2023)
Article history
Received:
November 04 2022
Accepted:
December 21 2022
Citation
Chong Teng, Daniel Huang, Junwei Lucas Bao; A spur to molecular geometry optimization: Gradient-enhanced universal kriging with on-the-fly adaptive ab initio prior mean functions in curvilinear coordinates. J. Chem. Phys. 14 January 2023; 158 (2): 024112. https://doi.org/10.1063/5.0133675
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