[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-118346-en":3,"doc-seo-118346-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},118346,13056703019404,"Miles","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",8,"Research & Report","Machine Learning Coupled Potential Energy Surfaces - Thesis Master of Science Chemistry","Machine learning methods for potential energy surfaces (PESs) have shown strong performance for isolated ground-state surfaces, while coupled excited-state PESs remain difficult due to non-differentiable adiabatic potentials at conical intersections. This work develops a smooth modeling strategy by learning nuclear-coordinate dependent characteristic polynomial coefficients of the potential matrix, enabling accurate reconstruction of coupled surfaces at conical-intersection seams. Validation is performed with ab initio MRCI across multiple molecules, including reproduction near minimum energy conical intersections and assessment against analytical MRCI solutions. The framework is extended to combined DFT/MRCI, where a Gaussian-process approach models local discontinuities as noise to obtain smooth, accurate DFT/MRCI(2) PES representations while matching ab initio branching spaces and geometries.","Machine Learning Coupled Potential Energy Surfaces  \nTzu Yu Wang  \nThesis submitted to the University of Ottawa in partial fulfillment of the requirements for the degree of Master of Science, Chemistry  \nDepartment of Chemistry and Biomolecular Sciences  \nFaculty of Science  \nUniversity of Ottawa  \nMichael S. Schuurman  \n© Tzu Yu Wang, Ottawa, Canada, 2025  \nAbstract  \nRecent advancements in machine learning (ML) for potential energy surfaces (PESs) have yielded promising results, with much of the focus on isolated ground-state surfaces. Extending machine learning to coupled excited state surfaces introduces significant challenges, however, particularly in regions of conical intersections. At these points, the adiabatic potentials are non-differentiable, complicating the application of standard ML techniques. In this work, we build on a previously proposed approach that overcomes this issue by learning the nuclear coordinate dependent characteristic polynomial coefficients of the potential matrix instead, which enables the construction of smooth, accurate machine learning models even at seams of conical intersections.  \nThe proposed approach is first validated at the ab initio multi-reference configuration interaction (MRCI) level of theory for various molecules. We examine the ability of the proposed model to accurately reproduce energies near a minimum energy conical intersection (MECI) and analyze its performance in capturing seams of conical intersection against analytical MRCI solutions. The results demonstrate that, through this approach, quantitatively accurate machine learning models of seams of conical intersection may be constructed.  \nWe further demonstrate the application of this framework to the combined density functional theory and multi-reference configuration interaction (DFT/MRCI) method. The selected configuration interaction nature of the method enables the calculation of accurate excitation energies at a low computational cost. However, the potential energy surfaces produced resemble smooth underlying surfaces contaminated with noise, rendering them locally non smooth. To mitigate this, we treat the local discontinuities in the potential surfaces as noise by explicitly optimizing a whitenoise kernel within a Gaussian process regression framework. We apply this method to optimize DFT/MRCI minimum energy conical intersection geometries and compare the results to ab initio MRCI solutions. While treating the locally discontinuous surface as noise limits the ability to achieve arbitrarily small energy gap at nominal intersections, the structures and branching spaces obtained are in strong agreement with ab initio data. This approach thus proves to be a viable method for generating smooth, accurate representations of DFT/MRCI(2) PESs.  \nAcknowledgements  \nFirst and foremost, I would like to express my heartfelt gratitude to Prof. Michael Schuurman for his unwavering patience and guidance over the past few years. I have learned so much under his mentorship. To Dr. Simon Neville, whose support has helped me grow in countless ways and who has become an irreplaceable mentor, I offer my deepest thanks. I am also grateful to all my lab members for their patience with my many questions and for helping me become a better scientist. Finally, I could not have embarked on this journey without the love and support of my family and my partner, who mean everything to me.  \nContents  \nAbstract ii  \nAcknowledgements iii  \nList of Figures vi  \nList of Tables viii  \nList of Abbreviations x  \n1 Motivation 1  \n2 Excited State Potential Energy Surfaces 4  \n2.1 Born-Oppenheimer Approximation ...................... 5  \n2.1.1 Diabatic States ............................. 10  \n2.2 Conical Intersections .............................. 13  \n2.2.1 Two-State Conical Intersections .................... 13  \n2.2.2 Three-State Conical Intersections ................... 18  \n2.2.3 Types of Conical Intersections ..................... 20  \n2.2.4 Met","cbCaiiUxBjx08Th5","https://ap.wps.com/l/cbCaiiUxBjx08Th5","pdf",6997816,1,125,"English","en",105,"# Motivation\n# Excited State Potential Energy Surfaces\n## Born-Oppenheimer Approximation\n## Conical Intersections\n## Electronic Structure Theory\n# Machine Learning of Potential Energy Surfaces\n## Smooth Overlap of Atomic Positions\n## Gaussian Process Regression\n# Learning Coupled Potential Energy Surfaces\n## Characteristic Polynomial Coefficients\n## Reproduction of Conical Intersections\n# DFT/MRCI Structure Optimization\n## Minimum Energy Conical Intersection Optimization and Characterization","[{\"question\":\"Why are coupled excited-state potential energy surfaces harder to learn than isolated ground-state surfaces?\",\"answer\":\"At conical intersections, adiabatic potentials become non-differentiable, which complicates standard machine learning workflows built on smooth inputs.\"},{\"question\":\"How does the thesis enable smooth machine learning models at seams of conical intersections?\",\"answer\":\"It learns characteristic polynomial coefficients of the potential matrix as functions of nuclear coordinates, allowing smooth and accurate construction of machine learning models even at conical-intersection seams.\"},{\"question\":\"How is the DFT/MRCI case handled when the learned potential surfaces become locally non-smooth?\",\"answer\":\"Local discontinuities are treated as noise by explicitly optimizing a whitenoise kernel within Gaussian process regression, improving smooth representations while keeping structures and branching spaces consistent with ab initio results.\"}]","Machine Learning Coupled Potential Energy Surfaces - Thesis Master of Science Chemistry | PDF",1785683206,315,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"machine-learning-coupled-potential-energy-surfaces-master-of-science-thesis-chemistry","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/machine-learning-coupled-potential-energy-surfaces-master-of-science-thesis-chemistry/118346/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-02",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"Why are coupled excited-state potential energy surfaces harder to learn than isolated ground-state surfaces?","Question",{"text":75,"@type":76},"At conical intersections, adiabatic potentials become non-differentiable, which complicates standard machine learning workflows built on smooth inputs.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the thesis enable smooth machine learning models at seams of conical intersections?",{"text":80,"@type":76},"It learns characteristic polynomial coefficients of the potential matrix as functions of nuclear coordinates, allowing smooth and accurate construction of machine learning models even at conical-intersection seams.",{"name":82,"@type":73,"acceptedAnswer":83},"How is the DFT/MRCI case handled when the learned potential surfaces become locally non-smooth?",{"text":84,"@type":76},"Local discontinuities are treated as noise by explicitly optimizing a whitenoise kernel within Gaussian process regression, improving smooth representations while keeping structures and branching spaces consistent with ab initio results.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]