[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-122227-en":3,"doc-seo-122227-105":29,"detail-sidebar-cat-0-en-105":90},{"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":11,"language":21,"language_code":22,"site_id":23,"html_lang":22,"table_of_contents":24,"faqs":25,"seo_title":26,"seo_description":14,"update_tm":27,"read_time":28},122227,13056703019404,"Miles","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",8,"Research & Report","Quantum Chemical Density Matrix Renormalization Group Method Boosted by Machine Learning","Machine learning (ML) is used to refine low-level quantum chemical calculations toward higher accuracy, an approach known as Δ-ML. The density matrix renormalization group (DMRG) offers a variational framework for strongly correlated quantum systems, typically balancing accuracy with high computational efficiency. This work shows that a simple ML model can substantially improve performance of the quantum chemical DMRG method while preserving efficiency, demonstrating practical benefits for reaching high-level accuracy.","Lawrence Berkeley National Laboratory  \nLBL Publications  \nTitle  \nQuantum Chemical Density Matrix Renormalization Group Method Boosted by Machine Learning  \nPermalink  \n[https://escholarship.org/uc/item/2r8757gr](https://escholarship.org/uc/item/2r8757gr)  \nJournal  \nThe Journal of Physical Chemistry Letters, 16(13)  \nISSN  \n1948-7185  \nAuthors  \nGolub, Pavlo  \nYang, Chao Vlček, Vojtěchet al.  \nPublication Date  \n2025-04-03  \nDOI  \n10.1021/acs.jpclett.5c00207  \nCopyright Information  \nThis work is made available under the terms of a Creative Commons Attribution License, available at [https://creativecommons.org/licenses/by/4.0/](https://creativecommons.org/licenses/by/4.0/)  \nPeer reviewed  \n[eScholarship.org](eScholarship.org) Powered by the California Digital Library  \nUniversity of California  \nThis article is licensed under CC-BY 4.0   \n[pubs.acs.org/JPCL](pubs.acs.org/JPCL)  Letter   \nQuantum Chemical Density Matrix Renormalization Group Method Boosted by Machine Learning  \nPavlo Golub, * Chao Yang, Vojťech Vľcek, and Libor Veis*  \n Cite This: J. Phys. Chem. Lett. 2025, 16, 3295−3301  \nRead Online  \nACCESS  \n Metrics & More  \n Article Recommendations  \n*sı   \nSupporting Information  \nDownloaded via 108.75.79.166 on April 10, 2025 at 17:25:24 (UTC) . See [https://pubs.acs.org/sharingguidelines](https://pubs.acs.org/sharingguidelines) for options on how to legitimately share published articles.  \nABSTRACT: The use of machine learning (ML) to refine low-level theoretical calculations to achieve higher accuracy is a promising and actively evolving approach known as Δ-ML. The density matrix renormalization group (DMRG) is a powerful variational approach widely used for studying strongly correlated quantum systems. High computational efficiency can be achieved without compromising accuracy. Here, we demonstrate the potential of a simple ML model to significantly enhance the performance of the quantum chemical DMRG method.  \nThe concept ofusing machine learning (ML) to refine low  \nlevel theoretical calculations, bringing them closer to high-level accuracy, is a promising and actively evolving approach known as Δ-ML.1 Various computational starting points have been explored in this context, including density functional theory (DFT)2−7 or Hartree−Fock (HF) singlereference calculations,8 and post-HF ab initio methods like second order Møller−Plesset perturbation thoery (MP2)9, 10 or coupled clusters with singles and doubles (CCSD).11 Additionally, variational two-electron reduced-density matrix (v2RDM) descriptions have been used as starting points.12 These methods are optimized against highly accurate, yet computationally intensive, benchmarks such as coupled clusters with perturbative triples [CCSD(T)] or complete active space configuration interaction (CASCI), aiming to achieve results that closely approximate high-level accuracy.  \nThe DMRG method 13, 14 is a powerful variational approach widely used for studying strongly correlated quantum systems.15 By optimizing the many-body wave function within a truncated Hilbert space, DMRG achieves high computational efficiency without compromising accuracy. In quantum chemistry applications, 16−20 DMRG typically approximates the ground state (or low-lying excited states) of a full configuration interaction (FCI) solution within a chosen orbital space, such as that defined by the CASCI framework. An example can be the π-orbital active space of polycyclic aromatic hydrocarbons (PAHs) presented below.  \nThe DMRG algorithm provides the wave function in a matrix product state (MPS) representation, which allows for an efficient and compact description of entangled quantum  \nstates.21 The FCI wave function, in the occupation basis representation, is expressed as  \n|FCI =  c 12 ... n|12 ··· n  \n{} (1)  \nwhere αi represents the occupation state of the i-th orbital, with αi ∈ |0 ⟩, |↓⟩, |↑⟩, |↓↑⟩. By successively applying singular value decomposition (SVD) to the FCI tensor cα1 α2... αn, t","cbCaitlrthyx7ieC","https://ap.wps.com/l/cbCaitlrthyx7ieC","pdf",3659799,1,"English","en",105,"## Abstract\n## Δ-ML concept and computational starting points\n## DMRG in quantum chemistry and MPS representation\n## MPGNN model and performance enhancement\n## Experimental/procedural details and discussion","[{\"question\":\"What is Δ-ML in the context of this work?\",\"answer\":\"Δ-ML refers to using machine learning to correct or refine lower-level theoretical calculations so they approach higher-level accuracy.\"},{\"question\":\"What role does DMRG play in the described methodology?\",\"answer\":\"DMRG is a variational method designed for strongly correlated quantum systems, providing efficient approximations by optimizing the many-body wave function in a truncated Hilbert space.\"},{\"question\":\"How does the proposed machine learning model improve quantum chemical DMRG?\",\"answer\":\"The study demonstrates that a simple ML model can significantly enhance the performance of the quantum chemical DMRG method without sacrificing computational efficiency.\"}]","Quantum Chemical Density Matrix Renormalization Group Method Boosted by Machine Learning | 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is Δ-ML in the context of this work?","Question",{"text":74,"@type":75},"Δ-ML refers to using machine learning to correct or refine lower-level theoretical calculations so they approach higher-level accuracy.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"What role does DMRG play in the described methodology?",{"text":79,"@type":75},"DMRG is a variational method designed for strongly correlated quantum systems, providing efficient approximations by optimizing the many-body wave function in a truncated Hilbert space.",{"name":81,"@type":72,"acceptedAnswer":82},"How does the proposed machine learning model improve quantum chemical DMRG?",{"text":83,"@type":75},"The study demonstrates that a simple ML model can significantly enhance the performance of the quantum chemical DMRG method without sacrificing computational 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