[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82969-en":3,"doc-seo-82969-105":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":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},82969,687197207639,"Asher","https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd",8,"Research & Report","EOM-CC Excited-State Gradients and Nonadiabatic Couplings on a Consumer GPU from a Contraction DAG with Laplace-Transform J/K Kernels","Unified, memory-bounded GPU implementation of equation-of-motion coupled-cluster (EOM-CC) excited-state gradients and interstate nonadiabatic coupling matrix elements (NACMEs) on a single 8GB consumer GPU. Both quantities are computed from one contraction directed acyclic graph: EOM-CC relaxation uses a reverse-mode transpose of the forward density build, avoiding per-state re-derivation. An AO-direct Laplace-transform J/K kernel resolves energy denominators without four-index tensors, while a two-sided Davidson yields eigenvectors from one device-resident, spin-pure solve. End-to-end validation matches finite differences and Psi4 results, and supports chromophore-scale runs using frozen natural virtual compression.","arXiv :2607 .05622v1 [physics .chem-ph] 6 Jul 2026  \nEOM-CC Excited-State Gradients and Nonadiabatic Couplings on a Consumer GPU from a Contraction-DAG with Laplace-Transform  \nJ/K Kernels  \nRuben Dario Guerrero ∗ ,†,‡  \n†Neuro TechNet S.A.S., 1108831, Bogot´a, Colombia  \n‡Quantum and Computational Chemistry Group (QCCG), Universidad Nacional de  \nColombia, Bogot´a, Colombia  \nE-mail: [rudaguerman@gmail.com](rudaguerman@gmail.com)  \nAbstract  \nWe present a unified, memory-bounded GPU realization of equation-of-motion coupled-cluster (EOM-CC) excited-state gradients and interstate nonadiabatic couplings (NACMEs) on a single 8GB consumer GPU. Both are built from one contraction directed acyclic graph: the EOM-CC relaxation is the reverse-mode transpose of the forward density build rather than a per-state re-derivation, and an atomic-orbital-direct Laplace-transform J/K kernel, made non-symmetric (Jx(A, B)  Jx(B, A)) by the transition densities, resolves every energy denominator with no four-index molecularorbital tensor; a two-sided Davidson returns both eigenvectors from one device-resident, spin-pure solve. The pipeline is validated end to end at small scale: gradients and NACMEs match finite differences across four spin multiplicities and full configuration interaction to \u003C 10 −12 for two electrons, and the excited-state gradient matches the  \nindependent Psi4 code to ≤4 .6×10−7 Eh/a0 from H2 O to aromatic benzene. The kernels and the ground-state solve reach chromophores (≤730 AO) in 8GB, and a frozennatural-virtual compression lets the eigensolver execute a complete excited-state gradient and Q–B NACME of the chlorophyll-core chromophore Mg-porphine (def2-SVP, 439 AO) on the card. We present that run as a capability demonstration—executed and translationally invariant to machine zero, but anchored only piece-wise and bounded by a direct convergence study at ∼ 10 −2 Eh/a0—not a converged spectroscopic result.  \nThe validated small-scale capability and the memory-bounded implementation are the contribution.  \n1 Introduction  \nWhen a molecule absorbs light it evolves on excited-state potential-energy surfaces and can return to the ground state through conical intersections —geometries where two electronic states become degenerate and the Born–Oppenheimer separation breaks down. Simulating this photochemistry — vision, photosynthesis, photovoltaics, DNA photoprotection — requires two quantities at every nuclear geometry: the gradient of each excited state (the force that drives the dynamics) and the nonadiabatic coupling matrix element (NACME, the rate at which neighbouring states exchange population near an intersection) . Computing both accurately for correlated wavefunctions is the central bottleneck of nonadiabatic dynamics.  \nWith equation-of-motion coupled cluster (EOM-CC), 1 ,2 the benchmark single-reference method for excited states, obtaining these quantities has traditionally meant re-deriving the response (relaxation) equations by hand for each state and running them on datacenter GPUs. Here we obtain both automatically—as the reverse-mode transpose (the same mechanism as backpropagation in machine learning) of a single contraction graph—and engineer the resulting non-symmetric Coulomb/exchange kernels to run within the 8GB budget of a consumer NVIDIA GeForce RTX 4060 (GPU performance is reported in Sect. 4.4), putting a capability that today needs a cluster allocation onto a card a student already owns.  \nEach ingredient of this construction has a mature literature, and we engage it directly so that the contribution is not overstated. EOM-CC excited-state gradients and nonadiabatic couplings are established quantities: the analytic EOM-CC gradient and its Lagrangian (Z-vector) formulation were developed by Stanton and Gauss 3 ,4 and implemented for spinconserving and spin-flip states by Krylov and co-workers, 5 while EOM-CC nonadiabatic and derivative couplings have been formulated and validated against multireferen","cbCairArosyQ320r","https://ap.wps.com/l/cbCairArosyQ320r","pdf",937051,2,1,72,"English","en",105,"# Introduction\n## Motivation: excited-state dynamics and conical intersections\n## Method: EOM-CC gradients and NACMEs with a single GPU pipeline\n## Related work and position of the contribution","[{\"question\":\"What do the gradients and NACMEs represent in excited-state photochemistry?\",\"answer\":\"The excited-state gradient is the force driving molecular dynamics on the excited-state potential-energy surface. The NACME is the matrix element governing how neighboring electronic states exchange population near conical intersections.\"},{\"question\":\"How does the proposed GPU method obtain EOM-CC relaxation for gradients without per-state re-derivation?\",\"answer\":\"It constructs both gradients and NACMEs from a single contraction directed acyclic graph, using the relaxation as the reverse-mode transpose of the forward density build, rather than re-deriving response equations separately for each state.\"},{\"question\":\"How are energy denominators handled efficiently within the GPU memory budget?\",\"answer\":\"An atomic-orbital-direct Laplace-transform J/K kernel resolves every energy denominator without four-index molecular-orbital tensors. Transition densities make the Coulomb/exchange kernels non-symmetric so the required denominators can be addressed within the same kernel framework.\"}]",1784184380,181,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"eom-cc-excited-state-gradients-and-nonadiabatic-couplings-on-a-consumer-gpu-from-a-contraction-dag-with-laplace-transform-jk-kernels","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,47,50],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":20},"https://docshare.wps.com/document/","Document",{"item":48,"name":12,"@type":43,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/eom-cc-excited-state-gradients-and-nonadiabatic-couplings-on-a-consumer-gpu-from-a-contraction-dag-with-laplace-transform-jk-kernels/82969/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-24","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What do the gradients and NACMEs represent in excited-state photochemistry?","Question",{"text":75,"@type":76},"The excited-state gradient is the force driving molecular dynamics on the excited-state potential-energy surface. The NACME is the matrix element governing how neighboring electronic states exchange population near conical intersections.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the proposed GPU method obtain EOM-CC relaxation for gradients without per-state re-derivation?",{"text":80,"@type":76},"It constructs both gradients and NACMEs from a single contraction directed acyclic graph, using the relaxation as the reverse-mode transpose of the forward density build, rather than re-deriving response equations separately for each state.",{"name":82,"@type":73,"acceptedAnswer":83},"How are energy denominators handled efficiently within the GPU memory budget?",{"text":84,"@type":76},"An atomic-orbital-direct Laplace-transform J/K kernel resolves every energy denominator without four-index molecular-orbital tensors. Transition densities make the Coulomb/exchange kernels non-symmetric so the required denominators can be addressed within the same kernel framework.","https://schema.org",{"og:url":51,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":51},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":20,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":52,"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"]