{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,13]],"date-time":"2025-11-13T12:40:34Z","timestamp":1763037634263,"version":"3.37.3"},"reference-count":102,"publisher":"IOP Publishing","issue":"3","license":[{"start":{"date-parts":[[2021,7,14]],"date-time":"2021-07-14T00:00:00Z","timestamp":1626220800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2021,7,14]],"date-time":"2021-07-14T00:00:00Z","timestamp":1626220800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/100010665","name":"H2020 Marie Sk\u0142odowska-Curie Actions","doi-asserted-by":"crossref","award":["722346"],"award-info":[{"award-number":["722346"]}],"id":[{"id":"10.13039\/100010665","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["Mach. Learn.: Sci. Technol."],"published-print":{"date-parts":[[2021,9,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Deep learning (DL) is applied to simulate non-adiabatic molecular dynamics of phenanthrene, using the time-dependent density functional based tight binding (TD-DFTB) approach for excited states combined with mixed quantum\u2013classical propagation. Reference calculations rely on Tully\u2019s fewest-switches surface hopping (FSSH) algorithm coupled to TD-DFTB, which provides electronic relaxation dynamics in fair agreement with various available experimental results. Aiming at describing the coupled electron-nuclei dynamics in large molecular systems, we then examine the combination of DL for excited-state potential energy surfaces (PESs) with a simplified trajectory surface hopping propagation based on the Belyaev\u2013Lebedev (BL) scheme. We start to assess the accuracy of the TD-DFTB approach upon comparison of the optical spectrum with experimental and higher-level theoretical results. Using the recently developed SchNetPack (Sch\u00fctt <jats:italic>et al<\/jats:italic> 2019 <jats:italic>J. Chem. Theory Comput.<\/jats:italic> \n                  <jats:bold>15<\/jats:bold> 448\u201355) for DL applications, we train several models and evaluate their performance in predicting excited-state energies and forces. Then, the main focus is given to the analysis of the electronic population of low-lying excited states computed with the aforementioned methods. We determine the relaxation timescales and compare them with experimental data. Our results show that DL demonstrates its ability to describe the excited-state PESs. When coupled to the simplified BL scheme considered in this study, it provides reliable description of the electronic relaxation in phenanthrene as compared with either the experimental data or the higher-level FSSH\/TD-DFTB theoretical results. Furthermore, the DL performance allows high-throughput analysis at a negligible cost.<\/jats:p>","DOI":"10.1088\/2632-2153\/abfe3f","type":"journal-article","created":{"date-parts":[[2021,7,13]],"date-time":"2021-07-13T11:32:07Z","timestamp":1626175927000},"page":"035039","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":9,"title":["On application of deep learning to simplified quantum-classical dynamics in electronically excited states"],"prefix":"10.1088","volume":"2","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1623-0594","authenticated-orcid":false,"given":"Evgeny","family":"Posenitskiy","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9412-2866","authenticated-orcid":false,"given":"Fernand","family":"Spiegelman","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Didier","family":"Lemoine","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"266","published-online":{"date-parts":[[2021,7,14]]},"reference":[{"key":"mlstabfe3fbib1","doi-asserted-by":"publisher","DOI":"10.1038\/ncomms13890","article-title":"Quantum-chemical insights from deep tensor neural networks","volume":"8","author":"Sch\u00fctt","year":"2017","journal-title":"Nat. Commun."},{"key":"mlstabfe3fbib2","doi-asserted-by":"publisher","DOI":"10.1002\/adma.201902765","article-title":"Machine learning interatomic potentials as emerging tools for materials science","volume":"31","author":"Deringer","year":"2019","journal-title":"Adv. Mater."},{"key":"mlstabfe3fbib3","doi-asserted-by":"publisher","DOI":"10.1088\/2632-2153\/ab9c3e","article-title":"Machine learning and excited-state molecular dynamics","volume":"1","author":"Westermayr","year":"2020","journal-title":"Mach. Learn.: Sci. Technol."},{"key":"mlstabfe3fbib4","doi-asserted-by":"publisher","first-page":"2336","DOI":"10.1021\/acs.jpclett.9b03664","article-title":"Quantum chemistry in the age of machine learning","volume":"11","author":"Dral","year":"2020","journal-title":"J. Phys. Chem. Lett."},{"key":"mlstabfe3fbib5","doi-asserted-by":"publisher","first-page":"3678","DOI":"10.1021\/acs.jctc.9b00181","article-title":"Physnet: A neural network for predicting energies, forces, dipole moments and partial charges","volume":"15","author":"Unke","year":"2019","journal-title":"J. Chem. Theory Comput."},{"author":"Meuwly","article-title":"Transformative applications of machine learning for chemical reactions","key":"mlstabfe3fbib6"},{"key":"mlstabfe3fbib7","doi-asserted-by":"crossref","DOI":"10.1613\/jair.301","article-title":"Reinforcement learning: a survey","author":"Kaelbling","year":"1996"},{"key":"mlstabfe3fbib8","doi-asserted-by":"publisher","DOI":"10.1063\/1.5023671","article-title":"Accelerating atomic structure search with cluster regularization","volume":"148","author":"S\u00f8rensen","year":"2018","journal-title":"J. Chem. Phys."},{"key":"mlstabfe3fbib9","doi-asserted-by":"publisher","first-page":"1486","DOI":"10.1021\/acs.jctc.6b01119","article-title":"Combining evolutionary algorithms with clustering toward rational global structure optimization at the atomic scale","volume":"13","author":"J\u00f8rgensen","year":"2017","journal-title":"J. Chem. Theory Comput."},{"key":"mlstabfe3fbib10","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.120.026102","article-title":"On-the-fly machine learning of atomic potential in density functional theory structure optimization","volume":"120","author":"Jacobsen","year":"2018","journal-title":"Phys. Rev. Lett."},{"key":"mlstabfe3fbib11","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.124.086102","article-title":"Efficient global structure optimization with a machine-learned surrogate model","volume":"124","author":"Bisbo","year":"2020","journal-title":"Phys. Rev. Lett."},{"key":"mlstabfe3fbib12","doi-asserted-by":"publisher","DOI":"10.1063\/1.5108871","article-title":"Atomistic structure learning","volume":"151","author":"J\u00f8rgensen","year":"2019","journal-title":"J. Chem. Phys."},{"key":"mlstabfe3fbib13","doi-asserted-by":"publisher","first-page":"503","DOI":"10.1002\/anie.199305031","article-title":"Neural networks in chemistry","volume":"32","author":"Gasteiger","year":"1993","journal-title":"Angewandte Chemie Int. Edn English"},{"key":"mlstabfe3fbib14","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1007\/BF02551274","article-title":"Approximation by superpositions of a sigmoidal function","volume":"2","author":"Cybenko","year":"1989","journal-title":"Math. Control Signals Syst."},{"key":"mlstabfe3fbib15","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1016\/0893-6080(89)90020-8","article-title":"Multilayer feedforward networks are universal approximators","volume":"2","author":"Hornik","year":"1989","journal-title":"Neural Netw."},{"key":"mlstabfe3fbib16","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.98.146401","article-title":"Generalized neural-network representation of high-dimensional potential-energy surfaces","volume":"98","author":"Behler","year":"2007","journal-title":"Phys. Rev. Lett."},{"key":"mlstabfe3fbib17","doi-asserted-by":"publisher","first-page":"6924","DOI":"10.1039\/C7SC02267K","article-title":"Machine learning molecular dynamics for the simulation of infrared spectra","volume":"8","author":"Gastegger","year":"2017","journal-title":"Chem. Sci."},{"key":"mlstabfe3fbib18","doi-asserted-by":"publisher","first-page":"2131","DOI":"10.1021\/acs.jpclett.7b00784","article-title":"Accurate neural network description of surface phonons in reactive gas\u2013surface dynamics: N2 + ru(0001)","volume":"8","author":"Shakouri","year":"2017","journal-title":"J. Phys. Chem. Lett."},{"key":"mlstabfe3fbib19","doi-asserted-by":"publisher","first-page":"1185","DOI":"10.1021\/acs.jpclett.9b00085","article-title":"Bridging the gap between direct dynamics and globally accurate reactive potential energy surfaces using neural networks","volume":"10","author":"Zhang","year":"2019","journal-title":"J. Phys. Chem. Lett."},{"key":"mlstabfe3fbib20","doi-asserted-by":"publisher","DOI":"10.1063\/1.4977050","article-title":"Neural network potentials for dynamics and thermodynamics of gold nanoparticles","volume":"146","author":"Chiriki","year":"2017","journal-title":"J. Chem. Phys."},{"key":"mlstabfe3fbib21","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.114.096405","article-title":"Molecular dynamics with on-the-fly machine learning of quantum-mechanical forces","volume":"114","author":"Zhenwei","year":"2015","journal-title":"Phys. Rev. Lett."},{"key":"mlstabfe3fbib22","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.120.143001","article-title":"Deep potential molecular dynamics: a scalable model with the accuracy of quantum mechanics","volume":"120","author":"Zhang","year":"2018","journal-title":"Phys. Rev. Lett."},{"key":"mlstabfe3fbib23","doi-asserted-by":"publisher","DOI":"10.1063\/1.5019779","article-title":"SchNet\u2014a deep learning architecture for molecules and materials","volume":"148","author":"Sch\u00fctt","year":"2018","journal-title":"J. Chem. Phys."},{"key":"mlstabfe3fbib24","doi-asserted-by":"publisher","DOI":"10.1063\/1.4928757","article-title":"Electronic spectra from TDDFT and machine learning in chemical space","volume":"143","author":"Ramakrishnan","year":"2015","journal-title":"J. Chem. Phys."},{"key":"mlstabfe3fbib25","doi-asserted-by":"publisher","first-page":"867","DOI":"10.1557\/mrc.2019.80","article-title":"Artificial neural network correction for density-functional tight-binding molecular dynamics simulations","volume":"9","author":"Zhu","year":"2019","journal-title":"MRS Commun."},{"key":"mlstabfe3fbib26","doi-asserted-by":"publisher","first-page":"2087","DOI":"10.1021\/acs.jctc.5b00099","article-title":"Big data meets quantum chemistry approximations: the \u03b4-machine learning approach","volume":"11","author":"Ramakrishnan","year":"2015","journal-title":"J. Chem. Theory Comput."},{"key":"mlstabfe3fbib27","doi-asserted-by":"publisher","first-page":"2339","DOI":"10.1002\/jcc.26004","article-title":"MLatom: a program package for quantum chemical research assisted by machine learning","volume":"40","author":"Dral","year":"2019","journal-title":"J. Comput. Chem."},{"key":"mlstabfe3fbib28","doi-asserted-by":"publisher","first-page":"178","DOI":"10.1016\/j.cpc.2018.03.016","article-title":"Deepmd-kit: a deep learning package for many-body potential energy representation and molecular dynamics","volume":"228","author":"Wang","year":"2018","journal-title":"Comput. Phys. Commun."},{"key":"mlstabfe3fbib29","doi-asserted-by":"publisher","first-page":"448","DOI":"10.1021\/acs.jctc.8b00908","article-title":"SchNetPack: a deep learning toolbox for atomistic systems","volume":"15","author":"Sch\u00fctt","year":"2019","journal-title":"J. Chem. Theory Comput."},{"key":"mlstabfe3fbib30","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1016\/0009-2614(90)87014-I","article-title":"The multi-configurational time-dependent Hartree approach","volume":"165","author":"Meyer","year":"1990","journal-title":"Chem. Phys. Lett."},{"key":"mlstabfe3fbib31","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/S0370-1573(99)00047-2","article-title":"The multiconfiguration time-dependent Hartree (MCTDH) method: a highly efficient algorithm for propagating wavepackets","volume":"324","author":"Beck","year":"2000","journal-title":"Phys. Rep."},{"key":"mlstabfe3fbib32","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1007\/BF01329203","article-title":"Bemerkung \u00fcber die angen\u00e4herte g\u00fcltigkeit der klassischen mechanik innerhalb der quantenmechanik","volume":"45","author":"Ehrenfest","year":"1927","journal-title":"Z. Phys."},{"key":"mlstabfe3fbib33","doi-asserted-by":"publisher","first-page":"1061","DOI":"10.1063\/1.459170","article-title":"Molecular dynamics with electronic transitions","volume":"93","author":"Tully","year":"1990","journal-title":"J. Chem. Phys."},{"key":"mlstabfe3fbib34","doi-asserted-by":"publisher","first-page":"334","DOI":"10.1016\/j.chemphys.2008.01.044","article-title":"Implementation of surface hopping molecular dynamics using semiempirical methods","volume":"349","author":"Fabiano","year":"2008","journal-title":"Chem. Phys."},{"key":"mlstabfe3fbib35","doi-asserted-by":"publisher","first-page":"7026","DOI":"10.1021\/acs.chemrev.7b00577","article-title":"Recent advances and perspectives on nonadiabatic mixed quantum\u2013classical dynamics","volume":"118","author":"Crespo-Otero","year":"2018","journal-title":"Chem. Rev."},{"key":"mlstabfe3fbib36","doi-asserted-by":"publisher","first-page":"e1370","DOI":"10.1002\/wcms.1370","article-title":"Nonadiabatic dynamics: the SHARC approach","volume":"8","author":"Mai","year":"2018","journal-title":"WIREs Comput. Mol. Sci."},{"key":"mlstabfe3fbib37","doi-asserted-by":"publisher","first-page":"3828","DOI":"10.1021\/acs.jpclett.0c00527","article-title":"Combining SchNet and SHARC: the SchNarc machine learning approach for excited-state dynamics","volume":"11","author":"Westermayr","year":"2020","journal-title":"J. Phys. Chem. Lett."},{"key":"mlstabfe3fbib38","doi-asserted-by":"publisher","first-page":"6702","DOI":"10.1021\/acs.jpclett.8b03026","article-title":"Deep learning for nonadiabatic excited-state dynamics","volume":"9","author":"Chen","year":"2018","journal-title":"J. Phys. Chem. Lett."},{"key":"mlstabfe3fbib39","doi-asserted-by":"publisher","first-page":"2725","DOI":"10.1021\/acs.jpclett.8b00684","article-title":"Inclusion of machine learning kernel ridge regression potential energy surfaces in on-the-fly nonadiabatic molecular dynamics simulation","volume":"9","author":"Hu","year":"2018","journal-title":"J. Phys. Chem. Lett."},{"key":"mlstabfe3fbib40","doi-asserted-by":"publisher","first-page":"5660","DOI":"10.1021\/acs.jpclett.8b02469","article-title":"Nonadiabatic excited-state dynamics with machine learning","volume":"9","author":"Dral","year":"2018","journal-title":"J. Phys. Chem. Lett."},{"key":"mlstabfe3fbib41","doi-asserted-by":"publisher","first-page":"8100","DOI":"10.1039\/C9SC01742A","article-title":"Machine learning enables long time scale molecular photodynamics simulations","volume":"10","author":"Westermayr","year":"2019","journal-title":"Chem. Sci."},{"key":"mlstabfe3fbib42","doi-asserted-by":"publisher","DOI":"10.1088\/2632-2153\/ab88d0","article-title":"Neural networks and kernel ridge regression for excited states dynamics of CH2NH 2+ : from single-state to multi-state representations and multi-property machine learning models","volume":"1","author":"Westermayr","year":"2020","journal-title":"Mach. Learn.: Sci. Technol."},{"key":"mlstabfe3fbib43","doi-asserted-by":"publisher","first-page":"13392","DOI":"10.1039\/C9CP01883B","article-title":"Bayesian machine learning for quantum molecular dynamics","volume":"21","author":"Krems","year":"2019","journal-title":"Phys. Chem. Chem. Phys."},{"key":"mlstabfe3fbib44","doi-asserted-by":"publisher","first-page":"4012","DOI":"10.1021\/acs.jctc.7b00507","article-title":"Direct quantum dynamics using grid-based wave function propagation and machine-learned potential energy surfaces","volume":"13","author":"Richings","year":"2017","journal-title":"J. Chem. Theory Comput."},{"key":"mlstabfe3fbib45","doi-asserted-by":"publisher","DOI":"10.1021\/acs.chemrev.0c00749","article-title":"Machine learning for electronically excited states of molecules","author":"Westermayr","year":"2020","journal-title":"Chem. Rev."},{"year":"1995","author":"Casida","first-page":"pp 155","key":"mlstabfe3fbib46"},{"key":"mlstabfe3fbib47","doi-asserted-by":"publisher","first-page":"12947","DOI":"10.1103\/PhysRevB.51.12947","article-title":"Construction of tight-binding-like potentials on the basis of density-functional theory: application to carbon","volume":"51","author":"Porezag","year":"1995","journal-title":"Phys. Rev. B"},{"key":"mlstabfe3fbib48","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1002\/(SICI)1097-461X(1996)58:2185::AID-QUA73.0.CO;2-U","article-title":"Calculations of molecules, clusters and solids with a simplified LCAO-DFT-LDA scheme","volume":"58","author":"Seifert","year":"1996","journal-title":"Int. J. Quantum Chem."},{"key":"mlstabfe3fbib49","doi-asserted-by":"publisher","DOI":"10.1098\/rsta.2012.0483","article-title":"Density functional tight binding","volume":"372","author":"Elstner","year":"2014","journal-title":"Phil. Trans. R. Soc. A"},{"key":"mlstabfe3fbib50","doi-asserted-by":"publisher","first-page":"7260","DOI":"10.1103\/PhysRevB.58.7260","article-title":"Self-consistent-charge density-functional tight-binding method for simulations of complex materials properties","volume":"58","author":"Elstner","year":"1998","journal-title":"Phys. Rev. B"},{"key":"mlstabfe3fbib51","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.63.085108","article-title":"Tight-binding approach to time-dependent density-functional response theory","volume":"63","author":"Niehaus","year":"2001","journal-title":"Phys. Rev. B"},{"key":"mlstabfe3fbib52","doi-asserted-by":"publisher","first-page":"1436","DOI":"10.1021\/acs.jctc.5b01231","article-title":"Nonadiabatic molecular dynamics for thousand atom systems: a tight-binding approach toward PYXAID","volume":"12","author":"Pal","year":"2016","journal-title":"J. Chem. Theory Comput."},{"key":"mlstabfe3fbib53","doi-asserted-by":"publisher","first-page":"174","DOI":"10.1016\/j.cpc.2017.08.012","article-title":"DFTBaby: a software package for non-adiabatic molecular dynamics simulations based on long-range corrected tight-binding TD-DFT(B)","volume":"221","author":"Humeniuk","year":"2017","journal-title":"Comput. Phys. Commun."},{"key":"mlstabfe3fbib54","doi-asserted-by":"publisher","first-page":"5846","DOI":"10.1021\/acs.jctc.7b01000","article-title":"Nonadiabatic dynamics of cycloparaphenylenes with TD-DFTB surface hopping","volume":"13","author":"Stojanovi\u0107","year":"2017","journal-title":"J. Chem. Theory Comput."},{"key":"mlstabfe3fbib55","doi-asserted-by":"publisher","first-page":"12139","DOI":"10.1039\/C9CP00603F","article-title":"Non-adiabatic molecular dynamics investigation of the size dependence of the electronic relaxation in polyacenes","volume":"21","author":"Posenitskiy","year":"2019","journal-title":"Phys. Chem. Chem. Phys."},{"key":"mlstabfe3fbib56","doi-asserted-by":"publisher","DOI":"10.1063\/5.0006831","article-title":"Non-adiabatic molecular dynamics with divide-and-conquer type large-scale excited-state calculations","volume":"152","author":"Uratani","year":"2020","journal-title":"J. Chem. Phys."},{"key":"mlstabfe3fbib57","doi-asserted-by":"publisher","DOI":"10.1063\/1.5135369","article-title":"Theoretical investigation of the electronic relaxation in highly excited chrysene and tetracene: the effect of armchair vs zigzag edge","volume":"152","author":"Posenitskiy","year":"2020","journal-title":"J. Chem. Phys."},{"key":"mlstabfe3fbib58","doi-asserted-by":"publisher","first-page":"1456","DOI":"10.1021\/acs.jpclett.9b03687","article-title":"Hot electron cooling in silicon nanoclusters via Landau\u2013Zener nonadiabatic molecular dynamics: size dependence and role of surface termination","volume":"11","author":"Smith","year":"2020","journal-title":"J. Chem. Theory Comput."},{"key":"mlstabfe3fbib59","first-page":"696","article-title":"Non-adiabatic crossing of energy levels","volume":"137","author":"Zener","year":"1932","journal-title":"Proc. R. Soc. A"},{"year":"1965","author":"Ter Haar","first-page":"pp 63","key":"mlstabfe3fbib60"},{"key":"mlstabfe3fbib61","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.84.014701","article-title":"Nonadiabatic nuclear dynamics of atomic collisions based on branching classical trajectories","volume":"84","author":"Belyaev","year":"2011","journal-title":"Phys. Rev. A"},{"key":"mlstabfe3fbib62","doi-asserted-by":"publisher","first-page":"8497","DOI":"10.1063\/1.463368","article-title":"The two-state linear curve crossing problems revisited. ii. Analytical approximations for the stokes constant and scattering matrix: the Landau\u2013Zener case","volume":"97","author":"Zhu","year":"1992","journal-title":"J. Chem. Phys."},{"key":"mlstabfe3fbib63","doi-asserted-by":"publisher","first-page":"6208","DOI":"10.1063\/1.464814","article-title":"The two-state linear curve crossing problems revisited. iii. Analytical approximations for stokes constant and scattering matrix: nonadiabatic tunneling case","volume":"98","author":"Zhu","year":"1993","journal-title":"J. Chem. Phys."},{"key":"mlstabfe3fbib64","doi-asserted-by":"publisher","first-page":"25883","DOI":"10.1039\/C4CP03498H","article-title":"Trajectory-based nonadiabatic molecular dynamics without calculating nonadiabatic coupling in the avoided crossing case: trans\u2013cis photoisomerization in azobenzene","volume":"16","author":"Yu","year":"2014","journal-title":"Phys. Chem. Chem. Phys."},{"key":"mlstabfe3fbib65","doi-asserted-by":"publisher","DOI":"10.1063\/1.5046757","article-title":"An efficient approximate algorithm for nonadiabatic molecular dynamics","volume":"149","author":"Hanasaki","year":"2018","journal-title":"J. Chem. Phys."},{"key":"mlstabfe3fbib66","doi-asserted-by":"publisher","first-page":"7433","DOI":"10.1063\/1.1508368","article-title":"Adiabatic time-dependent density functional methods for excited state properties","volume":"117","author":"Furche","year":"2002","journal-title":"J. Chem. Phys."},{"key":"mlstabfe3fbib67","doi-asserted-by":"publisher","first-page":"12772","DOI":"10.1063\/1.1824903","article-title":"Erratum: \u2018adiabatic time-dependent density functional methods for excited state properties\u2019 [j. chem. phys. 117, 7433 (2002)]","volume":"121","author":"Furche","year":"2004","journal-title":"J. Chem. Phys."},{"key":"mlstabfe3fbib68","doi-asserted-by":"publisher","first-page":"2589","DOI":"10.1002\/jcc.20697","article-title":"Analytical excited state forces for the time-dependent density-functional tight-binding method","volume":"28","author":"Heringer","year":"2007","journal-title":"J. Comput. Chem."},{"key":"mlstabfe3fbib69","doi-asserted-by":"publisher","first-page":"593","DOI":"10.1002\/jcc.22916","article-title":"Erratum: \u2018analytical excited state forces for the time-dependent density-functional tight-binding method\u2019 [j. comp. chem. 28, 2589]","volume":"33","author":"Heringer","year":"2011","journal-title":"J. Comput. Chem."},{"year":"2017","author":"Sch\u00fctt","first-page":"pp 991","key":"mlstabfe3fbib70"},{"key":"mlstabfe3fbib71","doi-asserted-by":"publisher","DOI":"10.1063\/1.3095491","article-title":"Simultaneous fitting of a potential-energy surface and its corresponding force fields using feedforward neural networks","volume":"130","author":"Pukrittayakamee","year":"2009","journal-title":"J. Chem. Phys."},{"key":"mlstabfe3fbib72","doi-asserted-by":"publisher","first-page":"1032","DOI":"10.1002\/qua.24890","article-title":"Constructing high-dimensional neural network potentials: a tutorial review","volume":"115","author":"Behler","year":"2015","journal-title":"Int. J. Quantum Chem."},{"key":"mlstabfe3fbib73","doi-asserted-by":"publisher","first-page":"4657","DOI":"10.1063\/1.467455","article-title":"Proton transfer in solution: molecular dynamics with quantum transitions","volume":"101","author":"Hammes-Schiffer","year":"1994","journal-title":"J. Chem. Phys."},{"key":"mlstabfe3fbib74","doi-asserted-by":"publisher","DOI":"10.1063\/1.2715585","article-title":"Critical appraisal of the fewest switches algorithm for surface hopping","volume":"126","author":"Granucci","year":"2007","journal-title":"J. Chem. Phys."},{"key":"mlstabfe3fbib75","doi-asserted-by":"publisher","DOI":"10.1063\/1.4829856","article-title":"Can we derive Tully\u2019s surface-hopping algorithm from the semiclassical quantum Liouville equation? Almost, but only with decoherence","volume":"139","author":"Subotnik","year":"2013","journal-title":"J. Chem. Phys."},{"year":"2009","author":"Heine","key":"mlstabfe3fbib76"},{"key":"mlstabfe3fbib77","doi-asserted-by":"publisher","first-page":"319","DOI":"10.1016\/j.chemphys.2008.02.061","article-title":"Nonadiabatic dynamics within the time dependent density functional theory: ultrafast photodynamics in pyrazine","volume":"349","author":"Werner","year":"2008","journal-title":"Chem. Phys."},{"key":"mlstabfe3fbib78","doi-asserted-by":"publisher","first-page":"10608","DOI":"10.1063\/1.1376633","article-title":"Direct semiclassical simulation of photochemical processes with semiempirical wave functions","volume":"114","author":"Granucci","year":"2001","journal-title":"J. Chem. Phys."},{"key":"mlstabfe3fbib79","doi-asserted-by":"publisher","DOI":"10.1063\/1.5006788","article-title":"Accuracy of trajectory surface-hopping methods: test for a two-dimensional model of the photodissociation of phenol","volume":"147","author":"Xie","year":"2017","journal-title":"J. Chem. Phys."},{"key":"mlstabfe3fbib80","doi-asserted-by":"publisher","DOI":"10.1063\/1.1953530","article-title":"Dissociative ionization of neon clusters nen, n=3 to 14: a realistic multisurface dynamical study","volume":"123","author":"Bonhommeau","year":"2005","journal-title":"J. Chem. Phys."},{"key":"mlstabfe3fbib81","doi-asserted-by":"publisher","first-page":"471","DOI":"10.1070\/RC2001v070n06ABEH000657","article-title":"Ultrafast nonradiative transitions between higher excited states in organic molecules","volume":"70","author":"Ermolaev","year":"2001","journal-title":"Russ. Chem. Rev."},{"key":"mlstabfe3fbib82","first-page":"pp 613","article-title":"Photophysical studies of jet-cooled PAHs: emission spectra, lifetimes and van der Waals clusters astrophysical implications","volume":"vol 312","author":"Brechignac","year":"1994"},{"year":"2009","author":"Frisch","key":"mlstabfe3fbib83"},{"key":"mlstabfe3fbib84","doi-asserted-by":"publisher","first-page":"1674","DOI":"10.1063\/1.1635798","article-title":"A global investigation of excited state surfaces within time-dependent density-functional response theory","volume":"120","author":"Wanko","year":"2004","journal-title":"J. Chem. Phys."},{"key":"mlstabfe3fbib85","doi-asserted-by":"publisher","first-page":"6267","DOI":"10.1021\/acs.jctc.9b00688","article-title":"Performances of density functional tight-binding methods for describing ground and excited state geometries of organic molecules","volume":"15","author":"Fihey","year":"2019","journal-title":"J. Chem. Theory Comput."},{"year":"2017","author":"Kingma","article-title":"Adam: a method for stochastic optimization","key":"mlstabfe3fbib86"},{"key":"mlstabfe3fbib87","article-title":"The atomic simulation environment\u2014a Python library for working with atoms","volume":"29","author":"Larsen","year":"2017","journal-title":"J. Phys.: Condens. Matter."},{"key":"mlstabfe3fbib88","doi-asserted-by":"publisher","first-page":"5593","DOI":"10.1021\/j150667a027","article-title":"Statistical-limit line broadening in the s2 state of phenanthrene in supersonic jets","volume":"88","author":"Amirav","year":"1984","journal-title":"J. Phys. Chem."},{"key":"mlstabfe3fbib89","doi-asserted-by":"publisher","first-page":"921","DOI":"10.1080\/00268978600102481","article-title":"Electronic spectra and intramolecular dynamics of phenanthrene in a supersonic free jet","volume":"59","author":"Ohta","year":"1986","journal-title":"Mol. Phys."},{"key":"mlstabfe3fbib90","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1039\/b001138j","article-title":"Towards disentangling coupled electronic\u2013vibrational dynamics in ultrafast non-adiabatic processes","volume":"115","author":"Blanchet","year":"2000","journal-title":"Faraday Discuss."},{"key":"mlstabfe3fbib91","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1016\/0301-0104(86)85151-5","article-title":"Determination of femtosecond lifetimes of higher excited singlet states by means of transient photophysical hole-burning. The s2 state of phenanthrene","volume":"110","author":"Dick","year":"1986","journal-title":"Chem. Phys."},{"key":"mlstabfe3fbib92","doi-asserted-by":"publisher","first-page":"10252","DOI":"10.1063\/1.467905","article-title":"Electronic absorption spectroscopy of matrix-isolated polycyclic aromatic hydrocarbon cations. ii. The phenanthrene cation (C14H10+) and its 1-methyl derivative","volume":"101","author":"Salama","year":"1994","journal-title":"J. Chem. Phys."},{"key":"mlstabfe3fbib93","doi-asserted-by":"publisher","first-page":"224","DOI":"10.1007\/s00214-003-0470-2","article-title":"Theoretical characterization of the absorption spectra of phenanthrene and its radical cation","volume":"110","author":"Gonz\u00e1lez-Luque","year":"2003","journal-title":"Theor. Chem. Acc."},{"key":"mlstabfe3fbib94","doi-asserted-by":"publisher","first-page":"16981","DOI":"10.1039\/C9CP03147B","article-title":"Ultrafast dynamics in polycyclic aromatic hydrocarbons: the key case of conical intersections at higher excited states and their role in the photophysics of phenanthrene monomer","volume":"21","author":"Nazari","year":"2019","journal-title":"Phys. Chem. Chem. Phys."},{"year":"2020","author":"Posenitskiy","article-title":"Non-adiabatic molecular dynamics of PAH-related complexes","key":"mlstabfe3fbib95"},{"key":"mlstabfe3fbib96","doi-asserted-by":"publisher","DOI":"10.1126\/sciadv.1603015","article-title":"Machine learning of accurate energy-conserving molecular force fields","volume":"3","author":"Chmiela","year":"2017","journal-title":"Sci. Adv."},{"key":"mlstabfe3fbib97","doi-asserted-by":"publisher","first-page":"722","DOI":"10.1021\/ar500432k","article-title":"The chemical space project","volume":"48","author":"Reymond","year":"2015","journal-title":"Acc. Chem. Res."},{"key":"mlstabfe3fbib98","doi-asserted-by":"publisher","first-page":"8732","DOI":"10.1021\/ja902302h","article-title":"970 million druglike small molecules for virtual screening in the chemical universe database GDB-13","volume":"131","author":"Blum","year":"2009","journal-title":"J. Am. Chem. Soc."},{"key":"mlstabfe3fbib99","doi-asserted-by":"publisher","DOI":"10.1038\/sdata.2014.22","article-title":"Quantum chemistry structures and properties of 134 kilo molecules","volume":"1","author":"Ramakrishnan","year":"2014","journal-title":"Sci. Data"},{"key":"mlstabfe3fbib100","doi-asserted-by":"publisher","DOI":"10.1063\/1.3604007","article-title":"Ultrafast internal conversion in ethylene. i. The excited state lifetime","volume":"134","author":"Tao","year":"2011","journal-title":"J. Chem. Phys."},{"key":"mlstabfe3fbib101","doi-asserted-by":"publisher","DOI":"10.1038\/srep35522","article-title":"Revealing deactivation pathways hidden in time-resolved photoelectron spectra","volume":"6","author":"Ruckenbauer","year":"2016","journal-title":"Sci. Rep."},{"year":"2020","author":"Posenitskiy","doi-asserted-by":"publisher","key":"mlstabfe3fbib102","DOI":"10.5281\/zenodo.4266393"}],"container-title":["Machine Learning: Science and Technology"],"original-title":[],"link":[{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/abfe3f","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/abfe3f\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/abfe3f\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/abfe3f\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,12,13]],"date-time":"2021-12-13T17:18:00Z","timestamp":1639415880000},"score":1,"resource":{"primary":{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/abfe3f"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,7,14]]},"references-count":102,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2021,7,14]]},"published-print":{"date-parts":[[2021,9,1]]}},"URL":"https:\/\/doi.org\/10.1088\/2632-2153\/abfe3f","relation":{},"ISSN":["2632-2153"],"issn-type":[{"type":"electronic","value":"2632-2153"}],"subject":[],"published":{"date-parts":[[2021,7,14]]},"assertion":[{"value":"On application of deep learning to simplified quantum-classical dynamics in electronically excited states","name":"article_title","label":"Article Title"},{"value":"Machine Learning: Science and Technology","name":"journal_title","label":"Journal Title"},{"value":"paper","name":"article_type","label":"Article Type"},{"value":"\u00a9 2021 The Author(s). Published by IOP Publishing Ltd","name":"copyright_information","label":"Copyright Information"},{"value":"2020-12-15","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2021-05-05","name":"date_accepted","label":"Date Accepted","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2021-07-14","name":"date_epub","label":"Online publication date","group":{"name":"publication_dates","label":"Publication dates"}}]}}