{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,7]],"date-time":"2026-08-07T15:33:04Z","timestamp":1786116784321,"version":"build-2736575974"},"reference-count":176,"publisher":"American Chemical Society (ACS)","issue":"31","license":[{"start":{"date-parts":[[2026,7,27]],"date-time":"2026-07-27T00:00:00Z","timestamp":1785110400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,7,27]],"date-time":"2026-07-27T00:00:00Z","timestamp":1785110400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,7,27]],"date-time":"2026-07-27T00:00:00Z","timestamp":1785110400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-045"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,8,6]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>The lowest electronically excited \u03c0\u03c0* states of conjugated hydrocarbons, as well as related heterocyclic compounds, pose a significant challenge for quantum chemical calculations. The difficulty arises from the need to achieve a balanced description of excited states with markedly different electronic characters, such as bright vs dark, ionic vs covalent, and singly vs doubly excited states. Here, we focus on the low-lying \u03c0\u03c0* states of five-member-ring heterocycles, such as furan, pyrrole and thiophene. We analyze the origins of the diverse excited-state characters from both molecular orbital and valence bond theory perspectives, employing pseudosymmetry arguments to bridge the two viewpoints and drawing comparisons with the \u03c0\u03c0* excited states of the cis-butadiene and benzene model systems. We further discuss the critical role of electronic correlation in obtaining a balanced description of excited states and explain why it is difficult, or sometimes impossible, to achieve high accuracy with commonly used electronic-structure approximations. As an illustration, we focus on results from standard time-dependent density functional theory approximations, as well as a series of algebraic diagrammatic construction methods with systematically improvable correlation levels through perturbative truncation schemes. Finally, we address the origins and implications of valence\u2013Rydberg mixing, which arguably remains an open question in excited-state quantum chemistry.<\/jats:p>","DOI":"10.1021\/acs.jpca.6c03644","type":"journal-article","created":{"date-parts":[[2026,8,4]],"date-time":"2026-08-04T13:10:15Z","timestamp":1785849015000},"page":"6198-6217","source":"Crossref","is-referenced-by-count":0,"title":["Low-Lying \u03c0\u03c0*\nExcited States in Five-Membered\nRing Heterocycles: A Continuing Challenge"],"prefix":"10.1021","volume":"130","author":[{"given":"Chaiyaporn","family":"Lakmuang","sequence":"first","affiliation":[{"name":"Ru\u0111er Bos\u030ckovic\u0301 Institute , , Bijenic\u030cka 54 , ,","place":["Zagreb, Croatia, 10000"]},{"name":"University of Zagreb , , Horvatovac 102a , ,","place":["Zagreb, Croatia, 10000"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0722-0159","authenticated-orcid":true,"given":"Thierry","family":"Tran","sequence":"additional","affiliation":[{"name":"Wroc\u0142aw University of Science and Technology , , ,","place":["Wroc\u0142aw, Poland, PL-50370"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5589-9776","authenticated-orcid":true,"given":"Antonio","family":"Prlj","sequence":"additional","affiliation":[{"name":"Ru\u0111er Bos\u030ckovic\u0301 Institute , , Bijenic\u030cka 54 , ,","place":["Zagreb, Croatia, 10000"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"316","published-online":{"date-parts":[[2026,7,27]]},"reference":[{"key":"2026080608135792200_cit1","doi-asserted-by":"crossref","DOI":"10.1002\/9783527637737","volume-title":"Modern Heterocyclic\nChemistry, 4 Volume Set","author":"Alvarez-Builla","year":"2011"},{"key":"2026080608135792200_cit2","doi-asserted-by":"crossref","DOI":"10.1002\/9781118380208","volume-title":"Heterocyclic Chemistry\nat a Glance","author":"Joule","year":"2012"},{"key":"2026080608135792200_cit3","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1016\/0301-0104(94)00386-O","article-title":"The electronic states\nof furan studied by VUV absorption, near-threshold electron energy-loss\nspectroscopy and ab initio multi-reference configuration interaction\ncalculations","volume":"192","author":"Palmer","year":"1995","journal-title":"Chem. Phys."},{"key":"2026080608135792200_cit4","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1016\/S0301-0104(98)00285-7","article-title":"The electronic\nstates of pyrrole\nstudied by optical (VUV) absorption, near-threshold electron energy-loss\n(EEL) spectroscopy and ab initio multi-reference configuration interaction\ncalculations","volume":"238","author":"Palmer","year":"1998","journal-title":"Chem. Phys."},{"key":"2026080608135792200_cit5","doi-asserted-by":"publisher","first-page":"275","DOI":"10.1016\/S0301-0104(98)00425-X","article-title":"The electronic\nstates of thiophene\nstudied by optical (VUV) absorption, near-threshold electron energy-loss\n(EEL) spectroscopy and ab initio multi-reference configuration interaction\ncalculations","volume":"241","author":"Palmer","year":"1999","journal-title":"Chem. Phys."},{"key":"2026080608135792200_cit6","doi-asserted-by":"publisher","first-page":"6184","DOI":"10.1021\/ja00067a038","article-title":"Theoretical\nstudy of the electronic spectra of cyclopentadiene, pyrrole, and furan","volume":"115","author":"Serrano-Andres","year":"1993","journal-title":"J. Am. Chem. Soc."},{"key":"2026080608135792200_cit7","doi-asserted-by":"publisher","first-page":"445","DOI":"10.1016\/j.cplett.2006.06.009","article-title":"An application of second and third-order\nn-electron valence state perturbation theory to the calculation of\nthe vertical electronic spectrum of furan","volume":"426","author":"Pastore","year":"2006","journal-title":"Chem.\nPhys. Lett."},{"key":"2026080608135792200_cit8","doi-asserted-by":"publisher","first-page":"6","DOI":"10.1016\/j.chemphys.2010.10.002","article-title":"A computational study of radiationless deactivation\nmechanisms of furan","volume":"379","author":"Stenrup","year":"2011","journal-title":"Chem. Phys."},{"key":"2026080608135792200_cit9","doi-asserted-by":"publisher","first-page":"3423","DOI":"10.1021\/ja973437o","article-title":"The electronic\nspectrum of furan","volume":"120","author":"Christiansen","year":"1998","journal-title":"J. Am. Chem. Soc."},{"key":"2026080608135792200_cit10","doi-asserted-by":"publisher","first-page":"737","DOI":"10.1063\/1.1578051","article-title":"Theoretical\nstudy of the low-lying excited singlet states of furan","volume":"119","author":"Gromov","year":"2003","journal-title":"J. Chem. Phys."},{"key":"2026080608135792200_cit11","doi-asserted-by":"publisher","first-page":"8","DOI":"10.1016\/S0009-2614(02)00122-7","article-title":"Study of excited states of furan\nand pyrrole by time-dependent density functional theory","volume":"355","author":"Burcl","year":"2002","journal-title":"Chem. Phys. Lett."},{"key":"2026080608135792200_cit12","doi-asserted-by":"publisher","DOI":"10.1007\/s00214-012-1237-4","article-title":"Spectrum simulation and decomposition\nwith nuclear\nensemble: formal derivation and application to benzene, furan and\n2-phenylfuran","volume":"131","author":"Crespo-Otero","year":"2012","journal-title":"Theor. Chem. Acc."},{"key":"2026080608135792200_cit13","doi-asserted-by":"publisher","first-page":"8591","DOI":"10.1021\/jp911602k","article-title":"A multireference coupled-cluster study of electronic\nexcitations in furan and pyrrole","volume":"114","author":"Li","year":"2010","journal-title":"J. Phys. Chem.\nA"},{"key":"2026080608135792200_cit14","doi-asserted-by":"publisher","first-page":"7853","DOI":"10.1063\/1.1316034","article-title":"Electronic\nexcitation spectra of furan and pyrrole: Revisited by the symmetry\nadapted cluster-configuration interaction method","volume":"113","author":"Wan","year":"2000","journal-title":"J. Chem. Phys."},{"key":"2026080608135792200_cit15","doi-asserted-by":"publisher","first-page":"184","DOI":"10.1016\/j.jms.2015.03.002","article-title":"A study of the excited electronic\nstates of normal and fully deuterated furan by photoabsorption spectroscopy\nand high-level ab initio calculations","volume":"315","author":"Holland","year":"2015","journal-title":"J. Mol.\nSpectrosc."},{"key":"2026080608135792200_cit16","doi-asserted-by":"publisher","first-page":"859","DOI":"10.1080\/00268979909482888","article-title":"Does density\nfunctional theory contribute to the understanding of excited states\nof unsaturated organic compounds?","volume":"97","author":"Tozer","year":"1999","journal-title":"Mol. Phys."},{"key":"2026080608135792200_cit17","doi-asserted-by":"publisher","first-page":"2312","DOI":"10.1063\/1.470926","article-title":"Theoretical study of\nthe excitation spectra of five-membered ring compounds: Cyclopentadiene,\nfuran, and pyrrole","volume":"104","author":"Nakano","year":"1996","journal-title":"J. Chem. Phys."},{"key":"2026080608135792200_cit18","doi-asserted-by":"publisher","first-page":"175","DOI":"10.1016\/S0301-0104(97)00256-5","article-title":"Polarization propagator\nstudy of electronic excitation\nin key heterocyclic molecules II. Furan","volume":"224","author":"Trofimov","year":"1997","journal-title":"Chem.\nPhys."},{"key":"2026080608135792200_cit19","doi-asserted-by":"publisher","first-page":"7526","DOI":"10.1063\/1.1465406","article-title":"Theoretical characterization of the lowest-energy absorption\nband of pyrrole","volume":"116","author":"Roos","year":"2002","journal-title":"J. Chem. Phys."},{"key":"2026080608135792200_cit20","doi-asserted-by":"publisher","DOI":"10.1063\/1.4861223","article-title":"A reinterpretation\nof the electronic spectrum of pyrrole:\nA quantum dynamics study","volume":"140","author":"Neville","year":"2014","journal-title":"J. Chem. 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Lett."},{"key":"2026080608135792200_cit23","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1016\/S0301-0104(96)00303-5","article-title":"Polarization propagator\nstudy of electronic excitation\nin key heterocyclic molecules I. Pyrrole","volume":"214","author":"Trofimov","year":"1997","journal-title":"Chem.\nPhys."},{"key":"2026080608135792200_cit24","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1016\/0009-2614(93)80061-S","article-title":"A theoretical study\nof the electronic spectrum of thiophene","volume":"211","author":"Serrano-Andre\u0301s","year":"1993","journal-title":"Chem.\nPhys. Lett."},{"key":"2026080608135792200_cit25","doi-asserted-by":"publisher","first-page":"18","DOI":"10.1016\/j.chemphys.2011.12.004","article-title":"Theoretical\nstudy of the radiationless deactivation mechanisms of photo-excited\nthiophene","volume":"397","author":"Stenrup","year":"2012","journal-title":"Chem. 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Phys."},{"key":"2026080608135792200_cit29","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1021\/jz5022087","article-title":"Qualitatively\nincorrect features in the TDDFT spectrum of thiophene-based compounds","volume":"6","author":"Prlj","year":"2015","journal-title":"J. Phys. Chem. Lett."},{"key":"2026080608135792200_cit30","doi-asserted-by":"publisher","first-page":"380","DOI":"10.1039\/B710380H","article-title":"Excited\nstates of thiophene: ring opening as deactivation mechanism","volume":"10","author":"Salzmann","year":"2008","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2026080608135792200_cit31","doi-asserted-by":"publisher","first-page":"393","DOI":"10.1039\/B710381F","article-title":"Ultrafast\ndynamics in thiophene investigated by femtosecond pump probe photoelectron\nspectroscopy and theory","volume":"10","author":"Weinkauf","year":"2008","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2026080608135792200_cit32","doi-asserted-by":"publisher","DOI":"10.1063\/1.3480361","article-title":"A resonance Raman spectroscopic\nand CASSCF investigation of the Franck-Condon region structural dynamics\nand conical intersections of thiophene","volume":"133","author":"Wu","year":"2010","journal-title":"J. Chem.\nPhys."},{"key":"2026080608135792200_cit33","doi-asserted-by":"publisher","first-page":"3426","DOI":"10.1021\/acs.jctc.1c00212","article-title":"Tailoring CIPSI expansions\nfor QMC calculations of electronic excitations: the case study of\nthiophene","volume":"17","author":"Dash","year":"2021","journal-title":"J. Chem. Theory Comput."},{"key":"2026080608135792200_cit34","doi-asserted-by":"publisher","DOI":"10.1063\/1.2889385","article-title":"Benchmarks for electronically\nexcited states: CASPT2, CC2, CCSD, and CC3","volume":"128","author":"Schreiber","year":"2008","journal-title":"J. Chem. Phys."},{"key":"2026080608135792200_cit35","doi-asserted-by":"publisher","DOI":"10.1063\/1.3518441","article-title":"Ultrafast\nphotodynamics of furan","volume":"133","author":"Fuji","year":"2010","journal-title":"J. Chem. Phys."},{"key":"2026080608135792200_cit36","doi-asserted-by":"publisher","first-page":"2025","DOI":"10.1039\/C6CP06240G","article-title":"Substituent effects on the relaxation dynamics of furan,\nfurfural and \u03b2-furfural: a combined theoretical\nand experimental approach","volume":"19","author":"Oesterling","year":"2017","journal-title":"Phys. Chem. Chem.\nPhys."},{"key":"2026080608135792200_cit37","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1016\/j.chemphys.2004.04.019","article-title":"Multi-mode-multi-state quantum dynamics\nof key five-membered heterocycles: spectroscopy and ultrafast internal\nconversion","volume":"304","author":"Ko\u0308ppel","year":"2004","journal-title":"Chem. Phys."},{"key":"2026080608135792200_cit38","doi-asserted-by":"publisher","DOI":"10.1063\/1.4845215","article-title":"Reaction surface\napproach to multimode vibronic coupling problems: General framework\nand application to furan","volume":"139","author":"Gromov","year":"2013","journal-title":"J. Chem. Phys."},{"key":"2026080608135792200_cit39","doi-asserted-by":"publisher","first-page":"10602","DOI":"10.1021\/acs.jctc.4c01263","article-title":"Non-adiabatic\ncouplings in surface hopping with tight binding density functional\ntheory: The case of molecular motors","volume":"20","author":"Di\u0301az Miro\u0301n","year":"2024","journal-title":"J. Chem.\nTheory Comput."},{"key":"2026080608135792200_cit40","doi-asserted-by":"publisher","first-page":"1478","DOI":"10.1039\/D5DD00044K","article-title":"Excited-state\nnonadiabatic dynamics in explicit solvent using machine learned interatomic\npotentials","volume":"4","author":"Tiefenbacher","year":"2025","journal-title":"Digit. Discov."},{"key":"2026080608135792200_cit41","doi-asserted-by":"publisher","first-page":"7787","DOI":"10.1039\/C5CP00019J","article-title":"Modeling ultrafast\nexciton deactivation\nin oligothiophenes via nonadiabatic dynamics","volume":"17","author":"Fazzi","year":"2015","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2026080608135792200_cit42","doi-asserted-by":"publisher","first-page":"14719","DOI":"10.1039\/C5CP01429H","article-title":"Excited state dynamics of thiophene\nand bithiophene: new insights into theoretically challenging systems","volume":"17","author":"Prlj","year":"2015","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2026080608135792200_cit43","doi-asserted-by":"publisher","first-page":"25662","DOI":"10.1039\/C7CP05061E","article-title":"Ab initio molecular dynamics of thiophene: The interplay\nof internal conversion and intersystem crossing","volume":"19","author":"Schnappinger","year":"2017","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2026080608135792200_cit44","doi-asserted-by":"publisher","first-page":"11544","DOI":"10.1021\/jp206893n","article-title":"Ab Initio trajectory surface-hopping study on ultrafast deactivation\nprocess of thiophene","volume":"115","author":"Cui","year":"2011","journal-title":"J. Phys. Chem. A"},{"key":"2026080608135792200_cit45","doi-asserted-by":"publisher","DOI":"10.1063\/1.4978289","article-title":"A new approach to molecular\ndynamics with non-adiabatic\nand spin-orbit effects with applications to QM\/MM simulations of thiophene\nand selenophene","volume":"146","author":"Pederzoli","year":"2017","journal-title":"J. Chem. Phys."},{"key":"2026080608135792200_cit46","doi-asserted-by":"publisher","first-page":"5809","DOI":"10.1021\/acs.jctc.0c00512","article-title":"Pragmatic Approach\nto Photodynamics: Mixed Landau-Zener Surface Hopping with Inter-system\nCrossing","volume":"16","author":"Suchan","year":"2020","journal-title":"J. Chem. Theory Comput."},{"key":"2026080608135792200_cit47","doi-asserted-by":"publisher","DOI":"10.1007\/s00214-021-02741-0","article-title":"Exploring\nthe effects of quantum\ndecoherence on the excited-state dynamics of molecular systems","volume":"140","author":"Heller","year":"2021","journal-title":"Theor. Chem. Acc."},{"key":"2026080608135792200_cit48","doi-asserted-by":"publisher","DOI":"10.1063\/5.0226105","article-title":"The \u201csimple\u201d\nphotochemistry of thiophene","volume":"161","author":"Parkes","year":"2024","journal-title":"J. Chem. Phys."},{"key":"2026080608135792200_cit49","doi-asserted-by":"publisher","first-page":"845","DOI":"10.1080\/00268970802665639","article-title":"Excited-state non-adiabatic\ndynamics simulations of pyrrole","volume":"107","author":"Vazdar","year":"2009","journal-title":"Mol. Phys."},{"key":"2026080608135792200_cit50","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1016\/j.chemphys.2010.07.014","article-title":"Non-adiabatic dynamics\nof pyrrole: Dependence of deactivation mechanisms on the excitation\nenergy","volume":"375","author":"Barbatti","year":"2010","journal-title":"Chem. Phys."},{"key":"2026080608135792200_cit51","doi-asserted-by":"publisher","first-page":"762","DOI":"10.1002\/qua.25049","article-title":"Effects of different\ninitial condition samplings on photodynamics\nand spectrum of pyrrole","volume":"116","author":"Barbatti","year":"2016","journal-title":"Int. J. Quantum Chem."},{"key":"2026080608135792200_cit52","doi-asserted-by":"publisher","DOI":"10.1063\/1.3651536","article-title":"Ab initio\nquantum dynamical study\nof the multi-state nonadiabatic photodissociation of pyrrole","volume":"135","author":"Faraji","year":"2011","journal-title":"J. Chem. Phys."},{"key":"2026080608135792200_cit53","doi-asserted-by":"publisher","first-page":"3316","DOI":"10.1039\/C4CP04571H","article-title":"Ab initio\nmultiple cloning simulations of pyrrole photodissociation: TKER spectra\nand velocity map imaging","volume":"17","author":"Makhov","year":"2015","journal-title":"Phys. Chem. Chem.\nPhys."},{"key":"2026080608135792200_cit54","doi-asserted-by":"publisher","first-page":"16227","DOI":"10.1039\/c3cp51199e","article-title":"Simulation\nof ultrafast photodynamics\nof pyrrole with a multiconfigurational Ehrenfest method","volume":"15","author":"Saita","year":"2013","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2026080608135792200_cit55","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1016\/j.jphotochem.2007.01.018","article-title":"Photoinduced multi-mode quantum dynamics of pyrrole\nat the 1\u03c0\u03c3*\u2013S0 conical intersections","volume":"190","author":"Lan","year":"2007","journal-title":"J. Photochem. Photobiol.,\nA"},{"key":"2026080608135792200_cit56","doi-asserted-by":"crossref","DOI":"10.1063\/1.2049250","article-title":"Photochemistry of pyrrole:\nTime-dependent quantum wave-packet description of the dynamics at\nthe 1\u03c0\u03c3*\u2013S0 conical intersections","volume":"123","author":"Vallet","year":"2005","journal-title":"J. Chem. Phys."},{"key":"2026080608135792200_cit57","doi-asserted-by":"publisher","DOI":"10.1063\/1.4907529","article-title":"Excited state\nnon-adiabatic dynamics\nof pyrrole: A time-resolved photoelectron spectroscopy and quantum\ndynamics study","volume":"142","author":"Wu","year":"2015","journal-title":"J. Chem. Phys."},{"key":"2026080608135792200_cit58","doi-asserted-by":"publisher","first-page":"19012","DOI":"10.1039\/C5CP02100F","article-title":"Timescales\nof N\u2013H bond dissociation in pyrrole: a nonadiabatic dynamics\nstudy","volume":"17","author":"Sapunar","year":"2015","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2026080608135792200_cit59","doi-asserted-by":"publisher","first-page":"38","DOI":"10.1016\/j.comptc.2019.03.012","article-title":"A XMS-CASPT2\nnon-adiabatic dynamics study on pyrrole","volume":"1155","author":"Heindl","year":"2019","journal-title":"Comput.\nTheor. Chem."},{"key":"2026080608135792200_cit60","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1016\/j.chemphys.2008.01.049","article-title":"Role of vibrational energy relaxation in the photoinduced\nnonadiabatic dynamics of pyrrole at the 1\u03c0\u03c3*\u2013S0 conical intersection","volume":"350","author":"Lan","year":"2008","journal-title":"Chem. Phys."},{"key":"2026080608135792200_cit61","doi-asserted-by":"publisher","DOI":"10.1063\/1.2711188","article-title":"Restricted open-shell Kohn-Sham theory: Simulation\nof the pyrrole photodissociation","volume":"126","author":"Frank","year":"2007","journal-title":"J. Chem. 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