{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,11]],"date-time":"2026-07-11T05:38:31Z","timestamp":1783748311545,"version":"3.55.0"},"reference-count":78,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,2,2]],"date-time":"2023-02-02T00:00:00Z","timestamp":1675296000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100006595","name":"UEFISCDI public institution under the Romanian Ministry of Education","doi-asserted-by":"publisher","award":["PN-III-P4-ID-PCE-2020-0770"],"award-info":[{"award-number":["PN-III-P4-ID-PCE-2020-0770"]}],"id":[{"id":"10.13039\/501100006595","id-type":"DOI","asserted-by":"publisher"}]},{"name":"MDPI","award":["PN-III-P4-ID-PCE-2020-0770"],"award-info":[{"award-number":["PN-III-P4-ID-PCE-2020-0770"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IJMS"],"abstract":"<jats:p>The equilibrium and conical intersection geometries of the benzene dimer were computed in the framework of the conventional, linear-response time-dependent and spin-flipped time-dependent density functional theories (known as DFT, TDDFT and SF-TDDFT) as well as using the multiconfigurational complete active space self-consistent field (CASSCF) method considering the minimally augmented def2-TZVPP and the 6\u201331G(d,p) basis sets. It was found that the stacking distance between the benzene monomers decreases by about 0.5 \u00c5 in the first electronic excited state, due to the stronger intermolecular interaction energy, bringing the two monomers closer together. Intermolecular-type conical intersection (CI) geometries can be formed between the two benzene molecules, when (i) both monomer rings show planar deformation and (ii) weaker (approximately 1.6\u20131.8 \u00c5 long) C\u2013C bonds are formed between the two monomers, with parallel and antiparallel orientation with respect to the monomer. These intermolecular-type CIs look energetically more favorable than dimeric CIs containing only one deformed monomer. The validity of the dimer-type CI geometries obtained by SF-TDDFT was confirmed by the CASSCF method. The nudged elastic band method used for finding the optimal relaxation path has confirmed both the accessibility of these intermolecular-type CIs and the possibility of the radiationless deactivation of the electronic excited states through these CI geometries. Although not as energetically favorable as the previous two CI geometries, there are other CI geometries characterized by the relative rotation of monomers at different angles around a vertical C\u2013C axis.<\/jats:p>","DOI":"10.3390\/ijms24032906","type":"journal-article","created":{"date-parts":[[2023,2,3]],"date-time":"2023-02-03T02:35:10Z","timestamp":1675391710000},"page":"2906","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Intermolecular-Type Conical Intersections in Benzene Dimer"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5347-1514","authenticated-orcid":false,"given":"Attila","family":"Bende","sequence":"first","affiliation":[{"name":"National Institute for Research and Development of Isotopic and Molecular Technologies, Donat Street, No. 67-103, 400283 Cluj-Napoca, Romania"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9207-8520","authenticated-orcid":false,"given":"Alex-Adrian","family":"Farca\u015f","sequence":"additional","affiliation":[{"name":"National Institute for Research and Development of Isotopic and Molecular Technologies, Donat Street, No. 67-103, 400283 Cluj-Napoca, Romania"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,2]]},"reference":[{"key":"ref_1","unstructured":"Klessinger, M., and Michl, J. (1995). Excited States and Photochemistry of Organic Molecules, VCH Publishers, Inc."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1021\/j150379a010","article-title":"The Crossing of Potential Surfaces","volume":"41","author":"Teller","year":"1937","journal-title":"J. Phys. Chem."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"783","DOI":"10.1351\/pac199567050783","article-title":"Conical intersections as a mechanistic feature of organic photochemistry","volume":"67","author":"Robb","year":"1995","journal-title":"Pure Appl. Chem."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1039\/cs9962500321","article-title":"Potential energy surface crossings in organic photochemistry","volume":"25","author":"Bernardi","year":"1996","journal-title":"Chem. Soc. Rev."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1146\/annurev.physchem.55.091602.094335","article-title":"BEYOND BORN-OPPENHEIMER: Molecular Dynamics Through a Conical Intersection","volume":"55","author":"Worth","year":"2004","journal-title":"Annu. Rev. Phys. Chem."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"621","DOI":"10.1146\/annurev-physchem-032210-103450","article-title":"Nonadiabatic Events and Conical Intersections","volume":"62","author":"Matsika","year":"2011","journal-title":"Annu. Rev. Phys. Chem."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1146\/annurev-physchem-052516-050721","article-title":"Dynamics at Conical Intersections","volume":"69","author":"Schuurman","year":"2018","journal-title":"Annu. Rev. Phys. Chem."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1016\/S0009-2614(97)01142-1","article-title":"Internal conversion in highly excited benzene and benzene dimer: Femtosecond time-resolved photoelectron spectroscopy","volume":"281","author":"Radloff","year":"1997","journal-title":"Chem. Phys. Lett."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/j.cplett.2008.12.069","article-title":"Ultrafast dynamics of the S1 excited state of benzene","volume":"469","author":"Parker","year":"2009","journal-title":"Chem. Phys. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2814","DOI":"10.1039\/C9CP06164A","article-title":"Methyl substitution effects on the non-adiabatic dynamics of benzene: Lifting three-state quasi-degeneracy at conical intersections","volume":"22","author":"Adachi","year":"2020","journal-title":"Phys. Chem. Chem. Phys."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1016\/j.chemphys.2004.04.018","article-title":"Excited state direct dynamics of benzene with reparameterized multi-reference semiempirical configuration interaction methods","volume":"304","author":"Toniolo","year":"2004","journal-title":"Chem. Phys."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1039\/c1fd00003a","article-title":"Time-resolved photoelectron spectroscopy from first principles: Excited state dynamics of benzene","volume":"150","author":"Thompson","year":"2011","journal-title":"Faraday Discuss."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"673","DOI":"10.1021\/ja00055a042","article-title":"An MC-SCF study of the S1 and S2 photochemical reactions of benzene","volume":"115","author":"Palmer","year":"1993","journal-title":"J. Am. Chem. Soc."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1016\/0009-2614(95)00718-J","article-title":"\u2019Classical wavepacket\u2019 dynamics through a conical intersection. Application to the S1\/S 0 photochemistry of benzene","volume":"242","author":"Smith","year":"1995","journal-title":"Chem. Phys. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"124307","DOI":"10.1063\/1.2839607","article-title":"Automatic generation of active coordinates for quantum dynamics calculations: Application to the dynamics of benzene photochemistry","volume":"128","author":"Lasorne","year":"2008","journal-title":"J. Chem. Phys."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"13017","DOI":"10.1021\/jp803740a","article-title":"Controlling S1\/S0 Decay and the Balance between Photochemistry and Photostability in Benzene: A Direct Quantum Dynamics Study","volume":"112","author":"Lasorne","year":"2008","journal-title":"J. Phys. Chem. A"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"064303","DOI":"10.1063\/1.3197555","article-title":"A model Hamiltonian to simulate the complex photochemistry of benzene II","volume":"131","author":"Penfold","year":"2009","journal-title":"J. Chem. Phys."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1016\/j.chemphys.2010.08.016","article-title":"A global picture of the S1\/S0 conical intersection seam of benzene","volume":"377","author":"Li","year":"2010","journal-title":"Chem. Phys."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"10252","DOI":"10.1063\/1.1361246","article-title":"Introduction of n-electron valence states for multireference perturbation theory","volume":"114","author":"Angeli","year":"2001","journal-title":"J. Chem. Phys."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"137219","DOI":"10.1016\/j.cplett.2020.137219","article-title":"Locating conical intersections using the quasidegenerate partially and strongly contracted NEVPT2 methods","volume":"744","author":"Nishimoto","year":"2020","journal-title":"Chem. Phys. Lett."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"903","DOI":"10.1088\/0034-4885\/38\/8\/001","article-title":"Excimers","volume":"38","author":"Birks","year":"1975","journal-title":"Rep. Prog. Phys."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"13916","DOI":"10.1039\/C8CP06354K","article-title":"Dynamics of benzene excimer formation from the parallel-displaced dimer","volume":"21","author":"Cardozo","year":"2019","journal-title":"Phys. Chem. Chem. Phys."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1016\/j.cplett.2006.05.123","article-title":"A theoretical study of singlet low-energy excited states of the benzene dimer","volume":"426","author":"Vico","year":"2006","journal-title":"Chem. Phys. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"7400","DOI":"10.1021\/acs.jpclett.1c01908","article-title":"Benzene Excimer and Excited Multimers: Electronic Character, Interaction Nature, and Aromaticity","volume":"12","author":"Casanova","year":"2021","journal-title":"J. Phys. Chem. Lett."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"653","DOI":"10.1021\/jp209190e","article-title":"Electronic States of the Benzene Dimer: A Simple Case of Complexity","volume":"116","author":"Diri","year":"2012","journal-title":"J. Phys. Chem. A"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1962","DOI":"10.1021\/acs.jpca.7b01070","article-title":"Rewriting the Story of Excimer Formation in Liquid Benzene","volume":"121","author":"Sadybekov","year":"2017","journal-title":"J. Phys. Chem. A"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"6743","DOI":"10.1063\/1.457342","article-title":"Excited state lifetimes and appearance potentials of benzene dimer and trimer","volume":"91","author":"Shinohara","year":"1989","journal-title":"J. Chem. Phys."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"12098","DOI":"10.1021\/ja0023579","article-title":"Chemistry of syn-o,o\u2019-Dibenzene","volume":"122","author":"Gan","year":"2000","journal-title":"J. Am. Chem. Soc."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"874102","DOI":"10.1155\/2014\/874102","article-title":"Mechanisms of Laser-Induced Reactions of Stacked Benzene Molecules: A Semiclassical Dynamics Simulation and CASSCF Calculation","volume":"2014","author":"Shu","year":"2014","journal-title":"Int. J. Photoenergy"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"10996","DOI":"10.1021\/ja073628j","article-title":"Ultrafast Deactivation Channel for Thymine Dimerization","volume":"129","author":"Groenhof","year":"2007","journal-title":"J. Am. Chem. Soc."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"14834","DOI":"10.1021\/ja304069f","article-title":"Electronic Excited States Responsible for Dimer Formation upon UV Absorption Directly by Thymine Strands: Joint Experimental and Theoretical Study","volume":"134","author":"Banyasz","year":"2012","journal-title":"J. Am. Chem. Soc."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Wang, H., and Chen, X. (2017). How Does Thymine DNA Survive Ultrafast Dimerization Damage?. Molecules, 22.","DOI":"10.3390\/molecules22010060"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"806415","DOI":"10.3389\/fbioe.2021.806415","article-title":"Theoretical study of light-induced crosslinking reaction between pyrimidine DNA bases and aromatic amino acids","volume":"9","author":"Bende","year":"2022","journal-title":"Front. Bioeng. Biotechnol."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"29165","DOI":"10.1039\/D2CP03702E","article-title":"New insight to the catechol photochemistry: The role of different monomer and dimer configurations in radiationless decay of S1 electronic excited state","volume":"24","author":"Bende","year":"2022","journal-title":"Phys. Chem. Chem. Phys."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"837","DOI":"10.1007\/s00214-007-0331-5","article-title":"Comparison of algorithms for conical intersection optimisation using semiempirical methods","volume":"118","author":"Keal","year":"2007","journal-title":"Theor. Chem. Acc."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"12749","DOI":"10.1021\/jp908032x","article-title":"Optimizing Conical Intersections by Spin-Flip Density Functional Theory: Application to Ethylene","volume":"113","author":"Minezawa","year":"2009","journal-title":"J. Phys. Chem A"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1016\/j.cplett.2009.05.067","article-title":"Dynamic electron correlation effect on conical intersections in photochemical ring-opening reaction of cyclohexadiene: MS-CASPT2 study","volume":"476","author":"Mori","year":"2009","journal-title":"Chem. Phys. Lett."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"27394","DOI":"10.1039\/C8CP04703K","article-title":"Discovery of conical intersection mediated photochemistry with growing string methods","volume":"20","author":"Aldaz","year":"2018","journal-title":"Phys. Chem. Chem. Phys."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"100007","DOI":"10.1016\/j.cpletx.2019.100007","article-title":"Exploring approximate geometries of minimum energy conical intersections by TDDFT calculations","volume":"737S","author":"Harabuchi","year":"2019","journal-title":"Chem. Phys. Lett."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"3253","DOI":"10.1021\/acs.jctc.9b00917","article-title":"Comparison of Spin-Flip TDDFT-Based Conical Intersection Approaches with XMS-CASPT2","volume":"16","author":"Winslow","year":"2020","journal-title":"J. Chem. Theory Comput."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1039","DOI":"10.1080\/00268970500417762","article-title":"Conical intersections and double excitations in time-dependent density functional theory","volume":"104","author":"Levine","year":"2006","journal-title":"Mol. Phys."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Ferr\u00e9, N., Filatov, M., and Huix-Rotllant, M. (2016). Density-Functional Methods for Excited States, Springer International Publishing.","DOI":"10.1007\/978-3-319-22081-9"},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Gonz\u00e1lez, L., and Lindh, R. (2020). Quantum Chemistry and Dynamics of Excited States, John Wiley & Sons, Ltd.. Chapter 2.","DOI":"10.1002\/9781119417774"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"5180","DOI":"10.1002\/anie.201300653","article-title":"Structure of the Benzene Dimer-Governed by Dynamics","volume":"52","author":"Schnell","year":"2013","journal-title":"Angew. Chem. Int. Ed."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"10200","DOI":"10.1021\/jp0469517","article-title":"Highly Accurate Coupled Cluster Potential Energy Curves for the Benzene Dimer: Sandwich, T-Shaped, and Parallel-Displaced Configurations","volume":"108","author":"Sinnokrot","year":"2004","journal-title":"J. Phys. Chem. A"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"4072","DOI":"10.1039\/b608623c","article-title":"Calculation of intermolecular interactions in the benzene dimer using coupled-cluster and local electron correlation methods","volume":"8","author":"Hill","year":"2006","journal-title":"Phys. Chem. Chem. Phys."},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Falama\u015f, A., Petran, A., Hada, A.M., and Bende, A. (2022). Dopamine Photochemical Behaviour under UV Irradiation. Int. J. Mol. Sci., 23.","DOI":"10.3390\/ijms23105483"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1038\/s41565-020-00791-2","article-title":"Intermolecular conical intersections in molecular aggregates","volume":"16","author":"Sommer","year":"2021","journal-title":"Nat. Nanotechnol."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"3251","DOI":"10.1021\/j100855a027","article-title":"Fluorescence yields of aromatic compounds","volume":"72","author":"Dawson","year":"1968","journal-title":"J. Phys. Chem."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"3160","DOI":"10.1063\/1.1674464","article-title":"Fluorescence Lifetime of Benzene and Benzene-d6 Vapor Excited to Single Vibronic Levels","volume":"53","author":"Selinger","year":"1970","journal-title":"J. Chem. Phys."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"1904","DOI":"10.1021\/j100612a005","article-title":"Natural and experimental fluorescence lifetimes of benzene in various solvents","volume":"78","author":"Luria","year":"1974","journal-title":"J. Phys. Chem."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1021\/ja00417a002","article-title":"Radiative and nonradiative transitions in solution. First excited singlet state of benzene and its methyl derivatives","volume":"98","author":"Quina","year":"1976","journal-title":"J. Am. Chem. Soc."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"034104","DOI":"10.1063\/1.5010895","article-title":"On the theoretical prediction of fluorescence rates from first principles using the path integral approach","volume":"148","author":"Neese","year":"2018","journal-title":"J. Chem. Phys."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"084106","DOI":"10.1063\/1.2834918","article-title":"Systematic optimization of long-range corrected hybrid density functionals","volume":"128","author":"Chai","year":"2008","journal-title":"J. Chem. Phys."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"154104","DOI":"10.1063\/1.3382344","article-title":"A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu","volume":"132","author":"Grimme","year":"2010","journal-title":"J. Chem. Phys."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1021\/ct300715s","article-title":"Long-Range Corrected Hybrid Density Functionals with Improved Dispersion Corrections","volume":"9","author":"Lin","year":"2013","journal-title":"J. Chem. Theory Comput."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1007\/s00214-010-0846-z","article-title":"Minimally augmented Karlsruhe basis sets","volume":"128","author":"Zheng","year":"2011","journal-title":"Theor. Chem. Accounts"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"3297","DOI":"10.1039\/b508541a","article-title":"Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy","volume":"7","author":"Weigend","year":"2005","journal-title":"Phys. Chem. Chem. Phys."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"e1327","DOI":"10.1002\/wcms.1327","article-title":"Software update: The ORCA program system, version 4.0","volume":"8","author":"Neese","year":"2018","journal-title":"Wiley INterdisciplinary-Rev.-Comput. Mol. Sci."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"224108","DOI":"10.1063\/5.0004608","article-title":"The ORCA quantum chemistry program package","volume":"152","author":"Neese","year":"2020","journal-title":"J. Chem. Phys."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1016\/S0009-2614(99)01149-5","article-title":"Time-dependent density functional theory within the Tamm-Dancoff approximation","volume":"314","author":"Hirata","year":"1999","journal-title":"Chem. Phys. Lett."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1016\/j.chemphys.2008.10.036","article-title":"Efficient, approximate and parallel Hartree-Fock and hybrid DFT calculations. A \u2019chain-of-spheres\u2019 algorithm for the Hartree-Fock exchange","volume":"356","author":"Neese","year":"2009","journal-title":"Chem. Phys."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"1057","DOI":"10.1039\/b515623h","article-title":"Accurate Coulomb-fitting basis sets for H to Rn","volume":"8","author":"Weigend","year":"2006","journal-title":"Phys. Chem. Chem. Phys."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"587","DOI":"10.1007\/s00214-007-0250-5","article-title":"Optimized accurate auxiliary basis sets for RI-MP2 and RI-CC2 calculations for the atoms Rb to Rn","volume":"117","author":"Hellweg","year":"2007","journal-title":"Theor. Chem. Accounts"},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"114104","DOI":"10.1063\/1.3479401","article-title":"Spin-flip time dependent density functional theory applied to excited states with single, double, or mixed electron excitation character","volume":"133","author":"Rinkevicius","year":"2010","journal-title":"J. Chem. Phys."},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"2538","DOI":"10.1021\/acs.jpclett.9b00712","article-title":"Excited-State Potential Energy Surfaces, Conical Intersections, and Analytical Gradients from Ground-State Density Functional Theory","volume":"10","author":"Mei","year":"2019","journal-title":"J. Phys. Chem. Lett."},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"4326","DOI":"10.1039\/C9CP06507E","article-title":"Spin-flip methods in quantum chemistry","volume":"22","author":"Casanova","year":"2020","journal-title":"Phys. Chem. Chem. Phys."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"9407","DOI":"10.1021\/acs.chemrev.1c00074","article-title":"Electronic Structure Methods for the Description of Nonadiabatic Effects and Conical Intersections","volume":"121","author":"Matsika","year":"2021","journal-title":"Chem. Rev."},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"242","DOI":"10.1002\/wcms.82","article-title":"Molpro: A general-purpose quantum chemistry program package","volume":"2","author":"Werner","year":"2012","journal-title":"WIREs Comput. Mol. Sci."},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"5053","DOI":"10.1063\/1.448627","article-title":"A second order multiconfiguration SCF procedure with optimum convergence","volume":"82","author":"Werner","year":"1985","journal-title":"J. Chem. Phys."},{"key":"ref_71","unstructured":"Werner, H.-J., Knowles, P.J., Knizia, G., Manby, F.R., Sch\u00fctz, M., Celani, P., Korona, T., Lindh, R., Mitrushenkov, A., and Rauhut, G. (2022, September 09). MOLPRO, 2012.1, A Package of Ab Initio Programs. Available online: https:\/\/www.molpro.net."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"9978","DOI":"10.1063\/1.1323224","article-title":"Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points","volume":"113","author":"Henkelman","year":"2000","journal-title":"J. Chem. Phys."},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"4929","DOI":"10.1021\/acs.jctc.1c00462","article-title":"Nudged Elastic Band Method for Molecular Reactions Using Energy-Weighted Springs Combined with Eigenvector Following","volume":"17","author":"Birgisson","year":"2021","journal-title":"J. Chem. Theor. Comput."},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"270","DOI":"10.1016\/0009-2614(83)80005-0","article-title":"Charge, bond order and valence in the ab initio scf theory","volume":"97","author":"Mayer","year":"1983","journal-title":"Chem. Phys. Lett."},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1002\/qua.560260111","article-title":"Bond order and valence: Relations to Mulliken\u2019s population analysis","volume":"26","author":"Mayer","year":"1984","journal-title":"Int. J. Quantum Chem."},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1002\/jcc.21600","article-title":"Gabedit\u2013A graphical user interface for computational chemistry softwares","volume":"32","author":"Allouche","year":"2011","journal-title":"J. Comput. Chem."},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1186\/1758-2946-4-17","article-title":"Avogadro: An advanced semantic chemical editor, visualization, and analysis platform","volume":"4","author":"Hanwell","year":"2012","journal-title":"J. Cheminform."},{"key":"ref_78","unstructured":"Dennington, R., Keith, T., and Millam, J. (2009). Gaussview 5.0.9, Semichem Inc."}],"container-title":["International Journal of Molecular Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1422-0067\/24\/3\/2906\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:22:19Z","timestamp":1760120539000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1422-0067\/24\/3\/2906"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,2]]},"references-count":78,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2023,2]]}},"alternative-id":["ijms24032906"],"URL":"https:\/\/doi.org\/10.3390\/ijms24032906","relation":{},"ISSN":["1422-0067"],"issn-type":[{"value":"1422-0067","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,2,2]]}}}