Spin-orbit coupling between electronic states of different multiplicity can be strongly coupled to molecular vibrations, and this interaction is becoming recognized as an important mechanism for controlling the course of photochemical reactions. Here, we show that the involvement of spin-vibronic coupling is essential for understanding the photophysics and photochemistry of heptamethine cyanines (Cy7), bearing iodine as a heavy atom in the C3' position of the chain and/or a 3H-indolium core, as potential triplet sensitizers and singlet oxygen producers in methanol and aqueous solutions. The sensitization efficiency was found to be an order of magnitude higher for the chain-substituted than the 3H-indolium core-substituted derivatives. Our ab initio calculations demonstrate that while all optimal structures of Cy7 are characterized by negligible spin-orbit coupling (tenths of cm-1) with no dependence on the position of the substituent, molecular vibrations lead to its significant increase (tens of cm-1 for the chain-substituted cyanines), which allowed us to interpret the observed position dependence.

Department of Chemistry Faculty of Science Masaryk University Kamenice 5 625 00 Brno Czech Republic

Department of Physical Chemistry University of Chemistry and Technology Prague Technické 5 166 28 Prague 6 Czech Republic

RECETOX Faculty of Science Masaryk University Kamenice 5 625 00 Brno Czech Republic

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Huang J.; Pu K. Activatable Molecular Probes for Second Near-Infrared Fluorescence, Chemiluminescence, and Photoacoustic Imaging. Angew. Chem., Int. Ed. 2020, 59, 11717.10.1002/anie.202001783. PubMed DOI

Zhang Y.; Bi J.; Xia S.; Mazi W.; Wan S.; Mikesell L.; Luck R. L.; Liu H. A near-infrared fluorescent probe based on a FRET rhodamine donor linked to a cyanine acceptor for sensitive detection of intracellular pH alternations. Molecules 2018, 23, 2679.10.3390/molecules23102679. PubMed DOI PMC

Li S.; Zhang D.; Xie X.; Ma S.; Liu Y.; Xu Z.; Gao Y.; Ye Y. A novel solvent-dependently bifunctional NIR absorptive and fluorescent ratiometric probe for detecting Fe3+/Cu2+ and its application in bioimaging. Sens. Actuators, B 2016, 224, 661.10.1016/j.snb.2015.10.086. DOI

Gao X.; Wu W.; Xi J.; Zheng H. Manipulation of monomer-aggregate transformation of a heptamethine cyanine ligand: near infrared chromogenic recognition of Hg2+. RSC Adv. 2017, 7, 32732.10.1039/C7RA03517A. DOI

Liu Y.; Chen M.; Cao T.; Sun Y.; Li C.; Liu Q.; Yang T.; Yao L.; Feng W.; Li F. A cyanine-modified nanosystem for in vivo upconversion luminescence bioimaging of methylmercury. J. Am. Chem. Soc. 2013, 135, 9869.10.1021/ja403798m. PubMed DOI

Shealy D. B.; Lipowska M.; Lipowski J.; Narayanan N.; Sutter S.; Strekowski L.; Patonay G. Synthesis, chromatographic separation, and characterization of near-infrared labeled DNA oligomers for use in DNA sequencing. Anal. Chem. 1995, 67, 247.10.1021/ac00098a002. DOI

Vus K.; Tarabara U.; Kurutos A.; Ryzhova O.; Gorbenko G.; Trusova V.; Gadjev N.; Deligeorgiev T. Aggregation behavior of novel heptamethine cyanine dyes upon their binding to native and fibrillar lysozyme. Mol. BioSyst. 2017, 13, 970.10.1039/C7MB00185A. PubMed DOI

Shen Z.; Prasai B.; Nakamura Y.; Kobayashi H.; Jackson M. S.; McCarley R. L. A near-infrared, wavelength-shiftable, turn-on fluorescent probe for the detection and imaging of cancer tumor cells. ACS Chem. Biol. 2017, 12, 1121.10.1021/acschembio.6b01094. PubMed DOI PMC

Nani R. R.; Gorka A. P.; Nagaya T.; Kobayashi H.; Schnermann M. J. Near-IR light-mediated cleavage of antibody–drug conjugates using cyanine photocages. Am. Ethnol. 2015, 127, 13839.10.1002/ange.201507391. PubMed DOI PMC

Stackova L.; Russo M.; Muchova L.; Orel V.; Vítek L.; Stacko P.; Klan P. Cyanine-Flavonol Hybrids for Near-Infrared Light-Activated Delivery of Carbon Monoxide. Chem. – Eur. J. 2020, 26, 13184.10.1002/chem.202003272. PubMed DOI PMC

Food U.; Administration D. In Approved drug products with therapeutic equivalence evaluations; US Food and Drug Administration (FDA): 2021.

Ogasawara Y.; Ikeda H.; Takahashi M.; Kawasaki K.; Doihara H. Evaluation of breast lymphatic pathways with indocyanine green fluorescence imaging in patients with breast cancer. World J. Surg. 2008, 32, 1924.10.1007/s00268-008-9519-7. PubMed DOI

Cao J.; Chi J.; Xia J.; Zhang Y.; Han S.; Sun Y. Iodinated cyanine dyes for fast near-infrared-guided deep tissue synergistic phototherapy. ACS Appl. Mater. Interfaces 2019, 11, 25720.10.1021/acsami.9b07694. PubMed DOI

Liu H.; Yin J.; Xing E.; Du Y.; Su Y.; Feng Y.; Meng S. Halogenated cyanine dyes for synergistic photodynamic and photothermal therapy. Dyes Pigm. 2021, 190, 10932710.1016/j.dyepig.2021.109327. DOI

Atchison J.; Kamila S.; Nesbitt H.; Logan K. A.; Nicholas D. M.; Fowley C.; Davis J.; Callan B.; McHale A. P.; Callan J. F. Iodinated cyanine dyes: a new class of sensitisers for use in NIR activated photodynamic therapy (PDT). Chem. Commun. 2017, 53, 2009.10.1039/C6CC09624G. PubMed DOI

Klan P.; Wirz J.. Photochemistry of Organic Compounds: From Concepts to Practice; 1st ed.; John Wiley & Sons Ltd.: Chichester, 2009.

Solov’ev K. N.; Borisevich E. A. Intramolecular heavy-atom effect in the photophysics of organic molecules. Phys.-Usp. 2005, 48, 231.10.1070/PU2005v048n03ABEH001761. DOI

Yang X.; Bai J.; Qian Y. The investigation of unique water-soluble heptamethine cyanine dye for use as NIR photosensitizer in photodynamic therapy of cancer cells. Spectrochim. Acta, Part A 2020, 228, 11770210.1016/j.saa.2019.117702. PubMed DOI

Li M.; Sun W.; Tian R.; Cao J.; Tian Y.; Gurram B.; Fan J.; Peng X. Smart J-aggregate of cyanine photosensitizer with the ability to target tumor and enhance photodynamic therapy efficacy. Biomaterials 2021, 269, 12053210.1016/j.biomaterials.2020.120532. PubMed DOI

Zhao X.; Yao Q.; Long S.; Chi W.; Yang Y.; Tan D.; Liu X.; Huang H.; Sun W.; Du J. An Approach to Developing Cyanines with Simultaneous Intersystem Crossing Enhancement and Excited-State Lifetime Elongation for Photodynamic Antitumor Metastasis. J. Am. Chem. Soc. 2021, 143, 12345.10.1021/jacs.1c06275. PubMed DOI

Jarman J. B.; Dougherty D. A. Charge-transfer heptamethine dyes for NIR singlet oxygen generation. Chem. Commun. 2019, 55, 5511.10.1039/C9CC01096C. PubMed DOI

Stackova L.; Muchova E.; Russo M.; Slavicek P.; Stacko P.; Klan P. Deciphering the Structure–Property Relations in Substituted Heptamethine Cyanines. J. Org. Chem. 2020, 85, 9776.10.1021/acs.joc.0c01104. PubMed DOI

Montagnon T.; Tofi M.; Vassilikogiannakis G. Using singlet oxygen to synthesize polyoxygenated natural products from furans. Acc. Chem. Res. 2008, 41, 1001.10.1021/ar800023v. PubMed DOI

Mathon B.; Choubert J.-M.; Miege C.; Coquery M. A review of the photodegradability and transformation products of 13 pharmaceuticals and pesticides relevant to sewage polishing treatment. Sci. Total Environ. 2016, 551, 712.10.1016/j.scitotenv.2016.02.009. PubMed DOI

Gorman A.; Killoran J.; O’Shea C.; Kenna T.; Gallagher W. M.; O’Shea D. F. In vitro demonstration of the heavy-atom effect for photodynamic therapy. J. Am. Chem. Soc. 2004, 126, 10619.10.1021/ja047649e. PubMed DOI

Stackova L.; Stacko P.; Klan P. Approach to a substituted heptamethine cyanine chain by the ring opening of Zincke salts. J. Am. Chem. Soc. 2019, 141, 7155.10.1021/jacs.9b02537. PubMed DOI

Autschbach J. Why the Particle-in-a-Box Model Works Well for Cyanine Dyes but Not for Conjugated Polyenes. J. Chem. Educ. 2007, 84, 1840.10.1021/ed084p1840. DOI

Champagne B.; Guillaume M.; Zutterman F. TDDFT investigation of the optical properties of cyanine dyes. Chem. Phys. Lett. 2006, 425, 105.10.1016/j.cplett.2006.05.009. DOI

Grimme S.; Neese F. Double-hybrid density functional theory for excited electronic states of molecules. J. Chem. Phys. 2007, 127, 154116.10.1063/1.2772854. PubMed DOI

Jacquemin D.; Wathelet V.; Perpète E. A.; Adamo C. Extensive TD-DFT Benchmark: Singlet-Excited States of Organic Molecules. J. Chem. Theory Comput. 2009, 5, 2420.10.1021/ct900298e. PubMed DOI

Fabian J. TDDFT-calculations of Vis/NIR absorbing compounds. Dyes Pigm. 2010, 84, 36.10.1016/j.dyepig.2009.06.008. DOI

Jacquemin D.; Zhao Y.; Valero R.; Adamo C.; Ciofini I.; Truhlar D. G. Verdict: time-dependent density functional theory “not guilty” of large errors for cyanines. J. Chem. Theory Comput. 2012, 8, 1255.10.1021/ct200721d. PubMed DOI

Schreiber M.; Buß V.; Fülscher M. P. The electronic spectra of symmetric cyanine dyes: A CASPT2 study. Phys. Chem. Chem. Phys. 2001, 3, 3906.10.1039/b103417k. DOI

Jacquemin D.; Perpète E. A.; Scalmani G.; Frisch M. J.; Kobayashi R.; Adamo C. Assessment of the efficiency of long-range corrected functionals for some properties of large compounds. J. Chem. Phys. 2007, 126, 144105.10.1063/1.2715573. PubMed DOI

Send R.; Valsson O.; Filippi C. Electronic Excitations of Simple Cyanine Dyes: Reconciling Density Functional and Wave Function Methods. J. Chem. Theory Comput. 2011, 7, 444.10.1021/ct1006295. PubMed DOI

Masunov A. E. Theoretical spectroscopy of carbocyanine dyes made accurate by frozen density correction to excitation energies obtained by TD-DFT. Int. J. Quantum Chem. 2010, 110, 3095.10.1002/qua.22923. DOI

Le Guennic B.; Jacquemin D. Taking up the cyanine challenge with quantum tools. Acc. Chem. Res. 2015, 48, 530.10.1021/ar500447q. PubMed DOI PMC

Moore B.; Autschbach J. Longest-wavelength electronic excitations of linear cyanines: the role of electron delocalization and of approximations in time-dependent density functional theory. J. Chem. Theory Comput. 2013, 9, 4991.10.1021/ct400649r. PubMed DOI

Zhekova H.; Krykunov M.; Autschbach J.; Ziegler T. Applications of Time Dependent and Time Independent Density Functional Theory to the First π to π* Transition in Cyanine Dyes. J. Chem. Theory Comput. 2014, 10, 3299.10.1021/ct500292c. PubMed DOI

Penfold T. J.; Gindensperger E.; Daniel C.; Marian C. M. Spin-vibronic mechanism for intersystem crossing. Chem. Rev. 2018, 118, 6975.10.1021/acs.chemrev.7b00617. PubMed DOI

Terenziani F.; Painelli A.; Katan C.; Charlot M.; Blanchard-Desce M. Charge instability in quadrupolar chromophores: Symmetry breaking and solvatochromism. J. Am. Chem. Soc. 2006, 128, 15742.10.1021/ja064521j. PubMed DOI

Hyun H.; Owens E. A.; Narayana L.; Wada H.; Gravier J.; Bao K.; Frangioni J. V.; Choi H. S.; Henary M. Central C–C bonding increases optical and chemical stability of NIR fluorophores. RSC Adv. 2014, 4, 58762.10.1039/C4RA11225C. PubMed DOI PMC

Ebaston T.; Nakonechny F.; Talalai E.; Gellerman G.; Patsenker L. Iodinated xanthene-cyanine NIR dyes as potential photosensitizers for antimicrobial photodynamic therapy. Dyes Pigm. 2021, 184, 10885410.1016/j.dyepig.2020.108854. DOI

Pham W.; Medarova Z.; Moore A. Synthesis and application of a water-soluble near-infrared dye for cancer detection using optical imaging. Bioconjugate Chem. 2005, 16, 735.10.1021/bc049700+. PubMed DOI

Song F.; Peng X.; Lu E.; Zhang R.; Chen X.; Song B. Syntheses, spectral properties and photostabilities of novel water-soluble near-infrared cyanine dyes. J. Photochem. Photobiol., A 2004, 168, 53.10.1016/j.jphotochem.2004.05.012. DOI

Hansch C.; Leo A.; Taft R. A survey of Hammett substituent constants and resonance and field parameters. Chem. Rev. 1991, 91, 165.10.1021/cr00002a004. DOI

Matikonda S. S.; Hammersley G.; Kumari N.; Grabenhorst L.; Glembockyte V.; Tinnefeld P.; Ivanic J.; Levitus M.; Schnermann M. J. Impact of cyanine conformational restraint in the near-infrared range. J. Org. Chem. 2020, 85, 5907.10.1021/acs.joc.0c00236. PubMed DOI PMC

Wang L.; Jin J.; Chen X.; Fan H.-H.; Li B. K. F.; Cheah K.-W.; Ding N.; Ju S.; Wong W.-T.; Li C. A cyanine based fluorophore emitting both single photon near-infrared fluorescence and two-photon deep red fluorescence in aqueous solution. Org. Biomol. Chem. 2012, 10, 5366.10.1039/c2ob25619c. PubMed DOI

Thavornpradit S.; Usama S. M.; Park G. K.; Shrestha J. P.; Nomura S.; Baek Y.; Choi H. S.; Burgess K. QuatCy: A Heptamethine Cyanine Modification With Improved Characteristics. Theranostics 2019, 9, 2856.10.7150/thno.33595. PubMed DOI PMC

Landsman M.; Kwant G.; Mook G.; Zijlstra W. Light-absorbing properties, stability, and spectral stabilization of indocyanine green. J. Appl. Physiol. 1976, 40, 575.10.1152/jappl.1976.40.4.575. PubMed DOI

Filatov M.; Huix-Rotllant M. Assessment of density functional theory based ΔSCF (self-consistent field) and linear response methods for longest wavelength excited states of extended π-conjugated molecular systems. J. Chem. Phys. 2014, 141, 02411210.1063/1.4887087. PubMed DOI

Peach M. J. G.; Williamson M. J.; Tozer D. J. Influence of Triplet Instabilities in TDDFT. J. Chem. Theory Comput. 2011, 7, 3578.10.1021/ct200651r. PubMed DOI

Kautsky H.; de Bruijn H. Frontier Orbitals, Combustion and Redox Transfer from a Fermionic-Bosonic Orbital Perspective. Naturwissenschaften 1931, 19, 1043.10.1007/BF01516190. DOI

Wang Z.; Toffoletti A.; Hou Y.; Zhao J.; Barbon A.; Dick B. Insight into the drastically different triplet lifetimes of BODIPY obtained by optical/magnetic spectroscopy and theoretical computations. Chem. Sci. 2021, 12, 2829.10.1039/D0SC05494A. PubMed DOI PMC

Semenova O.; Kobzev D.; Yazbak F.; Nakonechny F.; Kolosova O.; Tatarets A.; Gellerman G.; Patsenker L. Unexpected effect of iodine atoms in heptamethine cyanine dyes on the photodynamic eradication of Gram-positive and Gram-negative pathogens. Dyes Pigm. 2021, 195, 10974510.1016/j.dyepig.2021.109745. DOI

Krieg M.; Redmond R. W. Photophysical properties of 3, 3′-dialkylthiacarbocyanine dyes in homogeneous solution. Photochem. Photobiol. 1993, 57, 472.10.1111/j.1751-1097.1993.tb02321.x. PubMed DOI

Usama S. M.; Thavornpradit S.; Burgess K. Optimized heptamethine cyanines for photodynamic therapy. ACS Appl. Bio Mater. 2018, 1, 1195.10.1021/acsabm.8b00414. PubMed DOI

James N. S.; Chen Y.; Joshi P.; Ohulchanskyy T. Y.; Ethirajan M.; Henary M.; Strekowsk L.; Pandey R. K. Evaluation of polymethine dyes as potential probes for near infrared fluorescence imaging of tumors: Part-1. Theranostics 2013, 3, 692.10.7150/thno.5922. PubMed DOI PMC

Tanielian C.; Golder L.; Wolff C. Production and quenching of singlet oxygen by the sensitizer in dye-sensitized photo-oxygenations. J. Photochem. 1984, 25, 117.10.1016/0047-2670(84)87016-1. DOI

Yoshiharu U. Determination Of Quantum Yield Of Singlet Oxygen Formation By Photosensitization. Chem. Lett. 1973, 2, 743.10.1246/cl.1973.743. DOI

Gorka A. P.; Schnermann M. J. Harnessing cyanine photooxidation: from slowing photobleaching to near-IR uncaging. Curr. Opin. Chem. Biol. 2016, 33, 117.10.1016/j.cbpa.2016.05.022. PubMed DOI PMC

Strehmel B.; Schmitz C.; Kütahya C.; Pang Y.; Drewitz A.; Mustroph H. Photophysics and photochemistry of NIR absorbers derived from cyanines: key to new technologies based on chemistry 4.0. Beilstein J. Org. Chem. 2020, 16, 415.10.3762/bjoc.16.40. PubMed DOI PMC

Rüttger F.; Mindt S.; Golz C.; Alcarazo M.; John M. Isomerization and Dimerization of Indocyanine Green and a Related Heptamethine Dye. Eur. J. Org. Chem. 2019, 2019, 4791.10.1002/ejoc.201900715. DOI

Chen P.; Sun S.; Hu Y.; Qian Z.; Zheng D. Structure and solvent effect on the photostability of indolenine cyanine dyes. Dyes Pigm. 1999, 41, 227.10.1016/S0143-7208(98)00088-6. DOI

Feng L.; Chen W.; Ma X.; Liu S. H.; Yin J. Near-infrared heptamethine cyanines (Cy7): from structure, property to application. Org. Biomol. Chem. 2020, 18, 9385.10.1039/D0OB01962C. PubMed DOI

Bunce N. J. In Organic Photochemistry and Photobiology; Horspool, W. M., Song P.-S., Eds.; CRC Press: Boca Raton, 1994, p 1181.

Luo Y.-R.Handbook of Bond Dissociation Energies in Organic Compounds; CRC Press: Boca Raton, 2002, 10.1201/9781420039863. DOI

Nastasa V.; Pascu A.; Boni M.; Smarandache A.; Staicu A.; Pascu M. Insights into the photophysics of zinc phthalocyanine and photogenerated singlet oxygen in DMSO-water mixture. Colloids Surf., A 2016, 505, 197.10.1016/j.colsurfa.2016.04.050. DOI

El-Sayed M. A. Triplet state. Its radiative and nonradiative properties. Acc. Chem. Res. 1968, 1, 8.10.1021/ar50001a002. DOI

Pokhilko P.; Krylov A. I. Quantitative El-Sayed Rules for Many-Body Wave Functions from Spinless Transition Density Matrices. J. Phys. Chem. Lett. 2019, 10, 4857.10.1021/acs.jpclett.9b02120. PubMed DOI

Albrecht A. C. Vibronic—Spin-Orbit Perturbations and the Assignment of the Lowest Triplet State of Benzene. J. Chem. Phys. 1963, 38, 354.10.1063/1.1733665. DOI

Perun S.; Tatchen J.; Marian C. M. Singlet and triplet excited states and intersystem crossing in free-base porphyrin: TDDFT and DFT/MRCI study. ChemPhysChem 2008, 9, 282.10.1002/cphc.200700509. PubMed DOI

Minaev B.; Ågren H. Theoretical DFT study of phosphorescence from porphyrins. Chem. Phys. 2005, 315, 215.10.1016/j.chemphys.2005.04.017. DOI

Tatchen J.; Gilka N.; Marian C. M. Intersystem crossing driven by vibronic spin–orbit coupling: a case study on psoralen. Phys. Chem. Chem. Phys. 2007, 9, 5209.10.1039/b706410a. PubMed DOI

Alarcon E.; Edwards A. M.; Aspee A.; Borsarelli C. D.; Lissi E. A. Photophysics and photochemistry of rose bengal bound to human serum albumin. Photochem. Photobiol. Sci. 2009, 8, 933.10.1039/b901056d. PubMed DOI

Hoebeke M.; Damoiseau X. Determination of the singlet oxygen quantum yield of bacteriochlorin a: a comparative study in phosphate buffer and aqueous dispersion of dimiristoyl-L-alpha-phosphatidylcholine liposomes. Photochem. Photobiol. Sci. 2002, 1, 283.10.1039/b201081j. PubMed DOI

Muraseccosuardi P.; Gassmann E.; Braun A. M.; Oliveros E. Determination Of The Quantum Yield Of Intersystem Crossing Of Rose Bengal. Helv. Chim. Acta 1987, 70, 1760.10.1002/hlca.19870700712. DOI

Fang L.; Liu J. A.; Ju S.; Zheng F. G.; Dong W.; Shen M. R. Experimental and theoretical evidence of enhanced ferromagnetism in sonochemical synthesized BiFeO3 nanoparticles. Appl. Phys. Lett. 2010, 97, 242501.10.1063/1.3525573. DOI

Young R. H.; Brewer D.; Keller R. A. Determination Of Rate Constants Of Reaction And Lifetimes Of Singlet Oxygen In Solution By A Flash-Photolysis Technique. J. Am. Chem. Soc. 1973, 95, 375.10.1021/ja00783a012. DOI

Entradas T.; Waldron S.; Volk M. The detection sensitivity of commonly used singlet oxygen probes in aqueous environments. J. Photochem. Photobiol., B 2020, 204.10.1016/j.jphotobiol.2020.111787. PubMed DOI

Wilkinson F.; Helman W. P.; Ross A. B. Quantum Yields For The Photosensitized Formation Of The Lowest Electronically Excited Singlet-state Of Molecular Oxygen In Solution. J. Phys. Chem. Ref. Data 1993, 22, 113.10.1063/1.555934. DOI

Atkinson K. M.; Morsby J. J.; Kommidi S. S. R.; Smith B. D. Generalizable synthesis of bioresponsive near-infrared fluorescent probes: sulfonated heptamethine cyanine prototype for imaging cell hypoxia. Org. Biomol. Chem. 2021, 19, 4100.10.1039/D1OB00426C. PubMed DOI PMC

Kumar S.; Watkins D. L.; Fujiwara T. A tailored spirooxazine dimer as a photoswitchable binding tool. Chem. Commun. 2009, 4369.10.1039/b909496b. PubMed DOI

Choi H. S.; Nasr K.; Alyabyev S.; Feith D.; Lee J. H.; Kim S. H.; Ashitate Y.; Hyun H.; Patonay G.; Strekowski L.; Henary M.; Frangioni J. V. Synthesis and In Vivo Fate of Zwitterionic Near-Infrared Fluorophores. Angew. Chem., Int. Ed. 2011, 50, 6258.10.1002/anie.201102459. PubMed DOI PMC

Schulz-Senft M.; Gates P. J.; Sönnichsen F. D.; Staubitz A. Diversely halogenated spiropyrans - Useful synthetic building blocks for a versatile class of molecular switches. Dyes Pigm. 2017, 136, 292.10.1016/j.dyepig.2016.08.039. DOI

Strekowski L.; Mason J. C.; Lee H.; Say M.; Patonay G. Water-soluble pH-sensitive 2,6-bis(substituted ethylidene)-cyclohexanone/hydroxy cyanine dyes that absorb in the visible/near-infrared regions. J. Heterocycl. Chem. 2004, 41, 227.10.1002/jhet.5570410213. DOI

Miertuš S.; Scrocco E.; Tomasi J. Electrostatic interaction of a solute with a continuum. A direct utilizaion of AB initio molecular potentials for the prevision of solvent effects. Chem. Phys. 1981, 55, 117.10.1016/0301-0104(81)85090-2. DOI

Körzdörfer T.; Sears J. S.; Sutton C.; Brédas J.-L. Long-range corrected hybrid functionals for π-conjugated systems: Dependence of the range-separation parameter on conjugation length. J. Chem. Phys. 2011, 135, 204107.10.1063/1.3663856. PubMed DOI

Grimme S. A simplified Tamm-Dancoff density functional approach for the electronic excitation spectra of very large molecules. J. Chem. Phys. 2013, 138, 244104.10.1063/1.4811331. PubMed DOI

Neese F. Software update: the ORCA program system, version 4.0. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2018, 8, e132710.1002/wcms.1327. DOI

Neese F. The ORCA program system. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2012, 2, 73.10.1002/wcms.81. DOI

Neese F.; Wennmohs F.; Becker U.; Riplinger C. The ORCA quantum chemistry program package. J. Chem. Phys. 2020, 152, 224108.10.1063/5.0004608. PubMed DOI

Sandhoefer B.; Neese F. One-electron contributions to the g-tensor for second-order Douglas–Kroll–Hess theory. J. Chem. Phys. 2012, 137, 09410210.1063/1.4747454. PubMed DOI

Neese F. Efficient and accurate approximations to the molecular spin-orbit coupling operator and their use in molecular g-tensor calculations. J. Chem. Phys. 2005, 122, 03410710.1063/1.1829047. PubMed DOI