Skip to main content

Advertisement

SpringerLink
Log in

Practical treatment of singlet oxygen with density-functional theory and the multiplet-sum method

  • Regular Article
  • Published:
Theoretical Chemistry Accounts Aims and scope Submit manuscript

Abstract

Singlet oxygen (\(^1\)O\(_2\)) comes in two flavors—namely the dominant lower-energy \(a \,^1\Delta _g\) state and the higher-energy shorter-lived \(b \,^1\Sigma _g^+\) state—and plays a key role in many photochemical and photobiological reactions. For this reason, and because of the large size of the systems treated, many papers have appeared with density-functional theory (DFT) treatments of the reactions of \(^1\)O\(_2\) with different chemical species. The present work serves as a reminder that the common assumption that it is enough to fix the spin multiplicity as unity is not enough to insure a correct treatment of singlet oxygen. We review the correct group theoretical treatment of the three lowest energy electronic states of O\(_2\) which, in the case of \(^1\)O\(_2\) is often so badly explained in the relevant photochemical literature that the explanation borders on being incorrect and prevents, rather than encourages, a correct treatment of this interesting and important photochemical species. We then show how many electronic structure programs, such as a freely downloadable and personal-computer compatible Linux version of deMon2k, may be used, together with the multiplet sum method (MSM), to obtain a more accurate estimation of the potential energy curves (PECs) of the two \(^1\)O\(_2\) states. Applications of the MSM DFT method to \(^1\)O\(_2\) appear to be extremely rare as we were only able to find one correct application of the DFT MSM (or rather a very similar approach) to \(^1\)O\(_2\) in our literature search. Here we treat both the \(a \,^1\Delta _g\) and \(b \,^1\Sigma _g^+\) state with a wide variety of density-functional approximations (DFAs). Various strengths and weaknesses of different DFAs emerge through our application of the MSM method. In particular, the quality of the \(a \,^1\Delta _g\) excitation energy reflects how well functionals are able to describe the spin-flip energy in DFT while the quality of the \(b \,^1\Sigma _g^+\) excitation energy reflects how well functionals are able to describe the spin-pairing energy in DFT. Finally, we note that improvements in DFT-based excited-state methods will be needed to describe the full PECs of \(^1\)O\(_2\) including both the equilibrium bond lengths and dissociation behavior.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17

Similar content being viewed by others

References

  1. Lavoisier A (1789) Traité élémentaire de Chimie, présenté dans un ordre nouveau et d’après les décovertes modernes. Chez Cuchet, Paris

  2. Borden WT, Hoffmann R, Stuyver T, Chen B (2017) Dioxygen: what makes this triplet diradical kinetically persistent? J Am Chem Soc 139:9010

    Article  CAS  PubMed  Google Scholar 

  3. Kearns DR (1971) Physical and chemical properties of singlet molecular oxygen. Chem Rev 71:395

    Article  CAS  Google Scholar 

  4. Ryter SW, Tyrrell RM (1998) Singlet molecular oxygen (\(^1\)O\(_2\)): a possible effector of eukaryotic gene expression. Free Radical Biol Med 24:1520

    Article  CAS  Google Scholar 

  5. DeRosa MC, Crutchley RJ (2002) Photosensitized singlet oxygen and its application. Coord Chem Rev 233–234:351

    Article  Google Scholar 

  6. Paterson MJ, Christiansen O, Jensen F, Ogilby PR (2006) Overview of theoretical and computational methods applied to the oxygen-organic molecule photosystem. Photochem Photobiol 82:1136

    Article  CAS  PubMed  Google Scholar 

  7. Ogilby PR (2010) Singlet oxygen: there is indeed something new under the sun. Chem Soc Rev 39:3181

    Article  CAS  PubMed  Google Scholar 

  8. Ziegler T, Rauk A, Baerends EJ (1977) On the calculation of multiplet energies by the Hartree-Fock-Slater method. Theor Chim Acta 4:877

    Google Scholar 

  9. Daul C (1994) Density functional theory applied to the excited states of coordination compounds. Int J Quantum Chem 52:867

    Article  CAS  Google Scholar 

  10. Etindele AJ, Maezono R, Melono RLM, Motapon O (2017) Influence of endohedral confinement of atoms on structural and dynamical properties of the C\(_{60}\) fullerene. Chem Phys Lett 685:395

    Article  CAS  Google Scholar 

  11. Darghouth AAMHM, Casida ME, Zhu X, Natarajan B, Su H, Humeniuk A, Mitrić R (2021) Effect of varying the TD-lc-DFTB range-separation parameter on charge and energy transfer in a model pentacene/buckminsterfullerene heterojunction. J Chem Phys 154:054102

    Article  CAS  PubMed  Google Scholar 

  12. Brunet L, Lyon DY, Hotze EM, Alvarez PJJ, Wiesner MR (2009) Comparative photoactivity and antibacterial properties of C\(_{60}\) fullerenes and titanium dioxide nanoparticles. Environ Sci Technol 43:4355

    Article  CAS  PubMed  Google Scholar 

  13. Hamblin MR (2018) Fullerenes as photosensitizers in photodynamic therapy: pros and cons. Photochem Photobiol Sci 17:1515

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  14. Yamakoshi Y, Umezawa N, Ryu A, Arakane K, Miyata N, Goda Y, Masumizu T, Nagano T (2003) Active oxygen species generated from photoexcited fullerene (C\(_{60}\)) as potential medicines: O\(_2^{-\bullet }\) versus \(^1\)O\(_2\). J Am Chem Soc 125:12803

    Article  CAS  PubMed  Google Scholar 

  15. Fueno H, Takenaka Y, Tanaka K (2011) Theoretical study on energy transfer from the excited C\(_{60}\) to molecular oxygen. Opt Spectrosc 111(2):248

    Article  CAS  Google Scholar 

  16. Zu Z (2020) Reactivities of singlet oxygen: open-shell or closed-shell? Phys Chem Chem Phys 22:13373

    Article  Google Scholar 

  17. Garavelli M, Bernardi F, Olivucci M, Robb MA (1998) DFT study of the reactions between singlet-oxygen and a carotenoid model. J Am Chem Soc 120:10210

    Article  CAS  Google Scholar 

  18. Yamaguchi K, Jensen F, Dorigo A, Houk K (1988) A spin correction procedure for unrestricted Hartree-Fock and Möller-Plesset wavefunctions for singlet diradicals and polyradicals. Chem Phys Lett 149:537

    Article  CAS  Google Scholar 

  19. Yamanaka S, Kawakami T, Nagao H, Yamaguchi K (1994) Effective exchange integrals for open-shell species by density functional methods. Chem Phys Lett 231:25

    Article  CAS  Google Scholar 

  20. Wittbrodt JM, Schlegel MBJ (1996) Some reasons not to use spin projected density functional theory. Chem Phys 105:6574

    CAS  Google Scholar 

  21. Al-Nu’airat J, Altarawneh M, Gao X, Westmoreland PR, Dlugogorski BZ (2017) Reaction of aniline with singlet oxygen (O\(_2\)\(^1\delta _g\)). J Phys Chem A 121:17

  22. National institute of standards and technologies computational chemistry comparison and benchmark data base. https://cccbdb.nist.gov/stgap3x.asp?im=90&ib=32&estate1=4&estate2=1. Last accessed 16 July 2021

  23. Farooq Z, Chestakov DA, Yan B, Groenenboom GC, van der Zande WJ, Parker DH (2014) Photodissociation of singlet oxygen in the UV region. Phys Chem Chem Phys 16:3305

  24. Geudtner G, Calaminici P, Carmona-Espindola J, del Campo JM, Dominguez-Soria VD, Flores-Moreno R, Gamboa GU, Goursot A, Kster AM, Reveles J U, Mineva T, Vasquez-Perez JM, Vela A, Zuñiga-Gutierrez B, Salahub D (2012) deMon2k. WIREs: Comput Mol Sci 2:548

  25. Krupenie PH (1972) The spectrum of molecular oxygen. J Phys Chem Ref Data 1:423

    Article  CAS  Google Scholar 

  26. Saxon RP, Liu B (1977) Ab initioconfiguration interaction study of the valence states of O\(_2\). J Chem Phys 67

  27. van Vroonhoven MCGN, Groenenboom GC (2002) Reassignment of the O\(_2\) spectrum just below dissociation threshold based on ab initio calculations. J Chem Phys 117:5240

    Google Scholar 

  28. Rohatgi A (2021) WebPlotDigitizer: Webbased plot digitizer. https://apps.automeris.io/wpd/. Last accessed 3 June 2021

  29. Laing M (1989) The three forms of molecular oxygen. J Chem Ed 66:453

    Article  CAS  Google Scholar 

  30. Wikipedia, Singlet oxygen. https://en.wikipedia.org/wiki/Singlet_oxygen. Last accessed 24 June (2021)

  31. Carlton TS (2006) Why the lower-energy term of singlet dioxygen has a doubly occupied \(\pi ^*\) orbital. J Chem Ed 83:477

    Article  CAS  Google Scholar 

  32. Hyde KE (1975) Methods for obtaining Russell-Saunders term symbols from electronic configurations. J Chem Ed 52:87

    Article  CAS  Google Scholar 

  33. NIST (2021) National institute of standards and technologies atomic spectra database. https://physics.nist.gov/PhysRefData/ASD/levels form.html. Last accessed 22 June

  34. Stuyver T, Chen B, Zeng T, Geerlings P, Proft FD, Hoffmann R (2019) Do diradicals behave like radicals? Chem Rev 119:11291

    Article  CAS  PubMed  Google Scholar 

  35. Friedrichs J, Frank I (2009) Mechanism of electrocyclic ring-opening of diphenyloxirane: 40 years after Woodward and Hoffmann. Chem Eur J 15:10825

  36. Casida ME, Huix-Rotllant M (2012) Progress in time-dependent density-functional theory. Ann Rev Phys Chem 63:287

    Article  CAS  Google Scholar 

  37. Koster AM et al (2021) deMon2k: density of Montreal, version 5.0 the deMon developers, Cinvestav, Mexico City (2018). http://www.demonsoftware.com/public html/index.html. Last accessed 3 July 2021

  38. de la Lande A, Alvarez-Ibarra A, Hasnaoui K, Cailliez F, Wu X, Mineva T, Cuny J, Calaminici P, López-Sosa L, Geudtner G, Navizet I, Garcia Iriepa C, Salahub DR, Köster AM (1653) Molecular simulations with in demon2kQM-MM, a tutorial-review. Molecules 24

  39. Löwdin P (1955) Quantum theory of many-particle systems. II. Study of the ordinary Hartree-Fock approximation

  40. Myneni H, Casida ME (2017) On the calculation of \(\delta \langle {\hat{S}}^2 \rangle \) for electronic excitations in time-dependent density-functional theory. Comput Phys Comm 213:72

    Article  CAS  Google Scholar 

  41. Goerigk L, Mehta N (2019) A trip to the density functional theory zoo: Warnings and recommendations for the user. Aust J Chem 72:563

    Article  CAS  Google Scholar 

  42. Perdew JP, Schmidt K (2001) Jacob’s ladder of density functional approximations for the exchange-correlation energy. In: Doren VEV, Alseoy KV, Geerlings P (eds) Density functional theory and its applications to materials. American Institute of Physics, Melville, New York, p 1

  43. Perdew JP, Ruzsinsky A, Constantin LA, Sun J, Csonka G (2009) Some fundamental issues in ground-state density functional theory: a guide for the perplexed. J Chem Theor Comput 5:902

    Article  CAS  Google Scholar 

  44. O’Neill DP, Gill PMW (2005) Benchmark correlation energies for small molecules. Mol Phys 103:763

  45. Zhao Y, Truhlar DG (2007) The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals. Theor Chem Acc 120:215

    Article  Google Scholar 

  46. Fouqueau A, Mer S, Casida ME, Daku LML, Hauser A, Mineva T, Neese F (2004) Comparison of density functionals for energy and structural differences between the high [\(^5T_{2g}: (t_{2g})^4(e_g)^2\)] and low [\(^1A_{1g}: (t_{2g})^6(e_g)^0\)] spin states of the hexaquoferrous cation, [Fe(H\(_2\)O)\(_6\)]\(^{2+}\). J Chem Phys 120:9473

    Article  CAS  PubMed  Google Scholar 

  47. Fouqueau A, Casida ME, Daku LML, Hauser A, Neese F (2005) Comparison of density functionals for energy and structural differences between the high [\(^5T_{2g}: (t_{2g})^4(e_g)^2\)] and low [\(^1A_{1g}: (t_{2g})^6(e_g)^0\)] spin states of iron(II) coordination compounds: II. More functionals and the hexaminoferrous cation, [Fe(NH\(_3\))\(_6\)]\(^{2+}\). J Chem Phys 122:044110

  48. Ganzenmüller G, Berkaïne N, Fouqueau A, Casida ME, Reiher M (2005) Comparison of density functionals for differences between the high (\(^5T_{2g}\)) and low (\(^1A_{1g}\)) spin states of iron(II) coordination compounds: IV. Results for the ferrous complexes [Fe(L)(‘NHS\(_4\)’)]. J Chem Phys 122:234321

  49. Daku LML, Vargas A, Hauser A, Fouqueau A, Casida ME (2005) Assessment of density functionals for the high-spin/low-spin energy difference in the low-spin iron(II) tris(2,2’-bipyridine) complex. Chem Phys Chem 6:1393

  50. Zein S, Borshch SA, Fleurat-Lessard P, Casida ME, Chermette H (2007) Assessment of the exchange-correlation functionals for the physical description of spin transition phenomena by DFT methods: All the same? J Chem Phys 126:014105

    Article  PubMed  Google Scholar 

  51. Song S, Kim M, Sim E, Benali A, Heinonen O, Burke K (2018) Benchmarks and reliable DFT results for spin gaps of small ligand Fe(II) complexes. J Chem Theory Comput 14:2304

    Article  CAS  PubMed  Google Scholar 

  52. Morse PM (1929) Diatomic molecules according to the wave mechanics. II. Vibrational levels. Phys Rev 34:57

  53. Hohenberg P, Kohn W (1964) Inhomogeneous electron gas. Phys Rev 136:B864

    Article  Google Scholar 

  54. Kohn W, Sham LJ (1965) Self-consistent equations including exchange and correlation effects. Phys Rev 140:A1133

    Article  Google Scholar 

  55. Casida ME (1995) Generalization of the optimized effective potential model to include electron correlation: a variational derivation of the Sham-Schluter equation for the exact exchange-correlation potential. Phys Rev A 51:2005

    Article  CAS  PubMed  Google Scholar 

  56. Casida ME (2009) Review: time-dependent density-functional theory for molecules and molecular solids. J Mol Struct (Theochem) 914:3

  57. Casida ME (2021) Reconciling of the \(\Delta \)SCF and TDDFT approaches to excitation energies. In: DFT: a charge-transfer correction for TDDFT with GGA functionals on-line workshop proceedings of the joint ITP/INT workshop on time-dependent density functional theory. 15–17 April 1999, Institute for Theoretical Physics, University of California at Santa Barbara. http://www.itp.ucsb.edu/online/tddft c99/. Last accessed 25

  58. Casida ME, Gutierrez F, Guan J, Gadea F, Salahub DR, Daudey J (2000) Charge-transfer correction for improved time-dependent local density approximation excited-state potential energy curves: Analysis within the two-level model with illustration for H\(_2\) and LiH. J Chem Phys 113:7062

    Article  CAS  Google Scholar 

  59. Ziegler T, Seth M, Krykunov M, Autschbach J, Wang F (2009) On the relation between time-dependent and variational density functional theory approaches for the determination of excitation energies and transition moments. J Chem Phys 130:154102

    Article  PubMed  Google Scholar 

  60. Ziegler T, Krykunov M, Cullen J (2012) The implementation of a self-consistent constricted variational density functional theory for the description of excited states. J Chem Phys 136:124107

    Article  PubMed  PubMed Central  Google Scholar 

  61. Hirata S, Head-Gordon M (1999) Time-dependent density functional theory within the Tamm-Dancoff approximation. Chem Phys Lett 314:291

    Article  CAS  Google Scholar 

  62. Guan J, Casida ME, Salahub DR (2000) Time-dependent density-functional theory investigation of excitation spectra of open-shell molecules. J Mol Struct (Theochem) 527:229

    Article  CAS  Google Scholar 

  63. Casida ME, Ipatov A, Cordova F (2006) Linear-response time-dependent density-functional theory for open-shell molecules. In: Marques MAL, Ullrich C, Nogueira F, Rubio A, Gross EKU (eds) Time-dependent density-functional theory. Springer, Berlin, p 243. Lecture Notes in Physics

  64. Ipatov A, Cordova F, Joubert Doriol L, Casida ME (2009) Excited-state spin-contamination in time-dependent density-functional theory for molecules with open-shell ground states. J Mol Struct (Theochem) 914:60

  65. Slipchenko LV, Krylov AI (2003) Electronic structure of the trimethylenemethane diradical in its ground and electronically excited states: bonding, equilibrium geometries, and vibrational frequencies. J Chem Phys 118:6874

    Article  CAS  Google Scholar 

  66. Shao Y, Head-Gordon M, Krylov AI (2003) The spin-flip approach within time-dependent density functional theory: theory and applications to diradicals. J Chem Phys 118:4807

    Article  CAS  Google Scholar 

  67. Wang F, Ziegler T (2004) Time-dependent density functional theory based on a noncollinear formulation of the exchange-correlation potential. J Chem Phys 121:12191

    Article  CAS  PubMed  Google Scholar 

  68. Wang F, Ziegler T (2006) Use of noncollinear exchange-correlation potentials in multiplet resolutions by time-dependent density functional theory. Int J Quantum Chem 106:2545

    Article  CAS  Google Scholar 

  69. Minezawa N, Gordon MS (2009) Optimizing conical intersections by spin-flip density functional theory: application to ethylene. J Phys Chem A 113:12749

    Article  CAS  PubMed  Google Scholar 

  70. Huix-Rotllant M, Natarajan B, Ipatov A, Wawire CM, Deutsch T, Casida ME (2010) Assessment of noncollinear spin-flip Tamm-Dancoff approximation time-dependent density-functional theory for the photochemical ring-opening of oxirane. Phys Chem Chem Phys 12:12811

    Article  CAS  PubMed  Google Scholar 

  71. Cave RJ, Zhang F, Maitra NT, Burke K (2004) A dressed TDDFT treatment of the \(2\,^1A_g\) states of butadiene and hexatriene. Chem Phys Lett 389:39

    Article  CAS  Google Scholar 

  72. Maitra NT, Zhang F, Cave RJ, Burke K (2004) Double excitations within time-dependent density functional theory linear response. J Chem Phys 120:5932

    Article  CAS  PubMed  Google Scholar 

  73. Casida ME (2005) Propagator corrections to adiabatic time-dependent density-functional theory linear response theory. J Chem Phys 122:054111

    Article  Google Scholar 

  74. Huix-Rotllant M, Ipatov A, Rubio A, Casida ME (2011) Assessment of dressed time-dependent density-functional theory for the low-lying valence states of 28 organic chromophores. Chem Phys 391:120

    Article  CAS  Google Scholar 

  75. Casida ME, Huix-Rotllant M (2015) Many-body perturbation theory (MBPT) and time-dependent density-functional theory (TD-DFT): MBPT insights about what is missing in, and corrections to, the TD-DFT adiabatic approximation. In: Ferré N, Filatov M, Huix-Rotllant M (eds) Topics in current chemistry, special volume on density-functional methods for excited states. Springer

  76. Guan J, Wang F, Ziegler T, Cox H (2006) Time-dependent density functional study of the electronic potential energy curves and excitation spectrum of the oxygen molecule. J Chem Phys 125:044314

    Article  Google Scholar 

  77. Cembran A, Song LC, Mo YR, Gao J (2009) Block-localized density functional theory (BLDFT), diabatic coupling, and their use in valence bond theory for representing reactive potential energy surfaces. J Chem Theory Comput 5:2702

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  78. Ren HS, Provorse MR, Bao P, Qu ZX, Gao J (2016) Multistate density functional theory for effective diabatic electronic coupling. J Phys Chem Lett 7:2286

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  79. Grofe A, Chen X, Liu W, Gao J (2017) Spin-multiplet components and energy splittings by multistate density functional theory. J Phys Chem Lett 8:4838

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  80. Grofe A, Qu ZX, Truhlar DG, Li H, Gao J (2017) Diabatic-at-construction method for diabatic and adiabatic ground and excited states based on multistate density functional theory. J Chem Theory Comput 13:1176

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  81. Yang L, Grofe A, Reimers J, Gao J (2019) Multistate density functional theory applied with 3 unpaired electrons in 3 orbitals: the singdoublet and tripdoublet states of the ethylene cation. Chem Phys Lett 736:136803

    Article  Google Scholar 

  82. Wu Q, Voorhis TV (2006) Constrained density functional theory and its application in long-range electron transfer. J Chem Theory Comput 2:765

    Article  CAS  PubMed  Google Scholar 

  83. Wu Q, Cheng CL, Voorhis TV (2007) Configuration interaction based on constrained density functional theory: a multireference method. J Chem Phys 127:164119

    Article  PubMed  Google Scholar 

  84. Kaduk B, Voorhis TV (2010) Communication: conical intersections using constrained density functional theory-configuration interaction. J Chem Phys 133:061102

    Article  PubMed  Google Scholar 

  85. Kaduk B, Kowalczyk T, Voorhis TV (2012) Constrained density functional theory. Chem Rev 112:321

    Article  CAS  PubMed  Google Scholar 

  86. Mavros MG, Voorhis TV (2015) Communication: CDFT-CI couplings can be unreliable when there is fractional charge transfer. J Chem Phys 143:231102

    Article  PubMed  Google Scholar 

  87. de la Lande A, Salahub DR (2010) Derivation of interpretive models for long range electron transfer from constrained density functional theory. J Mol Struct (THEOCHEM) 943:115

  88. Řezác R, Lévy B, Demachy I, de la Lande A (2012) Robust and efficient constrained DFT molecular dynamics approach to biochemical modeling. J Chem Theory Comput 8:418

Download references

Acknowledgements

AJE, OM, and MEC met through the African School of Electronic Structure Methods and Applications (ASESMA) and are grateful for the learning and networking possibilities provided by ASESMA. MEC acknowledges a useful conversation with Andreas Köster regarding symmetry breaking. MEC been involved in the deMon developers group from the time of its creation. MEC is grateful to Pierre Girard for configuring the personal computer on which some of the calculations reported here were performed.

Author information

Authors and Affiliations

  1. University of Maroua, B.P. 814, Maroua, Cameroon

    Abraham Ponra & Ousmanou Motapon

  2. Higher Teachers Training College, University of Yaounde I, P.O. Box 47, Yaounde, Cameroon

    Anne Justine Etindele

  3. Laboratoire de Spectrométrie, Interactions et Chimie théorique (SITh) Département de Chimie Moléculaire (DCM, UMR CNRS/UGA 5250), Institut de Chimie Moléculaire de Grenoble (ICMG, FR2607), Université Grenoble Alpes (UGA), 301 rue de la Chimie, BP 53, 38041, Grenoble Cedex 9, France

    Mark E. Casida

Authors
  1. Abraham Ponra
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Anne Justine Etindele
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ousmanou Motapon
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Mark E. Casida
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mark E. Casida.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Published as part of the special collection of articles “20th deMon Developers Workshop.

Supplementary Information

Below is the link to the electronic supplementary material.

Supplementary material 1 (pdf 1962 KB)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ponra, A., Etindele, A.J., Motapon, O. et al. Practical treatment of singlet oxygen with density-functional theory and the multiplet-sum method. Theor Chem Acc 140, 154 (2021). https://doi.org/10.1007/s00214-021-02852-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00214-021-02852-8

Keywords

Search

Navigation