Skip to main content
Log in

Structural, optical and nonlinear optical properties and TD-DFT analysis of heteroleptic bis-cyclometalated iridium(III) complex containing 2-phenylpyridine and picolinate ligands

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

Abstract

In this work, we studied the structural, optical and nonlinear optical properties and UV–visible absorption spectrum of the heteroleptic bis-cyclometalated iridium(III) complex (tfmppy)2Ir(pic) recently synthesized with tfmppy = 5-trifluoromethyl-2-phenylpyridine and pic = picolinate. The calculations were performed by means of density functional theory (DFT) and time-dependent density functional (TD-DFT) methods using four functionals B3LYP, PBE0, CAM-B3LYP and M06-2X. Calculated geometric parameters agree with the experimental data. CAM-B3LYP and M06-2X lower the HOMO energy level and give a large energy gaps compared with B3LYP and PBE0. The four functionals show that LUMO is delocalized over \( \pi_{\text{ppy}}^{ * } \) orbital, and HOMO is contributed by \( \pi_{\text{ppy}} \) and dIr orbitals. The studied complex gets a remarkably large first-order NLO response. B3LYP would provide good estimates of the energy gap and shows the strongest values of the first hyperpolarizabilities βHRS; M06-2X and CAM-B3LYP functionals overestimate the gaps and lower βHRS values. PBE0 and B3LYP spectra agree better with the experimental spectrum in the visible region, while CAM-B3LYP and M06-2X are more accurate in UV-C region. Natural transition orbital analysis shows that the weak band observed at 468 nm corresponds to MLCT/LLCT charge transfer transitions and the intense band observed at 270 nm is mainly assigned to intra-ligand state.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Scheme 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  1. Daniel C, Gourlaouen C (2017) Chemical bonding alteration upon electronic excitation in transition metal complexes. Coord Chem Rev 344:131–149. https://doi.org/10.1016/j.ccr.2016.10.010

    Article  CAS  Google Scholar 

  2. Na H, Teets TS (2018) Highly luminescent cyclometalated iridium complexes generated by nucleophilic addition to coordinated isocyanides. J Am Chem Soc 140:6353–6360. https://doi.org/10.1021/jacs.8b02416

    Article  CAS  PubMed  Google Scholar 

  3. Ren X-F, Kang G-J, He Q-Q, Zheng C-Y, Ren X-K (2016) A theoretical analysis of the effects of electron-withdrawing substitutions on electronic structures and phosphorescent efficiency of a series of Ir(III) complexes with 2-phenylpyridine ligands. Theor Chem Acc. https://doi.org/10.1007/s00214-015-1773-9

    Article  Google Scholar 

  4. Vazart F, Latouche C (2015) Validation of a computational protocol to simulate near IR phosphorescence spectra for Ru(II) and Ir(III) metal complexes. Theor Chem Acc. https://doi.org/10.1007/s00214-015-1737-0

    Article  Google Scholar 

  5. Guelai A, Brahim H, Guendouzi A, Boumediene M, Brahim S (2018) Structure, electronic properties, and NBO and TD-DFT analyses of nickel(II), zinc(II), and palladium(II) complexes based on Schiff-base ligands. J Mol Model. https://doi.org/10.1007/s00894-018-3839-9

    Article  PubMed  Google Scholar 

  6. Liu H-W, Law WH-T, Lee LC-C, Lau JC-W, Lo KK-W (2017) Cyclometalated iridium(III) Bipyridine-Phenylboronic Acid Complexes as Bioimaging Reagents and Luminescent Probes for Sialic Acids. Chem Asian J 12:1545–1556. https://doi.org/10.1002/asia.201700359

    Article  CAS  PubMed  Google Scholar 

  7. Ma D-L, Lin S, Wang W, Yang C, Leung C-H (2017) Luminescent chemosensors by using cyclometalated iridium(III) complexes and their applications. Chem Sci 8:878–889. https://doi.org/10.1039/c6sc04175b

    Article  CAS  PubMed  Google Scholar 

  8. Sudheesh KV, Jayaram PS, Samanta A, Bejoymohandas KS, Jayasree RS, Ajayaghosh A (2018) A cyclometalated IrIII complex as a lysosome-targeted photodynamic therapeutic agent for integrated imaging and therapy in cancer cells. Chem Eur J 24:10999–11007. https://doi.org/10.1002/chem.201801918

    Article  CAS  PubMed  Google Scholar 

  9. Zhang Q-C, Xiao H, Zhang X, Xu L-J, Chen Z-N (2018) Luminescent oligonuclear metal complexes and the use in organic light-emitting diodes. Coord Chem Rev. https://doi.org/10.1016/j.ccr.2018.01.017

    Article  Google Scholar 

  10. Brahim H, Daniel C (2014) Structural and spectroscopic properties of Ir(III) complexes with phenylpyridine ligands: absorption spectra without and with spin–orbit-coupling. Comput Theor Chem 1040–1041:219–229. https://doi.org/10.1016/j.comptc.2014.01.030

    Article  CAS  Google Scholar 

  11. Dang W, Yang X, Feng Z, Sun Y, Zhong D, Zhou G, Wu Z, Wong W-Y (2018) Asymmetric tris-heteroleptic iridium(III) complexes containing three different 2-phenylpyridine-type ligands: a new strategy for improving the electroluminescence ability of phosphorescent emitters. J Mater Chem C. https://doi.org/10.1039/c8tc02940g

    Article  Google Scholar 

  12. Tamura Y, Hisamatsu Y, Kazama A, Yoza K, Sato K, Kuroda R, Aoki S (2018) Stereospecific synthesis of tris-heteroleptic tris-cyclometalated Iridium(III) complexes via different heteroleptic halogen-bridged iridium(III) dimers and their photophysical properties. Inorg Chem 57:4571–4589. https://doi.org/10.1021/acs.inorgchem.8b00323

    Article  CAS  PubMed  Google Scholar 

  13. Brahim H, Haddad B, Boukabene M, Brahim S, Ariche B (2017) Theoretical study of geometric structures and electronic absorption spectra of iridium(III) complexes based on 2-phenyl-5-nitropyridyl with different ancillary ligands. Comput Theor Chem 1101:8–19. https://doi.org/10.1016/j.comptc.2016.12.016

    Article  CAS  Google Scholar 

  14. Brahim H, Haddad B, Brahim S, Guendouzi A (2017) DFT/TDDFT computational study of the structural, electronic and optical properties of rhodium(III) and iridium(III) complexes based on tris-picolinate bidentate ligands. J Mol Model 23:344. https://doi.org/10.1007/s00894-017-3517-3

    Article  CAS  PubMed  Google Scholar 

  15. Minaev B, Minaeva V, Ågren H (2009) Theoretical study of the cyclometalated iridium(III) complexes used as chromophores for organic light-emitting diodes. J Phys Chem A 113:726–735. https://doi.org/10.1021/jp807429h

    Article  CAS  PubMed  Google Scholar 

  16. Boixel J, Guerchais V, Le Bozec H, Jacquemin D, Amar A, Boucekkine A, Colombo A, Dragonetti C, Marinotto D, Roberto D, Righetto S, De Angelis R (2014) Second-order NLO switches from molecules to polymer films based on photochromic cyclometalated platinum(II) complexes. J Am Chem Soc 136:5367–5375. https://doi.org/10.1021/ja4131615

    Article  CAS  PubMed  Google Scholar 

  17. Cariati E, Pizzotti M, Roberto D, Tessore F, Ugo R (2006) Coordination and organometallic compounds and inorganic–organic hybrid crystalline materials for second-order non-linear optics. Coord Chem Rev 250:1210–1233. https://doi.org/10.1016/j.ccr.2005.09.013

    Article  CAS  Google Scholar 

  18. Coe BJ (2006) Switchable nonlinear optical metallochromophores with pyridinium electron acceptor groups. Acc Chem Res 39:383–393. https://doi.org/10.1021/ar050225k

    Article  CAS  PubMed  Google Scholar 

  19. Doisneau G, Balavoine G, Fillebeen-Khan T, Clinet JC, Delaire J, Ledoux I, Loucif R, Puccetti G (1991) Synthesis and nonlinear optical properties of new bimetallic iron/palladium complexes. J Organomet Chem 421:299–304. https://doi.org/10.1016/0022-328x(91)86414-l

    Article  CAS  Google Scholar 

  20. Evans RC, Douglas P, Winscom CJ (2006) Coordination complexes exhibiting room-temperature phosphorescence: evaluation of their suitability as triplet emitters in organic light emitting diodes. Coord Chem Rev 250:2093–2126. https://doi.org/10.1016/j.ccr.2006.02.007

    Article  CAS  Google Scholar 

  21. Whittall IR, Humphrey MG, Houbrechts S, Maes J, Persoons A, Schmid S (1997) Organometallic complexes for nonlinear optics. 14. Syntheses and second-order nonlinear optical properties of ruthenium, nickel and gold σ-acetylides of 1,3,5-triethynylbenzene: X-ray crystal structures of 1-(HC≡C)-3,5-C6H3(trans-C≡CRuCl(dppm)2)2 and 1,3,5-C6H3(C≡CAu(PPh3))3. J Organomet Chem 544:277–283. https://doi.org/10.1016/s0022-328x(97)00320-3

    Article  Google Scholar 

  22. You Y, Nam W (2012) Photofunctional triplet excited states of cyclometalated Ir(III) complexes: beyond electroluminescence. Chem Soc Rev 41:7061. https://doi.org/10.1039/c2cs35171d

    Article  CAS  PubMed  Google Scholar 

  23. Yun S-J, Jeon J, Jin S-H, Kang SK, Kim Y-I (2017) Synthesis, structure, and OLEDs application of cyclometalated iridium(III) complexes utilizing substituted 2-phenylpyridine. Bull Korean Chem Soc 38:788–794. https://doi.org/10.1002/bkcs.11173

    Article  CAS  Google Scholar 

  24. Becke AD (1993) Density-functional thermochemistry. III. The role of exact exchange. J Chem Phys. https://doi.org/10.1063/1.464913

    Article  Google Scholar 

  25. Hohenberg P, Kohn W (1964) Inhomogeneous electron gas. Phys Rev 136:B864–B871. https://doi.org/10.1103/physrev.136.b864

    Article  Google Scholar 

  26. Lee C, Yang W, Parr RG (1988) Development of the Colle–Salvetti correlation-energy formula into a functional of the electron density. Phys Rev B 37:785–789. https://doi.org/10.1103/physrevb.37.785

    Article  CAS  Google Scholar 

  27. Adamo C, Barone V (1999) Toward reliable density functional methods without adjustable parameters: the PBE0 model. J Chem Phys 110:6158. https://doi.org/10.1063/1.478522

    Article  CAS  Google Scholar 

  28. Peach MJG, Helgaker T, Sałek P, Keal TW, Lutnæs OB, Tozer DJ, Handy NC (2006) Assessment of a Coulomb-attenuated exchange–correlation energy functional. Phys Chem Chem Phys 8:558–562. https://doi.org/10.1039/b511865d

    Article  CAS  PubMed  Google Scholar 

  29. Yanai T, Tew DP, Handy NC (2004) A new hybrid exchange–correlation functional using the Coulomb-attenuating method (CAM-B3LYP). Chem Phys Lett 393:51–57. https://doi.org/10.1016/j.cplett.2004.06.011

    Article  CAS  Google Scholar 

  30. Hohenstein EG, Chill ST, Sherrill CD (2008) Assessment of the performance of the M05-2X and M06-2X exchange-correlation functionals for noncovalent interactions in biomolecules. J Chem Theory Comput 4:1996–2000. https://doi.org/10.1021/ct800308k

    Article  CAS  PubMed  Google Scholar 

  31. Zhao Y, Truhlar DG (2008) Density functionals with broad applicability in chemistry. Acc Chem Res 41:157–167. https://doi.org/10.1021/ar700111a

    Article  CAS  PubMed  Google Scholar 

  32. Hay PJ, Wadt WR (1985) Ab initio effective core potentials for molecular calculations. Potentials for the transition metal atoms Sc to Hg. J Chem Phys 82:270. https://doi.org/10.1063/1.448799

    Article  CAS  Google Scholar 

  33. Hay PJ, Wadt WR (1985) Ab initio effective core potentials for molecular calculations. Potentials for K to Au including the outermost core orbitals. J Chem Phys 82:299. https://doi.org/10.1063/1.448975

    Article  CAS  Google Scholar 

  34. Binning RC, Curtiss LA (1990) Compact contracted basis sets for third-row atoms: Ga–Kr. J Comput Chem 11:1206–1216. https://doi.org/10.1002/jcc.540111013

    Article  CAS  Google Scholar 

  35. Krishnan R, Binkley JS, Seeger R, Pople JA (1980) Self-consistent molecular orbital methods. XX. A basis set for correlated wave functions. J Chem Phys 72:650. https://doi.org/10.1063/1.438955

    Article  CAS  Google Scholar 

  36. McLean AD, Chandler GS (1980) Contracted Gaussian basis sets for molecular calculations. I. Second row atoms, Z = 11–18. J Chem Phys 72:5639. https://doi.org/10.1063/1.438980

    Article  CAS  Google Scholar 

  37. Cancès E, Mennucci B, Tomasi J (1997) A new integral equation formalism for the polarizable continuum model: theoretical background and applications to isotropic and anisotropic dielectrics. J Chem Phys 107:3032. https://doi.org/10.1063/1.474659

    Article  Google Scholar 

  38. Cossi M, Barone V, Mennucci B, Tomasi J (1998) Ab initio study of ionic solutions by a polarizable continuum dielectric model. Chem Phys Lett 286:253–260. https://doi.org/10.1016/s0009-2614(98)00106-7

    Article  CAS  Google Scholar 

  39. Wiberg KB (1968) Application of the pople-santry-segal CNDO method to the cyclopropylcarbinyl and cyclobutyl cation and to bicyclobutane. Tetrahedron 24:1083–1096. https://doi.org/10.1016/0040-4020(68)88057-3

    Article  CAS  Google Scholar 

  40. Foster JP, Weinhold F (1980) Natural hybrid orbitals. J Am Chem Soc 102:7211–7218. https://doi.org/10.1021/ja00544a007

    Article  CAS  Google Scholar 

  41. Reed AE, Weinhold F (1983) Natural bond orbital analysis of near-Hartree–Fock water dimer. J Chem Phys 78:4066–4073. https://doi.org/10.1063/1.445134

    Article  CAS  Google Scholar 

  42. Reed AE, Weinhold F (1985) Natural localized molecular orbitals. J Chem Phys 83:1736–1740. https://doi.org/10.1063/1.449360

    Article  CAS  Google Scholar 

  43. Reed AE, Weinstock RB, Weinhold F (1985) Natural population analysis. J Chem Phys 83:735–746. https://doi.org/10.1063/1.449486

    Article  CAS  Google Scholar 

  44. Martin RL (2003) Natural transition orbitals. J Chem Phys 118:4775–4777. https://doi.org/10.1063/1.1558471

    Article  CAS  Google Scholar 

  45. Frisch MJ, Schlegel GWTHB, Scuseria GE, Robb MA, Cheeseman JR, Scalmani G, Barone V, Mennucci B, Petersson GA, Nakatsuji H, Caricato M, Li X, Hratchian HP, Izmaylov AF, Bloino J, Zheng G, Sonnenberg JL, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Vreven T, Montgomery JA Jr, Peralta JE, Ogliaro F, Bearpark M, Heyd JJ, Brothers E, Kudin KN, Staroverov VN, Kobayashi R, Normand J, Raghavachari K, Rendell A, Burant JC, Iyengar SS, Tomasi J, Cossi M, Rega N, Millam JM, Klene M, Knox JE, Cross JB, Bakken V, Adamo C, Jaramillo J, Gomperts R, Stratmann RE, Yazyev O, Austin AJ, Cammi R, Pomelli C, Ochterski JW, Martin RL, Morokuma K, Zakrzewski VG, Voth GA, Salvador P, Dannenberg JJ, Dapprich S, Daniels AD, Foresman JB, Ortiz JV, Cioslowski J, Fox DJ (2009) Gaussian 09. Gaussian Inc., Wallingford

    Google Scholar 

  46. Glendening ED, Badenhoop JK, Reed AE, Carpenter JE, Bohmaann JA, Morales CM, Weinhold F (2001) NBO 3.1. Theoretical Chemistry Institute, University of Wisconsin, Madison, WI, USA

  47. Hanwell MD, Curtis DE, Lonie DC, Vandermeersch T, Zurek E, Hutchison GR (2012) Avogadro: an advanced semantic chemical editor, visualization, and analysis platform. J Cheminform 4:17. https://doi.org/10.1186/1758-2946-4-17

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  48. Barbante GJ, Doeven EH, Francis PS, Stringer BD, Hogan CF, Kheradmand PR, Wilson DJD, Barnard PJ (2015) Iridium(III) N-heterocyclic carbene complexes: an experimental and theoretical study of structural, spectroscopic, electrochemical and electrogenerated chemiluminescence properties. Dalton Trans 44:8564–8576. https://doi.org/10.1039/c4dt03378g

    Article  CAS  PubMed  Google Scholar 

  49. Wang H-Y, Jing L-X, Wang H-Q, Ye J-T, Qiu Y-Q (2018) Improving the NLO response of bis-cyclometalated iridium(III) complexes by modifying ligands: a DFT study. J Organomet Chem 869:18–25. https://doi.org/10.1016/j.jorganchem.2018.05.017

    Article  CAS  Google Scholar 

  50. Altürk S, Avcı D, Tamer Ö, Atalay Y (2017) Comparison of different hybrid DFT methods on structural, spectroscopic, electronic and NLO parameters for a potential NLO material. Comput Theor Chem 1100:34–45. https://doi.org/10.1016/j.comptc.2016.12.007

    Article  CAS  Google Scholar 

  51. Lin L, Wang Z, Fan J, Wang C (2017) Theoretical insights on the electroluminescent mechanism of thermally activated delayed fluorescence emitters. Org Electron 41:17–25. https://doi.org/10.1016/j.orgel.2016.11.035

    Article  CAS  Google Scholar 

  52. Zhang G, Musgrave CB (2007) Comparison of DFT methods for molecular orbital eigenvalue calculations. J Phys Chem A 111:1554–1561. https://doi.org/10.1021/jp061633o

    Article  CAS  PubMed  Google Scholar 

  53. Castet F, Bogdan E, Plaquet A, Ducasse L, Champagne B, Rodriguez V (2012) Reference molecules for nonlinear optics: a joint experimental and theoretical investigation. J Chem Phys 136:024506. https://doi.org/10.1063/1.3675848

    Article  CAS  PubMed  Google Scholar 

  54. Borini S, Limacher PA, Lüthi HP (2009) A systematic analysis of the structure and (hyper)polarizability of donor-acceptor substituted polyacetylenes using a Coulomb-attenuating density functional. J Chem Phys 131:124105. https://doi.org/10.1063/1.3216825

    Article  CAS  PubMed  Google Scholar 

  55. Hadji D, Rahmouni A (2016) Molecular structure, linear and nonlinear optical properties of some cyclic phosphazenes: a theoretical investigation. J Mol Struct 1106:343–351. https://doi.org/10.1016/j.molstruc.2015.10.033

    Article  CAS  Google Scholar 

  56. Jacquemin D, Perpète EA, Medved M, Scalmani G, Frisch MJ, Kobayashi R, Adamo C (2007) First hyperpolarizability of polymethineimine with long-range corrected functionals. J Chem Phys 126:191108. https://doi.org/10.1063/1.2741246

    Article  CAS  PubMed  Google Scholar 

  57. Kamiya M, Sekino H, Tsuneda T, Hirao K (2005) Nonlinear optical property calculations by the long-range-corrected coupled-perturbed Kohn–Sham method. J Chem Phys 122:234111. https://doi.org/10.1063/1.1935514

    Article  CAS  PubMed  Google Scholar 

  58. Limacher PA, Mikkelsen KV, Lüthi HP (2009) On the accurate calculation of polarizabilities and second hyperpolarizabilities of polyacetylene oligomer chains using the CAM-B3LYP density functional. J Chem Phys 130:194114. https://doi.org/10.1063/1.3139023

    Article  CAS  PubMed  Google Scholar 

  59. Peach MJG, Cohen AJ, Tozer DJ (2006) Influence of Coulomb-attenuation on exchange–correlation functional quality. Phys Chem Chem Phys 8:4543–4549. https://doi.org/10.1039/b608553a

    Article  CAS  PubMed  Google Scholar 

  60. Peach MJG, Sueur CRL, Ruud K, Guillaume M, Tozer DJ (2009) TDDFT diagnostic testing and functional assessment for triazene chromophores. Phys Chem Chem Phys 11:4465. https://doi.org/10.1039/b822941d

    Article  CAS  PubMed  Google Scholar 

  61. Sekino H, Maeda Y, Kamiya M, Hirao K (2007) Polarizability and second hyperpolarizability evaluation of long molecules by the density functional theory with long-range correction. J Chem Phys 126:014107. https://doi.org/10.1063/1.2428291

    Article  CAS  PubMed  Google Scholar 

  62. Aubert V, Ordronneau L, Escadeillas M, Williams JAG, Boucekkine A, Coulaud E, Dragonetti C, Righetto S, Roberto D, Ugo R, Valore A, Singh A, Zyss J, Ledoux-Rak I, Le Bozec H, Guerchais VR (2011) Linear and nonlinear optical properties of cationic bipyridyl iridium(III) complexes: Tunable and photoswitchable? Inorg Chem 50:5027–5038. https://doi.org/10.1021/ic2002892

    Article  CAS  PubMed  Google Scholar 

  63. Hierlinger C, Cordes DB, Slawin AMZ, Colombo A, Dragonetti C, Righetto S, Roberto D, Jacquemin D, Zysman-Colman E, Guerchais V (2018) An investigation on the second-order nonlinear optical response of cationic bipyridine or phenanthroline iridium(III) complexes bearing cyclometallated 2-phenylpyridines with a triphenylamine substituent. Dalton Trans 47:8292–8300. https://doi.org/10.1039/c8dt00754c

    Article  CAS  PubMed  Google Scholar 

  64. Rossi E, Colombo A, Dragonetti C, Righetto S, Roberto D, Ugo R, Valore A, Williams JAG, Lobello MG, De Angelis F, Fantacci S, Ledoux-Rak I, Singh A, Zyss J (2013) Tuning the dipolar second-order nonlinear optical properties of cyclometalated platinum(II) complexes with tridentate N^C^N binding ligands. Chem Eur J 19:9875–9883. https://doi.org/10.1002/chem.201301131

    Article  CAS  PubMed  Google Scholar 

  65. Baccouche A, Peigné B, Ibersiene F, Hammoutène D, Boutarfaïa A, Boucekkine A, Feuvrie C, Maury O, Ledoux I, Bozec H (2010) Effects of the metal center and substituting groups on the linear and nonlinear optical properties of substituted styryl-bipyridine metal(II) dichloride complexes: DFT and TDDFT computational investigations and harmonic light scattering measurements. J Phys Chem A 114:5429–5438. https://doi.org/10.1021/jp1014065

    Article  CAS  PubMed  Google Scholar 

  66. Bureš F, Cvejn D, Melánová K, Beneš L, Svoboda J, Zima V, Pytela O, Mikysek T, Růžičková Z, Kityk IV, Wojciechowski A, AlZayed N (2016) Effect of intercalation and chromophore arrangement on the linear and nonlinear optical properties of model aminopyridine push–pull molecules. J Mater Chem C 4:468–478. https://doi.org/10.1039/c5tc03499j

    Article  Google Scholar 

  67. Hadji D, Rahmouni A (2015) Theoretical study of nonlinear optical properties of some azoic dyes. Mediterr J Chem 4:185–192. https://doi.org/10.13171/mjc.4.4.2015.15.07.22.50/hadji

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Houari Brahim.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hadji, D., Brahim, H. Structural, optical and nonlinear optical properties and TD-DFT analysis of heteroleptic bis-cyclometalated iridium(III) complex containing 2-phenylpyridine and picolinate ligands. Theor Chem Acc 137, 180 (2018). https://doi.org/10.1007/s00214-018-2396-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00214-018-2396-8

Keywords

Navigation