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Electronic fine structure calculation of metal complexes with three-open-shell s, d, and p configurations

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Abstract

The ligand field density functional theory (LFDFT) algorithm is extended to treat the electronic structure and properties of systems with three-open-shell electron configurations, exemplified in this work by the calculation of the core and semi-core 1s, 2s, and 3s one-electron excitations in compounds containing transition metal ions. The work presents a model to non-empirically resolve the multiplet energy levels arising from the three-open-shell systems of non-equivalent ns, 3d, and 4p electrons and to calculate the oscillator strengths corresponding to the electric-dipole 3d m → ns 13d m4p 1 transitions, with n = 1, 2, 3 and m = 0, 1, 2, …, 10 involved in the s electron excitation process. Using the concept of ligand field, the Slater-Condon integrals, the spin-orbit coupling constants, and the parameters of the ligand field potential are determined from density functional theory (DFT). Therefore, a theoretical procedure using LFDFT is established illustrating the spectroscopic details at the atomic scale that can be valuable in the analysis and characterization of the electronic spectra obtained from X-ray absorption fine structure or electron energy loss spectroscopies.

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References

  1. Chermette H (1998) Density functional theory: A powerful tool for theoretical studies in coordination chemistry. Coord Chem Rev 178–180:699

  2. Figgis BN, Hitchman MA (2000) Ligand field theory and its applications. Wiley-VCH, New York

    Google Scholar 

  3. Gerloch M, Slade RC (1973) Ligand field parameters. Cambridge University Press, Cambridge

  4. Newman DJ, Ng BKC (2000) Crystal field handbook. Cambridge University Press, Cambridge

  5. Judd BR (1998) Operator techniques in atomic spectroscopy. Princeton University Press, Princeton

    Book  Google Scholar 

  6. van Vleck JH (1935) Valence Strength and the Magnetism of Complex Salts. J Chem Phys 3:807

  7. Bethe H (1929) Termaufspaltung in Kristallen. Ann Phys 395:133

  8. Atanasov M, Ganyushin D, Sivalingam K, Neese F (2011) A modern first-principles view on ligand field theory through the eyes of correlated multireference wavefunctions. Struct Bond 143:149

  9. Aravena D, Atanasov M, Neese F (2016) Periodic Trends in Lanthanide Compounds through the Eyes of Multireference ab Initio Theory. Inorg Chem 55:4457

  10. Chilton NF, Lei H, Bryan AM, Grandjean F, Long GJ, Power PP (2015) Ligand field influence on the electronic and magnetic properties of quasi-linear two-coordinate iron(II) complexes. Dalton Trans 44:11202

  11. Atanasov M, Comba P, Daul CA (2008) Combined Ligand Field and Density Functional Theory Analysis of the Magnetic Anisotropy in Oligonuclear Complexes Based on FeIII−CN−MII Exchange-Coupled Pairs. Inorg Chem 47:2449

  12. Zbiri M, Atanasov M, Daul C, Garcia-Lastra J-M, Wesolowski TA (2004) Application of the density functional theory derived orbital-free embedding potential to calculate the splitting energies of lanthanide cations in chloroelpasolite crystals. Chem Phys Lett 397:441

  13. Haverkort MW, Zwierzycki M, Andersen OK (2012) Multiplet ligand-field theory using Wannier orbitals. Phys Rev B 85:165113

  14. Atanasov M, Daul CA (2003) A DFT based ligand field model for magnetic exchange coupling in transition metal dimmer complexes: (i) principles. Chem Phys Lett 379:209

  15. Goursot A, Chermette H (1985) Ligand field and Rydberg assignments of the PtCl42− spectrum: a relativistic MS-Xα study. Can J Chem 63:1407

  16. Atanasov M, Daul CA, Rauzy C (2004) A DFT Based Ligand Field Theory. Struct Bond 106:97

  17. Borel A, Daul CA, Helm L (2004) Hybrid ligand-field theory/quantum chemical calculation of the fine structure and ZFS in lanthanide(III) complexes. Chem Phys Lett 383:584

  18. Senn F, Helm L, Borel A, Daul CA (2012) Electronic fine structure calculation of [Gd(DOTA)(H2O)]– using LF-DFT: The zero field splitting. Comptes Rendus de Chimie 15:250

  19. Atanasov M, Baerends EJ, Baettig P, Bruyndonckx R, Daul C, Rauzy C, Zbiri M (2004) The calculation of ESR parameters by density functional theory: the g- and A-tensors of Co(acacen). Chem Phys Lett 399:433

  20. Atanasov M, Daul CA (2003) A DFT based ligand field model for magnetic exchange coupling in transition metal dimer complexes:: (ii) application to magnetic systems with more than one unpaired electron per site. Chem Phys Lett 381:584

  21. Senn F, Daul CA (2010) Calculation of 59Co shielding tensor σ using LF–DFT, THEOCHEM J Mol Struct 954:105

  22. Senn F, Zlatar M, Gruden-Pavlovic M, Daul C (2011) Computational analysis of tris(1,2-ethanediamine) cobalt(III) complex ion: calculation of the 59Co shielding tensor using LF-DFT. Monatsch Chem 142:593

  23. Ramanantoanina H, Urland W, Cimpoesu F, Daul C (2013) Ligand field density functional theory calculation of the 4f2 → 4f15d1 transitions in the quantum cutter Cs2KYF6:Pr3+. Phys Chem Chem Phys 15:13902

  24. Ramanantoanina H, Urland W, Garcia-Fuente A, Cimpoesu F, Daul C (2013) Calculation of the 4f1→4f05d1 transitions in Ce3+-doped systems by Ligand Field Density Functional Theory. Chem Phys Lett 588:260

  25. Ramanantoanina H, Urland W, Garcia-Fuente A, Cimpoesu F, Daul C (2014) Ligand field density functional theory for the prediction of future domestic lighting. Phys Chem Chem Phys 16:14625

  26. Ramanantoanina H, Urland W, Herden B, Cimpoesu F, Daul C (2015) Tailoring the optical properties of lanthanide phosphors: prediction and characterization of the luminescence of Pr3+-doped LiYF4. Phys Chem Chem Phys 17:9116

  27. Ramanantoanina H, Cimpoesu F, Göttel C, Sahnoun M, Herden B, Suta M, Wickleder C, Urland W, Daul C (2015) Prospecting Lighting Applications with Ligand Field Tools and Density Functional Theory: A First-Principles Account of the 4f7–4f65d1 Luminescence of CsMgBr3:Eu2+. Inorg Chem 54:8319

  28. Ramanantoanina H, Sahnoun M, Barbiero A, Ferbinteanu M, Cimpoesu F (2015) Development and applications of the LFDFT: the non-empirical account of ligand field and the simulation of the f–d transitions by density functional theory. Phys Chem Chem Phys 17:18547

  29. Ramanantoanina H, Kuri G, Daul C, Bertsch J (2016) Core electron excitations in U4+: modelling of the nd105f2 → nd95f3 transitions with n = 3, 4 and 5 by ligand field tools and density functional theory. Phys Chem Chem Phys 18:19020

  30. de Groot FMF, Fuggle JC, Thole BT, Sawatzky GA (1990) 2p x-ray absorption of 3d transition-metal compounds: An atomic multiplet description including the crystal field. Phys Rev B 42:5459

  31. DeBeer-George S, Petrenko T, Neese F (2008) Prediction of Iron K-Edge Absorption Spectra Using Time-Dependent Density Functional Theory. J Phys Chem A 112:12936

  32. Kawai J, Takami M, Satoko C (1990) Multiplet structure in Ni Kβ x-ray fluorescence spectra of nickel compounds. Phys Rev Lett 65:2193

  33. Matthew JAD, Strasser G, Netzer F (1983) Multiplet effects and breakdown of dipole selection rules in the 3d → 4f core-electron-energy-loss spectra of La, Ce, and Gd. Phys Rev B 27:5839

  34. Ilton ES, Bagus PS (2008) Ligand field effects on the multiplet structure of the U4f XPS of UO2. Surf Sci 602:1114

  35. de Groot F (2005) Multiplet effects in X-ray spectroscopy. Coord Chem Rev 249:31

  36. Thole BT, Cowan RD, Sawatzky GA, Fink J, Fuggle JC (1985) New probe for the ground-state electronic structure of narrow-band and impurity systems. Phys Rev B 31:6856

  37. Radtke G, Lazar S, Botton GA (2006) High-resolution EELS investigation of the electronic structure of ilmenites. Phys Rev B 74:155117

  38. Jahn HA, Teller E (1937), Stability of Polyatomic Molecules in Degenerate Electronic States. I. Orbital Degeneracy, Proc R Soc London, Ser A 161:220

  39. Bersuker IB (2006) The Jahn-teller effect. Cambridge University Press, Cambridge

    Book  Google Scholar 

  40. Yamamoto T (2008) Assignment of pre-edge peaks in K-edge x-ray absorption spectra of 3d transition metal compounds: electric dipole or quadrupole?. X-ray spectrom 37:572

  41. Westre TE, Kennepohl P, DeWitt JG, Hedman B, Hodgson KO, Solomon EI (1997) A Multiplet Analysis of Fe K-Edge 1s → 3d Pre-Edge Features of Iron Complexes. J Am Chem Soc 119:6297

  42. de Groot F, Vanko G, Glatzel P (2009) The 1s x-ray absorption pre-edge structures in transition metal oxides. J Phys Condens Matter 21:104207

  43. Mehadji C, Nour S, Chermette H, Cartier C, Menage S, Verdaguer M (1990) X-ray absorption of tetraoxomanganates (MnO4n−: Experimental and MS LSD computational studies. Chem Phys 148:95

  44. Mehdji C, Chermette H, Cartier C, Verdaguer M (1995) X-ray Absorption Near-Edge Structures of Chloroferrates [FeIICl4]2-, [FeIIICl4]-, and [FeIIICl6]3-: Experimental and MS-LSD Computational Studies. J Phys Chem 99:5568

  45. Hahn JE, Scott RA, Hodgson KO, Doniach S, Desjardins SR, Solomon EI (1982) Observation of an electric quadrupole transition in the X-ray absorption spectrum of a Cu(II) complex. Chem Phys Lett 88:595

  46. Wong J, Lytle FW, Messmer RP, Maylotte DH (1984) K-edge absorption spectra of selected vanadium compounds. Phys Rev B 30:5596

  47. Pantelouris A, Modrow H, Pantelouris M, Hormes J, Reinen D (2004) The influence of coordination geometry and valency on the K-edge absorption near edge spectra of selected chromium compounds. Chem Phys 300:13

  48. te Velde G, Bickelhaupt FM, van Gisbergen SJA, Guerra CF, Baerends EJ, Snijders JG, Ziegler T (2001) Chemistry with ADF. J Comput Chem 22:931

  49. Guerra CF, Snijders JG, te Velde G, Baerends EJ (1998) Towards an order-N DFT method. Theor Chem Accounts 99:391

  50. Baerends EJ, Ziegler T, Autschbach J, Bashford D, Berces A, Bickelhaupt FM, Bo C, Boerrigter PM, Cavallo L, Chong DP, Deng L, Dickson RM, Ellis DE, van Faassen M, Fan L, Fischer TH, Guerra CF, Ghysels A, Giammona A, van Gisbergen SJA, Götz AW, Groeneveld JA, Gritsenko OV, Grüning M, Gusarov S, Harris FE, van den Hoek P, Jacob CR, Jacobsen H, Jensen L, Kaminski JW, van Kessel G, Koostra F, Kovalenko A, Krykunov MV, van Lenthe E, McCormack DA, Michalak A, Mitoraj M, Neugebauer J, Nicu VP, Noodleman L, Osinga VP, Patchkovskii S, Philipsen PHT, Post D, Pye CC, Ravenek W, Rodriguez JI, Ros P, Shipper PRT, Schreckenbach G, Seldenthuis JS, Seth M, Snijders JG, Sola M, Swart M, Swerhone D, te Velde G, Vernooijs P, Versluis L, Vissher L, Visser O, Wang F, Wesolowski T, van Wezenbeek EM, Wiesenekker G, Wolff SK, Woo TK, Yarkolev AL (2014) ADF 2014.01, available at http://www.scm.com

  51. Vosko SH, Wilk L, Nusair M (1980) Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis. Can J Phys 54:1200

  52. Perdew JP, Burke K, Ernzerhof M (1996), - Generalized Gradient Approximation Made Simple, Phys Rev Lett 77:3865

  53. Slater JC (1960) Quantum theory of atomic structure, vol I. McGraw-Hill, New York

  54. Slater JC (1960) Quantum theory of atomic structure, vol II. McGraw-Hill, New York,

  55. Cowan RD (1981) The theory of atomic structure and spectra. Univesity of California Press, Berkeley

    Google Scholar 

  56. Griffith JS (1961) The theory of transition-metal ions. Cambridge University Press, Cambridge

    Google Scholar 

  57. Lever ABP (1968) Inorganic electronic spectroscopy. Elsevier, Amsterdam

  58. Hüfner S (1978) Optical spectra of transparent rare-earth compounds. Academic, New York

  59. Ramanantoanina H, Urland W, Cimpoesu F, Daul C (2014) The angular overlap model extended for two-open-shell f and d electrons. Phys Chem Chem Phys 16:12282

  60. JØrgensen CK (1962) Absorption spectra and chemical bonding in complexes. Pergamon, Oxford

  61. Krause MO, Olivier JH (1979) Natural widths of atomic K and L levels, Kα X‐ray lines and several KLL Auger lines. J Phys Chem Ref Data 8:329

  62. Ogasawara K, Iwata T, Koyama Y, Ishii T, Tanaka I, Dachi HA (2001) Relativistic cluster calculation of ligand-field multiplet effects on cation L2,3 x-ray absorption edges of SrTiO3, NiO, and CaF2. Phys Rev B 64:115413

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Acknowledgments

This work is partly supported by Swissnuclear. We also acknowledge the support from the ECOSTBio (COST Action CM1305).

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Correspondence to Harry Ramanantoanina.

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This manuscript is dedicated to our friend and colleague Henry Chermette in the celebration of his 70th birthday.

This paper belongs to Topical Collection Festschrift in Honor of Henry Chermette

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Ramanantoanina, H., Daul, C. Electronic fine structure calculation of metal complexes with three-open-shell s, d, and p configurations. J Mol Model 23, 243 (2017). https://doi.org/10.1007/s00894-017-3413-x

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