Advertisement

Multiconfigurational Approach to X-ray Spectroscopy of Transition Metal Complexes

  • Marcus LundbergEmail author
  • Mickaël G. DelceyEmail author
Chapter
Part of the Challenges and Advances in Computational Chemistry and Physics book series (COCH, volume 29)

Abstract

Close correlation between theoretical modeling and experimental spectroscopy allows for identification of the electronic and geometric structure of a system through its spectral fingerprint. This is can be used to verify mechanistic proposals and is a valuable complement to calculations of reaction mechanisms using the total energy as the main criterion. For transition metal systems, X-ray spectroscopy offers a unique probe because the core-excitation energies are element specific, which makes it possible to focus on the catalytic metal. The core hole is atom-centered and sensitive to the local changes in the electronic structure, making it useful for redox active catalysts. The possibility to do time-resolved experiments also allows for rapid detection of metastable intermediates. Reliable fingerprinting requires a theoretical model that is accurate enough to distinguish between different species and multiconfigurational wavefunction approaches have recently been extended to model a number of X-ray processes of transition metal complexes. Compared to ground-state calculations, modeling of X-ray spectra is complicated by the presence of the core hole, which typically leads to multiple open shells and large effects of spin–orbit coupling. This chapter describes how these effects can be accounted for with a multiconfigurational approach and outline the basic principles and performance. It is also shown how a detailed analysis of experimental spectra can be used to extract additional information about the electronic structure.

Keywords

Electronic structure Coordination complexes Metal–ligand bonding Molecular orbital theory Restricted active space 

Notes

Acknowledgements

We acknowledge financial support from the foundation Olle Engkvist Byggmastare and the Knut and Alice Wallenberg Foundation (Grant No. KAW-2013.0020). We thank Meiyuan Guo and Michael Odelius for useful discussions.

References

  1. 1.
    Ågren H, Jensen HJA (1987) An efficient method for the calculation of generalized overlap amplitudes for core photoelectron shake-up spectra. Chem Phys Lett 137(5):431–436Google Scholar
  2. 2.
    Ågren H, Flores-Riveros A, Jensen HJA (1989) An efficient method for calculating molecular radiative intensities in the vuv and soft x-ray wavelength regions. Phys Scr 40(6):745Google Scholar
  3. 3.
    Andersson K, Malmqvist PÅ, Roos BO, Sadlej AJ, Wolinski K (1990) Second-order perturbation theory with a casscf reference function. J Phys Chem 94(14):5483–5488Google Scholar
  4. 4.
    Angeli C, Cimiraglia R, Evangelisti S, Leininger T, Malrieu JP (2001) Introduction of n-electron valence states for multireference perturbation theory. J Chem Phys 114(23):10252–10264.  https://doi.org/10.1063/1.1361246Google Scholar
  5. 5.
    Aquilante F, Autschbach J, Carlson RK, Chibotaru LF, Delcey MG, De Vico L, Fdez Galván I, Ferre N, Frutos LM, Gagliardi L et al (2016) Molcas 8: new capabilities for multiconfigurational quantum chemical calculations across the periodic table. J Comput Chem 37(5):506–541PubMedGoogle Scholar
  6. 6.
    Atak K, Bokarev SI, Gotz M, Golnak R, Lange KM, Engel N, Dantz M, Suljoti E, Kühn O, Aziz EF (2013) Nature of the chemical bond of aqueous Fe2+ probed by soft X-ray spectroscopies and ab initio calculations. J Phys Chem B 117(41):12613–12618PubMedGoogle Scholar
  7. 7.
    Bagus PS, Nelin CJ, Ilton ES, Sassi MJ, Rosso KM (2017) Analysis of X-ray adsorption edges: L2,3 edge of FeCl\(_4^{-}\). J Chem Phys 147(22):224306.  https://doi.org/10.1063/1.5006223PubMedGoogle Scholar
  8. 8.
    Bernadotte S, Atkins AJ, Jacob CR (2012) Origin-independent calculation of quadrupole intensities in X-ray spectroscopy. J Chem Phys 137(20):204106PubMedGoogle Scholar
  9. 9.
    Blomberg MR, Siegbahn PE (1997) A comparative study of high-spin manganese and iron complexes. Theor Chem Acc 97(1–4):72–80Google Scholar
  10. 10.
    Bokarev SI, Dantz M, Suljoti E, Kühn O, Aziz EF (2013) State-dependent electron delocalization dynamics at the solute-solvent interface: soft-x-ray absorption spectroscopy and ab initio calculations. Phys Rev Lett 111(8):083002–083007PubMedGoogle Scholar
  11. 11.
    Bokarev SI, Khan M, Abdel-Latif MK, Xiao J, Hilal R, Aziz SG, Aziz EF, Kühn O (2015) Unraveling the electronic structure of photocatalytic manganese complexes by L-edge X-ray spectroscopy. J Phys Chem C 119(33):19192–19200Google Scholar
  12. 12.
    Booth GH, Thom AJW, Alavi A (2009) Fermion monte carlo without fixed nodes: a game of life, death, and annihilation in slater determinant space. J Chem Phys 131(5):054106.  https://doi.org/10.1063/1.3193710PubMedGoogle Scholar
  13. 13.
    Bunău O, Joly Y (2012) Full potential x-ray absorption calculations using time dependent density functional theory. J Phys: Condens Matter 24(21):215502. http://stacks.iop.org/0953-8984/24/i=21/a=215502
  14. 14.
    Cederbaum LS, Domcke W, Schirmer J (1980) Many-body theory of core holes. Phys Rev A 22:206–222.  https://doi.org/10.1103/PhysRevA.22.206
  15. 15.
    Chan GKL, Sharma S (2011) The density matrix renormalization group in quantum chemistry. Annu Rev Phys Chem 62(1):465–481.  https://doi.org/10.1146/annurev-physchem-032210-103338 (pMID: 21219144)
  16. 16.
    Chantzis A, Kowalska JK, Maganas D, DeBeer S, Neese F (2018) Ab initio wave function-based determination of element specific shifts for the efficient calculation of x-ray absorption spectra of main group elements and first row transition metals. J Chem Theory Comput 14(7):3686–3702.  https://doi.org/10.1021/acs.jctc.8b00249 (pMID: 29894196)
  17. 17.
    Coriani S, Christiansen O, Fransson T, Norman P (2012) Coupled-cluster response theory for near-edge x-ray-absorption fine structure of atoms and molecules. Phys Rev A 85:022507. https://link.aps.org/doi/10.1103/PhysRevA.85.022507
  18. 18.
    Cossi M, Barone V (2000) Solvent effect on vertical electronic transitions by the polarizable continuum model. J Chem Phys 112(5):2427–2435Google Scholar
  19. 19.
    Cramer S, DeGroot F, Ma Y, Chen C, Sette F, Kipke C, Eichhorn D, Chan M, Armstrong W (1991) Ligand field strengths and oxidation states from manganese L-edge spectroscopy. J Am Chem Soc 113(21):7937–7940Google Scholar
  20. 20.
    De Groot F (2001) High-resolution x-ray emission and x-ray absorption spectroscopy. Chem Rev 101(6):1779–1808PubMedGoogle Scholar
  21. 21.
    Douglas M, Kroll NM (1974) Quantum electrodynamical corrections to the fine structure of helium. Ann Phys 82(1):89–155Google Scholar
  22. 22.
    Ekström U, Norman P, Carravetta V, Ågren H (2006) Polarization propagator for x-ray spectra. Phys Rev Lett 97:143001. http://link.aps.org/doi/10.1103/PhysRevLett.97.143001
  23. 23.
    Engel N, Bokarev SI, Suljoti E, Garcia-Diez R, Lange KM, Atak K, Golnak R, Kothe A, Dantz M, Kühn O, Aziz EF (2014) Chemical bonding in aqueous ferrocyanide: experimental and theoretical X-ray spectroscopic study. J Phys Chem B 118(6):1555–1563PubMedGoogle Scholar
  24. 24.
    Forsberg N, Malmqvist PÅ (1997) Multiconfiguration perturbation theory with imaginary level shift. Chem Phys Lett 274(1):196–204Google Scholar
  25. 25.
    Gel’mukhanov F, Ågren H (1999) Resonant x-ray raman scattering. Phys Rep 312(3–6):87–330Google Scholar
  26. 26.
    Ghigo G, Roos BO, Malmqvist PÅ (2004) A modified definition of the zeroth-order Hamiltonian in multiconfigurational perturbation theory (CASPT2). Chem Phys Lett 396(1):142–149Google Scholar
  27. 27.
    Golnak R, Bokarev SI, Seidel R, Xiao J, Grell G, Atak K, Unger I, Thürmer S, Aziz SG, Kühn O et al (2016a) Joint analysis of radiative and non-radiative electronic relaxation upon X-ray irradiation of transition metal aqueous solutions. Sci Rep 6:24659PubMedPubMedCentralGoogle Scholar
  28. 28.
    Golnak R, Xiao J, Atak K, Unger I, Seidel R, Winter B, Aziz EF (2016b) Undistorted X-ray absorption spectroscopy using s-core-orbital emissions. J Phys Chem A 120(18):2808–2814PubMedGoogle Scholar
  29. 29.
    Grell G, Bokarev SI, Winter B, Seidel R, Aziz EF, Aziz SG, Kühn O (2015) Multi-reference approach to the calculation of photoelectron spectra including spin-orbit coupling. J Chem Phys 143(7):074104PubMedGoogle Scholar
  30. 30.
    Grell G, Bokarev SI, Winter B, Seidel R, Aziz EF, Aziz SG, Kühn O (2016) Erratum: multi-reference approach to the calculation of photoelectron spectra including spin-orbit coupling. J Chem Phys 143:074104 (2015). J Chem Phys 145(8):089901Google Scholar
  31. 31.
    de Groot F (2005) Multiplet effects in X-ray spectroscopy. Coord Chem Rev 249(1):31–63Google Scholar
  32. 32.
    Guo M, Källman E, Sørensen LK, Delcey MG, Pinjari RV, Lundberg M (2016a) Molecular orbital simulations of metal 1s2p resonant inelastic X-ray scattering. J Phys Chem A 120(29):5848–5855PubMedGoogle Scholar
  33. 33.
    Guo M, Sørensen LK, Delcey MG, Pinjari RV, Lundberg M (2016b) Simulations of iron K pre-edge X-ray absorption spectra using the restricted active space method. Phys Chem Chem Phys 18(4):3250–3259PubMedGoogle Scholar
  34. 34.
    Guo M, Källman E, Pinjari RV, Couto RC, Sørensen LK, Lindh R, Pierloot K, Lundberg M (2019) Fingerprinting electronic structure of heme iron by ab initio modeling of metal L-edge X-ray absorption spectra. J Chem Theory Comput 15(1):477–489. https://doi.org/10.1021/acs.jctc.8b00658
  35. 35.
    Hess BA (1986) Relativistic electronic-structure calculations employing a two-component no-pair formalism with external-field projection operators. Phys Rev A 33(6):3742Google Scholar
  36. 36.
    Hocking RK, Wasinger EC, de Groot FM, Hodgson KO, Hedman B, Solomon EI (2006) Fe L-edge XAS studies of K\(_4\)[Fe(CN)\(_6\)] and K\(3\)[Fe(CN)\(_6\)]: a direct probe of back-bonding. J Am Chem Soc 128(32):10442–10451PubMedGoogle Scholar
  37. 37.
    Holmes AA, Tubman NM, Umrigar CJ (2016) Heat-bath configuration interaction: an efficient selected configuration interaction algorithm inspired by heat-bath sampling. J Chem Theory Comput 12(8):3674–3680.  https://doi.org/10.1021/acs.jctc.6b00407 (pMID: 27428771)
  38. 38.
    Jan W, Michael W, Andreas D (2014) Calculating core-level excitations and x-ray absorption spectra of medium-sized closed-shell molecules with the algebraic-diagrammatic construction scheme for the polarization propagator. J Comput Chem 35(26):1900–1915.  https://doi.org/10.1002/jcc.23703, https://onlinelibrary.wiley.com/doi/abs/10.1002/jcc.23703
  39. 39.
    Jay RM, Norell J, Eckert S, Hantschmann M, Beye M, Kennedy B, Quevedo W, Schlotter WF, Dakovski GL, Minitti MP, Hoffmann MC, Mitra A, Moeller SP, Nordlund D, Zhang W, Liang HW, Kunnus K, Kubiek K, Techert SA, Lundberg M, Wernet P, Gaffney K, Odelius M, Föhlisch A (2018) Disentangling transient charge density and metalligand covalency in photoexcited ferricyanide with femtosecond resonant inelastic soft X-ray scattering. J Phys Chem Lett 9(12):3538–3543.  https://doi.org/10.1021/acs.jpclett.8b01429 (pMID: 29888918)
  40. 40.
    Jensen HJA, Jørgensen P, Ågren H (1987) Efficient optimization of large scale MCSCF wave functions with a restricted step algorithm. J Chem Phys 87(1):451–466Google Scholar
  41. 41.
    Johansson MP, Blomberg MR, Sundholm D, Wikström M (2002) Change in electron and spin density upon electron transfer to haem. Biochim Biophys Acta-Bioenerg 1553(3):183–187Google Scholar
  42. 42.
    Josefsson I, Kunnus K, Schreck S, Föhlisch A, de Groot F, Wernet P, Odelius M (2012) Ab initio calculations of X-ray spectra: atomic multiplet and molecular orbital effects in a multiconfigurational SCF approach to the L-Edge spectra of transition metal complexes. J Phys Chem Lett 3(23):3565–3570.  https://doi.org/10.1021/jz301479j
  43. 43.
    Klooster R, Broer R, Filatov M (2012) Calculation of x-ray photoelectron spectra with the use of the normalized elimination of the small component method. Chem Phys 395:122–127Google Scholar
  44. 44.
    Kroll T, Hadt RG, Wilson SA, Lundberg M, Yan JJ, Weng TC, Sokaras D, Alonso-Mori R, Casa D, Upton MH, Hedman B, Hodgson KO, Solomon EI (2014) Resonant inelastic X-ray scattering on ferrous and ferric bis-imidazole porphyrin and cytochrome c: nature and role of the axial methionine-Fe bond. J Am Chem Soc 136(52):18087–18099Google Scholar
  45. 45.
    Kroll T, Lundberg M, Solomon EI (2016) X-ray absorption and RIXS on coordination complexes. In: Van Bokhoven JA, Lamberti C (eds) X-ray absorption and X-ray emission spectroscopy: theory and applications. Wiley, Chichester, pp 407–435Google Scholar
  46. 46.
    Kubin M, Kern J, Gul S, Kroll T, Chatterjee R, Lchel H, Fuller FD, Sierra RG, Quevedo W, Weniger C, Rehanek J, Firsov A, Laksmono H, Weninger C, Alonso-Mori R, Nordlund DL, Lassalle-Kaiser B, Glownia JM, Krzywinski J, Moeller S, Turner JJ, Minitti MP, Dakovski GL, Koroidov S, Kawde A, Kanady JS, Tsui EY, Suseno S, Han Z, Hill E, Taguchi T, Borovik AS, Agapie T, Messinger J, Erko A, Föhlisch A, Bergmann U, Mitzner R, Yachandra VK, Yano J, Wernet P (2017) Soft x-ray absorption spectroscopy of metalloproteins and high-valent metal-complexes at room temperature using free-electron lasers. Struct Dyn 4(5):054307.  https://doi.org/10.1063/1.4986627
  47. 47.
    Kubin M, Guo M, Ekimova M, Baker ML, Kroll T, Källman E, Kern J, Yachandra VK, Yano J, Nibbering ET, Lundberg M, Wernet P (2018) Direct determination of absolute absorption cross sections at the L-Edge of dilute Mn complexes in solution using a transmission flatjet. Inorg Chem 57(9):5449–5462Google Scholar
  48. 48.
    Kubin M, Guo M, Ekimova M, Källman EJ, Kern J, Yachandra VK, Yano J, Nibbering ET, Lundberg M, Wernet P (2018) Cr L-edge X-ray absorption spectroscopy of CrIII (acac)\(_3\) in solution with measured and calculated absolute absorption cross sections. J Phys Chem B.  https://doi.org/10.1021/acs.jpcb.8b04190
  49. 49.
    Kubin M, Guo M, Kroll T, Löchel H, Källman E, Baker ML, Mitzner R, Gul S, Kern J, Föhlisch A, Erko A, Bergmann U, Yachandra VK, Yano J, Lundberg M, Wernet P (2018) Probing the oxidation state of transition metal complexes: a case study on how charge and spin densities determine Mn L-Edge X-ray absorption energies. Chem Sci.  https://doi.org/10.1039/C8SC00550H
  50. 50.
    Kubin M, Kern J, Guo M, Källman E, Mitzner R, Yachandra VK, Lundberg M, Yano J, Wernet P (2018) X-ray-induced sample damage at the Mn L-edge: a case study for soft X-ray spectroscopy of transition metal complexes in solution. Phys Chem Chem Phys 20:16817–16827Google Scholar
  51. 51.
    Kunnus K, Josefsson I, Rajkovic I, Schreck S, Quevedo W, Beye M, Grbel S, Scholz M, Nordlund D, Zhang W, Hartsock RW, Gaffney KJ, Schlotter WF, Turner JJ, Kennedy B, Hennies F, Techert S, Wernet P, Odelius M, Fhlisch A (2016) Anti-stokes resonant x-ray Raman scattering for atom specific and excited state selective dynamics. New J Phys 18(10):103011. http://stacks.iop.org/1367-2630/18/i=10/a=103011
  52. 52.
    Kunnus K, Josefsson I, Rajkovic I, Schreck S, Quevedo W, Beye M, Weniger C, Grbel S, Scholz M, Nordlund D, Zhang W, Hartsock RW, Gaffney KJ, Schlotter WF, Turner JJ, Kennedy B, Hennies F, de Groot FMF, Techert S, Odelius M, Wernet P, Fhlisch A (2016) Identification of the dominant photochemical pathways and mechanistic insights to the ultrafast ligand exchange of Fe(CO)\(_5\) to Fe(CO)\(_4\)EtOH. Struct Dyn 3(4):043204.  https://doi.org/10.1063/1.4941602
  53. 53.
    Kunnus K, Zhang W, Delcey MG, Pinjari RV, Miedema PS, Schreck S, Quevedo W, Schroeder H, Föhlisch A, Gaffney KJ, Lundberg M, Odelius M, Wernet P (2016) Viewing the valence electronic structure of ferric and ferrous hexacyanide in solution from the Fe and cyanide perspectives. J Phys Chem B 120(29):7182–7194.  https://doi.org/10.1021/acs.jpcb.6b04751
  54. 54.
    Liang W, Fischer SA, Frisch MJ, Li X (2011) Energy-specific linear response TDHF/TDDFT for calculating high-energy excited states. J Chem Theory Comput 7(11):3540–3547.  https://doi.org/10.1021/ct200485xPubMedGoogle Scholar
  55. 55.
    List NH, Kauczor J, Saue T, Jensen HJA, Norman P (2015) Beyond the electric-dipole approximation: a formulation and implementation of molecular response theory for the description of absorption of electromagnetic field radiation. J Chem Phys 142(24):244111PubMedGoogle Scholar
  56. 56.
    List NH, Saue T, Norman P (2017) Rotationally averaged linear absorption spectra beyond the electric-dipole approximation. Mol Phys 115(1–2):63–74Google Scholar
  57. 57.
    Liu Y, Persson P, Sundström V, Wärnmark K (2016) Fe N-heterocyclic carbene complexes as promising photosensitizers. Acc Chem Res 49(8):1477–1485PubMedGoogle Scholar
  58. 58.
    Lundberg M, Kroll T, DeBeer S, Bergmann U, Wilson SA, Glatzel P, Nordlund D, Hedman B, Hodgson KO, Solomon EI (2013) Metal-ligand covalency of iron complexes from high-resolution resonant inelastic X-ray scattering. J Am Chem Soc 135(45):17121–17134.  https://doi.org/10.1021/ja408072q (pMID: 24131028)
  59. 59.
    Ma D, Li Manni G, Gagliardi L (2011) The generalized active space concept in multiconfigurational self-consistent field methods. J Chem Phys 135(4):044128.  https://doi.org/10.1063/1.3611401PubMedGoogle Scholar
  60. 60.
    Maganas D, DeBeer S, Neese F (2014) Restricted open-shell configuration interaction cluster calculations of the L-Edge X-ray absorption study of TiO\(_2\) and CaF\(_2\) solids. Inorg Chem 53(13):6374–6385.  https://doi.org/10.1021/ic500197v (pMID: 24871209)
  61. 61.
    Malmqvist PÅ (1986) Calculation of transition density matrices by nonunitary orbital transformations. Int J Quantum Chem 30(4):479–494.  https://doi.org/10.1002/qua.560300404
  62. 62.
    Malmqvist PÅ, Rendell A, Roos BO (1990) The restricted active space self-consistent-field method, implemented with a split graph unitary group approach. J Phys Chem 94(14):5477–5482.  https://doi.org/10.1021/j100377a011
  63. 63.
    Malmqvist PÅ, Roos BO, Schimmelpfennig B (2002) The restricted active space (RAS) state interaction approach with spin-orbit coupling. Chem Phys Lett 357(3):230–240Google Scholar
  64. 64.
    Malmqvist PÅ, Pierloot K, Shahi ARM, Cramer CJ, Gagliardi L (2008) The restricted active space followed by second-order perturbation theory method: theory and application to the study of CuO\(_2\) and Cu\(_2\)O\(_2\) systems. J Chem Phys 128(20):204109PubMedGoogle Scholar
  65. 65.
    Nakata A, Imamura Y, Otsuka T, Nakai H (2006) Time-dependent density functional theory calculations for core-excited states: assessment of standard exchange-correlation functionals and development of a novel hybrid functional. J Chem Phys 124(9):094105.  https://doi.org/10.1063/1.2173987Google Scholar
  66. 66.
    Norell J, Jay RM, Hantschmann M, Eckert S, Guo M, Gaffney KJ, Wernet P, Lundberg M, Föhlisch A, Odelius M (2018) Fingerprints of electronic, spin and structural dynamics from resonant inelastic soft X-ray scattering in transient photo-chemical species. Phys Chem Chem Phys 20(10):7243–7253PubMedPubMedCentralGoogle Scholar
  67. 67.
    Norman P, Dreuw A (2018) Simulating X-ray spectroscopies and calculating core-excited states of molecules. Chem Rev 118(15):7208–7248Google Scholar
  68. 68.
    Penfold TJ, Reinhard M, Rittmann-Frank MH, Tavernelli I, Rothlisberger U, Milne CJ, Glatzel P, Chergui M (2014) X-ray spectroscopic study of solvent effects on the ferrous and ferric hexacyanide anions. J Phys Chem A 118(40):9411–9418PubMedGoogle Scholar
  69. 69.
    Pierloot K (2003) The CASPT2 method in inorganic electronic spectroscopy: from ionic transition metal to covalent actinide complexes. Mol Phys 101(13):2083–2094Google Scholar
  70. 70.
    Pierloot K, Phung QM, Domingo A (2017) Spin state energetics in first-row transition metal complexes: contribution of (3s3p) correlation and its description by second-order perturbation theory. J Chem Theory Comput 13(2):537–553.  https://doi.org/10.1021/acs.jctc.6b01005 (pMID: 28005368)
  71. 71.
    Pinjari RV, Delcey MG, Guo M, Odelius M, Lundberg M (2014) Restricted active space calculations of L-edge X-ray absorption spectra: From molecular orbitals to multiplet states. J Chem Phys 141(12):124116PubMedGoogle Scholar
  72. 72.
    Pinjari RV, Delcey MG, Guo M, Odelius M, Lundberg M (2015) Erratum: restricted active space calculations of L-edge X-ray absorption spectra: from molecular orbitals to multiplet states. J Chem Phys 141:124116 (2014)]. J Chem Phys 142(6):069901Google Scholar
  73. 73.
    Pinjari RV, Delcey MG, Guo M, Odelius M, Lundberg M (2016) Cost and sensitivity of restricted active-space calculations of metal L-edge X-ray absorption spectra. J Comput Chem 37(5):477–486PubMedGoogle Scholar
  74. 74.
    Preuße M, Bokarev SI, Aziz SG, Kühn O (2016) Towards an ab initio theory for metal L-edge soft X-ray spectroscopy of molecular aggregates. Struct Dynam 3(6):062601Google Scholar
  75. 75.
    Roemelt M, Maganas D, DeBeer S, Neese F (2013) A combined DFT and restricted open-shell configuration interaction method including spin-orbit coupling: application to transition metal L-edge X-ray absorption spectroscopy. J Chem Phys 138(20):204101PubMedGoogle Scholar
  76. 76.
    Roos BO (1980) The complete active space SCF method in a fock-matrix-based super-CI formulation. Int J Quantum Chem 18(S14):175–189.  https://doi.org/10.1002/qua.560180822
  77. 77.
    Roos BO, Lindh R, Malmqvist PÅ, Veryazov V, Widmark PO (2004) Main group atoms and dimers studied with a new relativistic ANO basis set. J Phys Chem A 108(15):2851–2858Google Scholar
  78. 78.
    Roos BO, Lindh R, Malmqvist PÅ, Veryazov V, Widmark PO (2005) New relativistic ANO basis sets for transition metal atoms. J Phys Chem A 109(29):6575–6579PubMedGoogle Scholar
  79. 79.
    Roos BO, Lindh R, Malmqvist PÅ, Veryazov V, Widmark PO (2016) Multiconfigurational quantum chemistry. Wiley, New YorkGoogle Scholar
  80. 80.
    van Schooneveld MM, Juhin A, Campos-Cuerva C, Schmitt T, de Groot FM (2013) Origin of low energy d-d excitations observed on wet chemically prepared cobalt bearing nanoparticles by 2p3d resonant X-ray emission spectroscopy. J Phys Chem C 117(27):14398–14407Google Scholar
  81. 81.
    Sørensen LK, Guo M, Lindh R, Lundberg M (2017) Applications to metal K pre-edges of transition metal dimers illustrate the approximate origin independence for the intensities in the length representation. Mol Phys 115(1–2):174–189Google Scholar
  82. 82.
    Sørensen LK, Kieri E, Srivastava S, Lundberg M, Lindh R (2019) Implementation of the exact semiclassical light-matter interaction using the Gauss-Hermite quadrature: A simple alternative to the multipole expansion. Phys Rev A 99(013419):1–11. https://doi.org/10.1103/PhysRevA.99.013419
  83. 83.
    Stein CJ, Reiher M (2016) Automated selection of active orbital spaces. J Chem Theory Comput 12(4):1760–1771.  https://doi.org/10.1021/acs.jctc.6b00156 (pMID: 26959891)
  84. 84.
    Stener M, Fronzoni G, de Simone M (2003) Time dependent density functional theory of core electrons excitations. Chem Phys Lett 373(1):115–123.  https://doi.org/10.1016/S0009-2614(03)00543-8
  85. 85.
    Stenrup M, Lindh R, Fdez Galván I (2015) Constrained numerical gradients and composite gradients: practical tools for geometry optimization and potential energy surface navigation. J Comput Chem 36(22):1698–1708PubMedGoogle Scholar
  86. 86.
    Suljoti E, Garcia-Diez R, Bokarev SI, Lange KM, Schoch R, Dierker B, Dantz M, Yamamoto K, Engel N, Atak K, Kuhn O, Bauer M, Rubensson JE, Aziz EF (2013) Direct observation of molecular orbital mixing in a solvated organometallic complex. Angew Chem Int Ed 52(37):9841–9844.  https://doi.org/10.1002/anie.201303310, https://onlinelibrary.wiley.com/doi/abs/10.1002/anie.201303310
  87. 87.
    Tanaka A, Jo T (1994) Resonant 3d, 3p and 3s photoemission in transition metal oxides predicted at 2p threshold. J Phys Soc JPN 63(7):2788–2807Google Scholar
  88. 88.
    Thürmer S, Seidel R, Eberhardt W, Bradforth SE, Winter B (2011) Ultrafast hybridization screening in Fe3+ aqueous solution. J Am Chem Soc 133(32):12528–12535PubMedGoogle Scholar
  89. 89.
    Van Schooneveld M, DeBeer S (2015) A close look at dose: toward l-edge xas spectral uniformity, dose quantification and prediction of metal ion photoreduction. J Electron Spectrosc Relat Phenom 198:31–56Google Scholar
  90. 90.
    Wang H, Bokarev SI, Aziz SG, Kühn O (2017) Ultrafast spin-state dynamics in transition-metal complexes triggered by soft-X-ray light. Phys Rev Lett 118(2):023001PubMedGoogle Scholar
  91. 91.
    Wasinger EC, De Groot FM, Hedman B, Hodgson KO, Solomon EI (2003) L-edge X-ray absorption spectroscopy of non-heme iron sites: experimental determination of differential orbital covalency. J Am Chem Soc 125(42):12894–12906PubMedGoogle Scholar
  92. 92.
    Wernet P, Kunnus K, Schreck S, Quevedo W, Kurian R, Techert S, de Groot FM, Odelius M, Föhlisch A (2012) Dissecting local atomic and intermolecular interactions of transition-metal ions in solution with selective X-ray spectroscopy. J Phys Chem Lett 3(23):3448–3453PubMedGoogle Scholar
  93. 93.
    Wernet P, Kunnus K, Josefsson I, Rajkovic I, Quevedo W, Beye M, Schreck S, Gruebel S, Scholz M, Nordlund D, Zhang W, Hartsock RW, Schlotter WF, Turner JJ, Kennedy B, Hennies F, de Groot FMF, Gaffney KJ, Techert S, Odelius M, Foehlisch A (2015) Orbital-specific mapping of the ligand exchange dynamics of Fe(CO)\(_5\) in solution. Nature 520(7545):78–81Google Scholar
  94. 94.
    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(27):6297–6314Google Scholar
  95. 95.
    Wilson SA, Kroll T, Decreau RA, Hocking RK, Lundberg M, Hedman B, Hodgson KO, Solomon EI (2013) Iron L-Edge X-ray absorption spectroscopy of oxy-picket fence porphyrin: experimental insight into Fe-O\(_2\) bonding. J Am Chem Soc 135(3):1124–1136Google Scholar
  96. 96.
    Yano J, Yachandra V (2014) Mn\(_4\)Ca cluster in photosynthesis: where and how water is oxidized to dioxygen. Chem Rev 114(8):4175–4205PubMedPubMedCentralGoogle Scholar
  97. 97.
    Zobel JP, Nogueira JJ, Gonzalez L (2017) The ipea dilemma in caspt2. Chem Sci 8:1482–1499.  https://doi.org/10.1039/C6SC03759C

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Chemistry - Ångström LaboratoryUppsala UniversityUppsalaSweden

Personalised recommendations