
CHEMICAL SHIFTS OF XRAY EMISSION SPECTRA AND EFFECTIVE STATES OF YTTERBIUM IN FLUORIDES: EMBEDDED CLUSTER MODELING OF YbF2 AND YbF3 CRYSTALS
V.M. Shakhova, Yu.V. Lomachuk, Yu.A. Demidov, L.V. Skripnikov,
N.S. Mosyagin, A.V. Zaitsevskii, A.V. Titov
Pages: 169174
DOI: 10.21175/RadJ.2017.03.035
Received: 24 MAR 2017, Received revised: 25 MAY 2017, Accepted: 5 JUL 2017, Published online: 23 DEC 2017
Abstract 
References 
Full Text (PDF)
The YbF_{2} and YbF_{3} crystals were studied within the embedded cluster model. The small core relativistic pseudopotentials for the central Yb atom (42 valence electrons) and embedding potentials for Yb and F atoms were constructed. Chemical shifts of K_{α1} and K_{α2} lines of Xray emission spectra (XES) were calculated using nonvariation onecenter restoration technique and relativistic density functional theory (relDFT) with the hybrid exchangecorrelation functional PBE0. It was done in the YbF_{9}Yb_{12}F_{24} cluster simulating the YbF_{3} crystal with respect to YbF_{8}Yb_{12}F_{24} one representing the YbF_{2} crystal. The resulting estimates are 628 meV for K_{α1} and 559 meV for K_{α2} and their weighted mean agrees within 10% with the experimental value, 557±27 meV. In turn, the weighted relativistic Hartree−Fock (relHF) calculation is higher on 20%. It indicates that the incorporation of electron correlation effects is essential for reproducing the K_{α1, 2} chemical shifts.
 K. Siegbahn, “From XRay to Electron Spectroscopy,” in Lecture Notes in Physics: Nishina Memorial Lectures, vol. 746,Osaka, Japan: Springer, 2009, ch. 8, pp. 137 – 228.
DOI: 10.1007/9784431770565_8
 O. I. Sumbaev, “Shift of K Xray lines associated with valency change and with isomorphous phase transitions in rare earths,” Phys. Usp., vol. 21, no. 2, pp. 141 – 154, 1978.
DOI: 10.1070/PU1978v021n02ABEH005519
 R. I. Karaziya, A. I. Udris, D. V. Grabauskas, “Use of the Chemical Shifts of Electron Levels in the Study of the Distribution of the Effective Charges of Atoms in Compounds,” J. Struct. Chem., vol. 18, no. 4, pp. 520 – 525, 1977.
DOI: 10.1007/BF00745283
 Y. V. Lomachuk, A. V. Titov, “Method for Evaluating Chemical Shifts of Xray Emission Lines in Molecules and Solids,” Phys. Rev. A, vol. 88, 062511, 2013.
DOI: 10.1103/PhysRevA.88.062511
 A. V. Titov, Y. V. Lomachuk and L. V. Skripnikov, “Concept of effective states of atoms in compounds to describe properties determined by the densities of valence electrons in atomic cores,” Phys. Rev. A, vol. 90, 052522, Nov. 2014.
DOI: 10.1103/PhysRevA.90.052522
 A. V. Titov, N. S. Mosyagin, A. N. Petrov, T. A. Isaev, D. P. DeMille, “Study of P,Tparity violation effects in polar heavyatom molecules,” in Progress in Theoretical Chemistry and Physics: Recent Advances in the Theory of Chemical and Physical Systems, vol. 15, J.P. Julien, J. Maruani, D. Mayou, S. Wilson, G. DelgadoBarrio, Eds., Dordrecht, Netherlands: Springer, 2006, ch, 12, pp. 253–283.
DOI: 10.1007/140204528X_12
 P. A. Christiansen, Y. S. Lee and K. S. Pitzer, “Improved ab initio effective core potentials for molecular calculations,” J. Chem. Phys., vol. 71, no. 11, pp. 4445–4450, 1979.
DOI: 10.1063/1.438197
 N. S. Mosyagin, A. V. Zaitsevskii and A. V. Titov, “Shapeconsistent relativistic effective potentials of small atomic cores, international review of atomic and molecular physics,” Int. Rev. At. Mol. Phys., vol. 1, no. 1, pp. 63 – 72, 2010.
Retrieved from: https://pdfs.semanticscholar.org/82f5/65187ec338407439d7cb111e58e53adfc19c.pdf; Retrieved on: Aug. 5, 2017
 A. V. Titov and N. S. Mosyagin, “Generalized relativistic effective core potential: Theoretical grounds,” Int. J. Quantum Chem., vol. 71, no. 5, pp. 359 – 401, 1999.
DOI: 10.1002/(SICI)1097461X(1999)71:5<359::AIDQUA1>3.0.CO;2U
 N. S. Mosyagin, A. V. Zaitsevskii, L. V. Skripnikov, A. V. Titov, “Generalized relativistic effective core potentials for actinides,” Int. J. Quantum Chem., vol. 116, no. 4, pp. 301 – 315, Feb. 2016.
DOI: 10.1002/qua.24978
 A. V. Titov and N. S. Mosyagin, “Generalized relativistic effective core potential method: Theory and calculations,” Russ. J. Phys. Chem., vol. 74, suppl. 2, pp. S376 – S387, 2000.
Retrieved from: https://arxiv.org/pdf/physics/0008160.pdf; Retrieved on: Aug. 5, 2017
 L. V. Skripnikov, A. N. Petrov, A. V. Titov, N. S. Mosyagin, “Electron electric dipole moment: Relativistic correlation calculations of the P,Tviolation effecting the ^{3}∆_{3} state of PtH^{+},” Phys. Rev. A, vol. 80, no. 6, 060501(R), Dec. 2009.
DOI: 10.1103/PhysRevA.80.060501
 L. V. Skripnikov, A. V. Titov, A. N. Petrov, N. S. Mosyagin, O. P. Sushkov, “Enhancement of the electron electric dipole moment in Eu^{2+},” Phys. Rev. A, vol. 84, no. 2, 022505, Aug. 2011.
DOI: 10.1103/PhysRevA.84.022505
 A. N. Petrov, “Hyperfine and Zeeman interactions of the a(1)[^{3}σ_{1}^{+}] state of PbO,” Phys. Rev. A, vol. 83, no. 2, 024502, Feb. 2011.
DOI: 10.1103/PhysRevA.83.024502
 J. Lee et al., “Optical spectroscopy of tungsten carbide for uncertainty analysis in electron electric dipole moment search,” Phys. Rev. A, vol. 87, no. 2, 022516, Feb. 2013.
DOI: 10.1103/PhysRevA.87.022516
 A. N. Petrov, L. V. Skripnikov, A. V. Titov, R. J. Mawhorter, “Centrifugal correction to hyperfine structure constants in the ground state of lead monofluoride,” Phys. Rev. A, vol. 88, no. 1, 010501(R), Jul. 2013.
DOI: 10.1103/PhysRevA.88.010501
 L. V. Skripnikov, A. V. Titov, “LCAObased theoretical study of PbTiO_{3} crystal to search for parity and time reversal violating interaction in solids,” J. Chem. Phys., vol. 145, no. 5, 054115, Aug. 2016.
DOI: 10.1063/1.4959973
 L. V. Skripnikov, “Combined 4component and relativistic pseudopotential study of ThO for the electron electric dipole moment search,” J. Chem. Phys., vol. 145, no. 21, 214301, Dec. 2016.
DOI: 10.1063/1.4968229 PMid: 28799403
 L. V. Skripnikov, A. D. Kudashov, A. N. Petrov, A. V. Titov, “Search for parity and timeandparity–violation effects in lead monofluoride (PbF): Ab initio molecular study,” Phys. Rev. A, vol. 90, no. 6, 064501, Dec. 2014.
DOI: 10.1103/PhysRevA.90.064501
 T. Petzel, O. Greis, “The vaporization behavior of ytterbium(III) fluoride and ytterbium(II) fluoride,” J. LessCommon Met., vol. 46, no. 2, pp. 197 – 207, May 1976.
DOI: 10.1016/00225088(76)902101
 B. V. Bukvetskii, L. S. Garashina, “CrystalChemical Investigation of the Orthorhombic Trifluorides of Samarium, Holmium, and Ytterbium,” Sov. J. Coord. Chem., vol. 3, pp. 791 – 795, 1977.
 I. V. Abarenkov, M. A. Boyko, “WaveFunctionBased Embedding Potential for IonCovalent Crystals,” Int. J. Quantum Chem., vol. 116, no. 3, pp. 211 – 236, Feb. 2016.
DOI: 10.1002/qua.25041
 R. A. Kendall, T. H. Dunning, Jr. and R. J. Harrison, “Electron affinities of the firstrow atoms revisited: systematic basis sets and wave functions,” J. Chem. Phys., vol. 96, no. 9, 6796, May 1992.
DOI: 10.1063/1.462569
 S. G. Semenov, M. E. Bedrina, A. V. Titov, “Quantumchemical Study of Ytterbium Fluorides and of Complex F_{2}YbF_{2}CeF_{2},” Russ. J. Gen. Chem., vol. 86, no. 6, pp. 1215 – 1220, Jun. 2016.
DOI: 10.1134/S1070363216060013
 J. S. Binkley, J. A. Pople, W. J. Hehre, “SelfConsistent Molecular Orbital Methods. 21. Small SplitValence Basis Sets for FirstRow Elements,” J. Am. Chem. Soc., vol. 102, no. 3, pp. 939 – 947, Jan .1980.
DOI: 10.1021/ja00523a008
 J. P. Perdew, K. Burke, M. Ernzerhof, “Generalized gradient approximation made simple,” Phys. Rev. Lett., vol. 77, no. 18, pp. 3865 – 3868, 1996.
DOI: 10.1103/PhysRevLett.77.3865 PMid: 10062328
 C. Adamo, V. Barone, “Toward reliable density functional methods without adjustable parameters: The PBE0 model,” J. Chem. Phys., vol. 110, no. 13, pp. 6158 – 6170, Apr. 1999.
DOI: 10.1063/1.478522
 C. van Wuellen, “A quasirelativistic twocomponent density functional and Hartree−Fock program,” Z. Phys. Chem., vol. 224, no. 34, pp. 413 – 426, 2010.
DOI: 10.1524/zpch.2010.6114
 L. V. Skripnikov, A. V. Titov, “Theoretical study of ThF^{+} in the search for t,pviolation effects: Effective state of a Th atom in ThF^{+} and ThO compounds,” Phys. Rev. A, vol. 91, no. 4, 042504, Apr. 2015.
DOI: 10.1103/PhysRevA.91.042504
 L. V. Skripnikov, A. N. Petrov and A. V. Titov, “Communication: Theoretical study of ThO for the electron electric dipole moment search,” J. Chem. Phys., vol. 139, no. 22, 221103, Dec. 2013
DOI: 10.1063/1.4843955 PMid: 24329049
 В. А. Шабуров и др, “Состояния промежуточной валентности иттербия в интерметаллических соединениях,” т. 24, но. 1, стр. 263 – 265, 1982. (V. A. Shaburov et al., “State of the intermediate valence ytterbium in intermetallic compounds,” Phys. Solid State, vol. 24, no. 1, pp. 263–265, 1982.)
