Article Cite This: Inorg. Chem. 2019, 58, 8735−8738
pubs.acs.org/IC
Theoretical Search for the Highest Valence States of the Coinage Metals: Roentgenium Heptafluoride May Exist Jeanet Conradie*,†,‡ and Abhik Ghosh*,† †
Department of Chemistry, University of Tromsø, N-9037 Tromsø, Norway Department of Chemistry, University of the Free State, 9300 Bloemfontein, Republic of South Africa
‡
Downloaded via GUILFORD COLG on July 27, 2019 at 09:56:11 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.
S Supporting Information *
ABSTRACT: We present here a relativistic density functional theory investigation of the penta- and heptavalent states of gold and roentgenium, employing the ZORA (zeroth order regular approximation to the Dirac equation) Hamiltonian, including spin−orbit coupling at the twocomponent level, and large all-electron relativistic Slater-type quadruple-ζ quadruple polarization (ZORA-STO-QZ4P) basis sets. Unsurprisingly, our calculations confirm the stability of the experimentally known complexes AuF6− and Au2F10 with respect to decomposition to trivalent Au products and F2. The calculations also predict that RgF6− and Rg2F10 should be even more stable with respect to an analogous decomposition pathway. Like an earlier DFT study (Inorg. Chem. 2007, 46 (13), 5338−5342), our calculations rule out the true heptavalent Au complex AuF7 as a stable species, preferring instead a Cs AuF5···F2 formulation. Remarkably, our calculations confirm a D5h pentagonal-bipyramidal structure of RgF7 as the global minimum, at an energy of approximately half an electron volt below the RgF5···F2 form.
■
INTRODUCTION Relativity has a destabilizing effect on d orbitals and has a significant effect on the chemistry of 5d elements,1 reaching a maximum for groups 10−12, i.e., Pt, Au, and Hg.2−7 Examples of such effects include the experimental observation of such high-valent complexes as PtF6,8 AuF6−,9,10 Au2F10,11 HgF4,12 and the IrO4+ cation.13−15 Relativistic density functional theory (DFT) calculations have suggested that even decavalent platinum might exist.16 Under high pressure, even AuF617 and IrF818 have been predicted to exist. Against this backdrop, one might reasonably expect that seventh-period elements will furnish their own share of molecules with unexpected valence states. A striking finding in this connection is that the group 14 element flerovium is volatile, consistent with a noble-gas-like zero-valent state, a result of the very large 7p 1/2−3/2 splitting.19−21 Another striking, albeit as yet experimentally unverified, prediction is that copernicium tetrafluoride (CnF4) should be much more stable than HgF4 with respect to F2 elimination.22 Herein, we report a relativistic DFT study of the penta- and heptavalent states of gold23 and roentgenium using the ZORA24,25(zeroth order regular approximation to the Dirac equation) Hamiltonian, including spin−orbit coupling at the two-component level, and large all-electron relativistic Slater-type quadruple-ζ quadruple polarization (ZORA-STOQZ4P) basis sets. The calculations have yielded a host of interesting insights, including the tantalizing prospect that the heptavalent state of the superheavy element roentgenium26−28 may exist in the form of the pentagonal-bipyramidal molecule RgF7.29
valence states of Ag, Au, and Rg to lower-valent products. A full set of calculations were performed with the excellent OLYP functional, based on the OPTX exchange functional.30,31 Selected electronic energies were also recomputed with TPSS,32,33 M06L,34,35 and B3LYP,36,37 although many of the B3LYP calculations failed to converge. DFT methods have been previously calibrated against CCSD(T) in a previous study of Au(V) and Au(VII),23 and based on our own experience,22 the present level of theory was deemed entirely reliable for qualitative conclusions vis-à-vis the relative stabilities of different valence states. Spin-unrestricted calculations at the scalar relativistic level also did not provide any indication of spin symmetry-breaking and of multideterminantal character, consistent with the large ligand field splitting energies expected for the square-planar, octahedral, and pentagonal-bipyramidal species investigated herein. The data afford a host of insights, as enumerated below. Octahedral minima were calculated for AgF6−, AuF6−, and RgF6−. While AgF6− was found to be marginally stable with respect to decomposition to AgF4− and F2, AuF6− and RgF6− were found to be unambiguously stable (Table 1). The energetics for the dimeric M2F10 species proved analogous. While Ag2F10 was found to be clearly unstable with respect to decomposition to Ag2F6 and F2, Au2F10 and Rg2F10 were found to be stable with respect to analogous decomposition. Moreover, as expected, the decomposition energies indicate that pentavalent roentgenium fluoride complexes are much more stable than the analogous gold complexes. The high calculated stabilities of RgF6− and Rg2F10 led us to investigate whether monovalent ligands other than fluoride might stabilize
■
RESULTS AND DISCUSSION Table 1 presents the calculated energies, enthalpies, and Gibbs free energies associated with decomposition of the highest © 2019 American Chemical Society
Received: April 18, 2019 Published: June 15, 2019 8735
DOI: 10.1021/acs.inorgchem.9b01139 Inorg. Chem. 2019, 58, 8735−8738
Article
Inorganic Chemistry Table 1. Selected ZORA/STO-QZ4P Reaction Energies (eV)a OLYP reaction −
−
AgF6 → AgF4 + F2 Ag2F10 → Ag2F6 + 2F2 AuF6− → AuF4− + F2 Au2F10 → Au2F6 + 2F2 AuCl6− → AuCl4− + Cl2 Au2Cl10 → Au2Cl6 + 2Cl2 Au(CF3)6− → Au(CF3)4− + (CF3)2 AuF7 (D5h) → AuF5·F2 (Cs) 2 AuF7 (D5h) → Au2F10 + 2F2 2AuF5···F2 (Cs) → Au2F10 + 2F2 RgF6− → RgF4− + F2 Rg2F10 → Rg2F6 + 2F2 RgCl6− → RgCl4− + Cl2 Rg2Cl10 → Rg2Cl6 + 2Cl2 Rg(CF3)6− → Rg(CF3)4− + (CF3)2 RgF7 (D5h) → RgF5···F2 (Cs) 2 RgF7 (D5h) → Rg2F10 + 2F2
ΔE
ΔU
ΔH
ΔG
0.6 −0.9 1.9 1.7 −1.1 −3.2 −3.1 −1.4 −4.2 −1.4 2.7 3.6 −0.1 −1.3 −2.5 0.6 0.4
0.5 −1.1 1.8 1.5 −1.1 −3.3 −3.1 −1.4 −4.2 −1.4 2.6 3.5 −0.2 −1.4 −2.5 0.6 0.3
0.5 −1.0 1.8 1.6 −1.1 −3.2 −3.0 −1.4 −4.2 −1.4 2.7 3.5 −0.2 −1.4 −2.5 0.6 0.3
0.0 −2.0 1.3 0.6 −1.6 −4.2 −3.6 −1.6 −4.1 −1.4 2.2 2.6 −0.7 −2.3 −3.1 0.4 −0.2
B3LYP ΔE
TPSS ΔE
M06L ΔE
−1.4 1.6
2.5
2.7
−2.9
−1.9
−1.6
−1.1
−1.4
nc
4.3
4.4
nc
−0.1
0.4
nc 0.7
0.6
a
nc = not converged.
Table 2. OLYP/ZORA-STO-QZ4P Bond Distances d1−d3 (Å) for Selected Moleculesa
distance (Å) molecule/ion −
AgF4 AuF4− RgF4− Ag2F6 Au2F6 Rg2F6 AgF6− AuF6− RgF6− Ag2F10 Au2F10 Rg2F10 AuF7 RgF7
point group
d1
D4h D4h D4h D2h D2h D2h Oh Oh Oh D2h D2h D2h D5h D5h
1.950 1.953 (1.911)b 2.008 1.892 1.895 1.941 1.931 1.937 (1.883)c 2.001 1.882 1.887 (1.865)c 1.947 1.948 1.992
d2
d3
2.060 2.069 (2.013) 2.147 1.916 1.969
1.909 1.917 (1.896) 1.973
2.052 2.060 2.126
a
Available experimental data are quoted within parentheses. bRef 38. cRef 11.
Table 2 shows that the OLYP/ZORA-STO-QZ4P optimiza-
the pentavalent state of Au and Rg. These calculations showed that chloride and trifluoromethyl in fact do not stabilize pentavalent Au and Rg. The gold results are of course in full qualitative accord with the experimental literature, where both the AuF6− anion and Au2F10 are well-known, structurally characterized species.
tions slightly overestimate the Au−F bond distances in AuF4−, AuF6−, and Au2F10.11,38 The neglect of counterions and the solid state environment in our calculations is a plausible explanation for a good fraction of these discrepancies. 8736
DOI: 10.1021/acs.inorgchem.9b01139 Inorg. Chem. 2019, 58, 8735−8738
Inorganic Chemistry
■
We then turned our attention to the possible existence of the heptavalent state, in the form of AuF7 and RgF7. Interestingly, although AuF7 was reported by Timakov et al. in 1986,39 more recent quantum chemical studies by Himmel and Riedel convincingly proved that the true heptavalent gold complex AuF7 is unstable, with geometry optimizations indicating a structure corresponding to AuF5···F2.23 In our own calculations as well, a Cs AuF5···F2 form was found to be 1.4 eV more stable than D5h pentagonal-bipyramidal AuF7 (Figure 1).
Article
COMPUTATIONAL METHODS
Relativistic density functional theory calculations were carried out with the ZORA (zeroth order regular approximation to the Dirac equation) Hamiltonian,24 including spin−orbit coupling at the twocomponent level, the OLYP exchange-correlation functional, and allelectron ZORA-STO/QZ4P basis sets, all as implemented in the ADF program system.41 Selected calculations were repeated with the TPSS, M06L, and B3LYP functionals. Zero-point energy and thermal corrections (vibrational, rotational, and translational) were made to the electronic energies in the calculation of the thermodynamic parameters. Enthalpy (H) and Gibbs free energy (G) were calculated as U = Eel + Enuc
(1)
H = U + RT
(2)
G = H − TS
(3)
where U is the gas-phase thermodynamic energy, Eel the total electronic energy, Enuc the nuclear internal energy (sum of vibrational, rotational, and translational energies and the zero-point energy correction), R the ideal gas constant, T the temperature, and S the entropy. The entropy (S) was calculated from the temperaturedependent partition function in ADF at 298.15 K.
■
ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.9b01139. Optimized Cartesian coordinates (PDF)
Figure 1. DFT/ZORA-STO-QZ4P calculated geometry (Cs) of the AuF5···F2 form of AuF7. Bond distances (Å) are given in the order OLYP, M06-L, and TPSS.
■
AUTHOR INFORMATION
Corresponding Authors
*E-mail:
[email protected] (J.C.). *E-mail:
[email protected] (A.G.).
Fascinatingly, a D5h pentagonal-bipyramidal geometry was predicted as the global minimum for RgF7, with the Cs RgF5··· F2 form some 0.6 eV higher in energy. As expected on the basis of simple crystal/ligand field theory arguments, an examination of the frontier MOs (spinors) revealed a (6dxz2)(6dyz2) configuration, where the equatorial RgF5 group is identified with the xy plane, and a substantial HOMO−LUMO gap of 1.34 eV. Decomposition of RgF7 to Rg2F10 and F2 was found to be associated with a small positive energy change and a small negative free energy change at room temperature. On balance, our calculations suggest that RgF7 should exist as a somewhat delicate isolated molecule.
ORCID
Jeanet Conradie: 0000-0002-8120-6830 Abhik Ghosh: 0000-0003-1161-6364 Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS This work was supported by the Research Council of Norway (Grant 262229 to A.G.) and the South African National Research Foundation (Grants 113327 and 96111 to J.C.).
■
■
CONCLUSION As expected, RgF6− and Rg2 F10 are predicted to be considerably more stable than their analogous Au compounds. We confirm that true heptavalent gold, in the form of AuF7, does not exist as a stable species. In contrast, D5h pentagonalbipyramidal RgF7 is a global minimum, more stable than a Cs RgF5···F2 form by some 0.6 eV. Thus, at least theoretically, the present calculations extend the known valence states of the coinage metals to seven. Given that the most stable roentgenium isotopes have half-lives of tens of seconds,40 atom-at-a-time experimental studies of Rg chemistry may prove realistic; the actual experimental realization of RgF7, however, remains an open question. More generally, there can be little doubt that the coming years will reveal many surprising examples of novel valence states among seventhperiod elements.
REFERENCES
(1) Pyykkö, P. Relativistic Effects in Chemistry: More Common Than You Thought. Annu. Rev. Phys. Chem. 2012, 63, 45−64. (2) Schwerdtfeger, P. Relativistic Effects in Properties Of Gold. Heteroat. Chem. 2002, 13, 578−587. (3) Pyykkö, P. Theoretical Chemistry of Gold. Angew. Chem., Int. Ed. 2004, 43, 4412−4456. (4) Pyykkö, P. Theoretical Chemistry of Gold. II. Inorg. Chim. Acta 2005, 358, 4113−4130. (5) Pyykkö, P. Theoretical Chemistry of Gold. II. Chem. Soc. Rev. 2008, 37, 1967−1997. (6) Leyva-Pérez, A.; Corma, A. Similarities and Differences between the “Relativistic” Triad Gold, Platinum, and Mercury in Catalysis. Angew. Chem., Int. Ed. 2012, 51, 614−635. (7) Gorin, D. J.; Toste, F. D. Relativistic Effects in Homogeneous Gold catalysis. Nature 2007, 446, 395−403. (8) Alvarez-Thon, L.; David, J.; Arratia-Pérez, R.; Seppelt, K. Ground State of Octahedral Platinum Hexafluoride. Phys. Rev. A: At., Mol., Opt. Phys. 2008, 77, 034502. 8737
DOI: 10.1021/acs.inorgchem.9b01139 Inorg. Chem. 2019, 58, 8735−8738
Article
Inorganic Chemistry
(29) For an exposition of the motivations underlying the theoretical study of hypothetical molecules, see the following: Hoffmann, R. Why Think Up New Molecules? Am. Sci. 2008, 96, 372−374. (30) Handy, N. C.; Cohen, A. Left-Right Correlation Energy. Mol. Phys. 2001, 99, 403−412. (31) Lee, C.; Yang, W.; Parr, R. G. Development of the ColleSalvetti Correlation-Energy Formula into a Functional of the Electron-Density. Phys. Rev. B 1988, 37, 785−789. (32) Tao, J.; Perdew, J. P.; Staroverov, V. N.; Scuseria, G. E. Climbing the Density Functional Ladder: Nonempirical MetaGeneralized Gradient Approximation Designed for Molecules and Solids. Phys. Rev. Lett. 2003, 91, 146401. (33) Staroverov, V. N.; Scuseria, G. E.; Tao, J.; Perdew, J. P. Comparative Assessment Of A New Nonempirical Density Functional: Molecules And Hydrogen-Bonded Complexes. J. Chem. Phys. 2003, 119, 12129−12137. (34) Zhao, Y.; Truhlar, D. G. A New Local Density Functional for Main-Group Thermochemistry, Transition Metal Bonding, Thermochemical Kinetics, and Noncovalent Interactions. J. Chem. Phys. 2006, 125, 194101−194118. (35) Zhao, Y.; Truhlar, D. G. 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. 2008, 120, 215−241. (36) Becke, A. D. A New Mixing of Hartree-Fock and Local DensityFunctional Theories. J. Chem. Phys. 1993, 98, 1372−1377. (37) Stephens, P. J.; Devlin, F. J.; Chabalowski, C. F.; Frisch, M. J. Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields. J. Phys. Chem. 1994, 98, 11623−11627. (38) Ellwanger, M. A.; Steinhauer, S.; Golz, P.; Beckers, H.; Wiesner, A.; Braun-Cula, B.; Braun, T.; Riedel, S. Taming the High Reactivity of Gold(III) Fluoride: Fluorido Gold(III) Complexes with N-Based Ligands. Chem. - Eur. J. 2017, 23, 13501−13509. (39) Timakov, A. A.; Prusakov, V. N.; Drobyshevskii, Y. V. Gold heptafluoride. Dokl. Akad. Nauk SSSR 1986, 291, 125−128. (40) Sonzogni, A. Interactive Chart of Nuclides; National Nuclear Data Center, Brookhaven National Laboratory. https://www.nndc. bnl.gov/nudat2/. (41) The ADF program system uses methods described in the following: te Velde, G. T.; Bickelhaupt, F. M.; Baerends, E. J.; Guerra, C. F.; van Gisbergen, S. J. A.; Snijders, J. G.; Ziegler, T. Chemistry with ADF. J. Comput. Chem. 2001, 22, 931−967.
(9) Leary, K.; Bartlett, N. A New Oxidation State of Gold: The Preparation and Some Properties of [AuF6]− Salts. J. Chem. Soc., Chem. Commun. 1972, 0, 903−904. (10) Leary, K.; Zalkin, A.; Bartlett, N. Crystal Structure of [Xe2F11]+[AuF6]−. J. Chem. Soc., Chem. Commun. 1973, 0, 131−132. (11) Hwang, I.; Seppelt, S. Gold Pentafluoride: Structure and Fluoride Ion Affinity. Angew. Chem., Int. Ed. 2001, 40, 3690−3693. (12) Wang, X.; Andrews, L.; Riedel, S.; Kaupp, M. Mercury Is a Transition Metal: The First Experimental Evidence for HgF4. Angew. Chem., Int. Ed. 2007, 46, 8371−8375. (13) Wang, G.; Zhou, M.; Goettel, J. T.; Schrobilgen, G. J.; Su, J.; Li, J.; Schlöder, T.; Riedel, S. Identification of An Iridium-Containing Compound with a Formal Oxidation State of IX. Nature 2014, 514, 475−477. (14) Pyykkö, P.; Xu, W. On the Extreme Oxidation States of Iridium. Chem. - Eur. J. 2015, 21, 9468−9473. (15) Hu, S.-X.; Li, W.-L.; Lu, J.-B.; Bao, J. B.; Yu, H. S.; Truhlar, D. G.; Gibson, J. K.; Marçalo, J.; Zhou, M.; Riedel, S.; Schwarz, W. H. E.; Li, J. On the Upper Limits of Oxidation States in Chemistry. Angew. Chem., Int. Ed. 2018, 57, 3242−3245. (16) Yu, H. S.; Truhlar, D. G. Oxidation State 10 Exists. Angew. Chem., Int. Ed. 2016, 55, 9004−9006. (17) Lin, J.; Zhang, S.; Guan, W.; Yang, G.; Ma, Y. Gold with + 4 and + 6 Oxidation States in AuF4 and AuF6. J. Am. Chem. Soc. 2018, 140, 9545−9550. (18) Lin, J.; Zhao, Z.; Liu, C.; Zhang, J.; Du, X.; Yang, G.; Ma, Y. IrF8 Molecular Crystal under High Pressure. J. Am. Chem. Soc. 2019, 141, 5409−5414. (19) Pitzer, K. S. Are Elements 112, 114, And 118 Relatively Inert Gases? J. Chem. Phys. 1975, 63, 1032. (20) Chaudhuri, R. K.; Chattopadhyay, S.; Mahapatra, U. S. Taming the Electronic Structure of Lead and Eka-lead (Flerovium) by the Relativistic Coupled Cluster Method. J. Phys. Chem. A 2013, 117, 8555−8567. (21) Yakushev, A.; Gates, J. M.; Türler, A.; Schädel, M.; Düllmann, Ch. E.; Ackermann, D.; Andersson, L.-L.; Block, M.; Brüchle, W.; Dvorak, J.; Eberhardt, K.; Essel, H. G.; Even, J.; Forsberg, U.; Gorshkov, A.; Graeger, R.; Gregorich, K. E.; Hartmann, W.; Herzberg, R.-D.; Heßberger, F. P.; Hild, D.; Hübner, A.; Jäger, E.; Khuyagbaatar, J.; Kindler, B.; Kratz, J. V.; Krier, J.; Kurz, N.; Lommel, B.; Niewisch, L.; Nitsche, H.; Omtvedt, J. P.; Parr, E.; Qin, Z.; Rudolph, D.; Runke, J.; Schausten, B.; Schimpf, E.; Semchenkov, A.; Steiner, J.; ThörlePospiech, P.; Uusitalo, J.; Wegrzecki, M.; Wiehl, N. Superheavy Element Flerovium (Element 114) Is a Volatile Metal. Inorg. Chem. 2014, 53, 1624−1629. (22) Ghosh, A.; Conradie, J. The Valence States of Copernicium and Flerovium. Eur. J. Inorg. Chem. 2016, 2016, 2989−2992. (23) Himmel, D.; Riedel, S. After 20 Years, Theoretical Evidence That “AuF7” Is Actually AuF5·F2. Inorg. Chem. 2007, 46, 5338−5342. (24) van Lenthe, E.; Baerends, E. J.; Snijders, J. G. Relativistic Regular Two-Component Hamiltonians. J. Chem. Phys. 1993, 99, 4597−4610. (25) van Lenthe, E.; Baerends, E. J.; Snijders, J. G. Relativistic Total Energy Using Regular Approximations. J. Chem. Phys. 1994, 101, 9783−9792. (26) Hofmann, S.; Ninov, V.; Heßberger, F. P.; Armbruster, P.; Folger, H.; Münzenberg, G.; Schött, H. J.; Popeko, A. G.; Yeremin, A. V.; Andreyev, A. N.; Saro, S.; Janik, R.; Leino, M. The New Element 111. Z. Phys. A: Hadrons Nucl. 1995, 350, 281−282. (27) Hancock, R. D.; Bartolotti, L. J.; Kaltsoyannis, N. Density Functional Theory-Based Prediction of Some Aqueous-Phase Chemistry of Superheavy Element 111. Roentgenium(I) Is the ‘Softest’ Metal Ion. Inorg. Chem. 2006, 45, 10780−10785. (28) Muñoz-Castro, A.; Carey, D. M.; Arratia-Perez, R.; Malli, G. L. Relativistic Effects in Bonding and Isomerization Energy of the Superheavy Roentgenium (111Rg) Cyanide. Polyhedron 2012, 39, 113−117. 8738
DOI: 10.1021/acs.inorgchem.9b01139 Inorg. Chem. 2019, 58, 8735−8738
