Article Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX
pubs.acs.org/IC
Reactivity of Superheavy Elements Cn, Nh, and Fl and Their Lighter Homologues Hg, Tl, and Pb, Respectively, with a Gold Surface from Periodic DFT Calculations Valeria Pershina* GSI Helmholtzzentrum für Schwerionenforschung GmbH, Planckstr. 1, 64291 Darmstadt, Germany S Supporting Information *
ABSTRACT: Adsorption energies of superheavy elements (SHEs) Cn, Nh, and Fl and their lighter homologues Hg, Tl, and Pb, respectively, on a Au(111) surface at different adsorbate coverages are predicted via periodic relativistic DFT calculations with the aim of assisting the outcome of related “one-atomat-a-time” gas-phase chromatography experiments. In agreement with previous DFT studies with the use of a cluster model, the present results for large supercells are indicative of high volatility of Cn. Thus, this element should not interact with the regular Au(111) surface at room temperature but should adsorb on it in a vacancy. Fl should moderately interact with such a surface under ambient conditions, while Nh should be the most reactive element with respect to gold. All three elements should, however, reveal much lower reactivity toward gold than their lighter homologues. The reasons for this are the strong relativistic stabilization and contraction of the 7s1/2 and 7p1/2 AOs. The obtained trend in the adsorption energy, Nh ≫ Fl > Cn, enables one to easily separate these elements from each other, as well as from their lighter homologues using gold or gold/quartz surfaces. compared with the Tads and ΔHads of their lighter homologues in the chemical groups and with Rn, as an extremely inert element.11−14 In this way, the similarity between these elements is assessed, allowing for proving the position of SHEs in respective chemical groups of the periodic table. In one of those techniques, thermochromatography, the chromatography column has a negative temperature gradient from room temperature to one much below zero (of about −180 °C).9,10 The surface of the column, i.e., of detectors located along it, is made of thin gold films produced by thermal vapor deposition. Using this technique, the volatility of Cn was studied.3 The Cn atom was found to adsorb onto gold at a Tads of about −50 °C (−ΔHads = 52+4 −3 kJ/mol). For comparison, Hg fully adsorbed on gold at the beginning on the column with −ΔHads of 98 kJ/mol12, and Rn adsorbed at the end of it at about −180 °C with a −ΔHads of 33 ± 2 kJ/mol.11 Thus, Cn was proven to be very volatile. However, a relatively large value of −ΔHads(Cn), larger than that of Rn, was interpreted as evidence of Cn−metal bond formation, typically a property of group12 elements. By having registered only very few events (e.g., produced atoms), the results of two experimental studies on the volatility of Fl using the same technique turned out to be contra3 dictory.3,5 They gave a −ΔHads of Fl on gold of 34+54 −11 kJ/mol 5 and >60 kJ/mol , respectively, with a different interpretation: the formation of a physisorption bond in the former and an
1. INTRODUCTION Man-made superheavy elements (SHEs) are unique in their nature; they have extremely short half-lives and low production rates.1,2 The study of their chemical properties is therefore very exciting and challenging due to strong relativistic effects on their electron shells. Elements whose properties are now the focus of experimental and theoretical studies are 112 (Cn), 113 (Nh), and 114 (Fl).3−7 Even though being members of group 12 and 14 elements, respectively, Cn and Fl were expected to be rather different from their lighter homologues Hg and Pb, respectively; they should be inert and volatile. The reason is that the closed- and quasiclosed shell ground-state electronic configurations, 6d107s2 and 7s27p1/22, respectively, and large relativistic stabilization and contraction of the 7s and 7p1/2 AOs are making these orbitals less accessible for chemical bonding.8 Nh is, on the contrary, expected to be rather reactive due to the availability of one unpaired electron in the ground-state configuration, 7s27p1/2. However, strong relativistic contraction and stabilization of the 7s1/2 and 7p1/2 AOs, as well as large spin−orbit (SO) splitting of the 7p-AOs, are also expected to significantly reduce its reactivity as compared to that of Tl. One way to characterize these elements chemically is to measure their adsorption properties on the surfaces of some materials. This is done with the use of special gas−solid chromatography techniques.9,10 In those experiments, the adsorption temperature, Tads, of SHEs is measured and the adsorption enthalpy, ΔHads, is deduced on its basis via adsorption models. Those quantities of SHEs are then © XXXX American Chemical Society
Received: January 16, 2018
A
DOI: 10.1021/acs.inorgchem.8b00101 Inorg. Chem. XXXX, XXX, XXX−XXX
Article
Inorganic Chemistry
2. METHODS AND DETAILS OF THE CALCULATIONS
intermetallic one in the latter cases. Therefore, further experiments are on the way to solving this contradiction.6 Nh was claimed to be observed in similar gas-phase chromatography experiments; however, its chemical form could not be established. NhOH could have been formed in a humid atmosphere.7 For decades our work has been devoted to the study of the electronic structure and properties of SHEs (see refs 2,15, and 16 for recent reviews). The atomic properties of Cn, Nh, and Fl were predicted by our group via ab initio Dirac−Coulomb coupled cluster (DC CC) calculations.17,18 The chemical bonding of Cn, Nh, and Fl with Au and with themselves was investigated using both the fully relativistic density functional theory (DFT) and ab initio CC molecular methods.19−22 The bond weakening of the SHE compounds with respect to that of the lighter homologues was established and was shown to be a relativistic effect. To render assistance to experiments on the volatility of Cn and Fl,3−6adsorption energies, Eads, of single atoms of group 12 elements Hg and Cn and of group 14 elements Pb and Fl on the Au(111) and Au(100) surfaces were predicted by our group via four-component (4c) DFT calculations for the M−Aun clusters.23,24 Eads was converged with the cluster size, where n reached 120. Obtained Eads proved to be in good agreement with experimental ΔHads of Cn and Pb.3,14 For Nh, ΔHads was also estimated via 4c-DFT calculation for the MAu (M = Tl and Nh) dimers.22 Works of other researches on the study of the interaction of Cn, Nh, and Fl with gold were also performed using smaller M−Aun clusters (n ≤ 37 for Cn and Fl and n ≤ 58 for Nh)25−29 and DFT calculations. Even though the results of those studies proved to be physically meaningful, the cluster model, even for a very large n, cannot properly treat the solid-state periodicity. In addition, the surface relaxation effects were taken into account by geometry optimization for only small Aun clusters (n = 3−625,26 and n = 20, 2127,28), while for larger Aun systems, the geometric parameters were fixed at their Au bulk values.25−29 In addition, for the optimized M−gold clusters, nonoptimal adsorption positions of adatoms were considered because of the difficulty of modeling such systems using molecular codes (e.g., only the on-top position of M in small M−Au n systems was managed25,27). Such positons, as the modeling of the gold surface via a few atoms, are not optimal for the treatment of real adsorption phenomenon on thin gold films used in the experiments. Periodic codes having all of the necessary features for the proper treatment of the adsorption phenomena have not, until recently, been used for the heaviest elements. In 2016, we published the first results on Eads of Cn, Nh, and Fl and their homologues Hg, Tl, and Pb, respectively, on a hydroxylated quartz surface.30,31 Excellent agreement with the experiment for the lighter elements has been achieved (the measurements for SHEs have not yet been performed). In the present work, we calculated Eads of Cn, Nh, and Fl, as well as of their lighter homologues Hg, Tl, and Pb on a Au(111) surface for the first time via periodic relativistic DFT calculations. The Au(111) surface was chosen because the theoretical and experimental studies on the morphology of thin gold films came to the conclusion that this modification, coming from the fcc crystal lattice, is the most stable with the lowest energy.32,33 The method of the calculations is described in Section 2, while the results and their discussion are in Section 3. The conclusions are given in Section 4.
The calculations for all of the systems of interest were performed with the use of the ADF BAND program package.34 This DFT method solves Kohn−Sham equations self-consistently. The zeroth-order regular approximation (ZORA) lies in the basis of it.35 An accuracy of the ZORA approximation for the treatment of heavy elements was assessed in several earlier publications.35−38 Also, a ZORA MP (model potential) method,39 a modification of ZORA,35 applied to the calculations of hydrides and oxides of Fl, showed excellent agreement for the equilibrium bond lengths, Re, and dissociation energies, De, with the 4c-DFT results.40 The adsorption process was simulated by the (1 × 1)M/Au(111) slab for the full coverage and by the (2 × 2)M/Au(111) and (4 × 4)M/Au(111) supercells (sc) for a lower coverage, all with 4 layers of Au atoms, i.e., having 32 and 64 gold atoms, respectively. The Au atoms of the lowest level were kept fixed in their positions obtained via the Au bulk geometry optimization (i.e., being frozen), while Au atoms in the three upper layers, as well as the adatoms, were all relaxed. All of the possible adsorption positions of the M atoms on the Au slab/ supercells were considered: “top”, “bridge”, “hollow1” (on top of the gold atoms in the second layer), and “hollow2” (on top of the gold atoms in the third layer). The geometry optimization was performed for all of the systems of interest at the scalar-relativistic (SR) level. The SO effects were taken into account as single point calculations for the SR optimized structures. Both the nonspin-polarized and the spinpolarized noncollinear approaches were used. Several exchange-correlation potentials, Vxc, were tested. We have found that, as was established earlier,41 the PW91 functional provides a better description of the Au−Au bond than the PBE and revPBE ones. This was also found for Eads of Hg on the Au(111) surface via periodic calculations with the use of the Vienna ab initio simulation package (VASP).42,43 For the adsorption of Cn, Nh, and Fl on quartz, revPBE was found to be more suitable.30,31 Dispersion corrected Vxc, e.g., revPBE-D3(BJ), important for Hg and Cn, is not available for elements heavier than Z = 92, so the presented results for SHEs are all obtained with the PW91 and revPBE functionals. For the lighter homologues, the revPBE-D3(BJ) functional was also used. The frozen core approximation was utilized with the smallest frozen core, as advised.34 This means that for Cn, Nh, and Fl, orbitals 1s through 5d are frozen, while 6s through 5f are explicitly included in the calculations of the integrals. ADF BAND includes basis sets for SHEs until Z = 120. These are the combinations of numerical atomic orbitals and Slater-type orbitals. Both TZP and TZ2P sets were used and were proven to be equally good for the required accuracy of Eads. The real space integration parameter, q, that governs the precision of the numerical integration, i.e., the relative precision 10−q in the integrals, was taken as 5. The kspace integration is done accurately using the quadratic tetrahedron method. The total number of unique k points was 5. (See refs 34 and 38 for details). According to the ADF methodology, the method gives the formation energy of a system, Ef, with respect to the isolated atoms. (The obtained Ef values are presented in the Supporting Information (SI)). The adsorption energy, Eads, was calculated using the following equation Eads(M − slab) = −[Ef (M − slab) − Ef (M) − Ef (slab)]
(1)
The Ef(M), called atomic corrections, were calculated using the ADF BAND code within the SR and SO approaches for each functional used. Spin polarization was found to be important only for Ef(M).
3. RESULTS AND DISCUSSION A. Gold Bulk. Before modeling the adsorption, calculations of the cohesive energy, Ecoh, of bulk gold were performed using the most popular exchange-correlation potentials, such as revPBE, PW91, and revPBE-D3(BJ). As expected, PW91 gave a good value of Ecoh of 3.34 eV at the SO level and lattice B
DOI: 10.1021/acs.inorgchem.8b00101 Inorg. Chem. XXXX, XXX, XXX−XXX
Article
Inorganic Chemistry Table 1. Calculated and Experimental Lattice Parameter, a (in Å), and Cohesive Energy, Ecoh (in eV/atom), of Gold revPBE
a
PW91
revPBE-D3BJa
revPBE-D3BJb
property
TZP
TZ2P
TZP
TZ2P
TZ2P
TZ2P
expc
a Ecoh (SR) Ecoh (SO)
4.196 2.59 2.65
4.184 2.66 2.82
4.168 3.10 3.27
4.157 3.17 3.34
4.077 3.87 4.05
4.056
4.065
4.06
3.81
SR geometry optimization + SO. bSO geometry optimization. cReference 44.
parameter a = 4.157 Å as compared to the experimental values of 3.81 eV and 4.065 Å,44 respectively. The revPBE-D3(BJ) potential gave an even better Ecoh(Au) of 4.06 eV and a of 4.056 Å, so this Vxc was also used for the calculations of the M− Au(111) slab/supercell systems (M = Hg, Tl, and Pb) to test its suitability for the treatment of adsorption phenomena. One can see (Table 1) that the SR and SO geometry optimization for Au gives practically the same Ecoh. B. Adsorption of Hg/Cn, Tl/Nh, and Pb/Fl on the Au(111) Surface. As was mentioned above, the adsorption of M on the Au(111) surface was modeled by the M(1 × 1)/ Au(111) slab for the full coverage and by the (2 × 2)M/ Au(111) and (4 × 4)M/Au(111) supercells for lower coverage. The full, or high coverage, are, however, academic cases for single atoms of SHEs. Four possible adsorption positions of M on those slab/supercells, “top”, “bridge”, “hollow1” (on top of the gold atoms in the second layer), and “hollow2” (on top of the gold atoms in the third layer) shown in Figures 1−4, were considered. The adsorption in a vacancy created by the top Au atom, as is shown in Figure 5 for a unit cell, has also been taken into account.
Figure 3. A (4 × 4)M/Au(111) supercell simulating adsorption of M on the Au(111) surface in the “hollow1” position: top and side views.
Figure 4. A (4 × 4)M/Au(111) supercell simulating adsorption of M on the Au(111) surface in the “hollow2” position: top and side views.
Figure 1. A (4 × 4)M/Au(111) supercell simulating adsorption of M on the Au(111) surface in the “top” position: top and side views. Figure 5. A (4 × 4)M/Au(111) supercell simulating adsorption of M on the Au(111) surface in a vacancy: top and side views.
Å) and also of Cn (3.20 Å)17 are much larger than half of the Au−Au distance of 2.874 Å. (The equilibrium Fl−Fl distance in the dimer is 3.547 Å at the DC CC level.21) Therefore, at the full (1 × 1) coverage, Fl pushes gold atoms of the upper layer away (Table 2). With increasing size of the supercell, i.e., with an increasing M−M separation, the Fl atom is more strongly bound to the Au(111) surface. Thus, at the (2 × 2) supercell, it interacts with gold with an energy of 0.41 eV (the SO value), and the upper Au layer is not so much distorted (Table 2). A further increase in the size of the supercell from (2 × 2)M/ Au(111) to (4 × 4)M/Au(111) resulted in an increase in the Eads of Fl of only 0.03 eV at the SR level and of 0.18 eV at the SO level (Table 2). The latter case corresponds to the situation where the Fl−Fl atoms are separated from each other by 11.496 Å. This excludes any Fl−Fl interaction, which was also checked by additional molecular ADF and CC calculations. (As was mentioned above, the Re of Fl2 is 3.547 Å.21) On the (4 × 4)
Figure 2. A (4 × 4)M/Au(111) supercell simulating adsorption of M on the Au(111) surface in the “bridge” position: top and side views.
We have found out that for the (1 × 1) slab, as well as for the (2 × 2) and (4 × 4) supercells, the most preferential adsorption position for all of the atoms of interest is the “hollow2” (see below and the SI). The results for Eads(Fl) in the “hollow 2” position, demonstrating a change in Eads with an increasing size of the supercell or decreasing coverage, are shown in Table 2, as an example. One can see that the full coverage of Fl is energetically unfavorable at the SO level. The Fl−Fl interactions are strong because the atomic radii of Fl (3.30 C
DOI: 10.1021/acs.inorgchem.8b00101 Inorg. Chem. XXXX, XXX, XXX−XXX
Article
Inorganic Chemistry
Table 2. Formation Energies, Ef, of the (1 × 1)M/Au(111), (2 × 2)M/Au(111), and (4 × 4)M/Au(111) Systems, Adsorption Energies of Fl, Eads(M-Ausc) (in eV), on those Slab and Supercells in a “Hollow-2” Position, the z(M) coordinate of the M atom and the Displacement (z Coordinate) of the Top Au(0,0,0) Atom, z(Au) (in Å), Calculated Using the PW91 Functionala property
app.
(1 × 1)M/Au(111)
(2 × 2)M/Au(111)b
(4 × 4)M/Au(111)c
Ef(M-Ausc)
SR SO SR SO SO SO SR SO
−14.70 −17.59 2.28 −0.18 2.475 −0.644 −11.88 −12.66
−52.04 −56.06 3.35 0.41 2.493 0.075 −48.14 −50.53
−193.80 −205.09 3.38 0.59 2.535 0.101 −189.87 −199.49
element Fl
Eads(M-Ausc) z(M) z(Au) Ef(Ausc)
Au
a Atomic (SP) corrections are (in eV): Ef(Fl) = −0.55 (SR) and −5.12 (SO). bThe unit cell consists of 32 atoms of Au and one atom of M. cThe unit cell consists of 64 atoms of Au and one atom of M.
systematic and are, therefore, discussed below for SHEs and their homologues (see SI; the revPBE values are also given there). The PW91 (SR and SO) calculated Eads for the (4 × 4)M/ Au(111) (M = Cn, Nh, and Fl) supercells in various adsorption positions of M are given in Table 4. (The values for the
supercell, the Fl atom is positioned further away from the Au surface than on the (2 × 2) one; however, the deviation of the upper Au atom from the original z(0) position is also larger. Overall, the M-surface distance slightly increases from the (2 × 2)M/Au(111) to the (4 × 4)M/Au(111) case. A further increase in the size of the supercell did not seem necessary, as it would result in huge computational costs with practically no change in Eads. Thus, the (4 × 4)M/Au(111) model should be related to the experimental case of the adsorption of single species of SHEs or at zero-coverage (for lighter elements). Therefore, the calculations of Eads for all of the elements of interest in various adsorption positions were performed for the (4 × 4)M/Au(111) supercell. The resulting Eads values for different Vxc (revPBE, PW91, and revPBE-D3(BJ)) for the (4 × 4)M/Au(111) (M = Hg, Tl, and Pb) supercells, where experimental data at zero coverage are available,12−14 are shown in Table 3. One can see that
Table 4. (SR and SO) Adsorption Energies, Eads (in eV), and the Adatom−Surface Distances (in Å) (in Parentheses) for the (4 × 4)M/Au(111) Supercell in Different Adsorption Positions of M (M = Cn, Nh and Fl), the PW91 Approximation
a
position
Hg
Tl
Pb
revPBE PW91 PW91 PW91 revPBE-D3(BJ) exp
hollow2 hollow2 vacancy hollow2 hollow2
unbound 0.47 (2.50) 1.01 (0.73) 0.42a; 0.35b 0.81 (2.70) 1.01c
0.23 (3.37) 2.21 (2.60) 2.65 (1.08)
1.31 (3.24) 2.38 (2.29) 3.05 (0.69)
2.63 (2.81) 2.49d
2.78 (2.46) 2.43e
approx.
Cn
top
SR SO SR SO SR SO SR SO SR SO ΔHads
unbound unbound unbound unbound unbound unbound 0.03 0.00 (6.11) 0.27 0.61 (1.45) 0.53a
bridge
Table 3. Adsorption Energies, Eads (in eV), and the Adatom− Surface Distances (in Å) (in Parentheses) for the (4 × 4)M/ Au(111) Supercell (M = Hg, Tl, and Pb) Calculated Using Various Vxc method (Vxc)
position
hollow1 hollow2 vacancy exp a
Nh 2.54 0.98 2.77 1.21 2.71 1.15 2.79 1.23 3.08 1.51
(3.11) (2.69) (2.46) (2.87) (1.59)
Fl 2.97 0.14 (2.44) 3.37 0.46 (2.42) 3.30 0.41 (2.36) 3.38 0.59 (2.54) 4.17 0.81 (1.13) b c 0.350.56 −0.11, ≥0.6
Reference 3. bReference 4. cReference 5.
different positions are needed for Monte Carlo simulations of distribution of single SHE events along the column used in the experiments). In the preferable “hollow2” position, Cn is still unbound to the Au(111) surface at the PW91 level, so the inclusion of the dispersion corrections in Vxc might be essential. (The revPBE gives even more unbound state for Cn.) However, it adsorbs rather well in a vacancy, with the energy of 60 kJ/mol. As expected, Nh and Fl are relatively well bound to the regular Au(111) surface, with Nh being the most reactive element. The Eads of Fl, as in the earlier cluster calculations,24,26 was found to be significant, in the range of chemisorption values. With respect to their lighter homologues, all of the three SHEs are, however, much less reactive with gold. This is an SO effect (compare the SR and SO values in Table 4). The SO decrease in Eads of Nh and Fl is mainly due to the relativistic SO stabilization of the SHE atoms: Ef(Nh) is −2.01 eV and Ef(Fl) is −5.12 eV, as compared to an Ef(Tl) of −0.77 eV and Ef(Pb) of −1.88 eV (at the PW91 SO level). Thus, large SO effects on the 7p1/2 AOs make these elements relatively inert. For Cn, the
b
Reference 42. Reference 43 (see for details of the calculations therein). cReference 12. dReference 13. eReference 14.
revPBE Vxc underestimates bonding, so Hg does not interact with the Au surface at all. The PW91 potential gives a reasonable Eads, even though it is somewhat underestimated, like for Hg; however, it is in good agreement with earlier DFT calculations,42,43 also what concerns establishing the preferential adsorption site (“hollow2”). The PW91 Eads for a vacancy is, as expected, larger and in better agreement with the experiment for Hg.12 (The experimental Eads of Hg is, however, an energy of desorption, deduced from Tads via models with some assumptions, so direct comparison is problematic.) The obtained revPBE-D3(BJ) Eads for Hg and Pb in the “hollow2” position seems to be closer to the experimental value than the PW91 one, but the Eads for Tl and Pb are overestimated. Consequently, the PW91 results were found to be most D
DOI: 10.1021/acs.inorgchem.8b00101 Inorg. Chem. XXXX, XXX, XXX−XXX
Article
Inorganic Chemistry relative inertness is a result of its closed-shell 6d107s2 ground state and the 7s1/2 AO relativistic stabilization. The calculated geometries show that the Nh−gold and Fl− gold separations are larger than those of their homologues Tl and Pb, respectively, in agreement with the earlier calculations for the M−Aun systems.24−27 The reason for that is the participation of the relativistically expanded 7p3/2 AOs of these SHEs in bonding in addition to the contracted 7p1/2 AOs (see below). Differences in Eads(Fl) in various adsorption positions with respect to the most preferable one, as well as in comparison with those from the earlier calculations24, are given in Table 5.
effective charges, QM, calculated in this work show that some electron density is transferred from the Cn, Nh, and Fl atoms to the gold ones: Cn 0.15 Au , Nh 0.26 Au , and Fl0.24Au. This can be compared with Hg0.17Au, Tl0.30Au, and Pb0.39Au, where the QM are larger. The charge transfer from M (M = Cn, Nh, and Fl) to Au can be explained by the differences in the electron affinities (EA) between these elements and gold: EA of Cn (no EA), Nh (0.68 eV), and Fl (no EA)15 are much smaller than EA(Au) of 2.31 eV.44 The charge density transfer from M to Au for diatomics was investigated in reference 27 by the charge-displacement (CD) analysis. In that case, the Hg−Au and Cn−Hg CD curves were found to be markedly different, and the latter one more closely resembled the Xe/Rn−Au systems, while PbAu and FlAu exhibited similar CD curves. This finding is in accordance with that from our earlier work (see Table 3 and Figure 8 in reference 20), where a similar phenomenon was observed for the MAu dimers. The QM calculated there via the 4c-DFT method are Hg0.14, Tl0.35, and Pb0.30 and Cn0.07, Nh0.22, and Fl0.31. Thus, QM for Pb and Fl are almost equal, and a reversal of the trend in QM between the 6p and 7p elements was observed in the seventh row of the periodic table from Fl on, so that for group 17 elements, the charges are At0.03 and Ts0.15. Thus, starting from Mc, the 7p elements are more electropositive than their 6p homologues. This reversal of the trend was explained by the different relationship between the energies of the 6p AOs (donating) of the 6p elements and that of the 6s(Au) AO (accepting) on the one hand and between the energies of the 7p AOs (particularly, relativistically destabilized 7p3/2 AOs) of SHEs (donating) and that of 6s(Au) AO on the other hand (see Figure 1 in reference 20 and explanations therein). In other words, it is explained by the reversal of the trends in the EAs between the sixth row and seventh row elements from group 14 onward (see Figure 13 in reference 20). In the case of the interaction of M with a gold surface, QM of Cn, Nh, and Fl, found in this work, are all smaller than those of Hg, Tl, and Pb, particularly in the case of the Pb/Fl couple. This is also in agreement with findings of reference 27, where similar differences in the charge shift from M to Aun (n = 7 and 20) were found between sixth row atoms Hg and Pb and seventh row ones Cn and Fl, respectively. This was explained27 by the extension of the charge shift from M to the lower layers of the Aun cluster. In the present calculations, we also observe the charge shift down to the fourth layer of gold; however, the upper gold layer is influenced the most. As a summary, the Eads values of Hg/Cn, Tl/Nh, and Pb/Fl on the Au(111) surface in comparison with the Eads values from
Table 5. Differences in the Adsorption Energy, Eads (in eV and in kJ/mol in Parentheses), of Fl in Various Adsorption Positions with Respect to the Most Favorable One on the Au(111) Surface Obtained by Different Calculations (SO Level) position
revPBEa
PW91a
B88/P86b
hollow2 hollow1 bridge top
0 0.01 (1) 0.07 (7) 0.60 (58)
0 0.18 (17) 0.13 (13) 0.45 (44)
0.12 (12) 0.26 (25) 0 0.24 (23)
a
Present periodic 2c-ADF BAND calculations. calculations.24
b
4c-DFT cluster
Thus, according to the present PW91 ADF BAND results, Fl should preferentially adsorb in the “hollow2” position with a difference of 0.45 eV (44 kJ/mol) with respect to the less advantageous “top” one. (A different preferential adsorption position found in reference 24 is, probably, due to the lack of relaxation). Overall, the present data confirm the 4c-DFT results,24 where Nh and Fl were shown to be chemically bound to the gold surface in all of the adsorption sites, while for Cn, only a vacancy was found to be binding. A Mulliken population analysis for the M−Aun (M = Hg/Cn, Tl/Nh, and Pb/Fl) clusters was performed in our earlier works.20−24 In agreement with those findings, the present analysis also indicates that participation of both the 7p1/2 and 7p3/2 AOs of Nh and Fl in bonding in the considered systems is significant, though smaller than that of the related 6p AOs in lighter homologues Tl and Pb, respectively. Thus, AO populations are 7s1/20.017p1/20.037p3/20.04 and 7s1/20.017p1/20.017p3/20.07 for the Nh and Fl systems in the “hollow2” position, respectively. For Cn, in the vacancy, the 7s AOs are mostly active with some admixture of the 6d and 7p AOs: 6d3/20.016d5/20.017s1/20.207p1/20.097p3/20.04. The Mulliken
Table 6. Summary of Predictions of the Adsorption Energies, Eads (in kJ/mol), of Hg, Cn, Tl, Nh, Pb, and Fl on the Au(111) Surface from the Relativistic Periodic and Cluster Calculations as Well as Experimental −ΔHads (in kJ/mol) of Hg, Tl, Pb, Cn, and Fl on Gold at Zero Coverage method
model
Hg
Cn
Tl
Nh
Pb
Fl
ADF-SOa ADF-SOb 2c/4c-DFT RECP-DFT exp. exp.
periodic periodic cluster cluster
45 97 54c 31e >65h 98 ± 3l
0 59 45c 23e h 52+4 −3
213 256 256d
119 146 129d 116f
230 294 232c
57 78 68c 47g k 34+54 −11 m ≥48
240i
234j
a This work, in a “hollow2” position. bThis work, in vacancy. cReference 24. dReference 28. eReference 25. fReference 29. gReference 26. hReference 3. iReference 13. jReference 14. kReference 4. lReference 12. mReference 5.
E
DOI: 10.1021/acs.inorgchem.8b00101 Inorg. Chem. XXXX, XXX, XXX−XXX
Article
Inorganic Chemistry
should weakly interact with gold at temperatures of about −50 °C. Fl should not interact with quartz and should adsorb rather well on gold at the beginning of the second section. Nh, like Tl, should adsorb at once on quartz and should not be transported further to the second section with gold detectors. This predicted behavior is in agreement with the related experiments on the adsorption of Hg, Tl, Pb, and Cn.3−5,12−14 Results of further experiments on Nh and Fl should complete the picture on the chemical characterization of these three exotic SHEs.
the previous cluster calculations24−26,28,29 and with experiments3−5,12−14 are given in Table 6 and are depicted for the present calculations in Figure 6. One can see that there is an
4. CONCLUSIONS The adsorption energies of superheavy elements Cn, Nh, and Fl, and their lighter homologues Hg, Tl, and Pb, respectively, on a Au(111) surface at different adsorbate coverages have been predicted via periodic relativistic DFT calculations. The aim of the study was to assist related one-atom-at-a-time gasphase chromatography experiments. The present approach allowed for modeling the gold (111) surface in the most optimal way. In a difference to the earlier results based on a cluster approach (with the use of molecular DFT codes), the relaxation effects were taken into account by the full geometry optimization of the large supercells. The most preferable adsorption position for all of the atoms of interest was found to be “hollow2” (on top of the Au atoms in the third layer from the top). Adsorption in a vacancy, as expected, proved to be much stronger. Overall, good agreement was shown between the present results using a periodic code and those obtained from the cluster model for the regular Au(111) surface. According to all of those calculations, Cn, Nh, and Fl were found to reveal a lower reactivity, or a higher volatility, over a gold surface than that of their lighter homologues in the chemical groups Hg, Tl, and Pb, respectively. The reason for that are the strong relativistic stabilization and contraction of the 7s1/2 and 7p1/2 AOs. Accordingly, Cn should not interact with a regular Au(111) surface but should adsorb on such a surface in a vacancy at room temperature; however, the inclusion of dispersion corrections could shift its Tads toward negative values. Fl should moderately interact with the regular Au(111) surface under ambient conditions. Nh should be the most reactive element with respect to gold. The obtained Eads(M) for these SHEs (Nh ≫ Fl > Cn) are found to be rather different, so these elements should be easily separated from each other and from their homologues by adsorption on gold or gold/quartz surfaces.
Figure 6. Adsorption enthalpies of SHEs, Cn, Nh, and Fl and their sixth row homologues, Hg, Tl, and Pb, respectively, from the present ADF BAND calculations in the “hollow2” (“hol.2”) and vacancy (vac.) sites and experimental values.2−5,12−14 See the data in Table 6.
overall agreement in the trends of the Eads in the groups and in the rows of the elements between these types of calculations, even though the absolute values slightly differ (the ADF PW91 ones are somewhat lower) due to the different models and exchange-correlation potentials. Thus, all of the SHEs under consideration should be much more volatile over gold than their lighter homologues in the groups, with the following trend in the seventh row: Nh ≪ Fl < Cn. As indicated above, the reason for the smaller reactivity of the SHEs are the strong relativistic effects on their AOs. In combination with the results of periodic calculations of Eads(M) on a hydroxylated quartz surface,30,31 the present data can serve as a guiding tool for gas-phase chromatography experiments6 with an array of detectors, where those of quartz (kept at room temperature) are followed by the gold-plated ones (with a temperature gradient from room temperature to about −160 °C); see Figure 7. The Eads(M) values on gold
■
ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.8b00101. The resulting formation energies, structures, and adsorption energies (PDF)
Figure 7. Predicted adsorption positions (schematic) of Cn, Nh, and Fl for gas-phase chromatography experiments with a combined SiO2/ gold surface.
■
(Table 6) and on quartz (noninteraction of Cn and Fl and 58 kJ/mol for Nh30,31) indicate that the separation of these elements can easily be reached. (See schematically shown adsorption positions of the SHEs, Figure 7.) Thus, Hg should not interact with quartz at room temperature but should adsorb right at the beginning of the second section on the column with gold-covered detectors. Cn should not interact with quartz but
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Valeria Pershina: 0000-0002-7478-857X Notes
The author declares no competing financial interest. F
DOI: 10.1021/acs.inorgchem.8b00101 Inorg. Chem. XXXX, XXX, XXX−XXX
Article
Inorganic Chemistry
■
(14) Haenssler, F.; Eichler, R.; Gäggeler, H. W.; Soverna, S.; Dressler, R.; Piguet, D. Thermochromatographic studies of 212Pb on metal surfaces. LCH-Report 2006, 2005, 3. (15) Pershina, V.; Theoretical Chemistry of the Heaviest Elements; The Chemistry of Superheavy Elements, 2013, 1, 135239. (16) Pershina, V. Electronic structure and properties of superheavy elements. Nucl. Phys. A 2015, 944, 578−613. (17) Pershina, V.; Borschevsky, A.; Eliav, E.; Kaldor, U. Prediction of the adsorption behavior of elements 112 and 114 on inert surfaces from ab initio Dirac-Coulomb atomic calculations. J. Chem. Phys. 2008, 128, 024707. (18) Pershina, V.; Borschevsky, A.; Eliav, E.; Kaldor, U. Atomic Properties of Element 113 and Its Adsorption on Inert Surfaces from ab initio Dirac-Coulomb Calculations. J. Phys. Chem. A 2008, 112, 13712−13716. (19) Pershina, V.; Anton, J.; Fricke, B. Intermetallic compounds of the heaviest elements and their homologs: The electronic structure and bonding of MM’, where M = Ge, Sn, Pb, and element 114, and M’=Ni, Pd, Pt, Cu, Ag, Au, Sn, Pb, and element 114. J. Chem. Phys. 2007, 127, 134310. (20) Pershina, V.; Borschevsky, A.; Anton, J.; Jacob, T. Theoretical predictions of trends in spectroscopic properties of gold containing dimers of the 6p and 7p elements and their adsorption on gold. J. Chem. Phys. 2010, 133, 104304. (21) Borschevsky, A.; Pershina, V.; Eliav, E.; Kaldor, U. Relativistic coupled cluster study of diatomic compounds of Hg, Cn, and Fl. J. Chem. Phys. 2014, 141, 084301. (22) Pershina, V.; Anton, J.; Jacob, T. Electronic structures and properties of MAu and MOH, where M = Tl and element 113. Chem. Phys. Lett. 2009, 480, 157−160. (23) Sarpe-Tudoran, C.; Fricke, B.; Anton, J.; Pershina, V. Adsorption of superheavy elements on metal surfaces. J. Chem. Phys. 2007, 126, 174702. (24) Pershina, V.; Anton, J.; Jacob, T. Theoretical predictions of adsorption behavior of elements 112 and 114 and their homologs Hg and Pb. J. Chem. Phys. 2009, 131, 084713. (25) Rykova, E. A.; Zaitsevskii, A.; Mosyagin, N. S. Relativistic effective core potential calculations of Hg and eka-Hg (E112) interactions with gold: spin-orbit density functional theory modelling of Hg-Aun and E112-Aun systems. J. Chem. Phys. 2006, 125, 241102. (26) Zaitsevskii, A.; van Wüllen, C.; Rykova, E. A. Two-component relativistic density functional modeling of the adsorption of element 114 (eka-led) on gold. Phys. Chem. Chem. Phys. 2010, 12, 4152−4156. (27) Rampino, S.; Storchi, L.; Belpassi, L. Gold-superheavy-element interaction in diatomics and cluster adducts: A combined fourcomponent Dirac-Kohn-Sham/charge-displacement study. J. Chem. Phys. 2015, 143, 024307. (28) Fox-Beyer, B. S.; van Wüllen, C. Theoretical modelling of the adsorption of thallium and element 113 atoms on gold using twocomponent density functional methods with effective core potentials. Chem. Phys. 2012, 395, 95−103. (29) Rusakov, A. A.; Demidov, Y. A.; Zaitsevskii, A. Estimating the adsorption energy of element 113 on a gold surface. Cent. Eur. J. Phys. 2013, 11, 1537−1541. (30) Pershina, V. A relativistic periodic DFT study on interaction of superheavy elements 112 (Cn) and 114 (Fl) and their homologs Hg and Pb, respectively, with a quartz surface. Phys. Chem. Chem. Phys. 2016, 18, 17750−17756. (31) Pershina, V. A theoretical study on the adsorption behavior of element 113 and its homolog Tl on a quartz surface: relativistic periodic DFT calculations. J. Phys. Chem. C 2016, 120, 20232−20238. (32) Crljen, Ž .; Lazić, P.; Šokčević, D.; Brako, R. Relaxation and reconstruction on (111) surfaces of Au, Pt, and Cu. Phys. Rev. B: Condens. Matter Mater. Phys. 2003, 68, 19541110.1103/PhysRevB.68.195411. (33) Mahmoodi, N.; Rushdi, A. I.; Bowen, J.; Sabouri, A.; Anthony, C. J.; Mendes, P. M.; Preece, J. A. Room temperature thermally evaporated thin Au film on Si suitable for application of thiol self-
ACKNOWLEDGMENTS The author is thankful to leading experimentalists in this area: A. Yakushev (GSI, Darmstadt), also for the picture of the experimental setup (Figure 7), and R. Eichler (PSI, Switzerland) for valuable discussions of experimental results and new ideas.
■
REFERENCES
(1) The Chemistry of Superheavy Elements, 2nd ed.; Schädel, M., Shaughnessy, D., Eds.; Springer-Verlag: Berlin, 2014. (2) Türler, A.; Pershina, V. Advances in the production and chemistry of the heaviest elements. Chem. Rev. 2013, 113, 1237−1312. (3) Eichler, R.; Aksenov, N. V.; Belozerov, A. V.; Bozhikov, G. A.; Chepigin, V. I.; Dmitriev, S. N.; Dressler, R.; Gäggeler, H. W.; Gorshkov, V. A.; Haenssler, F.; Itkis, M. G.; Laube, A.; Lebedev, V. Ya.; Malyshev, O. N.; Oganessian, Yu. Ts.; Petrushkin, O. V.; Piguet, D.; Rasmussen, P.; Shishkin, S. V.; Shutov, S. V.; Svirikhin, A. I.; Tereshatov, E. E.; Vostokin, G. K.; Wegrzecki, M.; Yeremin, A. V. Chemical characterization of element 112. Nature 2007, 447, 72−75. (4) Eichler, R.; Aksenov, N. V.; Albin, Yu. V.; Belozerov, A. V.; Bozhikov, G. A.; Chepigin, V. I.; Dmitriev, S. N.; Dressler, R.; Gäggeler, H. W.; Gorshkov, V. A.; Henderson, R. A.; Johnsen, A. M.; Kenneally, J. M.; Lebedev, V. Ya.; Malyshev, O. N.; Moody, K. J.; Oganessian, Yu. Ts.; Petrushkin, O. V.; Piguet, D.; Popeko, A. G.; Rasmussen, P.; Serov, A.; Shaughnessy, D. A.; Shishkin, S. V.; Shutov, A. V.; Stoyer, M. A.; Stoyer, N. J.; Svirikhin, A. I.; Tereshatov, E. E.; Vostokin, G. K.; Wegrzecki, M.; Wilk, P. A.; Wittwer, D.; Yeremin, A. V. Indication for a volatile element 114. Radiochim. Acta 2010, 98, 133−139. (5) 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.; Hild, D.; Hübner, A.; Jäger, E.; Khuyagbaatar, J.; Kindler, B.; Kratz, J. V.; Krier, J.; Kurz, N.; Lommel, B.; Niewisch, J.; Nitsche, H.; Omtvedt, J. P.; Parr, E.; Qin Zhi Rudolp, D.; Runke, J.; Schausten, B.; Schimpf, E.; Semchenkov, A.; Steiner, J.; ThörlePospiech, P.; Uusito, J.; Wegrzecki, M.; Wiehl, N. Superheavy element Flerovium (Element 114) is a volatile metal. Inorg. Chem. 2014, 53, 1624−1629. (6) Yakushev, A.; Eichler, R. Gas-phase chemistry of element 114, flerovium. EPJ Web Conf. 2016, 131, 07003. (7) Dmitriev, S. N.; Aksenov, N. V.; Albin, Y. V.; Bozhikov, G. A.; Chelnokov, M. L.; Chepygin, V. I.; Eichler, R.; Isaev, A. V.; Katrasev, D. E.; Lebedev, V. Ya.; Malyshev, O. N.; Petrushkin, O. V.; Porobanuk, L. S.; Ryabinin, M. A.; Sabel’nikov, A. V.; Sokol, E. A.; Svirikhin, A. V.; Starodub, G. Ya.; Usoltsev, I.; Vostokin, G. K.; Yeremin, A. V. Pioneering experiments on the chemical properties of element 113. Mendeleev Commun. 2014, 24, 253−256. (8) Pitzer, K. S. Are elements 112, 114, and 118 relatively inert gases? J. Chem. Phys. 1975, 63, 1032−1033. (9) Türler, A., Grerorich, K. E.; Experimental Techniques; The Chemistry of Superheavy Elements, 2014, 1, 261−30810.1007/978-3642-37466-1_5. (10) Gäggeler, H. W., Türler, A.; Gas-Phase Chemistry of Superheavy Elements; The Chemistry of Superheavy Elements, 20141, 415− 48410.1007/978-3-642-37466-1_8. (11) Eichler, R.; Schädel, M. Adsorption of radon on metal surfaces: a model study for chemical investigations of elements 112 and 114. J. Phys. Chem. B 2002, 106, 5413−5420. (12) Soverna, S.; Dressler, R.; Düllmann, C. E.; Eichler, B.; Eichler, R.; Gäggeler, H. W.; Haenssler, F.; Niklaus, J. P.; Piguet, D.; Qin, Z.; Türler, A.; Yakushev, A. Thermochromatographic studies of mercury and radon on transition metal surfaces. Radiochim. Acta 2005, 93, 1−8. (13) Serov, A. R.; Eichler, R.; Dressler, R.; Piguet, D.; Türler, A.; Vögele, A.; Wittwer, D.; Gäggeler, H. W. Adsorption interaction of carrier-free thallium species with gold and quartz surfaces. Radiochim. Acta 2013, 101, 421−425. G
DOI: 10.1021/acs.inorgchem.8b00101 Inorg. Chem. XXXX, XXX, XXX−XXX
Article
Inorganic Chemistry assembled monolayers in micro/nano-electromechanical-systems sensors. J. Vac. Sci. Technol., A 2017, 35 (4), 041514. (34) BAND2016, SCM Theoretical Chemistry; Vrije Universiteit, Amsterdam, The Netherlands, http://www.scm.com. (35) van Lenthe, E.; Snejders, J. G.; Baerends, E. J. The zero-order regular approximation for relativistic effects: The effect of spin-orbit coupling in closed shell molecules. J. Chem. Phys. 1996, 105, 6505− 6516. (36) van Lenthe, E.; Ehlers, A.; Baerends, E. J. Geometry optimization in the zero order regular approximation for relativistic effects. J. Chem. Phys. 1999, 110, 8943−8953. (37) Faas, S.; van Lenthe, J. H.; Hennum, A. C. An ab initio twocomponent relativistic methods including spin-orbit coupling using the regular approximation. J. Chem. Phys. 2000, 113, 4052−4059. (38) Olsen, R. A.; Philipsen, P. H. T.; Baerends, E. J. CO on Pt(111): A puzzle revisited. J. Chem. Phys. 2003, 119, 4522−4528. (39) van Wüllen, C. Molecular density functional calculations in the regular relativistic approximation: Method, application to coinage metal diatomics, hydrides, fluorides and chlorides, and comparison with first-order relativistic calculations. J. Chem. Phys. 1998, 109, 392− 399. (40) Liu, W.; van Wüllen, Ch.; Han, Y. K.; Choi, Y. J.; Lee, Y. S. Spectroscopic constants of Pb and Eka-lead compounds: comparison of different approaches. Adv. Quantum Chem. 2001, 39, 325−355. (41) Baker, T. A.; Friend, C. M.; Kaxiras, E. Effects of chlorine and oxygen coverage on the structure of the Au(111) surface. J. Chem. Phys. 2009, 130 (8), 084701. (42) Steckel, J. Density Function Theory Study of Mercury Adsorption on Metal Surfaces. Phys. Rev. B: Condens. Matter Mater. Phys. 2008, 77, 11541210.1103/PhysRevB.77.115412. (43) Lim, D.-H.; Aboud, S.; Wilcox, J. Investigation of Adsorption Behavior of Mercury on Au(111) from First Principles. Environ. Sci. Technol. 2012, 46, 7260−7266. (44) Haynes, W. M., Ed.; CRC Handbook of Chemistry and Physics; 93rd ed.; Taylor & Francis Ltd., 2012−2013.
H
DOI: 10.1021/acs.inorgchem.8b00101 Inorg. Chem. XXXX, XXX, XXX−XXX
