Ionization Potentials, Electron Affinities, Resonance Excitation

Dec 8, 2010 - The uncertainties of calculated IPs, EAs, and IR for Uus and At were reduced through an extrapolation procedure. The good consistency wi...
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13388

J. Phys. Chem. A 2010, 114, 13388–13394

Ionization Potentials, Electron Affinities, Resonance Excitation Energies, Oscillator Strengths, And Ionic Radii of Element Uus (Z ) 117) and Astatine Zhiwei Chang, Jiguang Li, and Chenzhong Dong* Key Laboratory of Atomic and Molecular Physics and Functional Material of Gansu ProVince, College of Physics and Electronic Engineering, Northwest Normal UniVersity, 730070 Lanzhou, China ReceiVed: August 6, 2010; ReVised Manuscript ReceiVed: September 28, 2010

Multiconfiguration Dirac-Fock (MCDF) method was employed to calculate the first five ionization potentials, electron affinities, resonance excitation energies, oscillator strengths, and radii for the element Uus and its homologue At. Main valence correlation effects were taken into account. The Breit interaction and QED effects were also estimated. The uncertainties of calculated IPs, EAs, and IR for Uus and At were reduced through an extrapolation procedure. The good consistency with available experimental and other theoretical values demonstrates the validity of the present results. These theoretical data therefore can be used to predict some unknown physicochemical properties of element Uus, Astatine, and their compounds. Introduction During the past decades, the synthesis of the superheavy elements (SHE) has made significant progress. The SHE with nuclear charge up to 118 have been produced, apart from Uus (Z ) 117).1–3 Very recently, with the collaboration of Russian and American scientists, the discovery of element Uus was announced by the Joint Institute for Nuclear Research in Dubna, Russia.4 Two isotopes of this element, 293Uus and 294Uus, were produced in the fusion reaction 48Ca+249Bk followed by the emission of four and three neutrons, respectively. They were identified through the corresponding alpha decay chains. The synthesis of Uus fills the gap on the periodic table up to element 118 and offers more details to study the heaviest known “island of stability”.5 With the great achievement of synthesis, another aspect of Uus may attract people’s interests that the strong relativistic effects may largely influence its atomic structure and further change its physicochemical property. For SHE, the relativistic effect does not only cause very large spin-orbit splitting but also makes the orbitals contract with small angular momenta and those expand with large angular momenta.6–9 Such modification of atomic orbitals would greatly change the behavior of SHE which may not follow the trends in their lighter homologues.9–11 Pershina and co-workers studied the volatility of element 112 and found, because of the high excitation energy (7s2 f 7s7p) resulting from the relativistic effect, element 112 had the lowest sublimation enthalpy of all the transition metals and behaved as a gas.12 Another recent study for element 113 shown that the trends in the atomic properties and adsorption enthalpy in group 13 reversed from In to element 113, reflecting the strong relativistic contraction and stabilization of the outer p1/2 orbitals, which were largest for element 113.13 Nash studied the atomic and molecular properties of elements 112, 114, and 118 and predicted that the 7p block elements (elements 113-118) would exhibit a much different chemistry than their 6p analogues which was principally due to the dramatic spin-orbit effects found in the 7p subshell.14 In addition, our previous studies on the Uuq (Z ) 114) found that, because of * To whom correspondence should be addressed. E-mail: dongcz@ nwnu.edu.cn.

the strong relativistic effect, there were high ionization potentials and excitation energies for Uuq, which lead to its stronger inert chemical properties in the group IVA.15 Chemical investigations for Uus are extremely difficult because of its very short lifetimes (only 14 and 78 ms halflives for 293Uus and 294Uus, respectively) and yields of a few atoms,4 theoretical calculations therefore can provide useful information for such experiments and may be the only way to investigate a particular aspect of its chemistry. The main purpose of the present work was to obtain the ionization potentials (IPs), electron affinity (EA), resonance excitation energies (EEs), and ionic radii (IR) of Uus, which were accurate enough to be used to predict some chemical properties of Uus. Such predictions are usually based on the theory of the Born-Haber cycle.16,17 The prediction involves the ionization potentials or electron affinities, enthalpies, and entropies of sublimation, formation, and solution. The enthalpies of formation and solution depend on the ionic radii. The IPs are also useful for the prediction of the volatility of SHE on the inert and metal surface.12 The EEs can be used to estimate the sublimation enthalpies for SHE18,19 and are also helpful in the atomic spectra measurement.20 To our knowledge, only a small number of calculations for atomic properties of Uus have been published so far. A. V. Mitin and C. V. Wu¨llen calculated the first IP and EA of Uus as well as its homologous elements Br, I, and At through two-component relativistic density-functional calculations.21 W. J. Liu and D. L. Peng calculated the first five IPs and EA of Uus using infiniteorder quasirelativistic density-functional method.22 C. Thierfelder and co-workers calculated the EA of Uus using the Hartree-Fock (HF) method and coupled-cluster method with single and double excitations (CCSD).23 At is the existing heaviest homologue of Uus and no available experiment data for its IPs, EA and IR owning to its short halflife.24 The reported theoretical values of EA for At range from 2.30 to 2.91 eV21,25–27 and the IPs for At have not been systematically studied. In the present work, the multiconfiguration Dirac-Fock (MCDF) method was adopted to calculate the IPs, EAs, EEs, and IR of Uus and At. To reduce the uncertainties resulting from incomplete inclusion of electron correlations, the same quantities of the homologue elements Cl, Br, and I were also obtained with the same computational

10.1021/jp107411s  2010 American Chemical Society Published on Web 12/08/2010

Element Uus (Z ) 117) and Astatine

J. Phys. Chem. A, Vol. 114, No. 51, 2010 13389

method. The size of these uncertainties of IPs, EAs, and IR for Uus and At were reduced by using a widely used extrapolation procedure, which is based on the periodic law of the chemical elements. This procedure has been successfully used in the previous calculations for the SHE 104,28 105,29 106,30 107,31 108,31 112,32 and 114.15 The present results were in good agreement with other available theoretical data and were helpful for further understanding of the physical and chemical behavior of Uus and At. Theoretical Method The MCDF method has been described in detail by Grant,33 so only a brief synopsis was presented here. The wave function of an atomic system can be expanded as a linear combination of CSFs nc

|ΨR(PJM)〉 )

∑ cr(R)|γrPJM〉

(1)

r)1

where J and P are the total angular momentum and parity of the system, respectively, M is the z component of the total angular momentum, and cr(R) is the mixing coefficient. A CSF is constructed from a product of single electron wave functions through a proper coupling of the angular momenta of the individual subshells and the antisymmetrization of the basis states. The MCDF self-consistent iteration method is used to obtain simultaneously the mixing coefficients and radial orbitals. Based on these orbitals, the relativistic configuration interaction (RCI) calculation is performed to include the Breit interaction and QED effects. Here the orbitals are fixed but the mixing coefficients were recalculated by diagonalizing the modified Hamiltonian. According to the time-dependent perturbation theory, once the initial and final state wave functions have been calculated, the Einstein spontaneous transition probability for the electric dipole transition can be given by34

AβR )

2π 2jβ + 1

∑ ∑ |〈R(PRJRMR)|O(1)|β(PβJβMβ〉|2 Mβ MR

(2) where O(1) is the electric dipole operator, jβ is the total angular momentum of the final state β, and |R(PRJRMR)〉 and |β(PβJβMβ)〉 are the wave functions of the initial atomic state R and final state β, respectively. Then the absorption oscillator strengths can be obtained from34

fβR )

2jβ + 1 (2jR + 1)2Rω2

AβR

(3)

where jR is the total angular momentum of the initial state R and ω is frequency of the photon absorbed by an atom from the initial state R to the final state β. The GRASP2K package,35 a modified and extended version of GRASP92,36 was used to calculate the wave functions of the atomic and ionic systems and the transition matrix elements. Computational Details We perform calculations for Cl, Br, and I to help gauge the accuracy of the calculations for Uus and At and as a means to

reduce the ab initio errors of these elements through extrapolation. First of all, the test calculations of IPs and EA for Cl were performed to investigate the optimizing schemes for the orbitals and the various correlations that were described by including corresponding CSFs. In our calculations, the atomic or ionic system was modeled as a core plus valence subshells. The {ns,np} orbitals were treated as valence subshells (n ) 3, 4, 5, 6, and 7 for Cl, Br, I, At, and Uus, respectively) and the rest as core. From the test calculations, it was found that the inclusion of the effects of core-valence (CV) correlation and core (CC) correlation required large scale configuration interaction (CI) calculations and these effects only contributed to the IPs and EA for about 0.3 eV. With the aim of providing reliable data to predict some chemical properties of Uus and At, the large scale calculations need much more time and are not necessary. Therefore, the CV and CC correlation effects were neglected and only valence (VV) correlation were included. All the neglected effects were compensated by using an extrapolation procedure described below. By increasing the maximum orbital angular momentum up to h, it was noticed that f and g orbitals were very important for the IPs and EAs. For the calculations of IPs and EAs, the CSFs from single and double excitation of the valence {ns,np} subshells into {ns,np,nd; (n + 1)s,(n + 1)p,(n + 1)d,(n + 1)f; (n + 2)s,(n + 2)p,(n + 2)d,(n + 2)f,(n + 2)g; (n + 3)s,(n + 3)p,(n + 3)d,(n + 3)f} were included to take into account the VV correlation. First, the self-consistent-field (SCF) calculations were performed for the ground states of atoms or ions under consideration in the extended optimal level (EOL) scheme. All the occupied orbitals were generated as spectroscopic orbitals and the others were treated as correlation orbitals. With a set of fixed orbitals, the correction of the Breit interaction with the low frequency approximation and the QED effects including the vacuum polarization (VP) and self-energy correction (SE) were estimated in the following RCI calculations. The SE part was estimated by using a “ratio method.37 It was found that neither had a large effect. For example, the contributions of QED effects only amount to 0.2-0.8% and the Breit corrections amount to 0.1-0.4% for the IPs and EA of E117. Comparing the calculated results and available experimental data (Table 1, Table 2), one can find that the discrepancies range from 0.162 to 1.240 eV. These uncertainties mainly come from the neglect of the CV and CC correlation. They were reduced by using an extrapolation procedure. This extrapolation procedure used is based on ideas from the finite difference method in numerical analysis38 and is described in application to elements 10428 and 105.29 There are two qualities in this procedure: the quantity R is equal to experimental IP (or EA) minus the MCDF IP (or EA); the quantity β is equal to R(m) - R(m - 1), where m is the principal quantum number and is equal to n - 1. The extrapolation procedure was based on two assumptions: (1) R is a quadratic function of the m, which implies that β(m) - β(m + 1) is the same for m equals 3, 4, or 5; (2) the ratio of β(m) of another charge stage is equal to the ratio of corresponding values of β(m) - β(m + 1). The uncertainty is assumed to be equal to one-half of the absolute value of β(m) plus one-half of the absolute value of β(m) - β(m + 1) for m equals 4 or 5. The differences between experimental and calculated IP or EA are relatively large because they contain the systematic error from two different atomic entities. In contrast, when one performs the excitation state calculation in the same atom or ion, the systematic error can be largely removed. Therefore, to control the number of CSFs which grows very fast with the size of the active set, a smaller active set was used to calculate

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Chang et al.

TABLE 1: Calculated the First Five Ionization Potentials (in eV) for At and Uus change in state 0+ f 1+

1+ f 2+

2+ f 3+

3+ f 4+

4+ f 5+

a

element 2

5

2

4

MCDF

expt.

R

β

extrapolated

other theory

a

0.289 0.291 0.299 (0.314)

0.002 0.008 (0.015)

9.35 ( 0.01

(0.336)

(0.022)

7.64 ( 0.01

9.24b 9.40c 7.57b 7.60d

0.039 0.042 (0.045) (0.048)

17.88 ( 0.02 15.33 ( 0.02

15.24d

(0.057) (0.007)

26.58 ( 0.05 22.74 ( 0.08

22.79d

39.65 41.91

42.06d

50.39 52.93

53.41d

Cl Br I At

[3s 4p ]3/2 f [3s 3p ]2 [4s24p5]3/2 f [4s24p4]2 [5s25p5]3/2 f [5s25p4]2 [6s26p5]3/2 f [6s26p4]2

12.679 11.523 10.152 9.040

Uus

[7s27p5]3/2 f [7s27p4]2

7.310

Cl+ Br+ I+ At+ Uus+ Cl2+ Br2+ I2+ At2+ Uus2+ Cl3+ Br3+ I3+ At3+ Uus3+ Cl4+ Br4+ I4+ At4+ Uus4+

[3s23p4]2 f [3s23p3]3/2 [4s24p4]2 f [4s24p3]3/2 [5s25p4]2 f [5s25p3]3/2 [6s26p4]2 f [6s26p3]3/2 [7s27p4]2 f [7s27p3]3/2 [3s23p3]2/2 f [3s23p2]0 [4s24p3]3/2 f [4s24p2]0 [5s25p3]3/2 f [5s25p2]0 [6s26p3]3/2 f [6s26p2]0 [7s27p3]3/2 f [7s27p2]0 [3s23p2]0 f [3s23p]1/2 [4s24p2]0 f [4s24p]1/2 [5s25p2]0 f [5s25p]1/2 [6s26p2]0 f [6s26p]1/2 [7s27p2]0 f [7s27p]1/2 [3s23p]1/2 f [3s2]0 [4s24p]1/2 f [4s2]0 [5s25p]1/2 f [5s2]0 [6s26p]1/2 f [6s2]0 [7s27p]1/2 f [7s2]0

23.537 21.275 18.773 17.473 14.877 39.445 34.660 29.288 26.247 22.407 53.042 46.729 40.189 39.334 41.591 67.608 59.377 50.976 50.071 52.614

12.968 11.814a 10.451a

23.814a 21.591a 19.131a

0.277 0.316 0.358 (0.403) (0.451) 0.165 1.240 0.272 (0.329) (0.335) 0.424 1.041 0.162 (0.316) (0.320) 0.192 0.225

39.61e 36e 29.56 ( 0.02f 53.465e 47.77 ( 0.03g 40.35 ( 0.02h 67.80e 59.60 ( 0.02i

(0.316) (0.320)

Ref 44. b Ref 21. c Ref 26. d Ref 22. e Ref 43. f Ref 46. g Ref 47. h Ref 48. i Ref 49.

TABLE 2: Calculated Electron Affinities (in eV) for At and Uus change in state 0+ f 1-

a

element

MCDF

expt.a

R

β

extrapolated

other theory

3.617 3.365 3.059

0.322 0.300 0.265 (0.217)

-0.019 -0.035 (-0.048)

2.38 ( 0.02

(0.156)

(-0.061)

1.45 ( 0.03

2.30b 2.8(2)a 2.91c 2.90d 1.47b 1.59e 1.37f

Cl Br I At

[4s24p5]3/2 f [4s24p6]0 [4s24p5]3/2 f [4s24p6]0 [5s25p5]3/2 f [5s25p6]0 [6s26p5]3/2 f [6s26p6]0

3.295 3.065 2.794 2.158

Uus

[7s27p5]3/2 f [7s27p6]0

1.281

Ref 25. b Ref 21. c Ref 26. d Ref 27. e Ref 22. f Ref 23.

the resonance excitation energies and absorption oscillator strengths: the CSFs from single and double excitation of the valence {ns,np} subshells into {ns,np,nd; (n + 1)s,(n + 1)p,(n + 1)d,(n + 1)f; (n + 2)s,(n + 2)p,(n + 2)d,(n + 2)f,(n + 2)g} were included. The Breit and QED corrections were also estimated. It was noticed that these two effects tend to cancel each other, which is similar to the calculations of the resonance transition energies for Lu and Lr.39 Therefore, these effects were neglected in the calculations of EEs. As can be seen in Table 3, the differences between experimental and MCDF calculated results are of the order 0.004-0.143 eV. Ionization Potentials and Electron Affinities. MCDF calculations were performed for the ground states of the Cl, Br, I, At, and Uus atoms as well as their cations and anions. The total energies obtained were thus used to calculate the first five IPs and EAs for these atoms. The calculated results and other theoretical data were presented in Tables 1 and 2, along with the available experimental values. For the first two IPs and EAs, the calculated results are about 0.3 eV lower than the experimental values. Based on the first assumption of the extrapolation procedure, we obtained the first two IPs and EAs for Uus and At, which were consistent with other theoretical

results. However, the discrepancies between the calculated and the experimental values for the third and fourth IPs of Br are relatively large (1.240 and 1.041 eV, respectively). The unexpected large discrepancies may come from the experimental errors and thus prevent us obtaining accurate results. Based on the second assumption of the extrapolation procedure, we obtained the third IPs of Uus and At from these values of Cl and I. The uncertainties of first three IPs and EAs of Uus and At are of the order of 0.01-0.08 eV. Our extrapolated results are in good agreement with available theoretical data. The extrapolation procedure sensitively depends on the qualities R of the lighter homologues. For the fourth IP of Uus and At, the R of Cl3+ (0.424 eV) is relatively too larger than that of I3+ (0.162 eV), which makes the extrapolation unreliable. Also, due to lack of the experimental value of the fifth IP of I, we can not obtained these data of Uus and At from extrapolation. Actually, because of the approximately same uncertainties from atomic core, one can find that the qualities R for Uus or At are virtually identical (about 0.3 eV) in different ionized stages. On the basis of this, we assumed that the R of the fourth and fifth IPs for Uus and At are the average of these qualities of their other charge states. The obtained fourth IP of Uus is close to the DFT

Element Uus (Z ) 117) and Astatine

J. Phys. Chem. A, Vol. 114, No. 51, 2010 13391

TABLE 3: Calculated Resonance Excitation Energies (in eV) and Oscillator Strengths for Cl, Br, I, and At and 117 (L, Length Gauge; V, Velocity Gauge) transition energies element Cl

Br

I

At

117

a

transitions 2

2 2 3p3/2 4s1/2]5/2 [3s 3p1/2 2 3 [3s 3p1/23p3/24s1/2]5/2 2 2 [3s23p1/2 3p3/2 4s1/2]3/2 3 [3s23p1/23p3/2 4s1/2]3/2 3 [3s23p1/23p3/2 4s1/2]3/2 2 2 [3s23p1/2 3p3/2 4s1/2]1/2 3 [3s23p1/23p3/2 4s1/2]1/2 2 2 [3s23p1/2 3p3/2 4s1/2]1/2 3 [3s23p1/23p3/2 4s1/2]1/2 2 2 [3s23p1/2 3p3/2 4s1/2]3/2 3 [3s23p1/23p3/2 4s1/2]3/2 3 [3s23p1/23p3/2 4s1/2]3/2 2 2 [4s24p1/2 4p3/2 5s1/2]5/2 3 [4s24p1/24p3/2 5s1/2]5/2 2 2 [4s24p1/2 4p3/2 5s1/2]3/2 3 [4s24p1/24p3/2 5s1/2]3/2 3 [4s24p1/24p3/2 5s1/2]3/2 2 2 [4s24p1/2 4p3/2 5s1/2]1/2 3 [4s24p1/24p3/2 5s1/2]1/2 2 2 [4s24p1/2 4p3/2 5s1/2]1/2 3 [4s24p1/24p3/2 5s1/2]1/2 2 2 [4s24p1/2 4p3/2 5s1/2]3/2 3 [4s24p1/24p3/2 5s1/2]3/2 3 [4s24p1/24p3/2 5s1/2]3/2 2 2 [5s25p1/2 5p3/2 6s1/2]5/2 3 [5s25p1/25p3/2 6s1/2]5/2 2 2 [5s25p1/2 5p3/2 6s1/2]3/2 3 [5s25p1/25p3/2 6s1/2]3/2 3 [5s25p1/25p3/2 6s1/2]3/2 2 2 [5s25p1/2 5p3/2 6s1/2]1/2 3 [5s25p1/25p3/2 6s1/2]1/2 2 2 [5s25p1/2 5p3/2 6s1/2]1/2 3 [5s25p1/25p3/2 6s1/2]1/2 2 2 [5s25p1/2 5p3/2 6s1/2]3/2 3 [5s25p1/25p3/2 6s1/2]3/2 3 [5s25p1/25p3/2 6s1/2]3/2 2 2 [6s26p1/2 6p3/2 7s1/2]5/2 3 [6s26p1/26p3/2 7s1/2]5/2 2 2 [6s26p1/2 6p3/2 7s1/2]3/2 3 [6s26p1/26p3/2 7s1/2]3/2 3 [6s26p1/26p3/2 7s1/2]3/2 2 2 [6s26p1/2 6p3/2 7s1/2]1/2 3 [6s26p1/26p3/2 7s1/2]1/2 2 2 [6s26p1/2 6p3/2 7s1/2]1/2 3 [6s26p1/26p3/2 7s1/2]1/2 2 2 [6s26p1/2 6p3/2 7s1/2]3/2 3 [6s26p1/26p3/2 7s1/2]3/2 3 [6s26p1/26p3/2 7s1/2]3/2 2 2 [7s27p1/2 7p3/2 8s1/2]5/2 3 [7s27p1/27p3/2 8s1/2]5/2 2 2 [7s27p1/2 7p3/2 8s1/2]3/2 3 [7s27p1/27p3/2 8s1/2]3/2 3 [7s27p1/27p3/2 8s1/2]3/2 2 2 [7s27p1/2 7p3/2 8s1/2]1/2 3 [7s27p1/27p3/2 8s1/2]1/2 2 2 [7s27p1/2 7p3/2 8s1/2]1/2 3 [7s27p1/27p3/2 8s1/2]1/2 2 2 [7s27p1/2 7p3/2 8s1/2]3/2 3 [7s27p1/27p3/2 8s1/2]3/2 3 [7s27p1/27p3/2 8s1/2]3/2

f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f

expt.a,b

MCDF 2

2 3 [3s 3p1/2 3p3/2 ]3/2 2 2 3 [3s 3p1/23p3/2]3/2 2 3 [3s23p1/2 3p3/2 ]3/2 2 3 [3s23p1/2 3p3/2 ]3/2 2 3 [3s23p1/2 3p3/2 ]3/2 2 3 [3s23p1/2 3p3/2 ]3/2 2 3 [3s23p1/2 3p3/2 ]3/2 2 3 [3s23p1/2 3p3/2 ]1/2 2 3 [3s23p1/2 3p3/2 ]1/2 2 3 [3s23p1/2 3p3/2 ]1/2 2 3 [3s23p1/2 3p3/2 ]1/2 2 3 [3s23p1/2 3p3/2 ]1/2 2 3 [4s24p1/2 4p3/2 ]3/2 2 3 [4s24p1/2 4p3/2 ]3/2 2 3 [4s24p1/2 4p3/2 ]3/2 2 3 [4s24p1/2 4p3/2 ]3/2 2 3 [4s24p1/2 4p3/2 ]3/2 2 3 [4s24p1/2 4p3/2 ]3/2 3 2 [4s24p1/2 4p3/2 ]3/2 2 3 4p3/2 ]1/2 [4s24p1/2 2 3 [4s24p1/2 4p3/2 ]1/2 2 3 [4s24p1/2 4p3/2 ]1/2 2 3 [4s24p1/2 4p3/2 ]1/2 2 3 [4s24p1/2 4p3/2 ]1/2 2 3 [5s25p1/2 5p3/2 ]3/2 2 3 [5s25p1/2 5p3/2 ]3/2 2 3 [5s25p1/2 5p3/2 ]3/2 2 3 [5s25p1/2 5p3/2 ]3/2 2 3 [5s25p1/2 5p3/2 ]3/2 2 3 [5s25p1/2 5p3/2 ]3/2 2 3 [5s25p1/2 5p3/2 ]3/2 2 3 [5s25p1/2 5p3/2 ]1/2 2 3 [5s25p1/2 5p3/2 ]1/2 2 3 [5s25p1/2 5p3/2 ]1/2 2 3 [5s25p1/2 5p3/2 ]1/2 2 3 [5s25p1/2 5p3/2 ]1/2 2 3 [6s26p1/2 6p3/2 ]3/2 2 3 [6s26p1/2 6p3/2 ]3/2 2 3 [6s26p1/2 6p3/2 ]3/2 2 3 [6s26p1/2 6p3/2 ]3/2 3 2 [6s26p1/2 6p3/2 ]3/2 2 3 6p3/2 ]3/2 [6s26p1/2 2 3 [6s26p1/2 6p3/2 ]3/2 2 3 [6s26p1/2 6p3/2 ]1/2 2 3 [6s26p1/2 6p3/2 ]1/2 2 3 [6s26p1/2 6p3/2 ]1/2 2 3 [6s26p1/2 6p3/2 ]1/2 2 3 [6s26p1/2 6p3/2 ]1/2 2 3 [7s27p1/2 7p3/2 ]3/2 2 3 [7s27p1/2 7p3/2 ]3/2 2 3 [7s27p1/2 7p3/2 ]3/2 2 3 [7s27p1/2 7p3/2 ]3/2 2 3 [7s27p1/2 7p3/2 ]3/2 2 3 [7s27p1/2 7p3/2 ]3/2 2 3 [7s27p1/2 7p3/2 ]3/2 2 3 [7s27p1/2 7p3/2 ]1/2 2 3 [7s27p1/2 7p3/2 ]1/2 2 3 [7s27p1/2 7p3/2 ]1/2 2 3 [7s27p1/2 7p3/2 ]1/2 2 3 [7s27p1/2 7p3/2 ]1/2

8.779 10.363 8.855 9.067 10.366 8.892 9.155 8.782 9.045 8.745 8.957 10.256 7.750 9.363 7.930 8.210 9.370 8.185 8.415 7.737 7.965 7.480 7.759 8.920 6.651 8.431 6.840 7.548 8.461 7.479 7.720 6.559 6.800 5.919 6.628 7.540 5.519 8.934 5.650 8.280 8.836 8.448 8.894 5.616 6.151 2.818 5.447 6.017 3.238 7.646 6.442 8.250 8.618 7.655 7.738 -1.309 -4.750 -1.344 4.641 8.321

oscillator strengths L

∆

8.922 10.430 8.988 9.203 10.430 8.920 9.173 8.920 9.173 8.878 9.094 10.320 7.865 9.409 8.048 8.330 9.412 8.293 8.551 7.836 8.094 7.591 7.873 8.955 6.774 8.504 6.955 7.665 8.499 7.550 7.834 6.608 6.892 6.012 6.722 7.556 5.523

0.143 0.067 0.133 0.136 0.064 0.028 0.018 0.138 0.128 0.133 0.137 0.064 0.115 0.046 0.118 0.120 0.042 0.108 0.136 0.099 0.129 0.111 0.114 0.035 0.123 0.073 0.115 0.117 0.038 0.071 0.114 0.049 0.092 0.093 0.094 0.016 0.004

5.732

0.082

3.95 3.49 1.30 5.09 2.60 2.01 1.10 2.26 2.02 1.64 0.92 2.02 0.96 3.81 3.34 2.82 7.19 3.85 1.42 1.72 1.94 2.96 4.18 2.72 4.27 3.95 5.57 1.67 0.73 2.98 1.83 3.99 2.11 2.18 2.41 3.51 1.73 1.38 8.25 1.50 0.97 0.85 0.43 2.49 7.87 3.49 1.58 1.02 2.56 3.38 2.02 1.32 1.25 9.76 6.60

× × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × ×

V -4

10 10-1 10-2 10-1 10-2 10-4 10-1 10-3 10-1 10-3 10-1 10-1 10-2 10-1 10-1 10-1 10-3 10-4 10-1 10-2 10-1 10-2 10-2 10-1 10-2 10-1 10-1 10-1 10-3 10-2 10-1 10-3 10-1 10-2 10-2 10-1 10-1 10-2 10-1 10-1 10-2 10-1 10-4 10-1 10-3 10-3 10-2 10-1 10-1 10-3 10-1 10-1 10-5 10-3 10-4

0.33 × 10-3 1.52 × 10-3

5.99 3.62 1.69 6.49 2.78 2.12 1.32 1.58 2.53 2.04 1.10 2.05 1.04 3.77 3.82 3.17 6.31 6.83 1.55 1.57 2.30 3.55 4.77 2.68 4.39 3.90 6.20 1.82 1.54 2.53 1.91 1.89 2.43 2.82 2.70 3.47 1.97 0.68 9.21 1.56 1.85 1.02 1.01 2.78 7.35 9.39 1.82 1.08 2.80 4.74 2.27 0.92 2.12 8.34 3.81

× × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × ×

10-4 10-1 10-2 10-1 10-2 10-4 10-1 10-3 10-1 10-3 10-1 10-1 10-2 10-1 10-1 10-1 10-3 10-4 10-1 10-2 10-1 10-2 10-2 10-1 10-2 10-1 10-1 10-1 10-3 10-2 10-1 10-3 10-1 10-2 10-2 10-1 10-1 10-2 10-1 10-1 10-2 10-1 10-4 10-1 10-3 10-3 10-2 10-1 10-1 10-3 10-1 10-1 10-5 10-3 10-4

3.96 × 10-3 1.33 × 10-3

Ref 44. b Ref 45; ∆ is the experimental value minus the calculated result.

results. However, the fifth IP of Uus is about 0.5 eV lower than the DFT results which has to be further confirmed. The strength of the chemical bond depends on the energies of atomic valence shells and their spatial distribution. Figure 1 shows the orbital energies of (n - 1)d, ns and np for Cl, Br, I,

At, and Uus. One can find that because of the relativistic effects, from I to Uus, the contraction of the ns orbitals and the spin-orbit splitting of (n - 1)d, np orbitals become so strong with the increasing atomic number. Due to such huge spin-orbit splitting of 7p, it was predicted that the oxidation state of 3+

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Chang et al.

Figure 1. Orbital energies diagram for the ground state of Cl, Br, I, At, and Uus.

would be especially important for Uus.10 As illustrated in Figure 2a, the first IPs of group 17 elements decrease in the order of F > Cl > Br > I > At > Uus, reflecting the expansion of the np3/2 orbitals. Apart from F, the EAs also show the same trend (Figure 2b). In contrast, as can be seen in Figure 2c, the fourth IP of Uus is higher than those of I and At, indicating the relativistic stabilization of the 7p1/2. These facts reveal the

increased reactivities in the charge states 1-, 0, 1+, 2+ and chemically inert in the charge states 3+, 4+, and 5+ for Uus. Resonance Excitation Energies and Oscillator Strengths. The calculated resonance excitation energies and absorption oscillator strengths for the atoms of Cl, Br, I, At, and Uus were presented in Table 3. Available experimental values were also shown and compared with the present results. The MCDF calculated excitation energies agree well with the experimental data with deviations ranging from 0.004 to 0.143 eV. The oscillator strengths computed by length and velocity gauges are also reasonably consistent with each other which further confirms that the present calculations are reliable. Meanwhile, from Table 2 2 7p3/2 8s1/2]1/2 f 3, one can find that the transitions [7s27p1/2 2 2 2 2 3 3 2 3 ]1/2 and [7s 7p1/27p3/2]1/2, [7s 7p1/27p3/28s1/2]1/2 f [7s 7p1/27p3/2 2 2 2 3 7p3/2 8s1/2]3/2 f [7s27p1/2 7p3/2 ]1/2 become impossible for [7s27p1/2 element Uus. These facts obviously reflect the strong contraction of the 8s1/2 orbital and the expansion of the 7p3/2 orbital. In addition, the strong line corresponding to the transition 2 2 2 3 7p3/2 8s1/2]5/2 f [7s27p1/2 7p3/2 ]3/2 at 3.238 eV just lies in [7s27p1/2 the prime energy region, which is suitable for observing lowlying level structure for superheavy atoms using the resonance ionization spectroscopy (RIS) technique.40 Radii. The atomic radius41 (AR) or Pauling-Type IR42 of an element is a fundamental property from which some other properties can be found such as hydration enthalpies and distribution coefficients in solvent extraction experiments. Slater

Figure 2. (a) First IP, (b) EA, and (c) fourth IP of group 17 elements. The first and fourth IPs and EA for F through I are experimental values (filled symbols),25,44,43 for At and Uus are our calculations (open symbols).

TABLE 4: Maxima Orbital Radii Rmax (in nm) for Cl, Br, I, At, and Uus in the Charge States 1- to 5+ elements

1- (np3/2)

0 (np3/2)

1+ (np3/2)

2+ (np3/2)

3+ (np1/2)

4+ (np1/2)

5+ (ns1/2)

Cl Br I At Uus

0.115 0.134 0.148 0.163 0.199

0.104 0.121 0.141 0.156 0.180

0.099 0.110 0.134 0.144 0.163

0.094 0.110 0.127 0.138 0.156

0.089 0.104 0.121 0.121 0.115

0.085 0.099 0.115 0.115 0.115

0.077 0.077 0.099 0.104 0.099

Element Uus (Z ) 117) and Astatine

J. Phys. Chem. A, Vol. 114, No. 51, 2010 13393

TABLE 5: Calculated Atomic Radii and Ionic Radii in the 1- Charge State (in nm) for At and Uus element

Rmax

R

expt.

Cl Br I At Uus

0.104 0.102a 0.121 0.120a 0.141 0.140a 0.156 0.180

-0.002 -0.001 -0.001 (-0.002) (-0.004)

ClBrIAtUus-

0.115 0.181d 0.134 0.196d 0.148 0.220d 0.163 0.199

0.066 0.062 0.072 (0.096) (0.134)

a

β

extrapolated

other theory

0.001 0.000 (-0.001) 0.154 ( 0.001 0.153b (-0.002) 0.176 ( 0.001 0.177b 0.176c -0.004 0.01 (0.024) (0.038)

0.259 ( 0.009 0.333 ( 0.012

Ref 50. b Ref 21. c Ref 22. d Ref 51.

had found a direct correlation between the value of the maximum charge density of the outmost valence shell, Rmax, and the AR or IR.41 As discussed by Slater, the AR approximately equals to the corresponding Rmax and the IR is larger or smaller than the Rmax due to the different definitions. In Table 4, we displayed the values of Rmax for atoms of Cl, Br, I, At, and Uus as well as their anions and cations. The experimental values of AR and IR of 1- charge state are available for Cl, Br, and I. With the same strategy used in the calculations of IPs and EAs, the AR and IR of 1- charge state of Uus and At were obtained by extrapolation. The extrapolation procedure used is illustrated in Table 5. The value of R is equal to the difference between the corresponding values of the AR or IR and Rmax(np3/2). The value of β is equal to R(m) - R(m - 1). It gives AR(At) ) 0.154 ( 0.001 nm, AR(Uus) ) 0.176 ( 0.001 nm, and IR(At-) ) 0.259 ( 0.009 nm, IR(Uus-) ) 0.333 ( 0.013 nm. Conclusion In this paper, we present the first five ionization potentials, electron affinities, resonance excitation energies, oscillator strengths, and radii for element Uus and its homologue element At. Main valence correlation effects were taken into account and the Breit interaction and QED effects were estimated. The uncertainties of calculated IPs, EAs, and IR for Uus and At resulting from incomplete inclusion of the correlation effects and all other effects were reduced through an extrapolation procedure. The present results are in good agreement with available experimental and other theoretical values and can be used for the predictions of some important physicochemical properties of element Uus and At and their compounds in comparison with the lighter homologues. Acknowledgment. We gratefully thank Professor V. Pershina and Professor S. Fritzsche for helpful advice. We also greatly appreciate the referee’s valuable suggestions on the estimation of self-energy correction. This work was supported by the National Nature Science Foundation of China (Grant No. 10774122, 10876028, 10847007, 10964010), the specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20070736001) and the Foundation of Northwest Normal University (NWNU-KJCXGC-03-21). References and Notes (1) Hofmann, S.; Mu¨nzenberg, G. ReV. Mod. Phys. 2000, 72, 733. (2) Oganessian, Y. T.; Utyonkov, V. K.; Lobanov, Y. V.; Abdullin, F. S.; Polyakov, A. N.; Sagaidak, R. N.; Shirokovsky, I. V.; Tsyganov, Y. S.; Voinov, A. A.; Gulbekian, G. G.; Bogomolov, S. L.; Gikal, B. N.;

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