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The ionization energy of the superheavy element Og (Z = 118) and its homolog elements Ar, Kr, Xe, Rn, and their ions are systematically calculated by using the GRASP2K program based on the multi-configuration Dirac-Hartree-Fock (MCDHF) method, taking into account relativistic effects, electron correlation effects between valence shell electrons, quantum electrodynamics effects, and Breit interaction. To reduce the uncertainty of the ionization energy derived from electron correlation effects which are not fully considered, the ionization potential of the superheavy element Og0–2+ and its homolog element Rn0–2+ are extrapolated by the extrapolation method. The ionization energy of extrapolated Rn0–5+ and Og5+ coincide well with experimental and other theoretical values. These results can be used to predict the unknown physical and chemical properties of the atoms and compounds of the superheavy element Og. In addition, the calculation results of the electron orbital binding energy of the atomic valence shell of the superheavy element Og and its homolog elements Ar, Kr, Xe, and Rn under relativistic and non-relativistic conditions show that owing to the relativistic effect, there occur strong orbital contraction phenomena in the 7s orbital and 7p1/2 orbital and strong splitting phenomena in the 7p1/2 orbital and 7p3/2 orbital of Og, which may cause the physical and chemical properties of the superheavy element Og to differ from those of other homologs.
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Keywords:
- multi-configuration Dirac-Hartree-Fock method /
- superheavy element /
- ionization potential /
- orbital binding energy
[1] Düllmann C E 2017 Nucl. Phys. News 27 14
Google Scholar
[2] Oganessian Y T, Sobiczewski A, Ter-Akopian G M 2017 Phys. Scr. 92 023003
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[3] Kailas S 2014 Pramana 82 619
Google Scholar
[4] Safronova M, Budker D, DeMille D, Kimball D F J, Derevianko A, Clark C W 2018 Rev. Mod. Phys. 90 025008
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[5] Schädel M 2015 Philos. Trans. R. Soc. London, Ser. A 373 20140191
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[6] Heßberger F P 2013 ChemPhysChem 14 483
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[7] Öhrström L, Reedijk J 2016 Pure Appl. Chem. 88 1225
Google Scholar
[8] 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, Mezentsev A N, Iliev S, Subbotin V G, Sukhov A M, Subotic K, Zagrebaev V I, Vostokin G K, Itkis M G, Moody K J, Patin J B, Shaughnessy D A, Stoyer M A, Stoyer N J, Wilk P A, Kenneally J M, Landrum J H, Wild J F, Lougheed R W 2006 Phys. Rev. C 74 044602
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[9] Pyykko P 2011 Phys. Chem. Chem. Phys. 13 161
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[10] Desclaux J P 1973 At. Data Nucl. Data Tables 12 311
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[11] Fricke B, Greiner W, Waber J T 1971 Theor. Chim. Acta 21 235
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[12] Guo Y, Pašteka L F, Eliav E, Borschevsky A 2021 Advances in Quantum Chemistry (Musial M, Hoggan P E Ed.) (New York: Academic Press) pp107–123
[13] Hangele T, Dolg M, Hanrath M, Cao X, Schwerdtfeger P 2012 J. Chem. Phys. 136 214105
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[14] Dzuba V A, Berengut J C, Harabati C, Flambaum V V 2017 Phys. Rev. A 95 012503
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[15] Sato T K, Asai M, Borschevsky A, Beerwerth R, Kaneya Y, Makii H, Mitsukai A, Nagame Y, Osa A, Toyoshima A, Tsukada K, Sakama M, Takeda S, Ooe K, Sato D, Shigekawa Y, Ichikawa S I, Düllmann C E, Grund J, Renisch D, Kratz J V, Schädel M, Eliav E, Kaldor U, Fritzsche S, Stora T 2018 J. Am. Chem. Soc. 140 14609
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Google Scholar
[17] Sewtz M, Backe H, Dretzke A, Kube G, Lauth W, Schwamb P, Eberhardt K, Gruning C, Thorle P, Trautmann N, Kunz P, Lassen J, Passler G, Dong C Z, Fritzsche S, Haire R G 2003 Phys. Rev. Lett. 90 163002
Google Scholar
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Google Scholar
Ding X L, Dong C Z 2004 Acta Phys. Sin. 53 3326
Google Scholar
[19] Goidenko I, Labzowsky L, Eliav E, Kaldor U, Pyykkö P 2003 Phys. Rev. A 67 020102
Google Scholar
[20] Lackenby B G C, Dzuba V A, Flambaum V V 2018 Phys. Rev. A 98 042512
Google Scholar
[21] Eliav E, Kaldo U, Ishikawa Y, Pyykkö P 1996 Phys. Rev. Lett. 77 5350
Google Scholar
[22] Pershina V, Borschevsky A, Eliav E, Kaldor U 2008 J. Chem. Phys. 129 144106
Google Scholar
[23] Jerabek P, Schuetrumpf B, Schwerdtfeger P, Nazarewicz W 2018 Phys. Rev. Lett. 120 053001
Google Scholar
[24] Razavi A K, Hosseini R K, Keating D A, Deshmukh P C, Manson S T 2020 J. Phys. B: At. Mol. Opt. Phys. 53 205203
Google Scholar
[25] Indelicato P, Santos J P, Boucard S, Desclaux J P 2007 Eur. Phys. J. D 45 155
Google Scholar
[26] Pershina V 2019 Radiochim. Acta 107 833
Google Scholar
[27] Johnson E, Fricke B, Keller O L, Nestor C W, Tucker T C 1990 J. Chem. Phys. 93 8041
Google Scholar
[28] Fricke B, Johnson E, Rivera G M 1993 Radiochim. Acta 62 17
Google Scholar
[29] Johnson E, Pershina V, Fricke B 1999 J. Phys. Chem. A 103 8458
Google Scholar
[30] Johnson E F B, Jacob T, Dong C Z, Fritzsche S, Pershina V 2002 J. Chem. Phys. 116 1862
Google Scholar
[31] Yu Y J, Li J G, Dong C Z, Ding X B, Fritzsche S, Fricke B 2007 Eur. Phys. J. D 44 51
Google Scholar
[32] Yu Y J, Dong C Z, Li J G, Fricke B 2008 J. Chem. Phys. 128 124316
Google Scholar
[33] Liu J S, Wang X, Sang K C 2020 J. Chem. Phys. 152 204303
Google Scholar
[34] Chang Z, Li J, Dong C 2010 J. Phys. Chem. A 114 13388
Google Scholar
[35] Zhang D, Zhang F, Ding X, Dong C 2021 Chin. Phys. B 30 043102
Google Scholar
[36] Ding X, Wu C, Zhang D, Zhang M, Dong C 2021 J. Quant. Spectrosc. Radiat. Transfer 259 107426
Google Scholar
[37] Ding X, Zhang F, Yang Y, Zhang L, Koike F, Murakami I, Kato D, Sakaue H A, Nakamura N, Dong C 2020 Phys. Rev. A 101 042509
Google Scholar
[38] Grant I P 2007 Relativistic Quantum Theory of Atoms and Molecules (New York: Springer)
[39] Grant I P, McKenzie B J, Norrington P H, Mayers D F, Pyper N C 1980 Comput. Phys. Commun. 21 207
Google Scholar
[40] Mackenzie B, Grant I, Norrington P 1980 Comput. Phys. Commun. 21 233
Google Scholar
[41] Dyall K, Grant I, Johnson C, Parpia F, Plummer E 1989 Comput. Phys. Commun. 55 425
Google Scholar
[42] Parpia F A, Fischer C F, Grant I P 1996 Comput. Phys. Commun. 94 249
Google Scholar
[43] Jönsson P, Gaigalas G, Bieroń J, Fischer C F, Grant I P 2013 Comput. Phys. Commun. 184 2197
Google Scholar
[44] Fischer C F, Gaigalas G, Jönsson P, Bieroń J 2019 Comput. Phys. Commun. 237 184
Google Scholar
[45] Borschevsky A, Pašteka L F, Pershina V, Eliav E, Kaldor U 2015 Phys. Rev. A 91 020501
Google Scholar
[46] Gaston N, Schwerdtfeger P, Nazarewicz W 2002 Phys. Rev. A 66 062505
Google Scholar
[47] Glushkov A V, Ambrosov S V, Loboda A, Chernyakova Y G, Khetselius O Y, Svinarenko A A 2004 Nucl. Phys. A 734 E21
Google Scholar
[48] Kramida A, Ralchenko Y, Reader J, NIST ASD Team 2021 NIST Atomic Spectra Database (version 5.9), [Online], Available: https://physics.nist.gov/asd
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图 1 超重元素Og和其同主族元素Ar, Kr, Xe和Rn的价壳层电子轨道束缚能
Figure 1. Valence shell orbital energies diagram for the ground state of Ar, Kr, Xe, Rn and Og.
表 1 超重元素Og0–6+基态电子组态、总角动量(J)、宇称(P), 在不同关联模型和活动空间下产生的组态波函数数目. 其中, DHF表示单组态Dirac-Hartree-Fock计算. nSD表示电子单、双激发到主量子数为n的活动空间形成的电子关联模型, {nalb}表示n = a, l = 0, 1, 2
$, \cdots ,$ b的活动空间轨道, 其中n为量子数, l 为轨道量子数Table 1. Electron configuration, total angular momentum, parity, and number of configuration wave functions of the superheavy element Og0–6+ in different correlation models and active Spaces. DHF represents the single-configuration Dirac-Hartree-Fock calculation. nSD represents an electron association model formed by the single and double excitation of electrons to the active space where the principal quantum number is n. {nalb} represents the active space orbital of n = a, l = 0, 1, 2
$ , \cdots , $ b, where$ n $ is the principal quantum number and$ l $ is the orbital quantum number.电子组态 关联模型 活动空间 组态波函数数目 Og (J = 0+) [Rn]5f146d107s27p6 DHF {n 7l 1} 1 7SD {n 7l 2} 14 8SD 7SD + {n 8l 3} 143 9SD 8SD + {n 9l 4} 468 10SD 9SD + {n 10l 4} 987 11SD 10SD + {n 11l 4} 1700 12SD 11SD + {n 12l 4} 2607 Og1+ (J = 3/2–) [Rn]5f146d107s27p5 DHF {n 7l 1} 1 7SD {n 7l 2} 51 8SD 7SD + {n 8l 3} 758 9SD 8SD + {n 9l 4} 2738 10SD 9SD + {n 10l 4} 5982 11SD 10SD + {n 11l 4} 10490 12SD 11SD + {n 12l 4} 16262 Og2+ (J = 2+) [Rn]5f146d107s27p4 DHF {n 7l 1} 2 7SD {n 7l 2} 76 8SD 7SD + {n 8l 3} 1054 9SD 8SD + {n 9l 4} 3841 10SD 9SD + {n 10l 4} 8404 11SD 10SD + {n 11l 4} 14743 12SD 11SD + {n 12l 4} 22858 Og3+ (J = 3/2–) [Rn]5f146d107s27p3 DHF {n 7l 1} 3 7SD {n 7l 2} 66 8SD 7SD + {n 8l 3} 802 9SD 8SD + {n 9l 4} 2816 10SD 9SD + {n 10l 4} 6094 11SD 10SD + {n 11l 4} 10636 12SD 11SD + {n 12l 4} 16442 Og4+ (J = 0+) [Rn]5f146d107s27p2 DHF {n 7l 1} 2 7SD {n 7l 2} 22 8SD 7SD + {n 8l 3} 163 9SD 8SD + {n 9l 4} 500 10SD 9SD + {n 10l 4} 1031 11SD 10SD + {n 11l 4} 1756 12SD 11SD + {n 12l 4} 2675 Og5+ (J = 1/2–) [Rn]5f146d107s27p1 DHF {n 7l 1} 1 7SD {n 7l 2} 13 8SD 7SD + {n 8l 3} 96 9SD 8SD + {n 9l 4} 293 10SD 9SD + {n 10l 4} 606 11SD 10SD + {n 11l 4} 1035 12SD 11SD + {n 12l 4} 1580 Og6+ (J = 0+) [Rn]5f146d107s2 DHF {n 7l 1} 1 7SD {n 7l 2} 5 8SD 7SD + {n 8l 3} 17 9SD 8SD + {n 9l 4} 38 10SD 9SD + {n 10l 4} 68 11SD 10SD + {n 11l 4} 107 12SD 11SD + {n 12l 4} 155 
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表 2 超重元素Og及其同主族元素Ar, Kr, Xe, Rn的电离能(IP1—IP6)的计算值、外推值、误差以及其他理论值. 单位: eV. *表示实验测量值. 所有数据均保留到小数点后两位
Table 2. Calculated ionization energy (IP1–IP6, in eV) of the superheavy element Og and its homolog elements Ar, Kr, Xe and Rn by MCDHF method. Extrapolated, error, and other theoretical result are also given. *: Represents experimental measurements. All data is retained to two decimal digits.
元素 MCDHF NIST[48] α β 外推值 误差 Others IP1 Ar 15.50 15.76* 0.26 Kr 13.74 14.00* 0.26 0.00 Xe 11.85 12.13* 0.28 0.02 Rn 10.48 10.75* (0.32) (0.04) 10.80 0.04 10.76[12] Og 8.53 (0.38) (0.06) 8.91 0.06 8.86[13]
8.87[20]
8.91[22]
8.84[23]
8.88[12]IP2 Ar 27.36 27.63* 0.27 Kr 24.06 24.36* 0.30 0.03 Xe 20.63 20.98* 0.35 0.05 Rn 18.65 21.40±1.90 (0.42) (0.07) 19.07 0.07 18.99[12] Og 15.80 (0.51) (0.09) 16.31 0.09 16.19[12] IP3 Ar 40.45 40.74*±0.01 0.29 Kr 35.49 35.84*±0.02 0.35 0.06 Xe 30.60 31.05*±0.04 0.45 0.10 Rn 28.21 29.40±1.00 (0.59) (0.14) 28.80 0.14 Og 24.28 (0.77) (0.18) 25.05 0.18 IP4 Ar 58.96 59.58±0.18 0.62 Kr 50.48 50.85*±0.11 0.37 Xe 42.11 42.20*±0.20 0.09 Rn 37.88 36.90±1.70 (0.44) 38.32 1.53 Og 32.70 (0.55) 33.25 0.99 IP5 Ar 74.60 74.84±0.17 0.24 Kr 64.08 64.69*±0.20 0.61 Xe 54.38 54.10*±0.50 –0.28 Rn 52.83 52.90±1.90 (0.44) 53.27 2.13 Og 55.37 (0.55) 55.92 2.24 IP6 Ar 91.13 91.29* 0.16 Kr 78.07 78.49*±0.20 0.42 Xe 66.16 66.70* 0.54 Rn 64.42 64.00±2.00 (0.44) 64.86 2.59 Og 67.04 (0.55) 67.59 2.70
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表 3 超重元素Og及其同主族元素Ar, Kr, Xe和Rn的价壳层轨道在相对论和非相对论下的轨道束缚能(单位: a.u.). R表示相对论、NR表示非相对论结果(n = 3, 4, 5, 6, 7分别对应元素Ar, Kr, Xe和Rn)
Table 3. Relativistic and non-relativistic orbital binding energies (in a.u.) of the valence shell orbitals of superheavy element Og and its homolog elements Ar, Kr, Xe and Rn. R for relativistic, NR for non-relativistic (n = 3, 4, 5, 6, 7 correspond to elements Ar, Kr, Xe, Rn and Og, respectively).
轨道 Ar Kr Xe Rn Og R NR R NR R NR R NR R NR $ {n\mathrm{s}}_{1/2} $ 1.29 1.28 1.19 1.15 1.01 0.94 1.07 0.87 1.30 0.77 $ {n\mathrm{p}}_{1/2} $ 0.60 0.59 0.54 0.52 0.49 0.46 0.54 0.43 0.74 0.39 $ {n\mathrm{p}}_{3/2} $ 0.59 0.59 0.51 0.52 0.44 0.46 0.38 0.43 0.31 0.39
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[1] Düllmann C E 2017 Nucl. Phys. News 27 14
Google Scholar
[2] Oganessian Y T, Sobiczewski A, Ter-Akopian G M 2017 Phys. Scr. 92 023003
Google Scholar
[3] Kailas S 2014 Pramana 82 619
Google Scholar
[4] Safronova M, Budker D, DeMille D, Kimball D F J, Derevianko A, Clark C W 2018 Rev. Mod. Phys. 90 025008
Google Scholar
[5] Schädel M 2015 Philos. Trans. R. Soc. London, Ser. A 373 20140191
Google Scholar
[6] Heßberger F P 2013 ChemPhysChem 14 483
Google Scholar
[7] Öhrström L, Reedijk J 2016 Pure Appl. Chem. 88 1225
Google Scholar
[8] 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, Mezentsev A N, Iliev S, Subbotin V G, Sukhov A M, Subotic K, Zagrebaev V I, Vostokin G K, Itkis M G, Moody K J, Patin J B, Shaughnessy D A, Stoyer M A, Stoyer N J, Wilk P A, Kenneally J M, Landrum J H, Wild J F, Lougheed R W 2006 Phys. Rev. C 74 044602
Google Scholar
[9] Pyykko P 2011 Phys. Chem. Chem. Phys. 13 161
Google Scholar
[10] Desclaux J P 1973 At. Data Nucl. Data Tables 12 311
Google Scholar
[11] Fricke B, Greiner W, Waber J T 1971 Theor. Chim. Acta 21 235
Google Scholar
[12] Guo Y, Pašteka L F, Eliav E, Borschevsky A 2021 Advances in Quantum Chemistry (Musial M, Hoggan P E Ed.) (New York: Academic Press) pp107–123
[13] Hangele T, Dolg M, Hanrath M, Cao X, Schwerdtfeger P 2012 J. Chem. Phys. 136 214105
Google Scholar
[14] Dzuba V A, Berengut J C, Harabati C, Flambaum V V 2017 Phys. Rev. A 95 012503
Google Scholar
[15] Sato T K, Asai M, Borschevsky A, Beerwerth R, Kaneya Y, Makii H, Mitsukai A, Nagame Y, Osa A, Toyoshima A, Tsukada K, Sakama M, Takeda S, Ooe K, Sato D, Shigekawa Y, Ichikawa S I, Düllmann C E, Grund J, Renisch D, Kratz J V, Schädel M, Eliav E, Kaldor U, Fritzsche S, Stora T 2018 J. Am. Chem. Soc. 140 14609
Google Scholar
[16] Ramanantoanina H, Borschevsky A, Block M, Laatiaoui M 2022 Atoms 10 48
Google Scholar
[17] Sewtz M, Backe H, Dretzke A, Kube G, Lauth W, Schwamb P, Eberhardt K, Gruning C, Thorle P, Trautmann N, Kunz P, Lassen J, Passler G, Dong C Z, Fritzsche S, Haire R G 2003 Phys. Rev. Lett. 90 163002
Google Scholar
[18] 丁晓彬, 董晨钟 2004 物理学报 53 3326
Google Scholar
Ding X L, Dong C Z 2004 Acta Phys. Sin. 53 3326
Google Scholar
[19] Goidenko I, Labzowsky L, Eliav E, Kaldor U, Pyykkö P 2003 Phys. Rev. A 67 020102
Google Scholar
[20] Lackenby B G C, Dzuba V A, Flambaum V V 2018 Phys. Rev. A 98 042512
Google Scholar
[21] Eliav E, Kaldo U, Ishikawa Y, Pyykkö P 1996 Phys. Rev. Lett. 77 5350
Google Scholar
[22] Pershina V, Borschevsky A, Eliav E, Kaldor U 2008 J. Chem. Phys. 129 144106
Google Scholar
[23] Jerabek P, Schuetrumpf B, Schwerdtfeger P, Nazarewicz W 2018 Phys. Rev. Lett. 120 053001
Google Scholar
[24] Razavi A K, Hosseini R K, Keating D A, Deshmukh P C, Manson S T 2020 J. Phys. B: At. Mol. Opt. Phys. 53 205203
Google Scholar
[25] Indelicato P, Santos J P, Boucard S, Desclaux J P 2007 Eur. Phys. J. D 45 155
Google Scholar
[26] Pershina V 2019 Radiochim. Acta 107 833
Google Scholar
[27] Johnson E, Fricke B, Keller O L, Nestor C W, Tucker T C 1990 J. Chem. Phys. 93 8041
Google Scholar
[28] Fricke B, Johnson E, Rivera G M 1993 Radiochim. Acta 62 17
Google Scholar
[29] Johnson E, Pershina V, Fricke B 1999 J. Phys. Chem. A 103 8458
Google Scholar
[30] Johnson E F B, Jacob T, Dong C Z, Fritzsche S, Pershina V 2002 J. Chem. Phys. 116 1862
Google Scholar
[31] Yu Y J, Li J G, Dong C Z, Ding X B, Fritzsche S, Fricke B 2007 Eur. Phys. J. D 44 51
Google Scholar
[32] Yu Y J, Dong C Z, Li J G, Fricke B 2008 J. Chem. Phys. 128 124316
Google Scholar
[33] Liu J S, Wang X, Sang K C 2020 J. Chem. Phys. 152 204303
Google Scholar
[34] Chang Z, Li J, Dong C 2010 J. Phys. Chem. A 114 13388
Google Scholar
[35] Zhang D, Zhang F, Ding X, Dong C 2021 Chin. Phys. B 30 043102
Google Scholar
[36] Ding X, Wu C, Zhang D, Zhang M, Dong C 2021 J. Quant. Spectrosc. Radiat. Transfer 259 107426
Google Scholar
[37] Ding X, Zhang F, Yang Y, Zhang L, Koike F, Murakami I, Kato D, Sakaue H A, Nakamura N, Dong C 2020 Phys. Rev. A 101 042509
Google Scholar
[38] Grant I P 2007 Relativistic Quantum Theory of Atoms and Molecules (New York: Springer)
[39] Grant I P, McKenzie B J, Norrington P H, Mayers D F, Pyper N C 1980 Comput. Phys. Commun. 21 207
Google Scholar
[40] Mackenzie B, Grant I, Norrington P 1980 Comput. Phys. Commun. 21 233
Google Scholar
[41] Dyall K, Grant I, Johnson C, Parpia F, Plummer E 1989 Comput. Phys. Commun. 55 425
Google Scholar
[42] Parpia F A, Fischer C F, Grant I P 1996 Comput. Phys. Commun. 94 249
Google Scholar
[43] Jönsson P, Gaigalas G, Bieroń J, Fischer C F, Grant I P 2013 Comput. Phys. Commun. 184 2197
Google Scholar
[44] Fischer C F, Gaigalas G, Jönsson P, Bieroń J 2019 Comput. Phys. Commun. 237 184
Google Scholar
[45] Borschevsky A, Pašteka L F, Pershina V, Eliav E, Kaldor U 2015 Phys. Rev. A 91 020501
Google Scholar
[46] Gaston N, Schwerdtfeger P, Nazarewicz W 2002 Phys. Rev. A 66 062505
Google Scholar
[47] Glushkov A V, Ambrosov S V, Loboda A, Chernyakova Y G, Khetselius O Y, Svinarenko A A 2004 Nucl. Phys. A 734 E21
Google Scholar
[48] Kramida A, Ralchenko Y, Reader J, NIST ASD Team 2021 NIST Atomic Spectra Database (version 5.9), [Online], Available: https://physics.nist.gov/asd
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