2018 Table of Polarizabilities Lit.: P. Schwerdtfeger, J. K. Nagle, “2018 Table of Static Dipole Polarizabilities of the Neutral Elements in the Periodic Table”, Mol. Phys. (2019): https://doi.org/10.1080/00268976.2018.1535143 Last update: November 27, 2018 1 18 1 2 H He 1 2 4.50(0) 13 14 15 16 17 1.38(0) 3 4 5 6 7 8 9 10 2 Li Be B C N O F Ne 164(0) 37.7(1) 20.5(1) 11.3(2) 7.4(2) 5.3(2) 3.74(8) 2.66(0) 11 12 13 14 15 16 17 18 3 Na Mg Al Si P S Cl Ar 163(1) 71.2(4) 3 4 5 6 7 8 9 10 11 12 57.8(1) 37.3(7) 25(1) 19.4(1) 14.6(2) 11.1(0) 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 4 K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr 290(1) 161(4) 97(10) 100(10) 87(10) 83(12) 68(9) 62(4) 55(4) 49(3) 47(1) 38.7(3) 50(3) 40(1) 30(1) 29(1) 21(1) 16.8(0) 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 5 Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe 320(1) 197(1) 162(12) 112(13) 98(8) 87(6) 79(10) 72(10) 66(10) 26.1(1) 55(8) 46(2) 65(4) 53(6) 43(2) 38(4) 32.9(1) 27.3(2) 55 56 71 72 73 74 74 76 77 78 79 80 81 82 83 84 85 86 6 Cs Ba Lu Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn 401(1) 272(10) 137(7) 103(6) 74(20) 68(15) 62(3) 57(3) 54(7) 48(4) 36(3) 33.9(4) 50(2) 47(3) 48(4) 44(4) 42(4) 35(2) 87 88 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 7 Fr Ra Lr Rf Db Sg Bh Hs Mt Ds Rg Cn Nh Fl Mc Lv Ts Og 318(2) 246(4) 320(20) 112(10) 42(4) 40(4) 38(4) 36(4) 34(3) 32(3) 32(6) 28(2) 29(2) 31(4) 71(20) ? 76(15) 58(6) 119 120 8 Uue Ubn 169(4) 159(10) 57 58 59 60 61 62 63 64 65 66 67 68 69 70 6 La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb 215(20) 205(20) 216(20) 208(20) 200(20) 192(20) 184(20) 158(20) 170(20) 165(15) 156(10) 150(15) 144(15) 139(6) 89 90 91 92 93 94 95 96 97 98 99 100 101 102 7 Ac Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No 203(12) 217(54) 154(20) 129(17) 151(20) 132(20) 131(25) 144(25) 125(25) 122(20) 118(20) 113(20) 109(20) 110(6) Figure 1. Recommended values from Table 1 for the atomic polarizabilities (atomic units; estimated uncertainties in parentheses) of elements Z = 1-120. The various blocks of elements are color-coded: s-block, yellow; p-block, green; d-block, blue; f-block, orange. Acknowledgment PS thanks Ivan Lim, Gordon W. F. Drake (Windsor), Nicola Gaston (Auckland), Uwe Hohm (Braunschweig), Antonio Rizzo (Pisa), Jürgen Hinze (Bielefeld), Gary Doolen (Los Alamos National Laboratory), Dirk Andrae (Bielefeld), Vitaly Kresin (Los Angeles), Timo Fleig (Düsseldorf), Ajit Thakkar (Fredericton), Pekka Pyykkö (Helsinki), Zong-Chao Yan, (Brunswick), Juha Tiihonen (Helsinki) and Keith Bonin (Winston-Salem) for helpful discussions. Financial support from Marsden funding (17-MAU-021) by the Royal Society of New Zealand is gratefully acknowledged. JN thanks Bowdoin College for sabbatical leave support. 2 Table 1. Static scalar dipole polarizabilities (in atomic units) for neutral atoms. If not otherwise indicated by the state symmetry, ML (MJ) - averaged polarizabilities are listed; ML (MJ) respectively denotes that the polarizability for each ML (MJ) state can be found in the reference given. Abbreviations used (uncertainties given here consistently as ± values): exp.: experimentally determined value; NR: nonrelativistic; R: Relativistic, DK: Scalar relativistic Douglas-Kroll; MVD: mass-velocity-Darwin; SO: Spin-orbit coupled; SF: Dyall’s spin-free formalism (scalar relativistic); PP: relativistic pseudopotential; LDA: local (spin) density approximation; PW91: Perdew-Wang 91 functional; RPA: Random phase approximation; PolPot: Polarization potential; MBPT: many-body perturbation theory; CI: configuration interaction; CCSD(T): coupled cluster singles doubles (SD) with perturbative triples; FS Fock-space; CEPA: coupled electron pair approximation; MR: multi- reference; CAS: complete active space; VPA: variational perturbation approach. For all other abbreviations see text or references. If the symmetry of the state is not clearly specified as in Doolen’s calculations, the calculation was most likely set at a specific configuration (orbital occupancy) as listed in the Desclaux tables [1], reflecting the ground state symmetry of the specific atom. NB: 1 a.u. = 0.14818471 Å3 = 1.6487773 ´ 10–41 C m2/V. 3 Z Atom Refs. State aD Comments 1 H [2] 2S 4.5 NR, exact 2 [2,3] S1/2 4.49975149589 R, Dirac, variational, Slater basis/B-splines (more digits are given in ref 3) 2 [4] S1/2 4.49975149518 R, Dirac, Lagrange mesh method (more digits are given in this paper) 2 1 [3] S1/2 4.507107623 R, Dirac (as above), but with finite mass correction added for the H isotope 2 S1/2 4.50711±0.00003 recommended 1 4 2 He [5] S0 1.383191 R, Dirac, Breit-Pauli, QED, mass pol., correlated basis ( He) 1 [6] S0 1.38376079 R, Dirac, Breit-Pauli, QED, mass pol., exponentially correlated Slater ±0.00000023 functions (4He) 1 4 [7] S0 1.3837295330 R, Dirac, Breit, QED, recoil, … ( He) ±0.0000000001 1 [8,9] S0 1.383746±0.000007 exp. 1 [10] S0 1.383759±0.000013 exp. 1 S0 1.38375±0.00002 recommended 3 Li [11,12] 2S 164.05 NR, exponentially correlated Gaussians [18] + R/DK 2 7 [13] S1/2 164.084 R, Dirac, MBPT, Breit, QED, recoil ( Li) 2 7 [14] S1/2 164.1125±0.0005 Hylleraas basis, R(MV+Darwin+Breit), QED, recoil ( Li) 2 [15] S1/2 164.21 Frozen core Hamiltonian, semi-empirical polarization potential 2 [16] S1/2 164.0±3.4 exp. 2 [17] S1/2 164.2±1.1 exp. 2 S1/2 164.1125±0.0005 recommended 4 Z Atom Refs. State aD Comments 4 Be [11] 1S 37.755 NR, exponentially correlated Gaussians [18] 1 [19] S0 37.80±0.47 R, Dirac, coupled cluster 1 [20] S0 37.76±0.22 R, Dirac, CI+MBPT+ experimental data 1 [11,21] S0 37.739±0.030 R correction of –0.016 applied to value from ref [11] 1 [22] S0 37.86±0.17 R, Dirac, MBPT, CCSD 1 [23] S0 37.73±0.05 CCSD(T) 1 [24] S0 37.807 CI, expanded London formula 1 [25] S0 37.69 Combination of ab initio and semi-empirical methods 1 [26] S0 37.29 All-electron SCF plus valence CI 1 [27] S0 37.9 Model potential 37.74±0.03 recommended 2 5 B [28] P 20.47 NR, PNO-CEPA, ML res. 2 [29] P 20.43±0.11 NR, CCSD(T), ML res. 2 [30] P 20.59 R, SF, MRCI, ML res. 2 2 [30] P1/2/ P3/2 20.53/20.54 R, Dirac, MRCI, MJ res. 20.5±0.1 recommended 3 6 C [31] P 11.39 NR, CASPT2, ML res. 3 [29] P 11.67±0.07 NR, CCSD(T), ML res. 3 [32] P0 11.26±0.20 R, Dirac+Gaunt, CCSD(T) 11.3±0.2 recommended 7 N [28] 4S 7.43 NR, PNO-CEPA 4 [33] S 7.41 R, DK, CASPT2 4 [29] S 7.26±0.05 NR, CCSD(T) 4 [16,34] S3/2 7.6±0.4 exp. 4 [35,36] S3/2 7.28 exp. 7.4±0.2 recommended 5 Z Atom Refs. State aD Comments 3 8 O [28,86] P 5.41±0.11 NR, PNO-CEPA, ML res. 3 [31] P 5.4±0.7 NR, CASPT2, ML res. 3 [21,29] P 5.24±0.04 NR, CCSD(T), ML res. 3 [34] P2 5.2±0.4 exp. 5.3±0.2 recommended 2 9 F [28] P 3.76 NR, PNO-CEPA, ML res. 2 [37] P 3.76±0.06 NR, CASPT2, ML res. 2 [29] P 3.70±0.03 NR, CCSD(T), ML res. 3.74±0.08 recommended 10 Ne [38] 1S 2.68 NR, CCSD(T) 1 [39] S 2.665 NR, CC3 1 [39,40,41] S 2.666 R, CC3+FCI+DK3 correction 1 [42,43] S0 2.677±0.070 R, Dirac-Coulomb, non-linear PRCC 1 [44] S0 2.66063±0.00001 CCSD(T), ECP 1 [21] S0 2.661±0.005 R, CCSD(T) 1 [45] S0 2.663 exp. 1 [46] S0 2.6669±0.0008 exp. 1 [47] S0 2.66110±0.00003 exp. 2.66110±0.00003 recommended 2 11 Na [48] S1/2 162.6±0.3 R, SD all orders + exp.