Canadian Journal of Physics. The NIST compilation of ionization potentials revisited (I): From He-like to Xe-like ions

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1 The NIST compilation of ionization potentials revisited (I): From He-like to Xe-like ions Journal: Canadian Journal of Physics Manuscript ID cjp-6-5.r Manuscript Type: Article Date Submitted by the Author: 8-Dec-6 Complete List of Authors: Gil, Gabriel; Instituto de Cibernetica Matematica y Fisica, Departamento de Física Teórica; Istituto Nanoscienze Consiglio Nazionale delle Ricerche, S; Universita degli Studi di Modena e Reggio Emilia, Dipartimento di Scienze Fisiche, Informatiche e Matematiche Gonzalez, Augusto; Instituto de Cibernetica Matematica y Fisica, Departamento de Física Teórica Keyword: atomic ions, ionization potential, regularized perturbation theory, large- expansion, NIST Atomic Spectra Database

2 Page of Canadian Journal of Physics The NIST compilation of ionization potentials revisited (I): From He-like to Xe-like ions Gabriel Gil,, and Augusto Gonzalez Instituto de Cibernética, Matemática y Física, Havana, Cuba, S, CNR-Istituto di Nanoscienze, Modena, Italy, and Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Universitá degli studi di Modena e Reggio Emilia, Modena, Italy. The National Institute of Standards and Technology (NIST) database on ionization potentials for neutral atoms and ions is examined. For each isoelectronic sequence, we construct a regularized perturbative series based on the large- and N behaviors. Comparison of the NIST data with this series allows the identification of problematic values in the reported data. PACS numbers:..-r,..hq,.5.-p Physics is indeed a mature science. Large amounts of data, of very different kinds, have been accumulated along decades. Sometimes, a fresh look at these compilations, on the basis of simple -physically meaningfulmodels, leads to a qualitative understanding of the data. In previous papers,, on the basis of the scaling characteristic of Thomas-Fermi theory, we have shown that both the NIST data on ionization potentials of atomic ions, and the correlation energies of atomic ions can be accomodated along single universal curves. Recently, we went a step further and develop a simple model allowing the identification of problematic isolated reported values for the ionization potentials in a particular isoelectronic sequence. 7 In the present account, we systematically revisit the NIST ionization potential database in light of the new model. Because of the fact that the compilation is very often used for different purposes, indications of which data could be wrong and should be re-examined is of great importance. For instance, as commented in Refs. [5] and [6], accurate description of the spectra is useful in order to model some dynamical features of stellar sources, and also to interpret astronomical data. Our model for the ionization potential is a smooth interpolation that matches both the large- (heavy ion) and the N (anion) regions. 7 We call it the regularized perturbation theory (RPT). In our previous work, Ref. [7], the model is explained in detail and applied to the analysis of a few isoelectronic sequences, N =,8,9 and 6. Within this article, we analyze sequences from N =, He-like ions, to 5, Xe-like ions. We have used similar approaches in order to compute the energy of relatively large quantum dots, 8 atomic ions in a harmonic trap, 9 neutral atoms in traps, and Rydberg-like impurity levels in a quantum well. The RPT series for the ionization potential of an N- electron atomic ion with nuclear charge is written as (atomic units are used everywhere): 7, I p = a +a +a +a /. () Coefficients a and a are obtained from the large- limit. 7 a comes from the leading term (free electrons in the nuclear field), whereas a is computed in the nextto-leading approximation, where Coulomb repulsion between electrons is perturbatively treated. Relativistic corrections should be included because the NIST data span the range of nuclear charges up to very heavy ions, i.e., N. The next two terms of the series have the functional form suggested by higher-order perturbation theory on the Coulomb repulsion. However, in order to determine them, we shall follow a different strategy. We force expression () to match the expected value and the slope at = N. 7 Inthissense, itisa regularizedperturbative series. These conditions are written as follows: I p =N = E a, di p R d = s = dre κr /r. () =N dre κr E a is the electron affinity of the neutral atom with N electrons. The slope s, on the other hand, is computed in terms of E a and R, the latter is a characteristic radius of the (N )-electron system, which we estimate as the covalent radius. Note that κ = E a. The expression of the slope makes use of the fact that, at = N, the outer electron interacts with a neutral core. Thus, the interaction is short-ranged and the wave function at large distances is solely determined by the binding energy, i.e. E a. We use this function in order to perturbatively compute the residual Coulomb interaction of the outer electron with the core, when is slightly displaced from N. The explicit expression for s was derived earlier in Ref. []. Once the coefficients in Eq. () are determined, our RPT series provides an interpolation for intermediate values of. We show in Fig., in quality of example, the series for F-like ions (N = 9) along with the corresponding NIST data. R

3 Page of I p (a.u.) NIST Nonrel. Rel FIG.. (Color online) F-like ions (N = 9). Upper panel: I p taken from the NIST compilation along with our nonrelativistic (discontinuous, blue) and relativistically corrected (continuous, red) RPT predictions vs.. Curves are smooth at any scale. Lower panel: The difference between I p values reported by NIST and those stemming from the relativistic RPT series vs.. Reported error bars are shown. A 5-points running average curve (blue line) is used to identify problematic points. Inconsistencies at = 7 and 7 are noticed. The jump at = 5 5 lies within error bars. Problematic points are identified by comparison with a smoothed curve, which we construct by means of a 5- points running average. We notice that an abrupt change in I p could only be related to a rearrangement of the occupied electronic levels. This may take place as is increased. However, for > N + 5 or so, as may be verified also in the NIST compilation, the large- ordering of levels (free electrons in the field of the nucleus) is established. Thus, every jump or deviation beyond error bars in the smoothed NIST-RPT, not coinciding with a spectrum rearrangement point, can be taken as a signature of a possible problem. We stress that the NIST reported values are experimental points only when is very close to N. For larger, data come from calculations or interpolations and we may expect relatively high errors, as the reported error bars confirm. Remarkable deviations at = 7 (e.g., in Fig. ) are clear indications of points in the data that would require a further examination by the NIST team. Notably, the latter deviation is recurrent in of the isoelectronic sequences considered here (all coming from Ref. []). The abrupt jump at = 5 5, 5 albeit not problematic for F-like ions as confirmed in Fig., is indeed inconsistent for 5 isoelectronic sequences. The dispersion of the points for very heavy ions is also intriguing, although it may be related to rounding of the original data according to the estimated error bars. In the appendices, we examine isoelectronic sequences (five rows of the Mendeleev Table), from He-like to Xe-like ions. In this range, only the sequences which do not have a stable singly charged anion are excluded. Heavier ions, from Ba-like to Th-like, are to be analyzed in a subsequent paper 6. We hope that the present analysis will be helpful in order to improve the reference data. Some comments should be added to this figure. First, NIST and RPT values are relatively close even though no fitting parameters are used. The latter means that the RPT model contains the main contributions to I p. Second, the dependence of I p on seems smooth in the upper panel. It is difficult to distinguish a problematic point in the sequence, even if we change the scale. The reason is that there are large contributions to I p. The nuclear potential, for example, provides a term proportional to, and electron-electron repulsions a term proportional to. If we compute the difference NIST - RPT, such contributions are substracted and problematic points should become apparent. In principle, if RPT were an exact model, the mean value of NIST - RPT would be zero, and deviations from zero could only be related to experimental or computational uncertainties. Any point far from zero beyond error bars should be reexamined. Our model is not exact, thus we shall expect a smooth NIST - RPT dependence, as shown in the lower panel. ACKNOWLEDGMENTS The authors are grateful to the Caribbean Network for Quantum Mechanics, Particles and Fields (ICTP) for support. G.G. also acknowledge financial support from the European Community s FP7 through the Marie Curie ITN-INDEX. Appendix A: The He-like sequence (N = ) a =.5+.5 (/7.6), a = (/7.6), a =.68987, a =.68.

4 Page of Canadian Journal of Physics E a (H) =.776, s =.599. (A) The slope was computed from E a (H) and R cov (H) =.67. Here, and in the analysis below, data for E a and R cov are taken from Ref. []. E a (Li) =.75, s =.6. (B) The slope was computed from E a (Li) and R cov (Li) = FIG. A.. (Color online) He-like ions (N = ). The difference between I p values reported by NIST and those stemming from the relativistic RPT series vs.. Error bars are very small and can not be seen in the scale of the figure. No inconsistencies were detected. Let us comment on some features of the I p data for the He-like sequence shown in Fig. A.. In the range 6, the difference between our RPT series and the reported values is very well behaved. In the intermediate region, the maximum relative error is around.5%. When > 56, NIST-RPT rises. NIST ionization potentials in the range come mainly from ab intio Quantum Electrodynamics calculations by Artemyev et al., 7 which include finite nuclear-size effects. Our perturbative treatment of relativity cannot reproduce their results for very large. Appendix B: Second row elements. The Be-like sequence (N = ) a = (/7.6), a = (/7.6), a = , a = FIG. B.. (Color online) Be-like ions (N = ). The abrupt jump at = 5 5 can be, however, accomodated within error bars. The comparison between NIST and RPT I p values for the Be-like sequence shows an abrupt jump of.8 a.u. at = 5 5 (see Fig. B.). These are numbers based on Dirac-Fock calculations of I p computed by different groups. For 5, data come from Ref. [8], whereas for 5 almost all reported numbers come from Rodrigues et al. 5. We notice that, in Ref. [8], a formula likeeq.()isusedasafittocorrectthecomputedvalues. The observed jump is consistent with the natural dispersion of points, as suggested by the reported error bars. Thus, no inconsistency is detected.. The C-like sequence (N = 6) a = (/7.6), a = (/7.6), a =.965, a =.67. E a (B) =.76, s = (B) The slope was computed from E a (B) and R cov (B) =

5 Page 5 of FIG. B.. (Color online) C-like ions (N = 6). An inconsistency at = 7 and an abrupt jump at = 5 5) are noticed. FIG. B.. (Color online) N-like ions (N = 7). Deviations at = 6 and 7 are noticed. The analysis of NIST-RPT data for the C-like sequence (Fig. B.) also shows an abrupt jump of nearly. a.u. at = 5 5. As in the Be-like case, this jump is associated to changes in the calculation methodology. However, the jump exactly equals the reported error bars. Thus, we recommend revision of this data. In addition, an apparent deviation in the ionization potential is noticed at = 7. This number, corresponding to a tungsten heavy ion (W +68 ), was collected by NIST compilers Kramida and Reader with the help of a semi-empirical approach. Comparison with the average curve suggests that the reported value for W +68 is overestimated in.577 a.u. The N-like sequence (Fig. B.) presents noticeable jumps at = 6 and, once more, at = 7. The ionization potential for = 6 was taken from the paper by Sugar and Corliss. 9 According to our procedure, an overestimation of.5 a.u. is noticed. The = 7 case is again taken from Ref. []. It seems to be an inconsistent point, underestimated by.95 a.u. Data for = 5 come from the Dirac-Fock calculations by Biémont et al. 8 The reported large uncertainties in the data, of around.5 a.u., are consistent with the observed deviations. Notice, that error bars are remarkably high (from. to a.u.) for > 7.. The F-like sequence (N = 9). The N-like sequence (N = 7) a = (/7.6), a = (/7.6), a =.69, a =.566. E a (C) =.6657, s =.6. (B) The slope was computed from E a (C) and R cov (C) =.795. a = (/7.6), a = (/7.6), a =.79, a = E a (O) =.56759, s =.68. (B) The slope was computed from E a (O) and R cov (O) =.795. In the F-like sequence (see Fig. ), large deviations are noticed for = 7 and 7. I p for = 7 comes from Ref. [9], the very same paper by Sugar and Corliss cited in the N-like case. According to our Fig., it seems to be overestimated in.8 a.u.

6 Page 6 of Canadian Journal of Physics 5 On the other hand, = 7 belongs to the case of tungsten ions (W +65 ), and the I p value is, once more, taken from Ref. []. In this case, an underestimation of.7 a.u. is apparent. Finally, the observed jump at = 5 5 is consistent with the reported error bars. It is also worth mentioning the large error bars accompanying the data for The Ne-like sequence (N = ) The previously discussed abrupt jump at = 5 5, should be revised by the NIST team because the jump is greater than the data uncertainty. Ne-like ions were considered in Ref. [7] and are shown here for completeness. Appendix C: Third row elements. The Mg-like sequence (N = ) a = (/7.6), a = (/7.6), a =.8, a = a = (/7.6), a = (/7.6), a =.6996, a =.77. E a (F) =.985, s =.579. (B5) The slope was computed from E a (F) and R cov (F) = E a (Na) =.87, s =.9. (C) The slope was computed from E a (Na) and R cov (Na) = FIG. B.. (Color online) Ne-like ions (N = ). Inconsistencies at =,, 7, 7, and the abrupt jump at = 5 5 are noticed. A version of this figure was printed as part of Fig. in Ref. [7] FIG. C.. (Color online) Mg-like ions (N = ). Inconsistencies at =,, 5, 7 and 8, and a jump at = 5 5 are apparent. In the Ne-like sequence (Fig. B.), deviations at =,, and 7 are noticed. Points are related to Ref. [9]. We suggest correcting these values in -., +. and +.6 a.u., respectively. The = 7 case, is also clearly inconsistent. The ionization potential seems to be underestimated in.77 a.u. The Mg-like sequence (Fig. C.) shows clear deviations at =,, 5, 7 and 8. 9 The figure suggests corrections of -.5, -., +.6, -.8 and -.6 a.u. to these points, respectively. In principle, also the value at = qualifies as problematic, but once a smoother average curve is considered (e.g., based on 7 points instead of 5), it is no longer meeting our criterion (not shown).

7 Page 7 of 6 The jump at = 5 5 was discussed above. It is clearly not consistent with error bars, thus we suggest revision of these data. a = (/7.6), a = 5.86, a =.65.. The Si-like sequence (N = ) a = (/7.6), a = (/7.6), a =., a =.96. E a (Al) =.596, s =.966. (C) The slope was computed from E a (Al) and R cov (Al) = E a (Si) =.587, s =.87. (C) The slope was computed from E a (Si) and R cov (Si) = FIG. C.. (Color online) P-like ions (N = 5). A big jump at = 5 5, and a noticeable deviation at = 7 are apparent FIG. C.. (Color online) Si-like ions (N = ). Deviations at = 6 and =7 are remarkable. For the P-like sequence (Fig. C.), we suggest a revision of the data near = 5, and correcting the = 7 value in +.7 a.u.. The S-like sequence (N = 6) In the Si-like sequence (Fig. C.), a group of four points, = 6, seems to be out of the general trend. Thus, we use a 7-points running average (instead of 5- points) in order to create a smooth curve. We suggest using the top of the error bars as values for =, and the bottom of the error bars for = 6. The = 7 point, on the other hand, should be corrected in -.9 a.u.. The P-like sequence (N = 5) a = (/7.6), a = (/7.6), a = (/7.6), a =.8765, a = E a (P) =.759, s =.867. (C) The slope was computed from E a (P) and R cov (P) =

8 Page 8 of Canadian Journal of Physics FIG. C.. (Color online) S-like ions (N = 6). The only detected inconsistency is the deviation at = 7. Although error bars are relatively high for S-like ions (Fig. C.), we suggest a correction of +.9 a.u. to the = 7 value of I p. 5. The Cl-like sequence (N = 7) a = (/7.6), a =..6 (/7.6), a = 5.859, a =.9. E a (S) =.768, s =.89. (C5) The slope was computed from E a (S) and R cov (S) = Error bars are also relatively large for the Cl-like sequence (Fig. C.5). However, we suggest a revision of the data near = 5, which show a jump of.6 a.u., and using in the = 7 case the top value of the error bar. 6. The Ar-like sequence (N = 8) FIG. C.5. (Color online) Cl-like ions (N = 7). The jump at = 5 5, and the deviation at = 7 are noticeable. E a (Cl) =.775, s =.85. (C6) The slope was computed from E a (Cl) and R cov (Cl) = FIG. C.6. (Color online) Ar-like ions (N = 8). In this case, we distinguish only the deviation at = 7. a = (/7.6), a = (/7.6), a = 6., a = 9.9. In spite of the relatively large error bars for the Ar-like sequence (Fig. C.6), we suggest using the top of the error bar as the = 7 value of I p.

9 Page 9 of 8 Appendix D: Four row elements. The Ca-like sequence (N = ) a = (/7.6), a =.7.6 (/7.6), a = , a = 8.7. E a (Ca) =.99, s =.779. (D) The slope was computed from E a (Ca) and R cov (Ca) = E a (K) =.8, s =.767. (D) The slope was computed from E a (K) and R cov (K) = FIG. D.. (Color online) Sc-like ions (N = ). Only the = 7 point is distinguished FIG. D.. (Color online) Ca-like ions (N = ). Only the = 7 point is distinguished. Sc-like sequence (Fig. D.) is very similar to Ca-like case. We suggest correcting I p at = 7 in -. a.u.. The Ti-like sequence (N = ) The Ca-like sequence (Fig. D.) is the first with a rearrangement of the electronic spectrum with the increase of. For N the last two electrons occupy the s subshell, whereas for larger they move to the d orbital. The observed jump at = is surely related to this fact. On the other hand, we suggest using for I p at = 7 the bottom of its error bar. a = (/7.6), a = (/7.6), a = , a = 5.8. E a (Sc) =.6965, s =.759. (D). The Sc-like sequence (N = ) The slope was computed from E a (Sc) and R cov (Sc) =.665. a = (/7.6), a = (/7.6), a = 7.887, a = Ti-like sequence (Fig. D.) is also very similar to the previous cases (Ca- and Sc-like). We suggest correcting I p at = 7 in -.5 a.u.

10 Page of Canadian Journal of Physics FIG. D.. (Color online) Ti-like ions (N = ). Only the = 7 point is distinguished. 5. The Cr-like sequence (N = ) a = (/7.6), a = (/7.6), a =.96, a = E a (V) =.9866, s =.85. (D5) The slope was computed from E a (V) and R cov (V) = The V-like sequence (N = ) a = (/7.6), a = (/7.6), a = , a = E a (Ti) =.9, s = (D) The slope was computed from E a (Ti) and R cov (Ti) = FIG. D.5. (Color online) Cr-like ions (N = ). An apparent deviation at = is detected FIG. D.. (Color online) The V-like ions (N = ). No inconsistencies were detected. In the Cr-like sequence (Fig. D.5), we shall distinguish the problematic point at =, coming from the paper by Sugar and Musgrove. I p is overestimated in.8 a.u. 6. The Mn-like sequence (N = 5) a = (/7.6), a =.6.69 (/7.6), a =.5, a = 68.. E a (Cr) =.666, s =.95. (D6)

11 Page of FIG. D.6. (Color online) Mn-like ions (N = 5). No inconsistency is detected. FIG. D.7. (Color online) Co-like ions (N = 7). The only detected inconsistency is at = 7. The slope was computed from E a (Cr) and R cov (Cr) =.566. E a (Co) =.96, s =.66. (D8) 7. The Co-like sequence (N = 7) The slope was computed from E a (Co) and R cov (Co) = a = (/7.6), a = (/7.6), a =.98, a = E a (Fe) =.557, s = (D7) The slope was computed from E a (Fe) and R cov (Fe) = In the Co-like sequence (Fig. D.7), I p at = 7 is overestimated in.96 a.u. FIG. D.8. (Color online) Ni-like ions (N = 8). Inconsistencies are detected at =, 7, and 79. A version of this figure was printed as part of Fig. in Ref. [7]. 8. The Ni-like sequence (N = 8) a = (/7.6), a = (/7.6), a =.65, a = The Ni-like sequence (Fig. D.8) shows deviations at =, 7 and 79, the latter coming from the paper by Tragin et al.. As suggested by the figure, I p at = is overestimated in.7 a.u. Corrections of -. and -. a.u. should be added to the points at = 7 and 79, respectively.

12 Page of Canadian Journal of Physics Ni-like ions were considered in Ref. [7] and are shown here for completeness. 9. The Cu-like sequence (N = 9) a = (/7.6), a =.7.6 (/7.6), a = , a = E a (Ni) =.67, s =.995. (D9) The slope was computed from E a (Ni) and R cov (Ni) =.98. E a (Cu) =.569, s = (D) The slope was computed from E a (Cu) and R cov (Cu) = FIG. D.9. (Color online) Cu-like ions (N = 9). Small deviations at = 7 and 79 are noticed. A version of this figure was printed as part of Fig. in Ref. [7]. In the Cu-like sequence (Fig. D.9), slight deviations at = 7 and 79 are apparent. The data come from Ref. []. Points seem to be overestimated in.6 and.97 a.u., respectively. Cu-like ions were considered in Ref. [7] and are shown here for completeness.. The n-like sequence (N = ) a = (/7.6), a = (/7.6), a = 9.67, a = FIG. D.. (Color online) n-like ions (N = ). Inconsistencies are noticed at = 5,, 5 and 7. In the n-like sequence (Fig. D.), the data for = 5 is taken from the Dirac-Fock calculation of Ref. [5], while the value for = is due to Refs. [] and [5]. These potentials should be corrected in +.76 and -.5 a.u., respectively. On the other hand, = 5 ionization potential was collected from the relativistic multireference many-body perturbation theory calculations of Vilkas et al.. It seems to be overestimated in.87 a.u. The = 7 ionization potential comes from Ref. [], as before. It is. a.u. higher than the average curve.. The Ge-like sequence (N = ) a = (/7.6), a = (/7.6), a =.9568, a = E a (Ga) =.57966, s =.69. (D) The slope was computed from E a (Ga) and R cov (Ga) =.6.

13 Page of FIG. D.. (Color online) Ge-like ions (N = ). Only the = 7 point is distinguished. FIG. D.. (Color online) As-like ions (N = ). No inconsistencies are detected. In the Ge-like sequence (Fig. D.), I p at = 7 is overestimated in.6 a.u. The slope was computed from E a (As) and R cov (As) = The As-like sequence (N = ) a =.5+. (/7.6), a = (/7.6), a =.657, a = E a (Ge) =.58, s = (D) The slope was computed from E a (Ge) and R cov (Ge) = FIG. D.. (Color online) Se-like ions (N = ). Slight deviations at = 9 and are apparent.. The Se-like sequence (N = ) a =.5+. (/7.6), a = (/7.6), a =.7569, a =.876. E a (As) =.956, s =.77. (D) In the Se-like sequence (Fig. D.), we detect inconsistencies at = 9 and. I p at = 9 seems to be overestimated in. a.u. The number for I p in Mo +8 (i.e. =, N = ) comes from Refs. [] and []. It seems to be.59 a.u. higher than the average curve.. The Br-like sequence (N = 5) a =.5+. (/7.6),

14 Page of Canadian Journal of Physics a = (/7.6), a =.595, a = E a (Se) =.77, s =.5. (D) The slope was computed from E a (Se) and R cov (Se) = FIG. D.. (Color online) Br-like ions (N = 5). A smooth curve. No inconsistencies are detected FIG. D.5. (Color online) Kr-like ions (N = 6). No inconsistencies are detected. Appendix E: Fifth row elements. The Sr-like sequence (N = 8) a =.5+. (/7.6), a = (/7.6), a = 5.88, a = E a (Rb) =.785, s = (E) 5. The Kr-like sequence (N = 6) The slope was computed from E a (Rb) and R cov (Rb) =.69. a =.5+. (/7.6), a = (/7.6), a =.557, a =.6. E a (Br) =.65, s =.9. (D5) The slope was computed from E a (Br) and R cov (Br) = FIG. E.. (Color online) Sr-like ions (N = 8). An apparent deviation at = 7 is shown.

15 Page 5 of In the Sr-like sequence (Fig. E.), I p at = 7 is overestimated in. a.u.. The Y-like sequence (N = 9) E a (Y) =.78, s =.797. (E) The slope was computed from E a (Y) and R cov (Y) =.598. a =.5+. (/7.6), a = (/7.6), a =.75, a = 5.6. E a (Sr) =.767, s =.8. (E) The slope was computed from E a (Sr) and R cov (Sr) = FIG. E.. (Color online) r-like ions (N = ). The = 7 point is distinguished. In the r-like sequence (Fig. E.), I p at = 7 shows an overestimation of.7 a.u FIG. E.. (Color online) Y-like ions (N = 9). The only detected inconsistency is at = 7. In the Y-like sequence (Fig. E.), I p at = 7 should be corrected in -.8 a.u.. The r-like sequence (N = ) a =.5+. (/7.6), a = (/7.6), a = 6.7, a = The Nb-like sequence (N = ) a =.5+.9 (/7.6), a = (/7.6), a = 7.69, a = E a (r) =.5696, s =.988. (E) The slope was computed from E a (r) and R cov (r) =.995. In the Nb-like sequence (Fig. E.), I p at = 7 is overestimated in.6 a.u.

16 Page 6 of Canadian Journal of Physics In the Mo-like sequence (Fig. E.5), I p at = 7 should be corrected in -. a.u. 6. The Tc-like sequence (N = ) a =.5+.9 (/7.6), a = (/7.6), a = 9., a = FIG. E.. (Color online) Nb-like ions (N = ). The only detected inconsistency is the = 7 point. E a (Mo) =.779, s =.85. (E6) 5. The Mo-like sequence (N = ) The slope was computed from E a (Mo) and R cov (Mo) =.759. a =.5+.9 (/7.6), a =.96.7 (/7.6), a = , a = 5.5. E a (Nb) =.665, s =.99. (E5) TheslopewascomputedfromE a (Nb)andR cov (Nb) = FIG. E.5. (Color online) Mo-like ions (N = ). The only inconsistent point is = FIG. E.6. (Color online) Tc-like ions (N = ). Only the = 7 point is distinguished.. In the Tc-like sequence (Fig. E.6), I p at = 7 is overestimated in. a.u. 7. The Ru-like sequence (N = ) a =.5+.9 (/7.6), a = (/7.6), a = 9.96, a =

17 Page 7 of 6 E a (Tc) =.9, s =.65. (E7) The slope was computed from E a (Tc) and R cov (Tc) = FIG. E.7. (Color online) Ru-like ions (N = ). An inconsistency at = 7 is apparent FIG. E.8. (Color online) Rh-like ions (N = 5). There are apparent inconsistencies at = 9 5 and = The Pd-like sequence (N = 6) a =.5+.9 (/7.6), a = (/7.6), a =., a = In the Ru-like sequence (Fig. E.7), I p at = 7 is overestimated in.6 a.u. E a (Rh) =.769, s =.587. (E9) 8. The Rh-like sequence (N = 5) The slope was computed from E a (Rh) and R cov (Rh) =.5. a =.5+.9 (/7.6), a = (/7.6), a =.97, a = 6.5. E a (Ru) =.857, s =.65. (E8) The slope was computed from E a (Ru) and R cov (Ru) = In the Rh-like sequence (Fig. E.8), I p at = 9 is underestimated in.7 a.u., whereas the = 7 point is.6 a.u. higher than the average curve. FIG. E.9. (Color online) Pd-like ions (N = 6). Inconsistencies at = 55 and 7 are noticed.

18 Page 8 of Canadian Journal of Physics 7 In the Pd-like sequence (Fig. E.9), in addition to = 7, an apparent inconsistency at = 55 comes from the experimental work of Churilov et al. 6 The = 55 and 7 points are, respectively,. and.8 a.u. above the average curve. Data for 77 is the entire responsibility of Carlson et al. 7, who employ a simple spherical shell model in order to compute the ionization potentials. The indicated error bars are very high.. The Cd-like sequence (N = 8). The Ag-like sequence (N = 7) a =.5+.9 (/7.6), a = (/7.6), a = 5.88, a = 6.9. E a (Pd) =.66, s = (E) a =.5+.9 (/7.6), a = (/7.6), a = 7.77, a = E a (Ag) =.789, s = (E) The slope was computed from E a (Ag) and R cov (Ag) =.578. The slope was computed from E a (Pd) and R cov (Pd) = FIG. E.. (Color online) Cd-like ions (N = 8). Inconsistencies are detected at = 6 and 7. FIG. E.. (Color online) Ag-like ions (N = 7). The average curve is drawn (blue) in order to identify problematic points. Inconsistencies at = 6 and 7 are apparent. The = 95 point also distinguishes in spite of its huge error bar. A qualitatively different picture appears in the Ag-like sequence (Fig. E.). The maximum of RPT NIST diminished, as compared with the Pd-like sequence, but the dispersion of points has significantly increased. The problematic point at = 6 comes from Ref. [5]. It seems to be.9 a.u. below the average curve. I p at = 7, on the other hand, is underestimated in.75 a.u. In the Cd-like sequence (Fig. E.), I p at = 7 is underestimated in. a.u. The value at = 6, although having error bars near the 5-pts average, is deviating even more from an smoother 7-pts average curve (not shown).. The Sn-like sequence (N = 5) a =.5+.9 (/7.6), a = (/7.6), a = 7.9, a =

19 Page 9 of 8 E a (In) =.8, s = (E) The slope was computed from E a (In) and R cov (In) = FIG. E.. (Color online) Sb-like ions (N = 5). The = 7 point is distinguished FIG. E.. (Color online) Sn-like ions (N = 5). A deviation at = 7 is apparent. In the Sn-like sequence (Fig. E.), I p at = 7 shows a huge deviation of -.7 a.u. We may notice also that, apparently, there are crossing points at = 6 and 6. Thus the group of points in = 6 6 should be below the x axis. However, we do not have a precise way of estimating these potentials.. The Te-like sequence (N = 5) a =.5+.9 (/7.6), a = (/7.6), a =.6, a = E a (Sb) =.86, s =.568. (E) The slope was computed from E a (Sb) and R cov (Sb) = The Sb-like sequence (N = 5) a =.5+.9 (/7.6), a =.6.78 (/7.6), a =.6766, a = 68.. E a (Sn) =.85, s =.576. (E) The slope was computed from E a (Sn) and R cov (Sn) = In the Sb-like sequence (Fig. E.), I p at = 7 is underestimated in a.u. We have stressed previously the problem of = 6 6 ions for Sn-like case. A similar comment applies here FIG. E.. (Color online) Te-like ions (N = 5). A marked deviation at = 7 is noticed.

20 Page of Canadian Journal of Physics 9 In the Te-like sequence (Fig. E.), I p at = 7 is.668 a.u. below the average curve. In the I-like sequence (Fig. E.5), I p at = 7 is.668 a.u. below the average curve. Notice that underestimation of this point is systematical since the Ag sequence. 5. The I-like sequence (N = 5) 6. The Xe-like sequence (N = 5) a = (/7.6), a =.79.5 (/7.6), a =.566, a = E a (Te) =.7, s = (E5) The slope was computed from E a (Te) and R cov (Te) = a = (/7.6), a = (/7.6), a = 6.87, a = 69.. E a (I) =.6, s =.976. (E6) The slope was computed from E a (I) and R cov (I) = FIG. E.5. (Color online) I-like ions (N = 5). An inconsistency is detected at = FIG. E.6. (Color online) Xe-like ions (N = 5). Only the = 7 point shows a clear inconsistency. In the Xe-like sequence (Fig. E.6), I p at = 7 is underestimated in.799 a.u. R. Carcasses and A. Gonzalez, Phys. Rev. A 8, 5 (9). A. Odriazola, A. Gonzalez and E. Rasanen, Phys. Rev. A 9, 55 (). D.A. Kirzhnits, Yu.E. Lozovik, and G.V. Shpatakovskaya, Sov. Phys. Usp. 8, 69 (975); E.H. Lieb, Rev. Mod. Phys. 5, 6 (98); L. Spruch, Rev. Mod. Phys. 6, 5 (99). A. Kramida, Yu. Ralchenko, J. Reader, and NIST ASD Team (). NIST Atomic Spectra Database (ver. 5.), [Online]. Available: [, March ]. National Institute of Standards and Technology, Gaithersburg, MD. Access date: August,. 5 C.J. Sansonetti, G. Nave, J. Reader, F. Kerber, The Astrophysical Journal Supplement Series,, 5 (). 6 D.K. Nandy and B.K. Sahoo, A&A 56, A5 (). 7 G. Gil and A. Gonzalez, Can. J. Phys., DOI:.9/cjp (6).

21 Page of 8 A. Matulis and F.M. Peeters, J. Phys.: Cond. Matter 6, 775 (99). 9 A. Gonzalez, A. Perez, Int. J. Mod. Phys. B, 9 (998). A. Gonzalez, B. Partoens, A. Matulis, F.M. Peeters, Phys. Rev. B 59 (), 65 (998). A. Gonzalez, I. Mikhailov, Int. J. Mod. Phys. B, 69 (997). G. Gil, A. Gonzalez, Mod. Phys. Lett. B 7, 578 (). Royal Society of Chemistry website Data References: W.M. Haynes (ed.) CRC Handbook of Chemistry and Physics, CRC Press, Boca Raton, ; G.W.C. Kaye and T.H. Laby, Tables of Physical and Chemical Constants, Longman, Essex, 995. Access date: July,. A.E. Kramida, J. Reader, At. Data Nucl. Data Tables 9, 57 (6). 5 G.C. Rodrigues, P. Indelicato, J.P. Santos, P. Patt, F. Parente, At. Data Nucl. Data Tables 86, 7 (). 6 G. Gil and A. Gonzalez, The NIST compilation of ionization potentials revisited (II): From Ba-like to Th-like ions, in preparation. 7 A.N.Artemyev, V.M.Shabaev, V.A.Yerokhin, G.Plunien, and G. Soff, Phys. Rev. A 7, 6 (5). 8 E. Biémont, Y. Frémat, P. Quinet, At. Data Nucl. Data Tables 7, 7 (999). 9 J. Sugar, C. Corliss, J. Phys. Chem. Ref. Data, Suppl., (985). J. Sugar and A. Musgrove, J. Phys. Chem. Ref. Data, (99). N. Tragin, J.-P. Geindre, C. Chenais-Popovics, J.-C. Gauthier, J.-F. Wyart, E. Luc-Koenig, Phys. Rev. A 9, 85 (989). M.J. Vilkas, Y. Ishikawa, K. Hirao, Chem. Phys. Lett., (). S. Khatoon, M. S.. Chaghtai, and K. Rahimullah, Phys. Scr. 9, (979). J. Sugar and A. Musgrove, J. Phys. Chem. Ref. Data 7, 55 (988). 5 U. Litzén and J. Reader, Phys. Rev. A 6, (987). 6 S.S. Churilov, Y.N. Joshi, and A.N. Ryabtsev, J. Phys. B 7, 585 (99). 7 T.A. Carlson, C.W. Nestor Jr., N. Wasserman, J.D. Mcdowell, At. Data Nucl. Data Tables, 6 (97).