Empirical regularities of atomic ionization potentials

Chemicd Physics 13 (1976) 299-308 0 North-Holland Publishing Company

EMPIRICAL REGULARITIES OF ATOMIC 1ONIZATlON POTENTIALS Hideo SAMBE and Ronald H. FELTON School ofCkmistry, Georgia Insritrrte of

Technology,

ArZanra,Georgin30332. USA

Received S August 1975 Revised manuscript received 11 December 1975

Regularities of the averaged ionization potentials for atoms and ions containing up lo 18 electrons are studied in detail. It is shown that a twwariable function constructed from the averaged ionization potentials for each subshell is linear with respect to the degee of ionization q and the occupancy k of the $ or pk subshell. One Linearityincludes previous timdings as a special case, and the other introduces a new regukrity for atomic ionization potentials. Enisting atomic ionization potentials and electron affiiities are analned employing the regubritics, and improved values of thew?quantities as well as term and fme S~IUC~UIC separations in negative ions are derived.

I. Introduction Atomic ionization potentials (IPs) determined to an accuracy of 0.005 eV or better by direct observa-

tions are still limited to the first few degrees of ionization. Even for five- to ten-electron systems [l] , only the first three members of each isoelectronic Equence are measured with such accuracy. In the past, this lack of reliable IP data has hindered a detailed and systematic analysis of atomic IPs; on the other hand, reliable experimental atomic electron affinities have accumulated rapidly over the past few years [2]. Electron affinities, or zeroth IPs, greatly aid studies of regularities of 1Psby adding a member to each isoelectronic sequence, and it.is appropriate to reinvestigate these trends. AI1regularities found here are concerned with the energy differences between configuration centers, i.e., the average energiesof a configuration weighted

accordingto the degeneraciesof its levels. In quantum chemistry, this energy difference is often denoted as an average p to distinguish it from the,conventional, ground Ip. It is well known [3] that the average IPs of s2px configurations are, in contrast to the ground IPs, nearly linear with respect to k for each futed degree of ionization CJ.Edie and Rohrlich [4] noted that the slopes of these linear functions of k are also nearly linear with respect to q. Loti [S]

found that the difference between the ground IPs of s and s2 configurations of the same 4 is nearly a linear function of 4. For sk configurations, the average and the ground IPs are the same, and the difference between the IPs of s and s* is simply the slope along k. Therefore, combining the above observations, one can say

that the averageIF’sof sk and s2pk configurationsare nearly linear with respect to k for each fmed 4, and the slopes of these linear functions of k are also nearly linear with respect to 4. These two regularities,one along k and the other along 4, are the basis of the “horizontal” analysis [4] used extensiveiy by Zoilweg [6] to obtain atomic electron affinities. In this paper we introduce the two-variable functions J,dk, q) for each nl-subshell and show that J,,l(k, q) is a nearly linear function of either q or k. The observation of Edie and Rohrlich [4] results from the linearity of Xk J,,&k, q) with respect to 4 for np subshells; the finding of Lotz 151 corresponds to the same feature ofJ,,(l, q) with respect to 4 for nssubshells. These authors checked their respective linearity for atoms and positive ions but not for negative ions. The linearity of Jn,(k, q) with respect to k is a new result and is a reliable regularity which extends to negative ions. We restrict ourselves to atoms and ions containing up to 18 electrons. The primary sources of experi. mental results are Moore’s [7] tables of ionization

pote,ntials and

atomicenergylevelsand the veryrecent

reviewarticle on bindingenergiesin atomic negative -ionsby Hotop and Lineberger [2]. Pertinent data were taken from these references unless otherwise stated.

IPs and are easily obtained from energiesof the individual ievelsi For atoms and positive ions, these data are more abundant and accurate than for the IPs themselves; however,such data for negativeions are rare [2]. In

Employing the cited regularities of JJk, q), we have analyzed these data and given estimated corrections or improved values.

this section we extrapolate level and term intervals along isoelectronic sequences using the available data of negative ions as anchors and derive ground configuration centers.

2. Ground configuration centers

2.1. Term inrewals

Configurationcenters measured from the lowest levelsare required to convert ground LPsto average

A term center or the center of gravity of a term is defined as the weightedaverageenergy of the !eveis

(b)

J-

f,(2p’L)

9 I

1 1

2

3

5

4

6

7

(d)

I

I I 1

Fk. 1. Dependence

offi

andfi

g 2

3

4

5

6

7

J.eq. (1)) on q (= Z - N + 1). The required term centers are eveluated from ref. [7]

_.

H.

Qmbe, R.H. Felron/Empiricol

reguhrities

of atomic

ionization

potelltiok

301

belonging to a term with each weight given by the level degeneracy. Term intervals (the energy differences among the term centers) of the s2pk configuration can be specified by the corresponding Slater integrals, viz.,

177,

35,

16,

3,

for JI (2p3) sequence

178,

37,

16,

7,

for fl(3p2) sequence

101,

31,

16,

10,

fi(t7pk) z [npk(lD) - rrpk(3P)] /6,

if k= 2,4

178,

36,

12,

2,

if k = 3

and show that A2(1) = A2(2) is a poor approximation. A better empirical fit to the data is obtained by

5 [npk(‘D) - npkeS)] 19,

(1) f2(npk) G [npk(‘S) - npk(‘D)] /9, s [~rp~(“P)- ~rp~(~D)]16,

if k

q

24

A’(m) = (am t b)-X ,

if k = 3

where ~~p~(~~+lf.)denotes the term center of the =+lL term of the ns2npk configuration. The Slater integral, (1 /25)F2(pp), is denoted by fi and f2, when it is obtained from the lowest interval and the second lowest interval, respectively. The advantage of using fI and f2 over term intervals is the parallelism among different k’s, as is demonstrated in fig. 1. The quanti. ties, fi and f2, are evaluated from experimental data [7] and are plotted against the degree of ionization q in fig. 1, which emphasizes their dependence upon q as well as k. Here, q is defined as 2 - N + 1 with Z being the nuclear charge and N being the number of electrons of an atom or an ion. Note that 4 = 0 corresponds to a negative ion. As is expected from the screening or irregular doublet law [B] , fI and f2 exhibit an approximate linear increase with q;however, deviation from linearity is marked at the beginning of each isoelectronic sequence. For the extrapolation toward q = 0, one has to take account to the non-linearity. This is given by a secondorder difference, A2(m) = [fi:(q = m) -h(q

= m - I)]

- rj(q = m f 1) - fi(q = m)] .

(2)

Extrapolation to a negative ion consists of obtaining A2(1) from the remaining A*(m). The quadratic extrapolation of&(q) by Bates and Moiseiwitsch [V] which has been employed by Edie and Rohrlich [4] and by Zollweg [6] results in A2(l) = A2(2). Recent experimental results [2] on term separations of the negative ions, C-, Al- and Si-, yield the following values (cm-l) for A2(l), A!(2), A2(3), and A2{4):

forfl(3P3)sequence forf2(3p3) sequence

x = 2.1 ,

(4)

where o and b are parameters. Values of’]A2(nr)]-1/2.1 are plotted against m in fig. 2; extrapolation of (4) yields the missing values of A2(1). To determine 0 and b, we consider the foliowing points: values of lA2(~r~)(-1/2.1for higher WIare not reliable, and the similarity between 2p and 3p systems and the parallelism between k = 2 and k = 4 are significant. A2(1) values yield unique term intervals. Missing term intervals for high degrees of ionization in ref. [7] are obtained by an isoelectronic extrapolation similar to the one described above. The only difference is the value of x in (4); here we choose x = 3, as implied by E&en’s semi.empirical formula [lo] _Since the secondorder differences A2(m) are so small for high m, any positive value of x can predict very accurate term intervals for high q. Only values of A*(nz) for small q are sensitive to the choice of the value ofx. 2.2. Fine-structure separations Extrapolation of fine-structure separations toward q = 0 is carried out similarly to that of the term intervals.According to the spin or regular doublet law [Y] , the fourth root of the separation between two levels of a given term increases linearly with q. There is, however, a significant departure from linearity at the beginning of each sequence. Analyzing the second-order differences by eq. (4) with x = 4, we obtain the fine.stnre ture separations of negative ions. 2P and 2D terms of (~rp)~configurations are excluded, since the fourthpower progression now cannot be applied. For these cases, we have examined the second-order differences of the level intervals and extrapolated them to 4 = 0. 2.3. Results The fme-structure separations of negative ions are:

302.‘.

‘H. Bmbe, R.H. Fehon/Empiricuf regu@ities

of ororuic

parenltils

iontiorion

1.5lAT”*~’

ol

f2(2pkl

al

f&3phI

1.4-

1.1-

1.1-

1.1-

(bq-1/2.l

b.4/3

1.3-

Fig 2. !A*(m)[+*.’

versus m for each isoelectronic

sequence offi(n&.

A+)

is in cm+.

A’(l)

values rae obtained from straight

Liles

listed in table 1 anh compared there with values [ 1l] cited in ref. [2]. The excellent agreement beyeen this work and ref. [2] ,indicates that the three ISCF electronic extrapolation methods, ratio, logarithmic, .&&screeningparameter (our procedure essential!y amounts to the,extrapo!ation of this quantity), yield e&ntially.the same iesulis. The one datum available [2} for comparisonis the 482 + 2 cm-l icterval of s+(%‘)ti ic‘h aaJ ees well with extrapolated value of 489 cm-l f&nrj here.

The term separationsor energy differences between the excited term centt~s and ihe ground Levelof a configuration are listed and compared in table 2. Since we use the experimental results cited in table 2 &anchors, these data should be compared with results of previous extrapolations. Calcu!ationsof the configuration centers is straightfonvard, and the results are collected intable 3. It$iazed valuesin table 3 are obtained by the extrapoiation procedures describedabove, and the remainder are calculated with the data cited in ref. [7]

303

H. timbe, R.H. Felton/Empirical regrrbririesof atomic ionization porenrtils Table 1 Fine-structure separations in negative ions _-Separation (cm-‘)

Negative

ion

Term

Be-Up)

ZP 3P

WP2)

W2P3) N-(2~~)

2D 2P aP

W2P5) M_(3P) Au3P2)

*P 2P 3P

Si-(3p3) P_(3P4)

2D 2P 3P

S_(3PS)

2P

Thhbwork

‘excited - ‘ground 3/2-l/2 1-o 2-o 312-512 312-112 l-2 o-2 l/2--3/2 3/2-l/2 I-O 2-o 5/2-312 3/2-l/2 l-2 o-2 l/2-3/2

Ref. [2]

1. 3.’ 8. 3. G.l 58. 83. 180. 20. 25. 72. 9. 16. 193. 282. 489.

4*1 9*1 3*1 181+ 4 26 i 3 76 r 7 722 190 * 20 280 * 30 4BB t 11

Table 2 Term separations in negative ions

Negative ion

B-(2p2) U2P3) N-(Zp’j A1-(3pZ) Si-(3p3) U3P4)

Separations (ev)

Term

Ground center - level

-_-----

‘D-3P, ‘s-3P, 2D-4%,2

‘D-3P2 2P-‘%,,, WP, ‘D-3P. ‘VP, 2D-4S,,2 2p-4q2 ID-‘P2 WPz

This work

Ref. [12]

Ref. [13]

0.44 0.89

0.5% -

0.52

1.24 1.73 1.32 2.67 0.33 0.79 0.66 1.36

1.25

0.99 1.29 1.46 1.28 2.60 0.39 0.94 0.88 1.44

1.85

1.22 2.58 0.29 0.60 0.81 1.31

0.81 1.93 _____-.___-__~

0.77 1.80

0.82 1.94

-

Expt. 121

1.233 f 0.009

0.34 f 0.03 0.862 c 0.005 1.356 f 0.005 ----

Table 3 ConFigurationcenters measured frcm the lowest energy level (in eV) Confguration

9

(W2@Plk

0

1

2

3

4

5

6’

7

n=2

0.000 0.204

0.001 0.602 2.265 0.941 0.017

0.005 0.910 3.168 1.246 0.032

0.014 1.210 4.031 1.552 0.056

0.032 1.516 4.878 1.865 0.092

0.062 1.836 5.721 2.187 0.142

0.108 2.177 6.545 2.529 0.211

0.177 2.548 7.368 2.89;1 0.300

0.009 0.399 1.402 0.580 0.036

0.024 0.569 1.835 0.738 0.059

0.046

0.079

0.734 2.233 0.895 0.090

0.906 2.613 1.056 0.129

0.123 1.090 2.984 I.226 0.178

0.183 1.290 3.350 1.407 0.241

0.259 1.513 3.713

k=l

k=2 k=3 k=4 k=S n=3

k=l k=2

k=3 k=4 k=5

1.140 0.619 0.007 0.002 0.166 0.839 0..406 0.020

1.600 0.3 17

3ac

H. Sombe, R.H. Felton/Empiriml

regrhritiek o/atomic

iodation

porentds

;

0.001 and 0.005 eV for k = 1,.5and k = 2,3,4, respectively and, correspondingly,error limits for separations between individual ten-k (tabie 2) are less than 0.01 eV.

Wehave studied the sensitivjty of the final configuration-center v&s to the slopes of.IA2(~)1-1/2.1. @orek-nple, .if vie let the line (A2(m)1-1/2.1of fl(jp4) pass thro’ugh the experimental nl = 3 point (see fig. 2), the’corresptindingcorifigurationcenter changesto 01401 eV from cited value of 0.406 eV. Indeed, this is the largestchange observed. Based upon’these considerations, we estimate the error limits in energiesof (fl~)~configuration centers as

3. Regularities of average ionization potentials

A set of parameters [@ok, q] specifies implicitly the nuclear chargeZ and the number of electrons N.

Coofiguration -_--_---_-

C[ (nP)L-‘, q +ll

/’

I,,[

Center

(“Dk,q 1 I

Ground iwet

[he) k-l, q c 1I

of

/ Configuration ___Y_I__I_

Center

I,[

I C[(nP)k,

(dlk,q

1

q I

I /

Grodnd

Level

of [(r& ‘, q 1

F~J.3. Relation betweenIg and Iav. Table 4 Values oTJnf(k, q) in eV 4

nl= 1s nl=2s

k

0

1

a:754

1

1

10.989

2

4

5

6

41.655

51.860

62.076

12.980 6.229

16.008 7.657

19.045 8.981

8.303 8.385 .8.699

10.304 10.364 10.773

12.328 12.353 12.806

0.917

3.930

6.943

nf=3s

‘1

1.221

2.507

3.793

31.442 9.957 5.045

nl=2p

1 2 3

0.525 0.653

2.366 2.516

4.328 4.453

6.322 5.436

0.772 -0.893

2.666 2.807

4.596 4.727

5.584 6.672

8.566

10.478

12.421

1.021

2.944

4.860 ..

6.787

8.797

10.884

13.000.

0.562 0.672 -0.794 0.897 I.015

1.799 1.877 I.963 2.052 2.150

2.881 3.027 3.076 3.159 3.251

4.040 4.109 4.176 4.228 4.350

j.457

6.436 6.853 5.568 6.354 6.573

8.145 7.974 6.463 7.313 7.718

4 5 nl’= 3p

1 2, 3 4 5:

.’

21.222

3

5.609

4.551 5.359 5.451

h! Shnrbe,R.H. FeltonfEnrpirical reguhrities of atomiciontiarionporenhfs

Fig. 4. Linarity of I&, refs. [2] and [7].

q) as a function of q, Ig da& from

Let us denote the configuration center of [(n$, q] measured from the ground level by C[(d)li, q], the values of which are already @ven in table 3 excepting the obvious cases of zero values. I,[(#, q] denotes the ground IP from an atom or an ion specified by [(nv, q] , and I,,[@I~~, q] denotes the corresponding average IP. he relationship between Ig and I,, is illustrated in fig. 3. The relation between Ig and I,, is

I,,WY>

41- Ig[bOk,41

= C[(?qP’,q + l]

- C[(tz$, q] .

(5)

The function Jnr defied as .m,(k 9) = Ia, [(~~k+l,

41- Ia”K4”Y41

(61

appears to exhibit many regularities. Values of I,,#, q) listed in table 4 are calculated from the $‘s given in refs. [2] and [7]. Since the Ig data cited in ref. [7] for [(npjk, q > 41 are mostly extrapolate’d results, we can rely only on the J,,#c, q) values for q = 0 to 3 excepting I = s cases. Graphical representations of J&c, q) are shown in figs. 4,5, and 6. In fig. 6, we have sbiftzd the J,p(k, q) value by arbitrary amount To exhibit greater detail. For the (2~)~ system, there

I

I

1

2

,

4

3

F& 5. Linearity of J,,+k, q) as a function of q. Is data from refs. 121 and [7].

exist [I] slightly improved experimental IPs for q = 1 to 3 and accurately extrapolated IPs for q = 4 to 5. The J&k, q) computed from these data are plotted in figs. 7 and 8. By comparison with fig. 8, we beIieve that large deviations from straight-line behavior in fig. 6 are due to inaccurate Ig data of [7] , For q 2 4, the J2,(k, q) values cited in tabie 4 differ considerably from those computed in [l] and do not yield linear behavior. The regularity along q states that the tw@variable function J&k, q), within a given subshell, is a nearly linear function of 4 for each futed k and the deviation from linearity is the lesser the greater is k (see figs. 4, 5 and 7). The actual departures from linearity, i.e., the second-order differences, are smaller than 0.01, 0.01,0.03,0.0~ and 0.04 eV for Jls, J2s, JJs, Jzp(5, q) and JJp(5, q), respectively. Based upon these examples and Elden’s values of J2p (fig. 7), we believe that this regularity holds over a wide range of q for every J&z, 4). previously, Lotz [5] found linearity of

H. Smbe, R.H.FeIton/Empirical~e~brities arrdatomic

‘I

ionizah

patentid

J&,q

9-

nI-

s54-

1

2

3

4

Fig. 6. Liriearity ofJ,,+k, q) as a function of refs (21 and (71.

5

k. Ig datafrom

J,&, q) for q 2 1, The finding of Edie and Rohrlich [4] and Zollweg [6] amounts to linearity of the averagedJR,, (7). alongQfOrQ21. Tile regularity along k states that the two-variable functibn J&c,

Q) is a nearly iinear function of k for

each fixed Q (see fig.6 and 8). Usingthe Jnp data for 4 = 0 and 1, the estimated deviation from Iinearity is less than 0.01 eV. Relying on the linear behavior for higher Q show-n in fig. 8, we conclude that the cited k-regularityholds for q 2 2 in both 2p” and 3pk subghells. The slopes of the straight lines in figs.6 and 8 .are plotted in fig. 9. For q >, 1, there appears to exist a smooth progressionalong 4, but at 4 = 0 this,tendency fails completely, which accounts for the inability .of.Elden+ semi-empiricalformula [ 1,IO] to predict accurate electron affinities.

Fe. 7. Linearityof J#, q) as a function ofq. Ig p”ta from refs. [ !] and 121. The I data from [7] does not peld this linea behavior for q 3 f , Another remarkablecharacter of the J&c, Q) function is the similarity between JIp(k, 0) and J$k, 0) (see fig. 5 and table 4). Fig.9 demonstrates that the slopes of this function tend to a common value for Q= 0. Wehave calculatedJ+(5,0) = 0.94 eV and J$5,0) = 0.83 eV from experimental results [2,7,14]. These valuesagainindicate that all (n~)~ systems yield more or less the sameJn (k, q) valuesat Q = 0. A similartendency exists for Qflsy systems (fig.4). Zollweg [6] noted this tendency earlier for the averagedJ,,, givenby (7).

4. Analyses 4.I, h7ectronaflinities The recommendedelectron affinities by Hotop and Iineberpr [2] are analyzed here. If we adopt

H. Sambe, RH. FeltonfEmptiical

regularities of atomic ionbction potenitik

307

B

0 1

2

3

ZP 4

3P 5

9.1 1.1

I

c I.

1

1

I

I

2

3

1

4

1

5

Fig, 8. Liiearity of Jzp(k, 4) as a function al k. Ig data from refs. [ 1) and [ 21. Compare with fig. 6, especially, J,&3,3). The Ig data from (71 does not yield this linear behavior for q 3 4. their recommended values for (np>k systems, we fmd considerable departures from the k-regularity in both the 2p and 3p subshells.However, if we use asleIectron affinities -0.14 and 0.43 eV for N- and Al-, respectively, instead of their recommended values of -0.07 (kO.08) for N- and 0.46 (kO.03) for Al-; the resultingJflp(k, 0) functions yield the k-regularity with the deviationsas small as the neutral atomic cases. These values of J,,,,(k, 0) were cited in table 4. Based upon this observation, we recommend the improved values-0.14 (20.02) eV for N- and 0.43 (20.02) eV for Al-. The values of JnI(l ,O)cited in table 4 are obtained by enforcing the regularitiesfound here excepting the value of J$,@), which is calculated with 1,,(1s)*, 0] = 0.754 eV and&[ ls,O] = 0 (see ref. [15] for the last equation). Upon replacement of the electron affinities of N- and Al-, the recommended values of Hotop and Lineberger agree remarkably well with the regularitiesclaimed here. With the term-separation results in table 2, we predict that ‘D state of P is not bound. Improved values of the recommended electron affinities are summarizedin table 5.

4.2. Ionization potentids of positive ions It can be noted in table 4 that J,,(k, 4) values for

Fig. 9. Slopes of lines diplayed in 6 and 8 versus q,

4 > 4, especiallyJ3,(3, 9 > 4), depart considerably from the regularitiesclaimed and indicate that previously employed extrapolation methods for IP are less accurate than that advanced here. Wehave reestimated IPs for positive ions and listed in table 6 the differences between our values and those cited by Moore [7]. An accurate determination of an IP, say Ig[(3p)“, 51, fmes the parameter z5, and thus gives the absolute difference with respect to Moore’s values for all IPs characterized by IS[(~P)~, 51. Although accurate to only SO.01 eV, we have listed IF corrections to 0.001 eV to avoid round-off errors.

Acknowledgement Wewish to thank the National Institutes of Health (AM-14344)for partial support of this work. References [l] B. Edlin, in: Topics in modern physics, eds. W.E. Brittin and H. Odabasi (Colorado Associated Univ. Press, Boulder, 1971) p. 133. [2] H. Hotop and W.C. Lineberger, J. Phys. Chem. Ref. Data 4 (1975) 539.

308

H. Sambe. R.H. Felton/Empiricol

reguhriries of atomic

iorlization

prentds

Table 5 Values of recommended atomic electron afftities _~____--_--------_

~--

states 2

Electron affmities (eV)

Atom

7N

13 Al 15 G

23

4s

-

Negative ion

This work

2p4 3P

-0.14 t 0.02

2g 2D3” - 2p4 d

0.92 f 0.02

2p3 2P 3P 2fi,,z

0.77 $0.02 0.43 ? 0.02 0.10 f 0.02

- 2p4 1s; - 3p23Po 3P 2p,,2 - 3p* ‘D, 3p3 4S,,2 - 3p’ ‘Da --

---_ Ref. [ 21 -0.a7 f 0.08

.

1.0 0.9 0.46 0.12

2 0.3 + 0.3 + 0.03 f 0.03

==0

-0.07 f 0.02

Table 6

Estimated correction (eV) to Moore’s ionization potential vdues [7] -----------

? Ill = 3s

1 2

2p

1 2 3

Ill=

(Moore’s IP) - (estimated IP) in eV --~-~-_____~-__-_ q=2 3 4 --_-----___--__---

4

rrl= 3p

5

0.000 +x4 -0.106 +x4

5 6

--

--

-0.000 + 1s 0.032 + xs

6 0.000 + xe 0.061 +xe

0.003 +ys 0.003 +y, -0.003 + y, 0.019 cys 0.011 +y,

0.000 + )I4 0.000 + y4 -0.026 +y4 0.154 + y4 0.095 +y4

-0.167 +yr -0.167 +yr -0.202 + ys 0.077 + y5

-0.229 fY6 -0.225 + yg -0.279 + ya 0.037 + Y6

-0.034 +ys

-0.115 +ys

-0.003 + y3

0.157 +y,

0.166 ty,

0.229 + y,

0.091 + z4 0.372 + z4 0.732 + z4

0.476 + z, 0.596 + .rs 1.065 f zs

0.000 + 2s 0.679 + ze 1.124 + ze

-0.039 + zq -0.075 + z4 -0.092 + zq

0.181 t z5 0.015 + z5 0.000 + zg

-0.005 t Z6

0.102 + z3

1 2 3

o.015+z2 -0.023 + 2s 0.002 + z2

4

-0.007 + z*

0.058 + z3

5

-0.016 + zs

0.007 + ‘3

6

-0.016 + :2

O.ODO + fg

0.097 ffs 0.083 + z3

See, for example, refs. [4] and [lo]. J.W.Edie and F. Rohrlich, J. Chem. Phys. 36 (1962) 623. IV. Lot-r, J. Opt. Sot. Am. 57 (1967) 873. R.J. ZoBweg, J. Chem. Phys. 50 (1969) 4251. C.E. Moore, Ionization potentials and ionization limits derived from the analyses of optical spectra, Nat. Stand Ref. Dah Ser. 34 (Nat Bur. Stand., U.S.A., 1970). IS. Bowen and R.A. Millikan, Phyr Rev. 24 (1924) 209. D-R. Batesand B.L. Moireiwitsch,Proc. Phys. Sot. (London) A68 (1955) 540. B. Eldbn, in: Handbuch der Physik, Vol. 27 (Springer, Berlin, 1964) pp. 171-174. The lground of C-(2D) listed in ref. [2] at table 9 is 3/2 instead of 512. According to [7], the /ground of *D io the N isoelectronic sequence is 5/2 up to AlVIl. Furthermore, the C-(‘D) interval was found by the logarithmic isoelectronic extrapolation, so that the interval cannot change the sign with this procedure.

-0.347 + i6 -0.347 + zg ---

Thesetwo facts imply that the Aground of C-(‘D) listed io ref. [2] is simply a printing error. [12] E. Clementi and A.D. McLean, Phys. Rev. 133 (1964) A419; E. Clementi, A.D. McLean, D.L. Raimondi and M. Yoslimine, Phys. Rev. 133 (1964) A1274. [ 131 B.L. Moiseiwitsch,Advan. Atomic and Mol. Phys. 1 (1965) 61. [ 141 C.E. Moore, Natl. Bur. Std. (U.S.) Circ. 467 (1949, 1958). [15) The [Is,01 parameter set implies thatN = 1 and Z = 0. Since the binding energy of an electron under a constant potential (Z = 0) is zero, we haveI&ls,O] = 0. It is interesting that the q-regularity ‘ofIJs yields 0.756 cV for the H- affinity, which is exactly the same as the value obtained by a stellar detachment’observation [ 161. [16] R.S. Berry, Chem. Revs 69 (1969) 533.