The Configurations 4dⁿ + 4d^{n − 1} 5s in Doubly-Ionized Atoms of the Palladium Group

Abstract

Four hundred and eighty-three energy levels belonging to the low even configurations of the third spectra of the palladium group are predicted by the use of interpolation formulas for the interaction parameters.

1. Introduction

In the present paper we describe a systematic treatment of the low even configurations of the sequence¹ of the third spectra of the palladium group. This treatment is analogous to the treatments of the second spectra of the iron group [1],² the second spectra of the palladium group [2], and the third spectra of the iron group [3] described in three previous papers.

The approximation used in this work is, as in the the previous papers, the Slater approximation with several improvements. We have included the interaction between the configurations 4dⁿ, 4dⁿ −5s, we have taken different values for the corresponding parameters B, C and α of the two configurations, we have considered the L(L +1) correction as well as the spin-orbit interaction.

The main stages of this treatment are the following:

1. The Slater approximation, improved by the above mentioned corrections, is used to calculate the energy levels of each spectrum. After diagonalizing (“Diag.”) the energy matrices, the interaction-parameters are considered as free parameters and the best fit to the experimental material is achieved by least-squares calculations (“L.S.”). We call this stage “the separate treatment.”

2. The corresponding interaction-parameters of all the spectra of the sequence are expressed as linear functions (in some cases, with a small quadratic correction) of the atomic number. Only the coefficients of these interpolation formulas (“general parameters”) retain the role of free parameters. Thus, the whole sequence, containing several hundreds of energy levels, is treated as a single problem (“general treatment”) with quite a small number of free parameters.

In the sequence from Y III to Cd III, theory predicts, for the configurations 4dⁿ + 4d^{n −1}5s, 209 terms which split into 483 levels. Unfortunately, the experimental material is rather scarce. Only 56 terms splitting into 130 levels were found reliable and could be fitted with the calculated levels. In most spectra the number of known terms does not exceed the number of electrostatic-interaction parameters; thus, a separate treatment of one spectrum loses a great deal of its significance. Such separate treatments were performed only as an introduction to the interpolative treatment, which is rather reliable even in this case, since the number of parameters rs reduced by the use of interpolation formulas for them.

In the following, we shall first give an account of the situation and the separate calculations in the various spectra, and then describe the general treatment.

Most of the experimental material used in this paper was taken from Moore’s Atomic Energy Levels, [4] later referred to as AEL. Unless other sources are explicitly mentioned, it means that the experimental matter was taken from AEL.

2. Notations

The symbols for the parameters are the usual ones. The parameters A, B, C, ζ refer to the configuration dⁿ, while A′, B′, C′, ζ′ refer to the configuration d^n−ls.

In the actual calculations of the separate treatment A′ was replaced by S′ = A′ − A. In the general treatment A and A′ were replaced by the centers of gravity of the configurations, M and M′, and the difference D′ = M′ − M was expressed by an interpolation formula like the interaction parameters.

The parameter G = G₂(ds) measures the exchange interaction between d and s electrons, H=R²(dd, ds)/35 is the parameter of the interaction between the configurations dⁿ and d^{n −1}s, and α is the parameter of the L(L + l)-correction.

“Diag.” is an abbreviation for “diagonalization,” “L.S.” is an abbreviation for “least-squares calculation.”

3. The Mean Error

Two kinds of mean-error are used in this paper. The “level-mean-error,” Δ, is defined by the formula

$$\mathrm{\Delta }=\sqrt{\Sigma {\mathrm{\Delta }}_1^2/(n-m)}$$ (1)

where the Δ_L are the differences between the observed levels and the calculated levels fitted to them, n is the number of observed levels, and m is the number of free parameters. The “term-mean-error,” Δ′, (the term, “mean error” as denned in this paper is identical to the concept, “residual standard deviation” used in statistical analysis) is defined by the formula

$${\mathrm{\Delta }}^{\prime }=\sqrt{\Sigma {\mathrm{\Delta }}_{\text{T}}^2/\left(n_{\text{T}}-m_{\text{E}}\right)}$$ (2)

where the Δ_T are the differences between the observed terms and calculated terms fitted to them, n_T is the number of observed terms, and m_E is the number of the free electrostatic parameters.

The calculation of Δ is easier, since our least-squares program furnishes $\sum {\mathrm{\Delta }}_{\text{L}}^2$; the abbreviation “mean-error” means the level-mean-error.

In fact, Δ′ is a more serious criterion of the precision of our approximations, as the levels belonging to the same term are strongly correlated, while in the definition of Δ they are considered independent.

4. Survey of the Various Spectra

Y iii − (4d+5s)

This spectrum consists of two terms and needs for its description two electrostatic parameters, so that a separate treatment is meaningless. On the other hand in the general treatment it supplies reliable points for the interpolation formulae of D′ and ζ.

The observed and calculated levels are given in table 7.

Zr iii − (4d² + 4d5s)

These configurations consist of 7 terms which split into 13 levels. In AEL 6 experimental terms, splitting into 12 levels, are reported; only the ¹S of d² is unknown.

Here, too, a separate treatment is not fully significant, since 6 electrostatic parameters are necessary. Nevertheless, a separate treatment was performed in order to get some preliminary information about the more stable parameters: D′, B, G, ζ, ζ.′.

Initial values for the parameters were taken from Zr II [2]. In L.S. 1, the parameter H was frozen and the mean error was 4 because the number of free electrostatic parameters is equal to the number of known terms.

The parameters of the various stages of the calculation are given in table 1, the observed and calculated energy levels in table 8.

Nb iii − (4d³ + 4d²5s)

In these configurations theory predicts 15 terms which split into 35 levels. In a paper of L. Iglesias [5] 11 experimental terms, splitting into 28 levels are reported.

Parameters for Diag. 1 were prepared by comparison with the parameters of NB II and Zr II [2]. It turned out that the level assigned by Iglesias as ²D₃/₂ is actually the ²P_3/2 of d³.

In L.S. 1 we got a mean error of 34.

The estimates of parameters of the various stages of the calculation are given in table 2, the energy levels in table 9.

Mo iii − (4d⁴ + 4d³5s)

These configurations consist of 27 terms, which split into 72 levels. In AEL only the level ⁵D₄ and the 5 levels belonging to the ⁵F of d³s are reported. Since the ground level d^{4 5}D₀ is unknown, Rico and Catalan estimated the value of the ⁵D₄ to be 1500 cm⁻¹, and added to all the known levels an unknown additive constant x. (Note, there is no connection between the unknown numerical constant “x”, introduced by Rico and Catalan, and the variable x = n − 6 defined in eq (5a) in the section on the interpolative treatment.)

Because of these circumstances we did not even include Mo III in the General Least Squares (G.L.S.) calculation, but, using the improved coefficients of the interpolation formulae achieved in the G.L.S., we calculated the interaction parameters of Mo III. Then the matrices of d⁴ + d³s were diagonalized with the use of the interpolated parameters, and thus, we obtained predictions for the levels of Mo III.

Using the calculated values of the (⁴F)⁵F one gets for x the value 340. For ⁵D₄ we got the value 1807 cm⁻¹ and this gives x = 307. We suppose that the uncertainty of x is of the order of magnitude of the term-mean-error of the G.L.S. which is 91 cm⁻¹.

The predicted levels of Mo III are given in table 10.

Tc iii − (4d⁵ + 4d⁴5s)

In these configurations theory predicts 40 terms which split into 100 levels. Unfortunately, no level was observed. Using the results of the G.L.S. the interaction parameters of Tc III were interpolated, and then the energy matrices of these configurations were diagonalized. In this way the energy levels could be calculated.

The predicted levels of Tc III are given in table 11.

Ru iii − (4d⁶ + 4d⁵5s)

These configurations consist of 48 terms, which split into 108 levels. In AEL only 7 levels are reported: The ⁵D of d⁶, and the ⁷S and the ⁵S of d⁵s.

Obviously, no separate treatment was performed, but in the G.L.S. these few data furnished more points for D′, G, and ζ. Of course, the main role of the G.L.S. in this case was to calculate all the levels of Ru III.

The observed and calculated energy levels are given in table 12.

Rh iii − (4d⁷ + 4d⁶5s)

In these configurations theory predicts 33 terms, which split into 82 levels. In AEL all these levels are reported. Only the b²S of d⁶s is considered doubtful.

Even at the preliminary stage of estimating parameters for the first diagonalization we had serious doubts as to the reliability of the experimental material. It is well known that the difference between two terms of d⁶s having the same parent term of d⁶ is determined by the parameter G = G₂(4d5s). This parameter is very stable for all spectra of the transition elements and also does not change considerably for all spectra of the same sequence. In the present spectrum we could get for the parameter G values which were different from each other by about 1000 cm⁻¹, depending upon the choice of the parent term. Only the difference between (⁵D)⁴D and (⁵D)⁶D was consistent with the interpolated value of G.

Since the experimental levels did not seem reliable we decided to perform Diag. 1 with interpolated parameters and to use its results for a more detailed critique of the observed levels. We got a very bad fit. The deviations between the calculated levels and those reported in AEL were frequently more than 10000 cm⁻¹. In order to check if there exists any set of parameters which will give calculated values close to the observed ones we included in the first least-squares calculation (“L.S. 1a”) 81 levels. Only the b²S which is reported as doubtful was excluded. We got a mean error of 3094 cm⁻¹. In L.S. 1b only 33 levels were included. We did not include 42 levels belonging to 4d⁶5s. The terms b²D, a²F, a²H of 4d⁷ were also included. The mean error reduced to 273, . but B′ and C′ assumed nonreasonable values. In L.S. 1c from the configuration d⁶s only the levels of (⁵D) ⁶D and (⁵D) ⁴D were left. The values of B′ and C′ were frozen and we got a mean error of 235. It should be noted that in L.S. 1c we used 6 free electrostatic parameters and 2 frozen ones for the description of only 7 observed terms. Thus, the separate treatment lost its physical significance and we could not use it for further critique of the remaining reported levels.

In the G.L.S. calculations, it turned out that also the other doublets of 4d⁷ were doubtful. Finally, only 16 levels were included in the calculation: the ⁴F and ⁴P of 4d⁷ and the (⁵D) ⁶D and (⁵D) ⁴D of d⁶s.

After these calculations had been finished, we had the opprotunity to discuss the results with A. G. Shenstone and he told us that he had reached similar conclusions by comparing the spectrum of Rh III to the isoelectronic spectrum of Ru II, which he analyzed later.

We hope that the predictions of the G.L.S. will help to revise the analysis of this spectrum.

The parameters of the various stages of the calculation are given in table 3, the levels are given in table 13.

Pd iii − (4d⁸ + 4d⁷5s)

In these configurations theory predicts 21 terms which split into 47 levels. In AEL 19 terms, splitting into 45 levels, are reported. Only the ¹S of 4d⁸ and the high ¹D of 4d⁷5s were not observed. The level assigned as b ³D₁ is reported in AEL as doubtful. It also deviates by about 700 cm⁻¹ from its calculated value, thus we did not include this level in the calculations.

In L.S. 1 the mean error was 157 and in L.S. 2 it reduced to 110. Because of the big distance between the configurations 4d⁷5s and 4d⁸ and the weak interaction between them the parameter H is not stable. Pd III is the only spectrum in the sequence in which the number of experimental levels is sufficient to make also the results of the separate treatment quite reliable.

The estimates of parameters of the various stages of the calculation are given in table 4. The observed and calculated levels are given in table 14.

Ag iii − (4d⁹ + 4d⁸5s)

These configurations consist of 8 terms which split into 18 levels. In AEL only the ²S of d⁸s is not reported, and the ⁴P_1/2 of d⁸s is doubtful. Since also the deviation of this level from its calculated value is rather big, we excluded it from the calculations.

After performing Diag. 1 we saw that the level ²P_1/2 deviates by more than 1000 cm⁻¹ from its calculated value. In L.S. la, where it was included, the mean error was 461. In L.S. 1B, from which it was excluded, the mean error reduced to 112. Hence, we did not include this level in the general least squares.

Not having a sufficient amount of experimental material the parameter H was frozen in L.S. 1a and 1b. After having an interpolation formula for the parameter H we could see that we forced H to assume a value which was much bigger than the correct one. Since in the configuration d⁸s the parameters H and α can compensate each other, this also caused an unjustified increase of α.

The estimates of parameters of the various stages of the calculation are reported in table 5, the energy levels – in table 15.

Cd iii − (4d¹⁰ + 4d⁹5s)

These configurations include only three terms which split into 5 levels. All are experimentally known.

There is no sense to perform any separate calculation of this spectrum. By including it in the G.L.S. we got an additional value for each of the parameters D′, G, ζ′.

The observed and calculated levels are given in table 16.

5. The Interpolative Treatment of the Whole Sequence

5.1. General Description of the Procedure

In the general (interpolative) treatment the whole sequence is considered as one system, and the coefficients of the interpolation formulas are given the role of free parameters. We call these coefficients “General Parameters.”

The parameters B, B′, C, C′, G, H, and α are represented by linear expressions of the form

$$\text{P}(n)=\overline{\text{P}}+\mathrm{\Delta }\text{P}\cdot x,$$ (3)

and the parameters D′, ζ, ζ′ by quadratic expressions of the form

$$\text{P}(n)=\overline{\text{P}}+\mathrm{\Delta }\text{P}\cdot x+{\mathrm{\Delta }}_2\text{P}\cdot y,$$ (4)

where

$$x=n-6^{\prime }$$ (5a)

and

$$y=x^2-10$$ (5b)

Here n is the total number of electrons in the states 4d and 5s. We consider only the coefficients $\overline{P}$, ΔP, and Δ₂P as independent parameters (the “general parameters”). The substitution of x and y for n and n² is used in order to get fairly orthogonal parameters.

By fitting the interpolation-formulas to the parameters of the separate treatments we obtain a set of initial general parameters. Using these parameters, we diagonalized the matrices of all spectra of the sequences; this is the “General Diagonalization” (“G. Diag.”).

In the “General Least-Squares” (“G.L.S.”) the known levels of all the spectra are compared with the results of the General Diagonalization. In this unified least-squares calculation only the general parameters specified in table 6 and the normalization parameters M(dⁿ) are considered as free parameters.

5.2. The Actual Calculations

As a consequence of the separate treatment which was described in the previous chapter we had for the general treatment only 56 reliable observed terms which split into 130 levels. Because of the relatively small amount of experimental material we were forced to use also the results of Zr III and Ag III (which are not quite reliable) for the calculation of the initial interpolation formulas. For the formulas of D′, ζ, and ζ′ even the information from Y III or Cd III was used.

In the G.L.S. we had 30 free parameters: 22 general parameters and 8 additive parameters M(dⁿ). 25 of them are electrostatic interaction parameters and 5 are spin-orbit interaction parameters.

A total of 483 levels, belonging to 209 terms, were calculated. The level mean error of the G.L.S. is

$$\underset{\_}{{\mathrm{\Delta }}_{\text{G.L.S.}}=77{\text{ cm}}^{-1}},$$

and the term-mean-error is

$$\underset{\_}{{{\mathrm{\Delta }}^{\prime }}_{\text{G.L.S.}}=91{\text{ cm}}^{-1}}.$$

The general parameters of the G. Diag. and the improved general parameters which were obtained in the G.L.S. are given in table 6.

6. Conclusions

We shall use the results in order to evaluate the relative importance of the various improvements to the Slater approximation used in the present paper. Generally speaking an interaction (or a correction-term) is important if, relative to other sequences of the transition elements [1–3] the parameter representing it has a large value and a small relative statistical uncertainty.

We see that the spin-orbit interaction is quite important, and it is certainly the most important correction in the right-hand side of the period. This fact can be seen also from the very mixed assignments given to the levels in tables 7 through 16.

The differences (B′ − B), (C′ − C), and (ζ′ − ζ) are much bigger than the uncertainties of these parameters. This means that it is important to allow these parameters to assume different values for the configurations 4dⁿ and 4d^{n −1}5s.

The estimates of the parameter α is considerably smaller than in the iron group, but its standard error is much smaller than its value. This means that it is still necessary in order to improve the fit between the theoretical and experimental levels.

Contrary to the results in the first [6] and second [2] spectra of the palladium group, the interaction between the configurations 4dⁿ and 4d^{n −1}5s is rather unimportant in the right hand side of the present sequence. This fact manifests itself in the large standard errors of H and the small values it assumes.

Out of 10 spectra of the sequence there are 8 in which the amount of experimental material is not sufficient for a reliable separate treatment. Thus, in this sequence the interpolative method is not only the more reliable one – practically it is the only method which enables us to predict the energy-levels for all the third spectra of the palladium group. We hope that these predictions will help in their experimental observation.

An Additional Remark.

The calculations reported in the present paper had been completed about five years ago and then the results were sent to several spectroscopy groups. Some weeks ago, after the stencils for the preprints of this paper had already been typed, we received from Rico a reprint of his paper [7] on the spectrum of Mo III. In table I of his paper he compares his observed levels with our theoretical calculations and the fit is quite good. Checking these results we found out, that by adding to all the calculated levels of Mo III 80 cm⁻¹ the fit is very much improved and we get a mean error of 95 cm⁻¹ with M(d⁴) heing the only free parameter. In table 10 we have added the observed levels of Mo III enclosed in brackets in order to indicate that they were not included in the G.L.S.

The author also was informed by L. Iglesias that now she is making a new analysis of Rh III. Hence, we already know that the calculations reported in the present paper actually help in the further analysis of the third spectra of the Pd group.

7. Tables of Results* Part A: Parameters

Table 1.

Parameters of Zr iii − (4d² + 4d5s)

	Diag. 1	L.S. 1*	G.L.S.
A	4840	4807±3	4741
S′	16560	16481±3	16593
B	530	525±0.3	532
C	1600	1829±2	1757
G	3000	2350±3	2454
H	400	fixed	376
α	25	23±0.4	34
ζ	450	410±1.4	411
ζ′	450	454±2.4	461
Δ		4

^*In tables 1–6 the number following the ± sign is the L.S. standard error of the parameter estimate.

Table 2.

Parameters of Nb iii − (4d³ + 4d²5s)

	Diag. 1	L.S. 1	G.L.S.
A	9260	9308±26	9224
S′	25650	26330±52	26485
B	550	563±2	559
B′	550	593±2	592
C	2200	2054±10	2018
C′	2200	2188±16	2210
G	2400	2386±19	2424
H	400	383±7	334
α	0	30±1	33
ζ	560	544±11	535
ζ′	560	589±11	597
Δ		34

Table 3.

Parameters of Rh iii − (4d⁷ + 4d⁶5s)

	Diag. 1	L.S. 1a	L.S. 1b	L.S. 1c	G.L.S.
A	11650	12717±1790	11792±1560	11621±146	11895
S′	56750	62083±2454	70184±1570	57185±222	56964
B	669	801±104	651±14	647±21	667
B′	713	980±52	1336±74	fixed	716
C	3068	3616±547	3288±57	3293±56	3062
C′	3194	3844±290	2926±76	fixed	3178
G	2296	2316±297	2276±35	2304±33	2304
H					166
α	28	fixed	fixed	24±17	29
ζ	1324	1110±677	1146±64	1141±60	1291
ζ′	1450	1673±490	1395±78	1381±102	1401
n		81	33	22	16
Δ		3094	273	235

n = number of levels included in the L. S. calculations.

Table 4.

Parameters of Pd iii − (4d + 5s)⁸

	Diag. 1	L.S. 1	Diag. 2	L.S. 2	G.L.S.
A	8100	7613±105	7600	7602±90	7663
S′	65100	65836±159	65836	65827±121	65818
B	800	699±13	699	695±9	694
B′	800	747±5	747	744±3	747
C	2500	3221±92	3221	3322±67	3328
C′	3100	3429±25	3429	3445±18	3420
G	2270	2277±24	2277	2274±18	2274
H	385	146±56	235	30±70	124
α	40	31±4	31	28±3	28
ζ	1300	1664±72	1664	1519±43	1545
ζ′	1530	1681±26	1681	1666±18	1667
Δ		157		110

Table 5.

Parameters of Ag iii − (4d + 5s)⁹

	Diag. 1	L.S. 1a	L.S. 1b	G.L.S.
A	1840	1595±400	1689±93	1655
S′	75290	75465±480	75037±115	75125
B′	770	841±33	804±8	778
C′	3210	3063±319	3377±78	3662
G	2270	2413±127	2236±33	2244
H	400	fixed	fixed	82
α	20	68±37	50±9	27
ζ	1730	1846±261	1846±61	1825
ζ′	1730	2031±162	1978±38	1959
Δ		461	112

Table 6.

General parameters in the third spectra of the palladium-group

	G. Diag.	G.L.S.
D̅′	48792	48746±34
ΔD′	8657	8666±10
Δ2D′	85	98±5
B̅	640	640±4
ΔB	28	27±1
B̅′	691	685±2
ΔB′	34	31±1
C̅	2756.9	2803±23
ΔC	232.4	262±8
C̅′	2939.9	2939±14
ΔC′	250.7	243±6
G̅	2318	2334±10
ΔG	−24	−31±6
H̅	250	208±24
ΔH	−40	−42±6
α̅	30	31±2
Δα	0	−0.9±0.7
ζ̅	1190	1193±16
Δζ	221	215±6
ζ̅′	1293	1291±12
Δζ′	232	227±4
Δ2ζ = Δ2ζ′	15.5	13±2
Level mean error		77
Term mean error		91

Tables of Results Part B: Energy Levels

Table 7.

Observed and calculated levels of Y iii

Conf.	Term	J	Observed	G.L.S.
				Calc.	O–C
4d	a2D	3/2	0.0	18	−18
		5/2	724.8	802	−77
5s	a2S	1/2	7466.2	7371	95

Table 8.

Observed and calculated levels of Zr iii

Conf.	Term	J	Observed	G.L.S
				Calc.	O–C
d2	a3F	2	0.00	−1	1
		3	681.0	683	−2
		4	1486.4	1488	−2
d2	a1D	2	5741.55	5725	16
d2	a3P	0	8062.07	8045	17
		1	8325.65	8312	13
		2	8838.21	8833	5
d2	a1G	4	11048.70	11067	−18
ds	(2D)a3D	1	18398.87	18382	17
		2	18802.79	18796	7
		3	19533.35	19532	1
d2	1S	0	(13832.0?)	24518
ds	(2D)b1D	2	25066.25	25122	−56

Table 9.

Observed and calculated levels of Nb iii

Iglesias	Conf.	Term	J	Observed	G.L.S.		Calc. g
					Calc.	O–C
	d3	a4F	3/2	0.0	63	−63	0.403
			5/2	515.8	565	−49	1.029
			7/2	1176.6	1208	−32	1.237
			9/2	1939.0	1949	−10	1.331
	d3	a4P	1/2	8664.3	8614	50	2.430
			3/2	8607.5	8562	45	1.629
			5/2	9593.7	9486	108	1.596
	d3	a2G	7/2	9236.1	9215	21	0.890
			9/2	9804.5	9761	44	1.098
	d3	2P	1/2		10753		0.904
a2D		2P + 4P + 2D	3/2	10912.2	10959	−46	1.307
	d3	a2H	9/2	12916.4	12856	60	0.925
			11/2	13263.8	13183	81	1.091
	d3	2D + 2P	3/2		12894		0.928
		2D	5/2	13094.0	13041	53	1.203
	d3	a2F	7/2	19861.0	19907	−46	1.142
			5/2	19975.0	20061	−86	0.857
	d2s	(3F)b4F	3/2	25220.2	25248	−28	0.403
			5/2	25735.2	25759	−23	1.029
			7/2	26463.7	26481	−18	1.238
			9/2	27373.5	27382	−9	1.333
	d3	2D	5/2		31463		1.197
			3/2		31785		0.800
	d2s	(3F)b2F	5/2	33658.0	33650	8	0.894
			7/2	35079.2	35060	19	1.141
	d2s	(3P)b4P	1/2	34514.5	34500	15	2.664
			3/2	34807.2	34797	10	1.704
		4P + 2D	5/2	34989.8	34983	7	1.507
	d2s	(1D)b2D	3/2	36535.7	36577	−42	0.832
		2D + 4P	5/2	37114.7	37105	10	1.258
	d2s	(1G)b2G	9/2	40875.2	40939	−64	1.112
			7/2	40943.9	40959	−15	0.891
	d2s	(3P)2P	1/2		43004		0.672
			3/2		43729		1.328
	d2s	(1S)2S	1/2		57154		1.997

Table 10.

Observed and calculated levels of Mo iii

Conf.	Term	J	Observed	G.L.S.		Calc. g
				Calc.	O–C
d4	5D	0	(0.00)	40	(−40)
		1	(243.10)	275	(−32)	1.500
		2	(669.60)	688	(−18)	1.499
		3	(1225.20)	1224	(1)	1.498
		4	(1873.80	1847	(27)	1.497
d4	3P	0	(11271.30)	11328	(−57)
		1	(12509.80)	12554	(−44)	1.493
		2	(14357.30)	14373	(−16)	1.491
d4	3H	4	(12630.31)	12634	(−4)	0.843
		5	(13201.34)	13201	(0)	1.043
		6	(13741.54)	13701	(41)	1.167
d4	3F	2	(13927.76)	13923	(5)	0.675
	3F+3G	3	(13947.40)	13924	(23)	1.015
	3F+3G+3H	4	(14295.85)	14233	(63)	1.185
d4	3G+3F	3	(15672.25)	15835	(−163)	0.822
		4	(16143.15)	16224	(−81)	1.067
	3G	5	(16763.14)	16629	(134)	1.190
d4	3D	3	(19390.90)	19391	(0)	1.329
		2	19783.28	19493	290	1.160
		1	(19995.50)	19806	(190)	0.509
d4	1I	6		19754		1.003
d4	1G	4		20377		1.008
d4	1S	0		22555
d4	1D	2		23221		1.011
d4	1F	3		26903		1.005
d4	3P	2	(30992.50)	31086	(−93)	1.495
		1	(32292.70)	32323	(−30)	1.493
		0	(32887.80)	32976	(−88)
d4	3F	4	(31932.50)	31970	(−37)	1.245
		3	(32142.80)	32252	(−109)	1.082
		2	(32126.50)	32112	(15)	0.672
d3s	(4F)5F	1	(32419.44)	32439	(−20)	0.010
		2	(32844.04)	32854	(−10)	1.000
		3	(33453.10)	33459	(−6)	1.249
		4	(34226.01)	34227	(−1)	1.349
		5	(35130.10)	35122	(8)	1.398
d4	1G	4		36033		1.005
d3s	(4P)5P	1	(42405.50)	42389	(17)	2.473
	5P+3F	2	(42665.90)	42652	(14)	1.378
	5P	3	(43462.69)	43420	(43)	1.596
d3s	(4F)3F+5P	2	(42605.84)	42526	(80)	1.112
	(4F)3F	3	(43562.61)	43557	(6)	1.142
		4	(44656.23)	44646	(10)	1.231
d3s	(2G)3G	3		46227		0.763
		4	(46557.96)	46544	(14)	1.053
		5	(46581.03)	46921	(−340)	1.185
d4	1D	2		47541		1.007
d3s	(2P)3P	0		48707
	3P+3D	1	(48753.45)	48636	(117)	1.159
		2	(49052.05)	48972	(80)	1.383
d3s	(2H)3H	4		49460		0.835
		5		50272		1.048
		6		50459		1.167
d3s	3D+3P+1P	1		50200		0.946
	3D+3P	2		51289		1.284
	3D	3		51204		1.333
d3s	(2G)1G	4		52519		0.985
d3s	(4P)3P	0		53082
	3P+1P+3D	1		52528		1.284
	(4P)3P	2		53858		1.487
d3s	(2H)1H	5		54931		1.002
d3s	1P+3P	1		55174		1.133
d3s	(a2D)1D	2		56633		1.001
d3s	(2F)3F	4		58811		1.249
		3		58960		1.084
		2		59121		0.672
d4	1S	0		61910
d3s	(2F)1F	3		64072		1.004
d3s	(b2D)3D	3		71596		1.329
		2		71793		1.165
		1		71940		0.500
d3s	(b2D)1D	2		76887		1.000

Table 11.

Calculated levels of Tc iii

Conf.	Term	J	G.L.S.	Cale. g
d5	6S	5/2	−2	1.997
d5	4G	5/2	19179	0.586
		7/2	19343	0.988
		9/2	19442	1.172
		11/2	19398	1.271
d5	4P+4D	5/2	20987	1.510
		3/2	21308	1.564
		1/2	21759	2.207
d5	4D	7/2	23007	1.422
	4D+4P	5/2	23849	1.430
		3/2	23850	1.354
		1/2	23502	0.456
d5	2I	11/2	28153	0.933
		13/2	28521	1.077
d5	2D+2F	5/2	29536	1.075
	2D+4F	3/2	30299	0.681
d5	4F+2G	9/2	31308	1.292
	4F+2F	7/2	31291	1.182
	4F	5/2	31746	1.015
	4F+2D	3/2	32463	0.534
d5	2F+4F	7/2	32182	1.171
	2F+2D	5/2	33789	1.002
d5	2H+2G+4F	9/2	33612	1.028
	2H	11/2	34954	1.083
d5	2G	7/2	34555	0.915
	2G+2H	9/2	35662	1.034
d5	2F	7/2	36640	1.146
		5/2	36655	0.872
d5	2S	1/2	39605	1.997
d5	2D	3/2	44478	0.801
		5/2	44737	1.193
d4s	(5D)6D	1/2	44705	3.322
		3/2	45063	1.864
		5/2	45607	1.656
		7/2	46287	1.585
		9/2	47069	1.553
d5	2G	9/2	49288	1.111
		7/2	49405	0.891
d4s	(5D)4D	1/2	56604	0.053
		3/2	57168	1.205
		5/2	57959	1.367
		7/2	58847	1.427
d5	2P	3/2	58686	1.317
		1/2	58938	0.660
d4s	(a3P)4P	1/2	61309	2.613
		3/2	62857	1.716
		5/2	65015	1.584
d4s	(3H)4H	7/2	61772	0.670
		9/2	62063	1.001
		11/2	62579	1.141
		13/2	63139	1.228
d4s	(a3F)4F	3/2	63738	0.419
	(a3F)4F+4G	5/2	63609	0.928
		7/2	63808	1.156
		9/2	64055	1.278
d5	2D	5/2	64334	1.195
		3/2	64525	0.805
d4s	(3G)4G + 4F	5/2	65388	0.692
		7/2	66037	1.041
		9/2	66416	1.188
	(3G)4G	11/2	66569	1.259
d4s	(a3P)2P + 4D	1/2	68826	0.564
	(a3P)2P	3/2	71968	1.309
d4s	(3H)2H	9/2	69062	0.933
	2H + 2I	11/2	69934	1.071
d4s	(3D)4D	7/2	69731	1.420
		5/2	69916	1.356
		3/2	69973	1.206
	4D + 2P	1/2	70649	0.170
d4s	(a3F)2F	7/2	70791	1.066
d4s		5/2	71320	0.882
	(1I)2I	13/2	72399	1.079
	2I + 2H	11/2	72703	0.949
d4s	(3G)2G	7/2	72503	0.899
	(3G)2G + (1G)2G	9/2	73239	1.112
d4s	(1G)2G + (3G)2G	9/2	74267	1.098
	2G + 2F	7/2	74648	0.966
d4s	(a1S)2S	1/2	76572	1.966
d4s	(1D)2D + (3D)2D	3/2	76635	0.807
		5/2	77879	1.197
d4s	(3D)2D + (1D)2D	5/2	77018	1.187
		3/2	78766	0.809
d4s	(1F)2F	7/2	81046	1.153
		5/2	81264	0.891
d4s	(b3P)4P	5/2	83340	1.585
		3/2	84675	1.697
		1/2	85616	2.650
d4s	(b3F)4F	9/2	84019	1.330
		7/2	84506	1.227
		5/2	84501	1.019
		3/2	84305	0.442
d4s	(b3F)2F + 2G	7/2	90827	1.039
	(b3F)2F	5/2	91454	0.860
d4s	(b3P2P	3/2	91036	1.334
		1/2	92733	0.678
d4s	(b1G)2G	9/2	91658	1.113
	2G + 2F	7/2	92142	0.993
d4s	(b1D)2D	3/2	104753	0.800
		5/2	104764	1.200
d4s	(b1S)2S	1/2	120665	1.999

Table 12.

Observed and calculated levels of Ru iii

Conf.	Term	J	Observed	G.L.S.		Calc. g
				Calc.	O–C
d6	a5D	4	0.0	−35	35	1.496
		3	1158.8	1139	20	1.498
		2	1826.3	1827	−1	1.498
		1	2266.3	2279	−12	1.498
		0	2476.0	2495	−19
d6	3H+3F+3G	4		15028		0.994
	3H+3G	5		15326		1.066
	3H	6		15081		1.162
d6	3P	2		15092		1.486
		1		18412		1.454
		0		19048
d6	3F+3H	4		16824		1.043
	3F+3G	3		16857		1.025
	3F	2		17357		0.677
d6	3G+3H	5		18612		1.167
	3G+3F	4		19611		1.062
		3		19878		0.814
d6	3D	1		22495		0.550
		2		22319		1.171
		3		22644		1.328
d6	1I	6		23289		1.004
d6	1G	4		24503		1.006
d5s	(6S)a7S	3	27162.8	27177	−14	1.997
d6	1S	0		27242
d6	1D	2		28412		1.008
d6	1F	3		31296		1.007
d6	2P	0		34942
		1		35818		1.498
		2		38006		1.491
d6	3F	4		36927		1.244
		3		37559		1.079
		2		37008		0.671
d5s	(6S)a5S	2	41111.7	41121	−9	1.992
d6	1G	4		42394		1.005
d5s	(4G)5G	2		51433		0.345
		3		51551		0.924
		4		51674		1.152
		5		51743		1.266
		6		51703		1.332
d5s	(4P)5P+5D	3		53614		1.600
		2		53937		1.701
		1		54432		2.257
d6	1D	2		54879		1.013
d5s	(4D)5D	4		55985		1.493
	5D+5P	3		57107		1.542
		2		57152		1.600
		1		56727		1.726
	5D	0		56198
d5s	(4G)3G	3		60682		0.771
		4		60980		1.054
		5		60957		1.195
d5s	(4P)3P+3D	2		62624		1.323
		1		63453		1.033
	3P	0		64541
d5s	(2I)3I	5		64001		0.847
		6		64093		1.030
		7		64422		1.143
d5s	(4D)3D+5F	3		65012		1.294
	3D	2		66051		1.152
	3D+3P	1		66262		0.669
d5s	(4F)5F+3P	1		65273		0.316
	5F	2		65408		1.054
	5F+3D	3		65724		1.275
	5F	4		65554		1.336
		5		65454		1.382
d5s	3D+3F+5F	3		66565		1.216
	3D+3F+1D	2		69516		1.006
	3D+5F+3P	1		68811		0.497
d5s	3F+3D+3P	2		67522		0.984
	3F+3G+3D	3		70165		1.040
	3F	4		68919		1.241
d5s	(2I)1I+3H	6		68535		1.002
d5s	3H+3G	4		70311		0.923
		5		72693		1.110
	3H+1I	6		72408		1.139
d5s	3G+3H	5		70511		1.126
		4		72228		0.965
	3G+3F	3		71472		0.908
d6	1S	0		71104
d5s	(a2D)1D+3F	2		73602		0.892
d5s	(2F)3F	2		73625		0.705
	3F+1F	3,		73412		1.059
		4		73715		1.227
d5s	(4F)3F+1G	4		74832		1.184
	3F+1F	3		74904		1.063
	3F	2		76138		0.738
d5s	(2F)1F+3F	3		75145		1.050
d5s	(2H)1H	5		76539		1.008
d5s	(2G)1G+3F	4		77177		1.071
d5s	(2S)3S	1		77522		1.997
d5s	(2F)1F	3		78799		1.027
d5s	(2S)1S	0		82821
d5s	(b2D)3D	1		82910		0.502
		2		83073		1.161
		3		83477		1.311
d5s	(b2D)1D	2		87968		0.999
d5s	(2G)3G	5		88207		1.200
		4		88335		1.051
		3		88434		0.754
d5s	(2G)1G	4		92963		1.001
d5s	(2P)3P	2		99093		1.490
		1		99316		1.486
		0		99513
d5s	(2P)1P+3D	1		103479		0.923
d5s	(c2D)3D	3		105494		1.333
		2		105701		1.172
		1		106119		0.595
d5s	(c2D)1D	2		110249		1.003

Table 13.

Observed and calculated levels of Rh iii

Conf.	Term	J	Observed	G.L.S.		Calc. g
				Calc.	O–C
d7	a4F	9/2	0.0	−25	25	1.327
		7/2	2147.8	2124	24	1.236
		5/2	3485.7	3476	9	1.031
		3/2	4322.0	4328	−6	0.414
d7—	a4P	5/2	11062.3	11060	2	1.592
	4P + 2P	3/2	10997.1	11085	−88	1.642
		1/2	12469.8	12519	−50	2.507
d7	2G	9/2		13092		1.093
		7/2		15229		0.893
d7	2P+2D+4P	3/2		16334		1.250
	2P+4P	1/2		18451		0.827
d7	2H	11/2		17317		1.091
		9/2		19500		0.931
d7	2D	5/2		18436		1.203
	2D+2P	3/2		21873		0.960
d7	2F	5/2		26798		0.863
		7/2		27889		1.140
d7	2D	3/2		42251		0.800
		5/2		43173		1.196
d6s	(5D)a6D	9/2	43022.0	43010	12	1.552
		7/2	44394.4	44385	9	1.584
		5/2	45278.2	45274	4	1.654
		3/2	45876.6	45876	1	1.862
		1/2	46227.1	46230	−3	3.317
d6s	(5D)a4D	7/2	54632.2	54576	56	1.418
		5/2	56125.7	56109	17	1.370
		3/2	57012.5	57013	0	1.200
		1/2	57531.3	57545	−14	0.023
d6s	(3H)4H	13/2		62412		1.227
	4H+4G	11/2		62573		1.153
	4H+4G+4F	9/2		62416		1.091
		7/2		62857		0.796
d6s	(a3P)4P	5/2		62555		1.585
		3/2		65466		1.574
		1/2		67426		2.523
d6s	4F+4H	9/2		64224		1.191
		7/2		64732		1.081
	4F+4G	5/2		64864		0.957
	(3F)4F	3/2		65263		0.492
d6s	4G+4H	11/2		66126		1.236
	4G+4F	9/2		67620		1.175
		7/2		68041		1.020
		5/2		67796		0.668
d6s	(3H)2H	11/2		69678		1.091
	2H+2G	9/2		69710		0.964
d6s	2F+2G+4D	7/2		70567		1.123
	(3F)2F	5/2		72351		0.871
d6s	2P+4D+4P	3/2		70583		1.345
	2P+2S	1/2		73950		0.842
d6s	(3D)4D	1/2		70819		0.159
	4D+2P	3/2		71264		1.236
	4D	5/2		70984		1.361
		7/2		71445		1.363
d6s	(3G)2G	9/2		73708		1.089
		7/2		74718		0.909
d6s	(1I)2I	13/2		74084		1.080
		11/2		74354		0.939
d6s	(a1G)2G	9/2		76094		1.096
	2G+2F	7/2		76404		0.945
d6s	(3D)2D	3/2		77596		0.821
		5/2		77834		1.191
d6s	2S+2P+4P	1/2		79502		1.847
d6s	(a1D)2D	5/2		80313		1.204
		3/2		80439		0.810
d6s	(1F)2F	7/2		82984		1.157
		5/2		83130		0.886
d6s	(b3P)4P	1/2		85311		2.601
		3/2		86279		1.718
		5/2		88927		1.579
d6s	(b3F)4F	9/2		87320		1.328
		7/2		88264		1.221
		5/2		88099		1.013
		3/2		87453		0.412
d6s	(d3P)2P	1/2		92424		0.687
		3/2		95311		1.330
d6s	2F+2G	7/2		94021		1.093
	(b3F)2F	5/2		94542		0.862
d6s	(b1G)2G	9/2		95741		1.114
	2G+2F	7/2		96104		0.940
d6s	(b1D)2D	5/2		110016		1.200
		3/2		110018		0.801
d6s	(b1S)2S	1/2		128531		1.999

Table 14.

Observed and calculated levels of Pd iii

AEL	Conf.	Term	j	Observed	G.L.S.		Calc. g
					Calc.	O–C
	d8	a3F	4	0.0	2	−2	1.248
			3	3229.7	3227	3	1.083
			2	4687.3	4728	40	0.714
a1D	d8	a3P+1D	2	10230.5	10330	−99	1.284
		3p	1	13470.3	13394	76	1.500
			0	13699.1	13636	63
a3P2	d8	a1D+3P	2	14634.3	14768	−133	1.168
	d8	a1G	4	17880.4	17824	56	1.002
	d8	1S	0		41196
	d7s	(4F)a5F	5	52915.9	52885	31	1.395
			4	55088.8	55040	49	1.344
			3	56741.5	56697	44	1.248
			2	57845.0	57806	39	1.002
			1	58527.3	58492	36	0.017
	d7s	(4F)b3F	4	62560.9	62397	163	1.242
			3	65255.4	65181	74	1.151
			2	67079.4	66986	94	0.694
	d7s	(4P)a5P	3	65708.0	65689	19	1.595
			2	65788.3	65817	−29	1.754
			1	67151.4	67195	−44	2.403
	d7s	(2G)a3G	5	69985.8	70034	−49	1.185
		3G+3H	4	71047.2	71027	20	1.022
		3G	3	72786.1	72791	−4	0.759
	d7s	(2P)3P	2	72745.0	72859	−113	1.381
		3P+1P+3D	1	73002.6	73096	−93	1.259
		(2P)3P+(4P)3P	0	74281.1	74320	−38
	d7s	(2H)a3H	6	74673.3	74741	−67	1.167
			5	75967.6	75971	−4	1.040
		3H+1G	4	78581.1	78525	56	0.890
	d7s	1G+3H+3G	4	75403.0	75336	67	0.957
	d7s	(4P)c3P	2	75455.0	75447	8	1.430
			1	76055.8	76193	−137	1.346
		(4P)3P+(2P)3P	0	78732.5	78682	50
	d7s	(a2D)a3D	3	76231.4	76235	−4	1.331
		3D+1D+3P	2	78169.8	78125	45	1.176
		3D+3P+1P	1	78120.0	78210	−90	1.049
	d7s	(2H)a1H	5	80805.1	80802	3	1.012
	d7s	1P+3D+3P	1	82620.3	82809	−189	0.925
	d7s	(a2D)c1D+3P+3D	2	83204.3	83113	91	1.074
	d7s	(2F)c3F	2	85420.7	85494	−74	0.678
			3	85830.4	85940	−110	1.084
			4	86795.2	86937	−142	1.246
	d7s	(2F)a1F	3	90684.3	90857	−173	1.004
	d7s	(b2D)b3D	1	(103529.4?)	102858		0.501
			2	103549.6	103296	254	1.160
			3	104419.1	104124	295	1.327
	d7s	(b2D)1D	2		108183		1.002

Table 15.

Observed and calculated levels of Ag iii

Conf.	Term	J	Observed	G.L.S.		Calc. g
				Cale.	O–C
d9	a2D	5/2	0	23	−23	1.200
		3/2	4607	4587	20	0.800
d8s	(3F)a4F	9/2	63250	63283	−33	1.332
		7/2	65764	65744	20	1.226
		5/2	68145	68146	−1	1.031
		3/2	69351	69360	−9	0.440
d8s	(3F)a2F	7/2	71691	71579	113	1.151
	2F+2D+4P	5/2	73934	73955	−21	1.135
d8s	4P+2F	5/2	76406	76415	−9	1.284
	4P+2D	3/2	77413	77476	−63	1.426
	4P	1/2	(79326?)	78938		2.656
d8s	2D+4P+2P	3/2	80131	80213	−82	1.189
	2D+4P	5/2	82231	82363	−132	1.236
d8s	2P+2D	3/2	85182	85216	−34	1.212
		1/2	(87477)	85512		0.682
d8s	(1G)a2G	9/2	85599	85703	−104	1.113
		7/2	85727	85760	−33	0.893
d8s	(1S)2S	1/2		111864		1.994

Table 16.

Observed and calculated levels of Cd iii

Conf.	Term	J	Observed	G.L.S.		Calc. g
				Calc.	O–C
d10	a1S	0	0.0	−72	72
d9s	(2D)a3D	3	80454.3	80540	−86	1.332
		2	82354.6	82361	−6	1.125
		1	86219.5	86237	‒18	0.500
d9s	(2D)a1D	2	88871.8	88834	38	1.042