We present a theoretical explanation for observed regularities in s -electron binding energies in lNs2 and lNs: viewed as a function of N, the curves form straight lines, joined continuously at the half-filled shell. The change in slope can be interpreted as an effective exchange integral Gl(l, s). We show that values of the exchange integral obtained from fitting ionization-energy curves generally agree with values obtained in other ways.
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σ = rms deviation
Reference 5.
Reference 10–12.
Reference 18.
Reference 15.
Y point excluded.
Reference 16.
Reference 22.
Reference 3.
Value for P (N = 3), Ref. 23.
Value for As (N = 3), Ref. 24.
TABLE II
fNs − fN binding energies and positions of fNs configurations for the +3 lanthanides. Extrapolated values from
References 26 and 27. Number in parentheses is the estimated standard deviation error in the last digit of the quoted value.
Calculated from w(fNs) − w(fN) and IP’s. Errors indicated in parentheses are 0.1 eV + error of Ref. 27.
Values in parentheses are estimates of Brewer (Ref. 28). Experimental values from Ref. 27.
TABLE III
Slopes (a and a′) and intercepts (b and b′) for extrapolation of lanthanide IP’s fNs → fN (all values in cm−1).
a
b
a′
b′
σ
+1 → +2
HF
1270 ± 10
79 655 ± 70
885 ± 7
82 354 ± 71
77
Exp.
1428 ± 10
80 797 ± 29
1076 ± 10
83 262 ± 32
72
Exp.-HF
158
1142
231
908
+2 → +3
HF
2102 ± 4
139 219 ± 13
1621 ± 2
142 581 ± 43
19
Exp.
2261 ± 11
141 438 ± 54
1688 ± 14
145 449 ± 57
114
Exp.-HF
159
2219
67
2868
+3 → +4
HF
3022 ± 8
208 360 ± 38
2444 ± 8
212 408 ± 40
54
Exp.-HF
160
3296
−97
5048
(Extrapolated)
Exp.
3182
211 656
2347
217 236
(Extrapolated)
Comparison with experimental fourth IPs
W(lNs) − W(lN)
Calc.
Exp.
N = 1
Pr
214 840
214 130 ± 160
N = 13
Lu
247 760
247 680 ± 160
TABLE IV
Slopes (a and a′) and intercepts (b and b′) for extrapolation from lanthanides to actinides.
Reference 34.
The ground level is not fNs2 and the extent of CI in the low levels is unknown so calculation of the fNs2 → fNs binding energy is not possible.
Because of CI in these elements these numbers may not correspond to an observable quantity.
Tables (5)
TABLE I
Constants from least squares fits of binding energies (lNs2 → lNs or lNs → lN) vs N (all values are in cm−1)
σ = rms deviation
Reference 5.
Reference 10–12.
Reference 18.
Reference 15.
Y point excluded.
Reference 16.
Reference 22.
Reference 3.
Value for P (N = 3), Ref. 23.
Value for As (N = 3), Ref. 24.
TABLE II
fNs − fN binding energies and positions of fNs configurations for the +3 lanthanides. Extrapolated values from
References 26 and 27. Number in parentheses is the estimated standard deviation error in the last digit of the quoted value.
Calculated from w(fNs) − w(fN) and IP’s. Errors indicated in parentheses are 0.1 eV + error of Ref. 27.
Values in parentheses are estimates of Brewer (Ref. 28). Experimental values from Ref. 27.
TABLE III
Slopes (a and a′) and intercepts (b and b′) for extrapolation of lanthanide IP’s fNs → fN (all values in cm−1).
a
b
a′
b′
σ
+1 → +2
HF
1270 ± 10
79 655 ± 70
885 ± 7
82 354 ± 71
77
Exp.
1428 ± 10
80 797 ± 29
1076 ± 10
83 262 ± 32
72
Exp.-HF
158
1142
231
908
+2 → +3
HF
2102 ± 4
139 219 ± 13
1621 ± 2
142 581 ± 43
19
Exp.
2261 ± 11
141 438 ± 54
1688 ± 14
145 449 ± 57
114
Exp.-HF
159
2219
67
2868
+3 → +4
HF
3022 ± 8
208 360 ± 38
2444 ± 8
212 408 ± 40
54
Exp.-HF
160
3296
−97
5048
(Extrapolated)
Exp.
3182
211 656
2347
217 236
(Extrapolated)
Comparison with experimental fourth IPs
W(lNs) − W(lN)
Calc.
Exp.
N = 1
Pr
214 840
214 130 ± 160
N = 13
Lu
247 760
247 680 ± 160
TABLE IV
Slopes (a and a′) and intercepts (b and b′) for extrapolation from lanthanides to actinides.
Reference 34.
The ground level is not fNs2 and the extent of CI in the low levels is unknown so calculation of the fNs2 → fNs binding energy is not possible.
Because of CI in these elements these numbers may not correspond to an observable quantity.