Skip to main content
. 2022 Jan 20;61(4):1817–1830. doi: 10.1021/acs.inorgchem.1c01525

Table 2. Slater Integrals and Spin–Orbit Coupling Constants for the Lanthanide Trivalent Cations (Ln3+)a.

Ln configuration F2 (4f, 4f) F4 (4f, 4f) F6 (4f, 4f) F2 (2p, 4f) G2 (4f, 4f) G4 (2p, 4f) F2 (3d, 4f) F4 (3d, 4f) G1 (3d, 4f) G3 (3d, 4f) G5 (3d, 4f) ξ (4f) ξ (2p) ξ (3d)
La 4f0 0.000 0.000 0.000                 0.000    
  2p54f1 0.000 0.000 0.000 1.305 0.116 0.075           0.091 281.477  
  3d94f1 0.000 0.000 0.000       7.063 3.167 4.723 2.761 1.905 0.092   6.799
Ce 4f1 0.000 0.000 0.000                 0.087    
  2p54f2 12.436 7.808 5.619 1.408 0.130 0.083           0.106 304.694  
  3d94f2 12.628 7.940 5.717       7.486 3.384 5.073 2.968 2.048 0.107   7.446
Pr 4f2 12.227 7.670 5.518                 0.103    
  2p54f3 12.920 8.114 5.839 1.508 0.143 0.092           0.123 329.429  
  3d94f3 13.096 8.235 5.929       7.889 3.591 5.410 3.166 2.186 0.123   8.139
Nd 4f3 12.725 7.985 5.744                 0.119    
  2p54f4 13.381 8.404 6.048 1.604 0.156 0.100           0.140 355.758  
  3d94f4 13.543 8.516 6.132       8.275 3.790 5.734 3.357 2.318 0.141   8.879
Pm 4f4 13.197 8.282 5.959                 0.136    
  2p54f5 13.823 8.682 6.248 1.698 0.169 0.109           0.159 383.763  
  3d94f5 13.975 8.787 6.326       8.650 3.983 6.049 3.543 2.447 0.160   9.668
Sm 4f5 13.648 8.566 6.163                 0.155    
  2p54f6 14.251 8.950 6.441 1.790 0.182 0.117           0.180 413.526  
  3d94f6 14.393 9.049 6.515       9.014 4.171 6.357 3.724 2.572 0.180   10.510
Eu 4f6 14.083 8.839 6.360                 0.175    
  2p54f7 14.665 9.209 6.628 1.881 0.195 0.126           0.202 445.137  
  3d94f7 14.800 9.303 6.698       9.368 4.354 6.657 3.901 2.695 0.202   11.405
Gd 4f7 14.505 9.103 6.550                 0.197    
  2p54f8 15.070 9.462 6.809 1.970 0.208 0.134           0.226 478.688  
  3d94f8 15.197 9.551 6.876       9.715 4.533 6.951 4.075 2.815 0.225   12.357
Tb 4f8 14.915 9.360 6.734                 0.221    
  2p54f9 15.465 9.709 6.987 2.057 0.221 0.142           0.251 514.272  
  3d94f9 15.586 9.794 7.050       10.055 4.709 7.240 4.245 2.933 0.251   13.368
Dy 4f9 15.315 9.610 6.914                 0.246    
  2p54f10 15.852 9.951 7.160 2.143 0.234 0.151           0.279 551.991  
  3d94f10 15.968 10.032 7.221       10.389 4.882 7.524 4.412 3.049 0.278   14.439
Ho 4f10 15.707 9.854 7.089                 0.273    
  2p54f11 16.233 10.188 7.330 2.228 0.247 0.159           0.308 591.947  
  3d94f11 16.343 10.265 7.389       10.718 5.052 7.803 4.577 3.163 0.307   15.575
Et 4f11 16.091 10.094 7.261                 0.302    
  2p54f12 16.607 10.421 7.497 2.312 0.260 0.167           0.339 634.250  
  3d94f12 16.713 10.496 7.554       11.042 5.219 8.080 4.740 3.276 0.337   16.777
Tm 4f12 16.469 10.330 7.431                 0.333    
  2p54f13 16.975 10.650 7.662 2.395 0.273 0.176           0.372 679.013  
  3d94f13 17.077 10.722 7.716       11.362 5.385 8.352 4.901 3.387 0.371   18.048
Yb 4f13 16.841 10.561 7.597                 0.366    
  2p54f14 17.339 10.876 7.824 2.477 0.285 0.184           0.408 726.353  
  3d94f14 17.437 10.946 7.877       11.677 5.548 8.622 5.060 3.497 0.406   19.391
a

All values are in electronvolts. In the spectroscopy calculations, the Slater integrals were scaled by 0.8 to correct for the Hartree–Fock approximations (see the text for details). Only the unfilled orbitals are shown in the configuration column.