Table 1.
Parameters* for the RM1 model for the trications of La, Ce and Pr.
Table 2.
Means and variances of the γ distribution fits for the UME(Ln-L)s computed for the N complexes for each lanthanide trication.
Table 3.
Means and Variances of the γ distribution fits for the UMEs computed for the N complexes for each lanthanide trication.
Table 4.
Sparkle/AM1, Sparkle/PM3, Sparkle/PM6, Sparkle/PM7, Sparkle/RM1 and RM1 unsigned mean errors for lanthanum(III) complexes.
Table 5.
Sparkle/AM1, Sparkle/PM3, Sparkle/PM6, Sparkle/PM7, Sparkle/RM1 and RM1 unsigned mean errors for cerium(III) complexes.
Table 6.
Sparkle/AM1, Sparkle/PM3, Sparkle/PM6, Sparkle/PM7, Sparkle/RM1 and RM1 unsigned mean errors for praseodymium(III) complexes.
Fig 1.
UME(Ln-Ln)s obtained using the RM1 model for the lanthanides and all five versions of the Sparkle Model: Sparkle/RM1, Sparkle/PM7, Sparkle/PM6, Sparkle/PM3 and Sparkle/AM1 for all complexes of the universe set for each of the lanthanide trications: La(III), Ce(III) and Pr(III).
The UMEs are calculated as the absolute value of the difference between the experimental and calculated Ln-Ln interatomic distances, summed up for all complexes, for each of the lanthanides.
Fig 2.
UME(Ln-O)s obtained using the RM1 model for the lanthanides and all five versions of the Sparkle Model: Sparkle/RM1, Sparkle/PM7, Sparkle/PM6, Sparkle/PM3 and Sparkle/AM1 for all complexes of the universe set for each of the lanthanide trications: La(III), Ce(III) and Pr(III).
The UMEs are calculated as the absolute value of the difference between the experimental and calculated Ln-O interatomic distances, summed up for all complexes, for each of the lanthanides.
Fig 3.
UME(Ln-N)s obtained using the RM1 model for the lanthanides and all five versions of the Sparkle Model: Sparkle/RM1, Sparkle/PM7, Sparkle/PM6, Sparkle/PM3 and Sparkle/AM1 for all complexes of the universe set for each of the lanthanide trications: La(III), Ce(III) and Pr(III).
The UMEs are calculated as the absolute value of the difference between the experimental and calculated Ln-N interatomic distances, summed up for all complexes, for each of the lanthanides.
Fig 4.
UME(Ln-C) obtained using the RM1 model for the lanthanides and all five versions of the Sparkle Model: Sparkle/RM1, Sparkle/PM7, Sparkle/PM6, Sparkle/PM3 and Sparkle/AM1 for all complexes of the universe set for each of the lanthanide trications: La(III), Ce(III) and Pr(III).
The UMEs are calculated as the absolute value of the difference between the experimental and calculated Ln-C interatomic distances, summed up for all complexes, for each of the lanthanides.
Fig 5.
UME(Ln-S) obtained using the RM1 model for the lanthanides and all five versions of the Sparkle Model: Sparkle/RM1, Sparkle/PM7, Sparkle/PM6, Sparkle/PM3 and Sparkle/AM1 for all complexes of the universe set for each of the lanthanide trications: La(III), Ce(III) and Pr(III).
The UMEs are calculated as the absolute value of the difference between the experimental and calculated Ln-S interatomic distances, summed up for all complexes, for each of the lanthanides. There are no Ho-S distances in the universe of Ho(III) complexes considered.
Fig 6.
UME(Ln-Cl)s obtained using the RM1 model for the lanthanides and all five versions of the Sparkle Model: Sparkle/RM1, Sparkle/PM7, Sparkle/PM6, Sparkle/PM3 and Sparkle/AM1 for all complexes of the universe set for each of the lanthanide trications: La(III), Ce(III) and Pr(III).
The UMEs are calculated as the absolute value of the difference between the experimental and calculated Ln-Cl interatomic distances, summed up for all complexes, for each of the lanthanides.
Fig 7.
UME(Ln-Br)s obtained using the RM1 model for the lanthanides and all five versions of the Sparkle Model: Sparkle/RM1, Sparkle/PM7, Sparkle/PM6, Sparkle/PM3 and Sparkle/AM1 for all complexes of the universe set for each of the lanthanide trications: La(III), Ce(III) and Pr(III).
The UMEs are calculated as the absolute value of the difference between the experimental and calculated Ln-Br interatomic distances, summed up for all complexes, for each of the lanthanides.
Fig 8.
UME(L-L’)s obtained using the RM1 model for the lanthanides and all five versions of the Sparkle Model: Sparkle/RM1, Sparkle/PM7, Sparkle/PM6, Sparkle/PM3 and Sparkle/AM1 for all complexes of the universe set for each of the lanthanide trications: La(III), Ce(III) and Pr(III).
The UMEs are calculated as the absolute value of the difference between the experimental and calculated interatomic distances between the coordinated atoms, L-L’, summed up for all complexes, for each of the lanthanides.
Fig 9.
UME(Ln-L’)s obtained using the RM1 model for the lanthanides and all five versions of the Sparkle Model: Sparkle/RM1, Sparkle/PM7, Sparkle/PM6, Sparkle/PM3 and Sparkle/AM1 for all complexes of the universe set for each of the lanthanide trications: La(III), Ce(III) and Pr(III).
Fig 10.
UMEs obtained using the RM1 model for the lanthanides and all five versions of the Sparkle Model: Sparkle/RM1, Sparkle/PM7, Sparkle/PM6, Sparkle/PM3 and Sparkle/AM1 for all complexes of the universe set for each of the lanthanide trications: La(III), Ce(III) and Pr(III).
Table 7.
Unsigned mean errors, UME(Eu-L)s and UMEs, for RM1 model for lanthanides, as compared to the respective experimental crystallographic values, obtained from the Cambridge Structural Database, for each of the 84 lanthanum(III) complexes.
Table 8.
Unsigned mean errors, UME(Gd-L)s and UMEs, for RM1 model for lanthanides, as compared to the respective experimental crystallographic values, obtained from the Cambridge Structural Database, for each of the 57 cerium(III) complexes.
Table 9.
Unsigned mean errors, UME(Tb-L)s and UMEs, for RM1 model for lanthanides, as compared to the respective experimental crystallographic values, obtained from the Cambridge Structural Database, [46–48] for each of the 65 praseodymium(III) complexes.
Fig 11.
Root mean square deviation fit and alignment of crystallographic and RM1 fully optimized structures of the tetramer of praseodymium, [Pr4Cl10(OH)2(thiazole)8(H2O)2][20].