Summary of the thermodynamic free energy changes relevant to address the difference in intermolecular affinity and in intermetallic interactions which control the speciation of f–f′ helicates under thermodynamic control in solution beyond statistical distributions mentioned in columns 4 and 7.

Helicate	Binding sites		ΔGstatperm (kJ mol−1)	ΔEmix1–2 (kJ mol−1)		ΔGstatexch (kJ mol−1)	Condition	Favoured speciesa	Ref.
[(L2)3(LnA)(2−n)(LnB)n]6+	N9–N6O3/N8–N7O2 b	—	0	—	−14.1 to −6.4	−3.4	—	Hetero	10
[(L3)3(La)(2−n)(Lu)n]6+	R–N9–N6O3 c	12.1	0	0d	—	−3.4	—	—	52
[(L6)3(LnA)(2−n)(LnB)n]6+	N6O3–N6O3	0	0	−0.6 to 0.4	−3.5 to −3.3	−3.4	—	Statistical	83
[(L5)3(LnA)(2−n)(LnB)n]6+	N9–N9	0	0	0	−3.4	−3.4	R LnA ≥ RGd and RLnB ≥ RGd	Statistical	65
[(L5)3(LnA)(2−n)(LnB)n]6+	N9–N9	0	0	1.6 to 2.3	−0.2 to 1.2	−3.4	R LnA < RGd or RLnB < RGd	Homo	65
[(L7)3(LnA)(3−n)(LnB)n]9+	N6O3–N9–N6O3	2.2 to 4.2	3.34	−0.6 to 0.2	−10.8 to −5.4	−5.4	—	Hetero	67
[(L8)3(La)(4−n)(Lu)n]12+	N6O3–N9–N9–N6O3	—	—	−2	−47.5	−22.2	—	Hetero	12
[(L43Zn)(LnA)(2−n)(LnB)n]8+	[ZnN6]–N9–N6O3	3.0 to 5.4	0	1.2 to 1.9	−3.6 to −0.4	−3.4	R LnA < RGd or RLnB < RGd	Homo	This work
[(L43Zn)(LnA)(2−n)(LnB)n]8+	[ZnN6]–N9–N6O3	5.4	0	−0.8	−7.5	−3.4	R LnA ≥ RGd and RLnB ≥ RGd	Hetero	This work

^aHomo resp. hetero = preference for homometallic, resp. heterometallic lanthanide complexes; statistical = no preference.

^bThe triple-stranded helicates exist as variable mixtures of HHH (N₉–N₆O₃) and HHT (N₈–N₇O₂) isomers.

^cR represents an organic tripod.

^dThe mixing energy is arbitrarily fixed to ΔE^mix_1–2 = 0.