Table 1 Electric fields and free energies of reductive elimination reaction in the Ga₄L₆¹²⁻ capsule.

Electric fields		E₁/MV cm⁻¹			E₂/MV cm⁻¹
Electric fields		Bulk water	Complexed water	Cage	Bulk water	Complexed water	Cage
RS
Uncatalyzed reaction		−21.49	59.73	N/A	−12.75	−14.89	N/A
Catalyzed reaction		−6.72	40.81	−0.21	−6.87	−7.97	−14.13
TS
Uncatalyzed reaction		−4.55	9.63	N/A	−15.81	−21.2	N/A
Catalyzed reaction		−51.63	19.30	27.27	−31.37	22.27	9.95
	\({\Delta G^{elec} = \mathop {\sum }\limits_i -0.048 ({\mathbf{\upmu }}_{{\it{TS}}}^i \cdot {\mathbf{E}}_{{\it{TS}}}^i - {\mathbf{\upmu }}_{{\it{RS}}}^i \cdot {\mathbf{E}}_{{\it{RS}}}^i)}\)
	\({\mathbf{\upmu }}_{{\it{RS}}}^1\)	\({\mathbf{\upmu }}_{{\it{RS}}}^i\)	\({\mathbf{\upmu }}_{{\it{TS}}}^1\)	\({\mathbf{\upmu }}_{{\it{TS}}}^2\)	Bulk water	Complexed water	Cage
Uncatalyzed reaction	−6.15	−2.83	−1.26	3.67	10.58	−11.29	N/A
Catalyzed reaction	−6.15	−2.83	2.05	0.71	9.02	−13.62	−1.04

The electric fields (E₁ and E₂, respectively) are given by the contribution from bulk water, a vicinal water, and from the nanocage for the reactant (RS) and transition state (TS) of the uncatalyzed and catalyzed reaction. Positive fields are defined in the opposite direction of the flow of electrons and contribute to stabilizing electrostatic effects. The bond dipoles \(({\mathbf{\upmu }}_{{\it{RS}}}^1,{\mathbf{\upmu }}_{{\it{RS}}}^2,{\mathbf{\upmu }}_{{\it{TS}}}^1,{\mathbf{\upmu }}_{{\it{TS}}}^2)\) were computed from the partial charges on the gold and carbon atoms, and using the bond length d_Au-Ci as shown in Supplementary Fig. 2 and Supplementary Table 1. The unit conversion factor for free energy \(\Delta G^{elec}\) from the projected electric field on the bond dipole in kcal/mol is 0.048. Color key: carbon = gray, phosphorous = orange, gold = yellow, hydrogen = white, oxygen=red

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