Table 1.

Analysis of main contributions to the standard rate constant for several Ni-N distances

R(Å) *	μ/ν †	Pμ ‡	§	¶	% contrib.∥
2.94	1/0	2.7 × 10-3	0.065	5.3 × 10-4	30
	2/0	2.1 × 10-4	0.587	1.5 × 10-3	61
3.04	2/0	3.8 × 10-6	0.215	6.8 × 10-3	42
	3/0	1.3 × 10-6	0.571	9.8 × 10-3	55
3.25	0/3	1.0	0.855	5.1 × 10-12	40
	4/0	4.3 × 10-11	0.917	1.6 × 10-1	58

^*The Ni-N distance of 2.94 Å is the shortest distance examined. The intermediate Ni-N distance of 3.04 Å is 0.04 Å larger than the dominant distance, and the Ni-N distance of 3.25 Å is the average equilibrium distance.

^†μ and ν correspond to the proton vibrational states for the reduced and oxidized states, respectively, of the catalyst.

^‡P_μ is the Boltzmann probability for state μ.

^§S_μν is the overlap integral between the proton vibrational wavefunctions associated with states μ and ν.

^¶ and is the effective free energy barrier at η = ε = 0.

^∥% contrib. is the percentage contribution to the overall standard rate constant at that distance R, , including only contributions greater than 10%.