Calculation of the Quantum-Mechanical Tunneling in Bound Potentials

Table 2

Thermal rate constants 𝑘(𝑇) for the asymmetric rectangular double well of Section 3.2. The first column lists the temperature, that is, 𝑘_𝐵𝑇 in units of the barrier height 𝑉_𝑏. The thermal rate constants obtained using (9) using exact energy levels and QM and QC transmission probabilities are given in the second and third columns, respectively. The last column contains the thermal rate constants obtained from QC tunneling probability and the energy levels of the reactant potential with infinitely high walls.

𝑘𝐵𝑇/𝑉𝑏	𝑇^QM𝐸^QM𝑛	𝑇^QC𝐸^QM𝑛	𝑇^QC𝐸^QC𝑛
0.01	6.91 (−13)	2.65 (−13)	7.38 (−15)
0.02	1.01 (−8)	3.80 (−9)	7.78 (−10)
0.04	1.23 (−6)	4.64 (−7)	2.52 (−7)
0.1	3.99 (−5)	2.67 (−5)	1.96 (−5)
0.2	1.31 (−3)	1.97 (−3)	2.41 (−3)
0.4	1.95 (−2)	2.66 (−2)	3.64 (−2)
1.0	0.134	0.159	0.198
2.0	0.286	0.320	0.371
4.0	0.450	0.483	0.533