Quantum Instanton Evaluations of the Thermal Rate Constants for Complex Systems

Table 1

Theoretical and experimental rate constants obtained for the 𝐻+𝐶𝐻₄→𝐻₂+𝐶𝐻₃ reaction. (𝜉_𝑎,𝜉_𝑏) is the saddle point of the quantum free energy surface. 𝑘_𝑄𝐼 is the quantum instanton rate constant. 𝑘_CVT/𝜇OMT is the rate constant of the canonical variational theory with microcanonical optimized multidimensional tunneling (CVT/μOMT) [46]. 𝑘^𝑎_exp𝑡 and 𝑘^𝑏_exp𝑡 are the experimental Arrhenius fits, 𝑘(𝑇)=2.18×10⁻²⁰𝑇^3.0exp(−4045/𝑇)[47] and 𝑘(𝑇)=6.78×10⁻²¹𝑇^3.156exp(−4406/𝑇) [48], respectively. Unit: 𝑐𝑚³𝑠⁻¹ for rates.

T (K)	(𝜉𝑎,𝜉𝑏)	𝑘QI	𝑘CVT/𝜇OMT	𝑘^𝑎exp𝑡	𝑘^𝑏exp𝑡
200	(0.93, 1.28)	3.30 (−22)		2.87 (−22)	3.36 (−23)
300	(1.05, 1.05)	7.80 (−19)	5.03 (−19)	8.20 (−19)	1.86 (−19)
400	(1.05, 1.05)	6.00 (−17)	4.16 (−17)	5.66 (−17)	1.82 (−17)
500	(1.04, 1.04)	9.00 (−16)	6.96 (−16)	8.35 (−16)	3.33 (−16)
600	(1.03, 1.03)	5.42 (−15)	5.00 (−15)	5.56 (−15)	2.57 (−15)
700	(1.02, 1.02)	2.40 (−14)		2.31 (−14)	1.19 (−14)
800	(1.02, 1.02)	7.13 (−14)	6.72 (−14)	7.10 (−14)	4.00 (−14)
900	(1.02, 1.02)	1.85 (−13)		1.78 (−13)	1.07 (−13)
1000	(1.02, 1.02)	3.97 (−13)	3.58 (−13)	3.82 (−13)	2.43 (−13)
2000	(1.00, 1.00)	1.52 (−11)	1.70 (−11)	2.31 (−11)	1.96 (−11)