Pollak Eli, Upadhyayula Sameernandan
Chemical and Biological Physics Department, Weizmann Institute of Science, 76100 Rehovoth, Israel.
J Chem Phys. 2024 May 14;160(18). doi: 10.1063/5.0211675.
The combination of vibrational perturbation theory with the replacement of the harmonic oscillator quantization condition along the reaction coordinate with an imaginary action to be used in the uniform semiclassical approximation for the transmission probability has been shown in recent years to be a practical method for obtaining thermal reaction rates. To date, this theory has been developed systematically only up to second order in perturbation theory. Although it gives the correct leading order term in an ℏ2 expansion, its accuracy at lower temperatures, where tunneling becomes important, is not clear. In this paper, we develop the theory to fourth order in the action. This demands developing the quantum perturbation theory up to sixth order. Remarkably, we find that the fourth order theory gives the correct ℏ4 term in the expansion of the exact thermal rate. The relative magnitude of the fourth order correction as compared to the second order term objectively indicates the accuracy of the second order theory. We also extend the previous modified second order theory to the fourth order case, creating an ℏ2 modified potential for this purpose. The resulting theory is tested on the standard examples-symmetric and asymmetric Eckart potentials and a Gaussian potential. The modified fourth order theory is remarkably accurate for the asymmetric Eckart potential.
近年来，振动微扰理论与沿反应坐标用虚作用量取代谐振子量子化条件相结合，用于传输概率的均匀半经典近似，已被证明是获得热反应速率的一种实用方法。迄今为止，该理论仅在微扰理论中系统地发展到二阶。尽管它在ħ²展开中给出了正确的主导项，但在隧道效应变得重要的较低温度下其准确性尚不清楚。在本文中，我们将该理论发展到作用量的四阶。这需要将量子微扰理论发展到六阶。值得注意的是，我们发现四阶理论在精确热速率展开中给出了正确的ħ⁴项。与二阶项相比，四阶修正的相对大小客观地表明了二阶理论的准确性。我们还将先前的修正二阶理论扩展到四阶情况，为此创建了一个ħ²修正势。所得理论在标准示例——对称和非对称埃卡特势以及高斯势上进行了测试。修正的四阶理论对非对称埃卡特势非常准确。
