Semiclassical transition-state theory based on fourth-order vibrational perturbation theory (VPT4-SCTST) is applied to compute the barrier transmission coefficient for the symmetric Eckart potential. For a barrier parametrized to mimic the H₂ + H exchange reaction, the results obtained are in excellent agreement with exact quantum calculations over a range of energy that extends down to roughly 1% of the barrier height, V₀, where tunneling is negligible. The VPT2-SCTST treatment, which is commonly used in chemical kinetics studies, also performs quite well but already shows an error of a few percent at ca. 0.8 V₀ where tunneling is still important. This suggests that VPT4-SCTST could offer an improvement over VPT2-SCTST in applications studies. However, the computational effort for VPT4-SCTST treatments of molecules is excessive, and any improvement gained is unlikely to warrant the increased effort. Nevertheless, the treatment of the symmetric Eckart barrier problem here suggests a simple modification of the usual VPT2-SCTST protocol that warrants further investigation.

中文翻译：

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基于四阶振动摄动理论的半经典过渡态理论：对称的埃克特屏障

应用基于四阶振动摄动理论的半经典过渡态理论（VPT4-SCTST）计算对称埃克特势的势垒传输系数。对于参数化模拟H ₂ + H交换反应的势垒，所获得的结果与在向下延伸至势垒可忽略的势垒高度V _0的大约1％的能量范围内的精确量子计算非常吻合。化学动力学研究中常用的VPT2-SCTST处理效果也相当好，但在大约5％时已经显示出百分之几的误差。0.8 V ₀在隧道仍然很重要的地方。这表明在应用研究中，VPT4-SCTST可以比VPT2-SCTST有所改进。但是，VPT4-SCTST分子治疗的计算量过多，并且所获得的任何改善都不太可能保证增加该量。尽管如此，这里对对称Eckart障碍问题的处理表明对常规VPT2-SCTST协议进行了简单修改，值得进一步研究。