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首页> 外文期刊>The journal of physical chemistry, A. Molecules, spectroscopy, kinetics, environment, & general theory >Improved Multidimensional Semiclassical Tunneling Theory
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Improved Multidimensional Semiclassical Tunneling Theory

机译：改进的多维半经典隧穿理论

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摘要

We show that the analytic multidimensional semiclassical tunneling formula of Miller et al. [Miller, W. H.; Hernandez, R.; Handy, N. C.; Jayatilaka, D.; Willets, A. Chem. Phys. Lett. 1990, 172, 62] is qualitatively incorrect for deep tunneling at energies well below the top of the barrier. The origin of this deficiency is that the formula uses an effective barrier weakly related to the true energetics but correctly adjusted to reproduce the harmonic description and anharmonic corrections of the reaction path at the saddle point as determined by second order vibrational perturbation theory. We present an analytic improved semiclassical formula that correctly includes energetic information and allows a qualitatively correct representation of deep tunneling. This is done by constructing a three segment composite Eckart potential that is continuous everywhere in both value and derivative. This composite potential has an analytic barrier penetration integral from which the semiclassical action can be derived and then used to define the semiclassical tunneling probability. The middle segment of the composite potential by itself is superior to the original formula of Miller et al. because it incorporates the asymmetry of the reaction barrier produced by the known reaction exoergicity. Comparison of the semiclassical and exact quantum tunneling probability for the pure Eckart potential suggests a simple threshold multiplicative factor to the improved formula to account for quantum effects very near threshold not represented by semiclassical theory. The deep tunneling limitations of the original formula are echoed in semiclassical high-energy descriptions of bound vibrational states perpendicular to the reaction path at the saddle point. However, typically ab initio energetic information is not available to correct it. The Supporting Information contains a Fortran code, test input, and test output that implements the improved semiclassical tunneling formula.
机译：我们证明了Miller等人的解析多维半经典隧穿公式。 [Miller，W. H .;埃尔南德斯（R.便利，北卡罗来纳州;贾亚蒂拉卡（D.） Willets，A。化学。物理来吧[1990，172，62]从质量上来说，对于远低于势垒顶部的能量的深隧穿是不正确的。此缺陷的根源在于，该公式使用了与真实能量学弱相关但有效调整的有效势垒，以再现谐波描述和鞍座点反应路径的非谐校正，这是由二阶振动微扰理论确定的。我们提出了一种经过分析的改进的半经典公式，该公式正确地包含了高能信息，并允许定性地正确表示深隧道。这是通过构造一个三段式复合Eckart电位来实现的，该电位在值和导数上都是连续的。该复合势具有解析势垒穿透积分，从该解析势垒积分可以得出半经典作用，然后用于定义半经典隧穿概率。复合势能的中间部分本身优于Miller等人的原始公式。因为它结合了由已知反应放热产生的反应势垒的不对称性。对纯Eckart势的半经典和精确量子隧穿概率的比较表明，对改进的公式而言，简单的阈值倍增因子可说明非常接近阈值的量子效应，而半经典理论并未对此加以说明。原始公式的深隧穿限制在与鞍点处垂直于反应路径的约束振动状态的半经典高能描述中得到了回应。但是，通常没有从头开始的能量信息来纠正它。支持信息包含实现改进的半经典隧道公式的Fortran代码，测试输入和测试输出。

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