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首页> 外文期刊>The Journal of Chemical Physics >Extremal path approach to rate constant calculations by the linearized semiclassical initial value representation
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Extremal path approach to rate constant calculations by the linearized semiclassical initial value representation

机译：用线性半经典初始值表示法求速率常数的极值路径法

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摘要

To extend the applicability of the linearlized initial value representation (LIVR) method to lower temperatures and realistic potentials, a generalization to barriers other than the inverted parabola is proposed. The LIVR method calculates rate constants of chemical reactions invovling quantum effects by weighting classical trajectories by the Wigner distribution function (WDF) of the Boltzmann-averaged flux opeator. These calculations can be performed efficiently if the WDF is avaiable in analytical form, which is the case for harmonic barriers only. The proposed generalization to anharmonic barriers is basedon the recognition that above a critical temperature T~* = hw/phik_B where omega is the curvature at the top of the barrier and k_B is the Boltzmann constant, the WDF is dominated by an extremal trajectory. The evaluation of WDFs and thus of thermal rate constants is thereby reduced to the search for the extremal path defined by a steepest-descent condition for the WDF. This extremal trajectory is the high-temperature analogue of the instanton (bounce path), which exists for temperatures lower than T~"/2. Explicit formulas are derived for the generation of realistic WDFs and barrier crossing rate constants for symmetric barriers of arbitrary shape. Approximations are introduced that will reduce the extra computational effort required for these anharmonic barriers. They are based on the fact that above the critical temperature the WDF of any anharmonic potential can be represented with good approximation in an analytical form anaglous to that of the parabolic barrier by the introduction of the effective parameters. Results obtained for two standard model potentials, the quartic potential and the symmetric Eckart barrier, are compared with the well-known parabolic barrier results. The formal and actual temperature limits for calculating tunneling rate constants and the extension of the method to asymmetric barriers are briefly discussed.
机译：为了将线性化的初始值表示（LIVR）方法的适用性扩展到更低的温度和现实势能，提出了对除倒抛物线以外的势垒的一般化方法。 LIVR方法通过使用Boltzmann平均通量运算器的Wigner分布函数（WDF）加权经典轨迹来计算涉及量子效应的化学反应的速率常数。如果WDF具有解析形式，则可以有效地执行这些计算，这仅适用于谐波势垒。提出的对非谐性障碍的概括是基于这样的认识，即在临界温度T〜* = hw / phik_B以上，其中ω是障碍物顶部的曲率，k_B是玻尔兹曼常数，WDF由极值轨迹控制。因此，对WDF的评估以及由此对热速率常数的评估都减少了对WDF的最速下降条件所定义的极值路径的搜索。该极值轨迹是瞬时子（反弹路径）的高温模拟，存在于温度低于T〜“ / 2时。存在显式，用于生成实际WDF和任意形状的对称障碍的障碍穿越速率常数。引入近似值将减少这些非谐波障碍所需的额外计算工作，它们基于以下事实：在临界温度以上，任何非谐波势的WDF都可以以类似于抛物线的解析形式很好地近似表示。通过引入有效参数，将两个标准模型势（四次势和对称Eckart势垒）获得的结果与众所周知的抛物线势垒结果进行比较，以计算隧道速率常数和简要讨论了将该方法扩展到不对称障碍的问题。

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