Anharmonicity of Coupled Torsions: The Extended Two-Dimensional Torsion Method and Its Use To Assess More Approximate Methods.

In this work we present the extended two-dimensional torsion (E2DT) method and use it to analyze the performance of several methods that incorporate torsional an-harmonicity more approximately for calculating rotational-vibrational partition functions. Twenty molecules having two hindered rotors were studied for temperatures between 100 and 2500 K. These molecules present several kinds of situation; they include molecules with nearly separable rotors, molecules in which the reduced moments of inertia changes substantially with the internal rotation and molecules presenting compound rotation. Partition functions obtained by the rigid-rotor harmonic oscillator approximation, a method involving global separability of torsions and the multi-structural methods without explicit potential coupling [MS-T(U)] and with explicit potential coupling [MS-T(C)] of torsions are compared to those obtained with a quantized version -called the extended two-dimensional torsion (E2DT) method- of the extended hindered rotor approximation of Vansteenkiste et al. (J. Chem. Phys. 2006, 124, 044314). In the E2DT method, quantum effects due to the torsional modes were incorporated by the two-dimensional non-separable method, which is a method that is based on the solution of the torsional Schrodinger equation and that includes full coupling in both the kinetic and potential energy. By comparing other methods to the E2DT method and to experimental thermochemical data, this study concludes that: the harmonic approximation yields very poor results at high temperatures; the global separation of torsions from the rest of degrees of freedom is not justified even when an accurate method to treat the torsions is employed; it is confirmed that methods based on less complete potential energy coupling of torsions, such as MS-T(U), are not accurate when dealing with rotors with different barrier heights; and more complete inclusion of torsional coupling to the method in MS-T(C), improves substantially the results in such a way that it could be used in cases where the E2DT method is unaffordable.

在这项工作中，我们提出了扩展二维扭转（E2DT）方法，并使用它来分析几种更近似地纳入扭转非谐性以计算转动 - 振动配分函数的方法的性能。对具有两个受阻转子的20种分子在100到2500 K的温度下进行了研究。这些分子呈现出几种情况；它们包括具有近乎可分离转子的分子、转动惯量的约化值随内转动大幅变化的分子以及呈现复合转动的分子。将刚性转子谐振子近似、一种涉及扭转全局可分离性的方法以及无明确势能耦合[MS - T(U)]和有明确势能耦合[MS - T(C)]的多结构方法所得到的配分函数，与范斯滕基斯特等人（《化学物理杂志》2006年，124卷，044314页）的扩展受阻转子近似的量子化版本——称为扩展二维扭转（E2DT）方法所得到的配分函数进行了比较。在E2DT方法中，扭转模式产生的量子效应通过二维不可分离方法纳入，该方法基于扭转薛定谔方程的求解，并且在动能和势能中都包含完全耦合。通过将其他方法与E2DT方法以及实验热化学数据进行比较，这项研究得出结论：谐振子近似在高温下产生非常差的结果；即使采用了一种精确的处理扭转的方法，将扭转从其余自由度中全局分离也是不合理的；证实了基于扭转势能耦合不太完全的方法，如MS - T(U)，在处理具有不同势垒高度的转子时是不准确的；并且在MS - T(C)方法中更完全地纳入扭转耦合，极大地改善了结果，以至于它可以在E2DT方法难以应用的情况下使用。