The absolute entropy of a flexible molecule can be approximated by the sum of a rigid-rotor-harmonic-oscillator (RRHO) entropy and a Gibbs–Shannon entropy associated to the Boltzmann distribution for the occupation of the conformational energy levels. Herein, we show that such partitioning, which has received renewed interest, leads to accurate entropies of single molecules of increasing size provided that the conformational part is estimated by means of a set of discretization and expansion techniques that are able to capture the significant correlation effects among the torsional motions. To ensure a reliable entropy estimation, we rely on extensive sampling as that produced by classical molecular dynamics simulations on the microsecond time scale, which is currently affordable for small- and medium-sized molecules. According to test calculations, the gas-phase entropy of simple organic molecules is predicted with a mean unsigned error of 0.9 cal/(mol K) when the RRHO entropies are computed at the B3LYP-D3/cc-pVTZ level. Remarkably, the same protocol gives small errors [<1 cal/(mol K)] for the extremely flexible linear alkane molecules (C_nH_2n+2, n = 14, 16, and 18). Similarly, we obtain well-converged entropies for a more challenging test of drug molecules, which exhibit more pronounced correlation effects. We also perform equivalent entropy calculations on a 76 amino acid protein, ubiquitin, by taking advantage of the cutoff-dependent formulation of an expansion technique (correlation-consistent multibody local approximation, CC-MLA), which incorporates genuine correlation effects among the neighboring dihedral angles. Moreover, we show that insightful descriptors of the coupled torsional motions can be obtained with the CC-MLA approach.

中文翻译：

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对柔性分子进行可靠和有洞察力的熵计算

柔性分子的绝对熵可以近似为刚性转子谐振子 (RRHO) 熵和与玻尔兹曼分布相关的吉布斯-香农熵之和，用于占据构象能级。在这里，我们表明，这种重新引起人们兴趣的分区会导致尺寸不断增加的单个分子的准确熵，前提是构象部分是通过一组能够捕获显着相关效应的离散化和扩展技术来估计的在扭转运动中。为了确保可靠的熵估计，我们依赖于经典分子动力学模拟在微秒时间尺度上产生的广泛采样，目前中小型分子可以负担得起。根据测试计算，当在 B3LYP-D3/cc-pVTZ 水平上计算 RRHO 熵时，预测简单有机分子的气相熵的平均无符号误差为 0.9 cal/(mol K)。值得注意的是，对于极其灵活的线性烷烃分子 (C_n H _{2 n +2}， n = 14、16 和 18）。同样，我们获得了收敛良好的熵，用于更具挑战性的药物分子测试，这些分子表现出更明显的相关效应。我们还通过利用扩展技术（相关一致多体局部近似，CC-MLA）的截止依赖性公式对 76 个氨基酸的蛋白质泛素进行等效熵计算，该技术结合了相邻二面角之间的真实相关效应角度。此外，我们表明可以使用 CC-MLA 方法获得耦合扭转运动的有见地的描述符。