从计算谱密度估算分子体系的构型熵和构型能量
Estimating configurational entropy and energy of molecular systems from computed spectral density
摘要：
从分子模拟数据估计构型熵的大多数方法产生上限，除了谐波系统，他们是准确的。问题出现在扩散系统和构象转变的存在。例如，基于协方差的方法在原子位置改变时会大大高估熵，并导致大的但不相关的空间方差。在这里，我们提出了一种称为频谱分辨估计（SRE）的熵，能量和自由能的方法，它是基于振动的频谱密度，并在固态物理中的准谐波分析的启发。与其他方法相比，它（a）产生熵的下限和自由能的上限，（b）不受扩散的破坏，（c）将熵贡献分配给光谱特征，从而揭示了这些贡献背后的局部化和运动类型。构象转变的空间范围没有影响。该方法适用于有限体积系统，对调和系统是精确的。溶剂分子的交换是生物大分子的特征。在这里，SRE为研究蛋白质等部分扩散系统的熵和自由能开辟了一条道路。它还可以研究通道，泵和酶，这些酶通常包含几个可以交换位置的内部功能性水分子。对特定运动的分配可以通过正常模式或局部模式分析来完成，包括通过带通滤波的可视化。因此，SRE提供了对构型熵起源的洞察，并有望支持从前药到工程蛋白质的分子的合理设计。本技术报告演示了如何通过评估量子力学分子动力学模拟计算的光谱来获得和分析小分子的热力学量。
英文摘要：
Most methods for estimating configurational entropy from molecular simulation data yield upper limits except for harmonic systems where they are exact. Problems arise at diffusive systems and the presence of conformational transitions. Covariance-based methods, for instance, can considerably overestimate entropy when atomic positions change and cause large, but irrelevant spatial variances. Here we propose a method called Spectrally Resolved Estimation (SRE) for entropy, energy and free energy which is based on the spectral density of vibrations and is inspired by the quasi-harmonic ansatz in solid-state physics. It (a) yields, in contrast with other methods, a lower limit of entropy and an upper limit of free energy, is (b) not corrupted by diffusion, (c) assigns entropic contributions to spectral features and thus reveals the localization and the type of motion underlying these contributions. The spatial extent of conformational transitions has no influence. The method applies to systems of finite volume and is exact for harmonic systems. The exchange of solvent molecules is characteristic of biological macromolecules. Here SRE opens an avenue to the entropy and free energy of partially diffusive systems like proteins. It also enables studying channels, pumps, and enzymes which often contain several internal, functional water molecules that can swap position. The assignment to particular motions can be done by normal modes or local mode analysis including visualization by band-pass filtering. Thus, SRE provides insight into the origin of configurational entropy and is expected to support the rational design of molecules from prodrugs up to engineered proteins. This technical report demonstrates how thermodynamic quantities are gained and analyzed for small molecules by evaluation of spectra computed by quantum mechanical molecular dynamics simulation.
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