Department of Chemistry and Department of Physics, Indiana University, 800 E. Kirkwood Ave, Bloomington, Indiana 47405, United States.
J Chem Theory Comput. 2011 Feb 8;7(2):256-68. doi: 10.1021/ct1005856. Epub 2011 Jan 12.
A new set of time-dependent deterministic sampling (TDDS) measures, based on local Shannon entropy, are presented to adaptively gauge the importance of various regions on a potential energy surface and to be employed in "on-the-fly" quantum dynamics. Shannon sampling and Shannon entropy are known constructs that have been used to analyze the information content in functions: for example, time-series data and discrete data sets such as amino acid sequences in a protein structure. Here the Shannon entropy, when combined with dynamical parameters such as the instantaneous potential, gradient and wavepacket density provides a reliable probe on active regions of a quantum mechanical potential surface. Numerical benchmarks indicate that the methods proposed are highly effective in locating regions of the potential that are both classically allowed as well as those that are classically forbidden, such as regions beyond the classical turning points which may be sampled during a quantum mechanical tunneling process. The approaches described here are utilized to improve computational efficiency in two different settings: (a) It is shown that the number of potential energy calculations required to be performed during on-the-fly quantum dynamics is fewer when the Shannon entropy based sampling functions are used. (b) Shannon entropy based TDDS functions are utilized to define a new family of grid-based electronic structure basis functions that reduce the computational complexity while maintaining accuracy. The role of both results for on-the-fly quantum/classical dynamics of electrons and nuclei is discussed.
提出了一组新的基于局部香农熵的时变确定性抽样（TDDS）度量方法，用于自适应地衡量势能面上各个区域的重要性，并应用于“实时”量子动力学中。香农抽样和香农熵是已知的构造，已被用于分析函数中的信息含量：例如，时间序列数据和离散数据集，如蛋白质结构中的氨基酸序列。在这里，香农熵与动力学参数（如瞬时势能、梯度和波包密度）相结合，为量子力学势能面的活跃区域提供了可靠的探测手段。数值基准表明，所提出的方法在定位经典允许区域和经典禁止区域方面非常有效，例如在经典转折点之外的区域，这些区域可能在量子力学隧穿过程中被采样。这里描述的方法用于提高两种不同设置中的计算效率：(a) 当使用基于香农熵的抽样函数时，在实时量子动力学中执行的势能计算的数量减少。(b) 基于香农熵的 TDDS 函数用于定义一组新的基于网格的电子结构基函数，在保持精度的同时降低计算复杂度。讨论了这两个结果在电子和核实时量子/经典动力学中的作用。
