Hait Diptarka, Head-Gordon Martin
Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry , University of California , Berkeley , California 94720 , United States.
Chemical Sciences Division , Lawrence Berkeley National Laboratory , Berkeley , California 94720 , United States.
J Phys Chem Lett. 2018 Nov 1;9(21):6280-6288. doi: 10.1021/acs.jpclett.8b02417. Epub 2018 Oct 19.
Approximate functionals used in practical density functional theory (DFT) deviate from the piecewise linear behavior of the exact functional for fractional charges. This deviation causes excess charge delocalization, which leads to incorrect densities, molecular properties, barrier heights, band gaps, and excitation energies. We present a simple delocalization function for characterizing this error and find it to be almost perfectly linear vs the fractional electron number for systems spanning in size from the H atom to the CH polyene. This causes the delocalization energy error to be a quadratic polynomial in the fractional electron number, which permits us to assess the comparative performance of 47 popular and recent functionals through the curvature. The quadratic form further suggests that information about a single fractional charge is sufficient to eliminate the principal source of delocalization error. Generalizing traditional two-point information like ionization potentials or electron affinities to account for a third, fractional charge-based data point could therefore permit fitting/tuning of functionals with lower delocalization error.
实际密度泛函理论（DFT）中使用的近似泛函偏离了精确泛函对于分数电荷的分段线性行为。这种偏差会导致电荷过度离域，进而导致密度、分子性质、势垒高度、带隙和激发能的计算错误。我们提出了一个简单的离域函数来表征这种误差，并发现对于从氢原子到多烯的一系列体系，该离域函数相对于分数电子数几乎呈完美的线性关系。这使得离域能误差成为分数电子数的二次多项式，从而使我们能够通过曲率评估47种常用和最新泛函的相对性能。二次形式进一步表明，关于单个分数电荷的信息足以消除离域误差的主要来源。因此，将传统的两点信息（如电离势或电子亲和势）推广到包含基于分数电荷的第三个数据点，可能允许对离域误差较低的泛函进行拟合/调整。
