标题： 基态能量并不总随着电子数的增加而凸性变化 显示英文标题

标题： Ground state energy is not always convex in the number of electrons

摘要： 我们提供了第一个反例，表明在外部库仑势中的电子基态能量并不总是电子数的凸函数。 这种凸性已被猜测了几十年，并在量子化学中起着重要作用。 我们的反例涉及六个远距离放置的具有小分数电荷的核。 显示3个电子的基态能量高于2个和4个电子能量的平均值。 我们还表明，核可以结合2个或4个电子，但不能结合3个电子。 本文提出了一个疑问，即能量凸性是否真的对所有可能的分子（具有整数电荷的核）成立。 显示英文摘要

摘要： We provide the first counterexample showing that the ground state energy of electrons in an external Coulomb potential is not always a convex function of the number of electrons. This convexity has been conjectured for decades and plays an important role in quantum chemistry. Our counterexample involves six nuclei with small fractional charges placed far apart. The ground state energy of 3 electrons is shown to be higher than the average of the energies for 2 and 4 electrons. We also show that the nuclei can bind 2 or 4 electrons, but not 3. This article raises the question of whether the energy convexity really holds for all possible molecules (with nuclei of integer charge).