标题： 基态能量并不总随着电子数的增加而呈现凸性 显示英文标题

标题： The 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。 这一性质在几十年中被认为成立，并在量子化学中起着重要作用。 我们的反例涉及由六个小分数电荷的核产生的外部势，这些核彼此相距很远。 证明了3个电子的基态能量高于2个和4个电子能量的平均值。 此外，我们表明核可以结合2个或4个电子，但不能结合3个。 尽管对于真实核（整数电荷）该猜想仍然开放，但我们的工作对一般原子和分子的能量凸性有效性提出了一些怀疑。 显示英文摘要

摘要： We provide the first counter-example 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 property had been conjectured to hold for decades and it plays an important role in quantum chemistry. Our counter-example involves an external potential generated by six nuclei of small fractional charges, placed far away from each other. The ground state energy of 3 electrons is proved to be higher than the average of the energies for 2 and 4 electrons. In addition, we show that the nuclei can bind 2 or 4 electrons, but not 3. Although the conjecture remains open for real nuclei (of integer charges), our work sets some doubt on the validity of the energy convexity for general atoms and molecules.