标题： 仅交换优化势与有限基组Kohn-Sham方法之间的关系；一个悖论的解决 显示英文标题

标题： Relation between exchange-only optimized potential and Kohn-Sham methods with finite basis sets; solution of a paradox

摘要： 给出了表明使用有限基组的交换唯象优化有效势（xOEP）方法通常不能得到 Hartree-Fock（HF）基态能量，而只能得到更高的能量的论据。 当完整的基组轨道乘积是线性相关的时，只有在从所用轨道基组产生的占据轨道和未占据轨道的所有乘积彼此线性无关的特殊情况下，才能通过基组xOEP方案获得HF基态能量。 然而，在这种情况下，导致HF基态能量的交换势表现出非物理的振荡，并且不代表Kohn-Sham（KS）交换势。 这些发现解决了Staroverov、Scuseria和Davidson看似矛盾的结果，即某些有限基组xOEP计算得出HF基态能量，尽管在实空间（或完整基组）表示中，xOEP基态能量总是高于HF能量。 此外，无论占据轨道和未占据轨道的乘积是否线性无关，都证明了基组xOEP方法仅在轨道基组和代表交换势的辅助基组相互平衡的情况下（即，轨道基组对于给定的辅助基组足够全面），才代表精确的交换唯象（EXX）KS方法，即适当的密度泛函方法。 否则，xOEP方法不表示EXX KS方法，并产生非物理的交换势。 显示英文摘要

摘要： Arguments showing that exchange-only optimized effective potential (xOEP) methods, with finite basis sets, cannot in general yield the Hartree-Fock (HF) ground state energy, but a higher one, are given. While the orbital products of a complete basis are linearly dependent, the HF ground state energy can only be obtained via a basis set xOEP scheme in the special case that all products of occupied and unoccupied orbitals emerging from the employed orbital basis set are linearly independent from each other. In this case, however, exchange potentials leading to the HF ground state energy exhibit unphysical oscillations and do not represent a Kohn-Sham (KS) exchange potential. These findings solve the seemingly paradoxical results of Staroverov, Scuseria and Davidson that certain finite basis set xOEP calculations lead to the HF ground state energy despite the fact that within a real space (or complete basis) representation the xOEP ground state energy is always higher than the HF energy. Moreover, whether or not the occupied and unoccupied orbital products are linearly independent, it is shown that basis set xOEP methods only represent exact exchange-only (EXX) KS methods, i.e., proper density-functional methods, if the orbital basis set and the auxiliary basis set representing the exchange potential are balanced to each other, i.e., if the orbital basis is comprehensive enough for a given auxiliary basis. Otherwise xOEP methods do not represent EXX KS methods and yield unphysical exchange potentials.