论文标题
Hartree-fock动能能否超过精确的动能？
Can the Hartree-Fock kinetic energy exceed the exact kinetic energy?
论文作者
论文摘要
自1920年代后期出现以来，Hartree-Fock（HF）近似一直是量子化学计算的重要工具，并且仍然是当今使用的大多数单一引用方法的起点。直觉表明，HF动能不应超过确切的动能，但是尽管有近世的发展，但不存在这种猜想的证据。从从缩放考虑因素得出的广义病毒定理开始，我们得出了适用于所有系统的动能差的一般表达。对于任何原子或离子，这可以微不足道地减少到众所周知的结果，即总能量是动能的负，并且由于相关能量永远不会阳性，因此在这种情况下证明了猜想。类似的考虑因素适用于其平衡键长的分子。我们对胡克原子（抛物线井中的两个电子）使用高度精确的计算来测试猜想，并在非平凡的情况下测试了猜想，并参数化密度功能和HF数量之间的差异，但没有发现猜想的违规行为。
The Hartree-Fock (HF) approximation has been an important tool for quantum-chemical calculations since its earliest appearance in the late 1920s, and remains the starting point of most single-reference methods in use today. Intuition suggests that the HF kinetic energy should not exceed the exact kinetic energy, but no proof of this conjecture exists, despite a near century of development. Beginning from a generalized virial theorem derived from scaling considerations, we derive a general expression for the kinetic energy difference that applies to all systems. For any atom or ion this trivially reduces to the well-known result that the total energy is the negative of the kinetic energy and since correlation energies are never positive, proves the conjecture in this case. Similar considerations apply to molecules at their equilibrium bond lengths. We use highly precise calculations on Hooke's atom (two electrons in a parabolic well) to test the conjecture in a non-trivial case, and to parameterize the difference between density-functional and HF quantities, but find no violations of the conjecture.
