In this article, we explore the construction of Hamiltonians with long-range interactions and their corrections using the short-range behavior of the wave function. A key aspect of our investigation is the examination of the one-particle potential, kept constant in our previous work, and the effects of its optimization on the adiabatic connection. Our methodology involves the use of a parameter-dependent potential dependent on a single parameter to facilitate practical computations. We analyze the energy errors and densities in a two-electron system (harmonium) under various conditions, employing different confinement potentials and interaction parameters. The study reveals that while the mean-field potential improves the expectation value of the physical Hamiltonian, it does not necessarily improve the energy of the system within the bounds of chemical accuracy. We also delve into the impact of density variations in adiabatic connections, challenging the common assumption that a mean field improves results. Our findings indicate that as long as energy errors remain within chemical accuracy, the mean field does not significantly outperform a bare potential. This observation is attributed to the effectiveness of corrections based on the short-range behavior of the wave function, a universal characteristic that diminishes the distinction between using a mean field or not.

中文翻译：

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探索平均场势和短程波函数行为在绝热连接中的作用


在本文中，我们探讨了具有长程相互作用的哈密顿量的构造及其使用波函数的短程行为的修正。我们研究的一个关键方面是检查在我们之前的工作中保持不变的单粒子势，以及其优化对绝热连接的影响。我们的方法涉及使用依赖于单个参数的参数相关势来促进实际计算。我们采用不同的限制势和相互作用参数，分析了各种条件下双电子系统（骈）的能量误差和密度。研究表明，虽然平均场势提高了物理哈密顿量的期望值，但它并不一定会在化学精度范围内提高系统的能量。我们还深入研究了绝热连接中密度变化的影响，挑战了平均场可以改善结果的常见假设。我们的研究结果表明，只要能量误差保持在化学精度范围内，平均场就不会明显优于裸电势。这一观察结果归因于基于波函数的短程行为的校正的有效性，这是一种普遍特征，减少了使用平均场与不使用平均场之间的区别。