An accurate treatment of effective core potentials (ECPs) requires care in continuum quantum Monte Carlo (QMC) methods. While most QMC studies have settled on the use of familiar non-local (NL) pseudopotentials with additional localization approximations, these approaches have been shown to result in moderate residual errors for some classes of molecular and solid state applications. In this work, we revisit an idea proposed early in the history of QMC ECPs that does not require localization approximations, namely, a differential class of potentials referred to as pseudo-Hamiltonians. We propose to hybridize NL potentials and pseudo-Hamiltonians to reduce residual non-locality of existing potentials. We derive an approach to recast pseudopotentials for 3d elements as hybrid pseudo-Hamiltonians with optimally reduced NL energy. We demonstrate the fidelity of the hybrid potentials by studying atomic ionization potentials of Ti and Fe and the binding properties of TiO and FeO molecules with diffusion Monte Carlo (DMC). We show that localization errors have been reduced relative to potentials with the same NL channels for Sc–Zn by considering the DMC energy change with respect to the choice of approximate localization. While localization error decreases proportionate to the reduced NL energy without a Jastrow, with a Jastrow, the degree of reduction decreases at higher filling of the d-shell. Our results suggest that a subset of existing ECPs may be recast in this hybrid form to reduce the DMC localization error. They also point to the prospect of further reducing this error by generating ECPs within this hybrid form from the start.

中文翻译：

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在扩散蒙特卡洛中混合伪汉密尔顿和非局部伪势。

有效核心电位（ECP）的准确处理需要采用连续量子蒙特卡罗（QMC）方法。虽然大多数QMC研究都以使用熟悉的非局部（NL）伪电位和其他局部逼近为基础，但这些方法已证明对于某些类型的分子和固态应用会产生中等程度的残留误差。在这项工作中，我们重新审视了QMC ECP历史上提出的不需要定位近似的想法，也就是称为伪哈密顿主义者的一类电位差。我们建议将NL势和伪哈密顿人杂交，以减少现有势的残留非局部性。我们推导了一种方法，可以将3d元素的伪电势重铸为具有最佳降低的NL能量的混合伪哈密顿函数。我们通过研究Ti和Fe的原子电离势以及TiO和FeO分子与扩散Monte Carlo（DMC）的结合特性来证明杂化势的保真度。我们显示，通过考虑DMC能量变化对近似定位的选择，相对于Sc-Zn的相同NL通道，相对于电位而言，定位误差已降低。尽管在没有Jastrow的情况下定位误差与降低的NL能量成比例地减小，但在具有Jastrow的情况下，减小的程度在d壳填充较高时减小。我们的结果表明，可以以这种混合形式重铸现有ECP的子集，以减少DMC定位错误。他们还指出了从一开始就通过在这种混合形式下生成ECP来进一步减少该错误的前景。