用廉价的无核电子三体关联因子优化双正交轨道用于量子Monte Carlo和互相关
Bi-orthonormal orbital optimization with a cheap core-electron free three-body correlation factor for Quantum Monte Carlo and Transcorrelation
摘要：
我们引入了一个新的三体关联因子，它被设计为在每个核周围的核心区域消失，并接近一个通用的价电子的两体关联因子。互相关哈密顿量用于优化双正交框架内的单个斯莱特行列式的轨道。Slater-Jastrow波函数在一组含有第二行元素和$3d$过渡金属元素的原子和分子系统上进行了优化。相关因子和轨道的优化，以及增加基组，导致所有测试系统的变分蒙特卡罗能量的系统性降低。重要的是，原子系统中获得的相关因子的最佳参数可转移到分子。另外，本相关因子在计算上是有效的，使用混合的分析-数值积分方案，其将昂贵的数值积分从$\mathbb{R}^6$减少到$\mathbb{R}^3$。
英文摘要：
We introduce a novel three-body correlation factor that is designed to vanish in the core region around each nucleus and approach a universal two-body correlation factor for valence electrons. The Transcorrelated Hamiltonian is used to optimize the orbitals of a single Slater determinant within a biorthonormal framework. The Slater-Jastrow wave function is optimized on a set of atomic and molecular systems containing both second-row elements and $3d$ transition metal elements. The optimization of the correlation factor and the orbitals, along with increasing the basis set, results in a systematic lowering of the Variational Monte Carlo energy for all systems tested. Importantly, the optimal parameters of the correlation factor obtained for atomic systems are transferable to molecules. Additionally, the present correlation factor is computationally efficient, using a mixed analytical-numerical integration scheme that reduces the costly numerical integration from $\mathbb{R}^6$ to $\mathbb{R}^3$.
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