利用应用于含数百个电子体系的反对称化 geminal 幂波函数，超越从头算扩散蒙特卡洛中的单参考固定节点近似
Beyond single-reference fixed-node approximation in ab initio Diffusion Monte Carlo using antisymmetrized geminal power applied to systems with hundreds of electrons
AI总结：
本文提出以反对称化 Geminal 幂波函数约束改进 DMC 固定节点面，超越单参考近似，并在 C$_{60}$ 等大体系中验证其精度与计算可行性。
摘要：
扩散蒙特卡洛（DMC）是一种用于投影出哈密顿量基态（GS）的精确技术。由于基态总是玻色性的，在费米子体系中，投影必须在施加反对称约束的同时进行，而这是一个非确定性多项式困难问题。因此在实践中，DMC 在电子结构问题上的应用通过采用固定节点（FN）近似来实现，即在具有固定预定义节点面的约束下执行 DMC。我们如何获得节点面？典型方法应用于具有数百甚至数千个电子的体系，即从用于获得单个 Slater 行列式的初步平均场方法（通常是密度泛函理论计算）获得节点面。这被称为“单参考”。本文提出一种适用于像 C$_{60}$ 富勒烯这样大体系的新方法，通过超越单参考来改进节点。实践中，我们采用一种隐式多参考拟设（带有分子轨道的反对称化 Geminal 幂波函数约束），在初步平均场方法上初始化，并通过最小化 FN-DMC 能量来优化决定节点面的波函数的少数参数，从而使其松弛。我们在若干例子中强调了所提方法相对于标准单参考方法的改进，并在可行情况下展示了其相对于标准多参考拟设的计算收益，这使该方法适用于大体系。我们还表明，依赖相对能量的物理性质（如结合能）在所提方案中是可负担且可靠的。
英文摘要：
Diffusion Monte Carlo (DMC) is an exact technique to project out the ground state (GS) of a Hamiltonian. Since the GS is always bosonic, in fermionic systems the projection needs to be carried out while imposing anti-symmetric constraints, which is a nondeterministic polynomial hard problem. In practice, therefore, the application of DMC on electronic structure problems is made by employing the fixed-node (FN) approximation, consisting of performing DMC with the constraint of having a fixed predefined nodal surface. How do we get the nodal surface? The typical approach, applied in systems having up to hundreds, or even thousands of electrons, is to obtain the nodal surface from a preliminary mean-field approach (typically, a density functional theory calculation) used to obtain a single Slater determinant. This is known as {\emph{single reference}}. In this paper, we propose a new approach, applicable to systems as large as the C$_{60}$ fullerene, which improves the nodes by going beyond the single reference. In practice, we employ an implicitly multireference ansatz (Antisymmetrized Geminal power wavefunction constraint with molecular orbitals), initialized on the preliminary mean-field approach, which is relaxed by optimizing a few parameters of the wave function determining the nodal surface by minimizing the FN-DMC energy. We highlight the improvements of the proposed approach over the standard single reference method on several examples and, where feasible, the computational gain over the standard multireference ansatz, which makes the methods applicable to large systems. We also show that physical properties relying on relative energies, such as binding energies, are affordable and reliable within the proposed scheme.
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