AI 中文总结
该研究提出ASyBGR方法，通过对称性缩减网格点，使势能面构建成本降低最多81%，VCI能量偏差低于1 cm⁻¹，验证了方法的有效性。
AI 中文摘要
构建基于网格的势能面（PES）成本可能过高，因为网格点数量随分子大小呈指数增长。分子对称性可通过消除对称等价点降低该成本。我们提出一种基于代数对称性的网格缩减方法ASyBGR，其能处理非阿贝尔群及高阶循环对称群。非坐标混合操作被编码为向量空间位串，高斯消元法和闭包可识别所有对称有效的符号变化模式，以及可关于原点减半网格的坐标轴。在存在简并子空间时，我们优化坐标基以最大化缩减效果。该方法通过比较使用全阶和对称缩减的四阶HDMR PES计算的振动组态相互作用（VCI）能量进行验证，测试分子涵盖广泛对称性范围。构建PES所需网格点数量最多减少81%，所有测试案例中VCI能量平均偏差低于1 cm⁻¹。全阶与对称缩减的势能面及偶极矩面间的相对均方根偏差（RRMSD）分别最多为10⁻³量级和10⁻²量级。
英文摘要
The construction of a grid-based potential energy surface (PES) can be prohibitively expensive as the number of grid points grows exponentially with molecular size. Molecular symmetry can reduce this cost by eliminating symmetry-equivalent points. We present an algebraic symmetry-based grid reduction method, ASyBGR, that is capable of handling non-Abelian and higher-order cyclic symmetry groups. Non-coordinate-mixing operations are encoded into a vector space bit-string, where Gaussian elimination and closure can identify all symmetry-valid sign change patterns and the coordinate axes whose grids can be halved about the origin. In the presence of degenerate subspaces, we optimize the coordinate basis to maximize reduction. The method was validated by comparing vibrational configuration interaction (VCI) energies calculated using the full and symmetry-reduced fourth-order HDMR PESs for molecules spanning a broad range of symmetries. The number of grid points required to construct the PES was reduced by as much as 81\%, while VCI energies deviated below 1 1/cm for all test cases on average. The relative root-mean-square deviation (RRMSD) between the full and symmetry-reduced potential energy and dipole moment surfaces were at most on the order of 10$^{-3}$ and 10$^{-2}$, respectively.
Comments32 pages, 2 tables
