School of Chemistry, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom.
J Chem Phys. 2012 Jun 21;136(23):234101. doi: 10.1063/1.4728026.
In situ optimization of a set of localized orbitals with respect to a systematically improvable basis set independent of the position of the atoms, such as psinc functions, would theoretically eliminate the correction due to Pulay forces from the total ionic forces. We demonstrate that for strict localization constraints, especially with small localization regions, there can be non-negligible Pulay forces that must be calculated as a correction to the Hellmann-Feynman forces in the ground state. Geometry optimization calculations, which rely heavily upon accurate evaluation of the total ionic forces, show much better convergence when Pulay forces are included. The more conventional case, where the local orbitals remain fixed to pseudo-atomic orbital multiple-ζ basis sets, also benefits from this implementation. We have validated the method on several test cases, including a DNA fragment with 1045 atoms.
针对原子位置独立的、可系统改进的基组（例如 psinc 函数），对一组局域轨道进行原位优化，理论上可以消除总离子力中由于 Pulay 力而产生的修正。我们证明，对于严格的局域化约束，特别是对于小的局域化区域，可能会存在不可忽略的 Pulay 力，必须将其作为基态下的海利曼-费曼力的修正来计算。几何优化计算严重依赖于总离子力的精确评估，当包含 Pulay 力时，收敛性会更好。对于局部轨道保持固定在伪原子轨道多 ζ 基组的更常规情况，这种实现也会受益。我们已经在几个测试案例上验证了该方法，包括一个含有 1045 个原子的 DNA 片段。
