论文标题
在晶体和螺旋中密度功能能的分析梯度中的非变化正交衍生物
Nonvanishing quadrature derivatives in the analytical gradients of density functional energies in crystals and helices
论文作者
论文摘要
结果表明，用多中心径向角网格评估的某些分析梯度中的正交衍生物即使在无限密度的网格极限，也不会消失，从而在被忽略时会导致严重的误差。所讨论的梯度是与晶体的晶格常数或具有螺钉对称性的链的螺旋角度相关的梯度。这与原子梯度中的正交衍生物相反，该梯度可以通过网格扩展任意地任意地使其缩小。不同的行为可追溯到网格点是否取决于取得能量导数的坐标。尽管在晶格 - 稳定梯度中的非变化正交衍生物被确定为由扩展的整合结构域引起的表面积分，但在螺旋 - 角度梯度中非呈现的正交衍生物的分析起源仍然未知。
It is shown that the quadrature derivatives in some analytical gradients of energies evaluated with a multi-centre radial-angular grid do not vanish even in the limit of an infinitely dense grid, causing severe errors when neglected. The gradients in question are those with respect to a lattice constant of a crystal or to the helical angle of a chain with screw axis symmetry. This is in contrast with the quadrature derivatives in atomic gradients, which can be made arbitrarily small by grid extension. The disparate behaviour is traced to whether the grid points depend on the coordinate with respect to which the derivative of energy is taken. Whereas the nonvanishing quadrature derivative in the lattice-constant gradient is identified as the surface integral arising from an expanding integration domain, the analytical origin of the nonvanishing quadrature derivative in the helical-angle gradient remains unknown.
