  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.
