xi = (qi - q0) * n,
where qi is the old coordinate of ith particle, xi = (xi, yi, zi ) is the new coordinate, q0 is the reference point which can be either the desiganted central particle or the center of mass of this local surface structure.
f(x, y) = axxx2 + 2axyxy + ayyy2 + a0
S = Sigmai(zi-f(xi, yi)) 2
with respect to axx, axy, ayy, a0.
( axx axy )
( axy ayy ) and get two principle axis and the correponding local curvatures (with a factor of 2). Note the parabolic curvatures now have signs to indicate directions ( positive as bending toward center of mass ).
Here is an illustration of the principle axis for a near-flat facet. Here is the local curvature distributions for the icosahedral gold cluster with 2624 atoms.
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