Stat inefficiency

[Pablo_Lopez_Rios]

The sweep does look like a quadric family: over the frames the surface goes from a closed ellipsoid, opens up, passes through something that looks like a hyperboloid, and closes back into an ellipsoid. That is what a family of second-order surfaces does, so at least in this region the node looks like a quadric in the scanned electron's coordinates rather than a curved plane.

Indeed, and there is probably a simple reason for the shapes - the trial wave function used in the plot is at heart a short-ish multideterminant expansion after all. What I tried to convey with the animation though is that a smooth, continuous backflow coordinate transformation x_i(R)=r_i+xi_i(R) cannot possibly take the Hartree-Fock node (a sphere) and make it go through this type of deformation because this would involve mapping points at infinity onto the surface of the sphere at some point in the animation, implying that xi_i(R) should diverge [i.e., so that Psi_HF is evaluated on the sphere (|xi_i|=r_sphere) when r_i is on the opened-up nodal surface at a point infinitely far from the origin].