[Pw_forum] Bader analysis, part II

[Steven Kirk]

Hello all,

Firstly, thank you for your responses to my previous enquiry regarding 
Bader analysis of the results produced by PWSCF.

I am strongly considering writing some code to add this capability to, 
for example, the PP program from PWSCF. I am primarily interested in 
point properties rather than integration over atomic basins: finding the 
critical points and bond paths would be a good start, together with the 
values of the charge density, Laplacian etc. at these points. 
Implementing basin definition and integration is a much more demanding 
task !

In order to find, for example, the bond critical points (BCPs), one 
could assume a starting point halfway between 2 neighbouring atoms, then
evaluate grad(rho) (the gradient of the charge density) at this point, 
and take small steps 'downhill' to exactly locate the BCP (where 
grad(rho) =0 ). This can be done using Newton-Raphson in 3D - I once 
implemented this in another code - you need to extract the Hessian 
matrix of the charge density.

If the wave function is represented by plane waves of the form exp( 
ikx), then weighting each of the plane waves with ik should allow one to 
extract grad(rho), and weighting with -k^2 should allow one to evaluate 
the Laplacian, at an arbitrary location x. Using plane waves has 
advantages over relatively crude 3D interpolations of gridded data in 
this case.

A good starting point, then, would be the ability to specify two atoms, 
find the BCP (if any) that exists between them, and extract the charge 
density and the Laplacian at the BCP. The bond path (the path linking 
the two atoms along which the charge density is maximal relative on any 
neigbouring path) would also be useful - sometimes these are *not* the 
expected straight lines !

I would be very grateful if any of the participants on this list or the 
developers can point me to an appropriate location in the code where it 
would be possible to 'splice in' this capability.

Many thanks in advance for any feedback on this topic,

Regards,
Steve Kirk