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functional derivatives

• To: mathgroup at christensen.cybernetics.net
• Subject: [mg419] functional derivatives
• From: P.Jemmer at sussex.ac.uk (Patrick Jemmer)
• Date: Mon, 23 Jan 95 17:28 GMT

Hello all:

I am using density functional theory for computing propertiesd
of atoms and molecules.

As part of this project I am deriving the background theory.
So, I need to get functional derivatives of functionals
of the form:

F( rho, modulus(gradient(rho)), laplacian(rho) )

I know the standard calculus of variations formula is:


delta f/ delta rho =

partial df/d rho - del.( partial df/ d del(rho) )
+ laplacian (partial df/ d laplacian(rho) )


I have tried using ther Mathematica opperation VariationalD,
but I think the problem with this is that it is designed
for functionals of 1-D functions only. and so works on:

delts f/ delta rho =

partial df/d rho - (d/d rho')(partial df/ d rho')
+ (d/d rho'')(partial df/ d rho'')


I was wondering how to make my own version of
VariationalD to do this sort of thing.

Any ideas much appreciated!

Thanks. Patrick.


-------------


Patrick Jemmer,

Theoretical Chemistry,
University of Sussex,
Falmer, Brighton.