# Re: CCL:WORDS LOCAL AND NONLOCAL IN DFT

*From*: Herbert Fruchtl <fruechtl %-% at %-% fecit.co.uk>
*Organization*: Fujitsu European Centre for Information
Technology
*Subject*: Re: CCL:WORDS LOCAL AND NONLOCAL IN DFT
*Date*: Thu, 22 Jun 2000 10:05:19 +0100

elewars wrote:
> Does any one know why DFT functionals without gradient corrections are
> called _local_, while gradient-corrected functionals are called
> _nonlocal_? I am not asking about the theory behind these, but why these
> terms are used. I know that nonlocal has a certain meaning in quantum
> physics; does it have some special meaning in connection with
> mathematical functions or functionals? The term nonlocal applied to
> gradient-corrected functional has been said to be mathematically wrong
> (A. St-Amant, Reviews in Computational chemistry, vol. 7, chapter 5,
> 1996; p. 223).
>
There is a mathematical theorem which states that if you know all
derivatives of an 'analytical function' (i.e. one that can be expressed
in a power series) in one point, you know the function in its complete
definition range.
Nonlocal functionals depend not only on the value of the density, but
also its derivatives (mostly only the first one, the gradient). The
gradient contains information about the surrounding area, not only the
point you look at. So the expression nonlocal my be not very intuitive,
but I don't think it's wrong.
HTH,
Herbert