From chemistry-request #at# server.ccl.net Thu Jun 22 05:06:42 2000 Received: from fecit-gate.fecit.co.uk (firewall-user*- at -*[193.119.134.250]) by server.ccl.net (8.8.7/8.8.7) with SMTP id FAA13324 for ; Thu, 22 Jun 2000 05:06:42 -0400 Received: by fecit-gate.fecit.co.uk; id KAA00693; Thu, 22 Jun 2000 10:12:09 +0100 Received: from suisei(192.168.101.50) by fecit-gate.fecit.co.uk via smap (V5.0) id xma000690; Thu, 22 Jun 00 10:11:09 +0100 Received: from fecit.co.uk (NT11.fecit.co.uk [192.168.101.116]) by suisei.fecit.co.uk (8.6.9/8.6.9) with ESMTP id KAA00086; Thu, 22 Jun 2000 10:15:40 +0100 Message-ID: <3951D6CF.2C12098F {*at*} fecit.co.uk> Date: Thu, 22 Jun 2000 10:05:19 +0100 From: Herbert Fruchtl Organization: Fujitsu European Centre for Information Technology X-Mailer: Mozilla 4.73 [en] (WinNT; U) X-Accept-Language: en MIME-Version: 1.0 To: elewars CC: chemistry: at :ccl.net Subject: Re: CCL:WORDS LOCAL AND NONLOCAL IN DFT References: <39511FD2.2F682830 |-at-| trentu.ca> Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit 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