From chemistry-request ":at:" ccl.net Wed Jul 21 09:17:02 2004 Received: from smtp-test.cshore.com (imgate1.cshore.com [209.113.151.8]) by server.ccl.net (8.12.8/8.12.8) with ESMTP id i6LEGx4s009107 for ; Wed, 21 Jul 2004 09:17:00 -0500 Received: from mailsrv.lorentzian.com (unknown [65.113.125.132]) by smtp-test.cshore.com (Postfix) with ESMTP id 77779AB69 for ; Wed, 21 Jul 2004 10:23:34 -0400 (EDT) Received: from svega.gaussian.com (unknown [193.0.9.49]) by mailsrv.lorentzian.com (Postfix) with ESMTP id A5286C972 for ; Wed, 21 Jul 2004 10:22:29 -0400 (EDT) Received: by svega.gaussian.com (Postfix, from userid 350) id 3752D4770D; Wed, 21 Jul 2004 10:24:03 -0400 (EDT) Date: Wed, 21 Jul 2004 10:24:03 -0400 To: chemistry.-at-.ccl.net Subject: Re: CCL:force constants of diatomics in GAUSSIAN-03 Message-ID: <20040721142403.GC18470.-at-.svega.gaussian.com> References: <40F5307B.1020909.-at-.xenon.spb.ru> <40FC1BDF.1010700.-at-.xenon.spb.ru> <40FD869D.4060002.-at-.xenon.spb.ru> <40FE5064.9030808.-at-.xenon.spb.ru> Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Disposition: inline In-Reply-To: <40FE5064.9030808.-at-.xenon.spb.ru> User-Agent: Mutt/1.5.6i From: frisch.-at-.gaussian.com (Michael Frisch) X-Spam-Status: No, hits=1.0 required=7.5 tests=NO_RDNS autolearn=no version=2.61 X-Spam-Checker-Version: SpamAssassin 2.61 (1.212.2.1-2003-12-09-exp) on servernd.ccl.net On Wed, Jul 21, 2004 at 03:15:48PM +0400, Dmitry Rozmanov wrote: Dmitry Rozmanov wrote > If this is the case, then I guess this is just a wrong way of doing things > and the force constants got by Gaussian are not correct at all. There is a > definition of the thing and there is no two way of calculation. > > ---Dmitry. > This is nonsense. The details are in a white paper on our web site, but the key point is that the force constant is the second derivative with respect to a normal mode displacement and the units for the normal mode, or equivalently the convention for what consititues a unit step, are arbitrary. For polyatomic molecules, one typically diagonalizes the force constant matrix in mass-weighted coordinates, so the natural unit step is a normalized displacement in these coordinates. This approach is general and applicable to any polyatomic molecule. In the particular case of H2 with the molecule along the x-axis, this normalized step would be (1/sqrt(2),0,0,1/sqrt(2),0,0) in the 6 cartesian coordinates. This unit step changes the H-H distance by sqrt(2). For the particular case of diatomic molecules when people calculate by hand, they use the distance between atoms as the coordinate, which simpler for diatomics but doesn't apply to polyatomics. In that coordinate system, a unit displacement changes the distance by 1 rather than sqrt(2), so the force constants (second derivatives of the energy) differ by a factor of 2. The corresponding reduced masses for the mode also differ by a factor of two and the frequency is the same. For the diatomic, the "by hand" coordinates give a reduced mass for the mode which is the same as the overall reduced mass for the molecule. For a general polyatomic molecule, the reduced mass corresponding to a particular mode is not an observable quantity and is not defined until one adopts a convention for the (arbitrary) size of a unit normal mode displacement. Mike Frisch