From chemistry-request@server.ccl.net Thu May 15 14:35:06 2003 Received: from marcy.nas.nasa.gov ([129.99.113.17]) by server.ccl.net (8.11.6/8.11.0) with ESMTP id h4FIZ5J20576 for ; Thu, 15 May 2003 14:35:06 -0400 Received: from localhost (ioana@localhost) by marcy.nas.nasa.gov (8.11.7+Sun/8.11.6/NAS 8.11.6-5n) with ESMTP id h4FIZ5q20355; Thu, 15 May 2003 11:35:05 -0700 (PDT) Date: Thu, 15 May 2003 11:35:05 -0700 (PDT) From: Ioana Cozmuta To: WU_GUOSHENG@Lilly.com cc: CHEMISTRY@ccl.net Subject: Re: CCL:Error estimation of gibbs free energy In-Reply-To: Message-ID: References: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=X-UNKNOWN Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from QUOTED-PRINTABLE to 8bit by server.ccl.net id h4FIZ6J20577 Hi Guosheng, > From the top of my head, that formula comes from a Taylor expansion in which you neglect the higher-order terms. Honestly, the best info I have on error propagation are my hand written notes from the courses I followed during undergrad/grad studies. However, if you do a search on google with the following terms: general formula error propagation it gives lots of references. The most frequently mentioned reference I see is Taylor, J. R., "An introduction to Error Analysis", University Science Books, 1982. I also think that any book on numerical analysis should have at least a chapter that covers error propagation. See also: http://mulliken.chem.hope.edu/~polik/Chem345-2000/errorpropagation.htm Regards, Ioana **************************************************************************** * Ioana Cozmuta, PhD * * * NASA-AMES Research Center * "Gravitation can not be held responsible* * Mail Stop 230-3 * for people falling in love" * * Moffet Field,CA 94035 * * * phone: (650) 604-0993 * Albert Einstein* * fax: (650) 604-0350 * (1879-1955) * **************************************************************************** On Thu, 15 May 2003 WU_GUOSHENG@Lilly.com wrote: > Dear Ioana, > > Could you please point out if there is any reference for your equation? > > I am sure there must be such kind of thing in some data analysis books, > but it's just inconvenient for me to find it at this moment. > > It seems to me the straightforwad way to get an error estimation is > by the basis calculus, like following (with similar presentation to > yours): > > for f = f(x1, x2, ...), > > (del_f)= (df/dx1)*(del_x1) + (df/dx2)*(del_x2) + ... > > Then, (del_f)^2 can be the next form, if one has the interest: > > (del_f)^2= (df/dx1)^2 * (del_x1)^2 + (df/dx2)^2 * (del_x2)^2 > + 2*(df/dx1)* (del_x1) * (df/dx2) * (del_x2) + ... > > So for your example if f= x+y then (del_f) = (del_x)+(del_y) > > if f = x*y then simply > del_f = x * (del_y) + y * (del_x) > > If one like, (del_f)/f = (del_x)/x + (del_y)/y > > or [(del_f)/f]^2 = (del_x/x)^2 + (del_y/y)^2 > + 2 * (del_x)*(del_y)/(x*y) > > Of course, for practical usage, one may overlook one or more terms if they > are much smaller than others. > - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - > Thanks for your attention. > > Sincerely, > > Guosheng > > Guosheng Wu, Ph.D. > Eli Lilly & Company > > > > > > Ioana Cozmuta > Sent by: Computational Chemistry List > 05/14/2003 01:32 PM > > > To: "'CHEMISTRY@ccl.net'" > cc: > Subject: CCL:Error estimation of gibbs free energy > > > Hi, > > The most general formula from which you can always estimate the error > del_f of a function f(x1, x2, x3, ...xn) is > > (del_f)^2= (df/dx1)^2*del_x1^2+(df/dx2)^2*del_x2^2+... > > where df/dxi are partial derivatives of the function f with respect to xi > (i=1,n) and del_xi are the individual errors. > > So for example if f= x+y then (del_f)^2 = (del_x1)^2+(del_x2)^2 > if f = x*y then (delf/f)^2= (del_x/x)^2+(del_y/y)^2 > > If x1, ...xn are functions of other variables I find the general formula > above (with derivatives) much easier to use. > > Ioana > > On Wed, 14 May 2003, VITORGE Pierre 094605 wrote: > > > d(dG) = square root([d(dH)]^2 + [d(dS)]^2) > > cannot be true, if dh=0 and T is constant the above Eq. gives > > d(dG) = d(dS) > > while it is of course > > d(dG) = T d(dS) > > > > You probably mean: > > d(DG) = square root([d(DH)]^2 + [(Td(DS)+(DS)dT)]^2)? > > or > > d(DG) = square root([d(DH)]^2 + [Td(DS)]^2 + [(DS)dT]^2)? > > > > Pierre Vitorge > > CEA DEN Saclay DPC/SECR/LSRM & UMR 8587 (CEA-CNRS-Universite d'Evry) > > Universite d'Evry UMR 8587 > > pierre.vitorge@cea.fr > > http://perso.club-internet.fr/vitorgen/pierre/pierre.html > > > > > > -----Message d'origine----- > > De: Dr. Richard L. Wood [mailto:rlw28@cornell.edu] > > Date: lundi 12 mai 2003 15:58 > > À: Wong Lai Ho > > Cc: CHEMISTRY@ccl.net > > Objet: CCL:Error estimation of gibbs free energy > > > > > > Wouldn't the following be true > > > > d(dG) = square root([d(dH)]^2 + [d(dS)]^2)? > > > > dG is delta G, d(dG) is the error in delta G, dH is delta H, d(dH) is > the > > error > > in delta H, dS is delta S and d(dS) is the error in delta S. > > > > This is taken from a simple error propagation analysis as taught in some > > physical/analytical chemistry laboratories. > > > > Richard > > > > Wong Lai Ho wrote: > > > > > Dear CCLers, > > > > > > I have a question regarding error estimation of the experimental > values of > > > gibbs free energy. > > > As we knows that: > > > delta G(formation) > > > = delta H(formation) > > > - Temp * [entropy(molecule)-sum(entropy(atoms to form the > molecules))] > > > > > > Can I claim that the experimental error bar of the gibbs free > energy(delta > > > G) is equal to the error bar of the enthalpy change of formation(delta > H)? > > > (since the error introduced by the entropy is usually very small) > > > Is there any papers or books talking about this error? > > > > > > I would be grateful if you can give some comments on this claim. > > > > > > Larry > > > > > > > -- > > Richard L. Wood, Ph. D. > > Physical/Computational Chemist > > Post-doctoral Associate > > Department of Chemistry > > Trinity University, San Antonio, TX 78212 > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > -= This is automatically added to each message by mailing script =- > CHEMISTRY@ccl.net -- To Everybody | CHEMISTRY-REQUEST@ccl.net -- To > Admins > Ftp: ftp.ccl.net | WWW: http://www.ccl.net/chemistry/ | Jan: jkl@ccl.net > > > > > > > >