From owner-chemistry@ccl.net Sun Nov 4 16:30:00 2012 From: "Arne Dieckmann adieckma%%googlemail.com" To: CCL Subject: CCL: ZPE in non-stationary points Message-Id: <-47842-121104162512-21366-n+Ozm/18DBLnSHt+qIhqcg*server.ccl.net> X-Original-From: Arne Dieckmann Content-Transfer-Encoding: 8bit Content-Type: text/plain; charset=utf-8 Date: Sun, 4 Nov 2012 13:25:04 -0800 Mime-Version: 1.0 (1.0) Sent to CCL by: Arne Dieckmann [adieckma]|[googlemail.com] Dear Sebastian, There are ways to do this, but I am not aware of a simple method. You could employ (ab initio) molecular dynamics and use metadynamics, thermodynamic integration or something like that to sample phase space and construct a free energy surface. Cheers, Arne On Nov 4, 2012, at 12:21 PM, "Sebastian Kozuch kozuchs|yahoo.com" wrote: > Jussi, You have a point here. Let me rephrase my question then: > Can you calculate the Gibbs energy of a system when you are not at a minimum or a TS? In other words, is there a simple way to calculate a potential GIBBS energy surface? > I'm not a specialist on this, but physically having a stretched molecule may only mean being at the geometrical limit of a high vibrationally state. In principle, there should be an equivalent to E+ZPE for each point of the curve of a reaction (as long as it is permitted by the uncertainty principle). Can someone share some light on this? > > Thanks, > > Sebastian > > > > ________________________________ > From: "Jussi Lehtola jussi.lehtola,,helsinki.fi" > To: "Kozuch, Sebastian " > Sent: Saturday, November 3, 2012 7:10 PM > Subject: CCL: ZPE in non-stationary points > > > Sent to CCL by: Jussi Lehtola [jussi.lehtola]^[helsinki.fi] > On Sat, 3 Nov 2012 16:05:34 -0700 (PDT) > "Sebastian Kozuch kozuchs]~[yahoo.com" wrote: >> Dear all, >> Does anyone know of a (simple) method to calculate ZPE and maybe >> Gibbs energies for geometries that are not stationary points (i.e. >> not a stable intermediate or a TS)? How valid is a typical frequency >> calculation for these geometries? > > Please elaborate on what you mean. > > Zero point vibrations only make sense in cases where the potential can > be expanded locally as a Taylor series as > V(r) ~ V(r0) + (r-r0)*d2V/dr2*(r-r0) > where d2V/dr2 is the Hessian computed at r0. This means that you must > be in a stationary point, since the first derivative (gradient) needs to > vanish. > > Secondly, any stationary point will not do, since otherwise you will > have a saddle point, meaning that vibrations do not exist in some > directions, instead the system is just unstable: when the system is > pushed in this direction, it will not start to oscillate around the > configuration in the stationary point, instead the perturbation will > just start growing. > > To calculate ZPE you need a bound system. This is not the case even for > all stationary points -- and even less for non-stationary points. > -- > -------------------------------------------------------- > Mr. Jussi Lehtola, M. Sc. Doctoral Student > jussi.lehtola{:}helsinki.fi Department of Physics > http://www.helsinki.fi/~jzlehtol University of Helsinki > Office phone: +358 9 191 50 632 Finland > -------------------------------------------------------- > Jussi Lehtola, FM Tohtorikoulutettava > jussi.lehtola{:}helsinki.fi Fysiikan laitos > http://www.helsinki.fi/~jzlehtol Helsingin Yliopisto > Työpuhelin: (0)9 191 50 632 > --------------------------------------------------------> the strange characters on the top line to the - - sign. You can also > > > E-mail to subscribers: CHEMISTRY- -ccl.net or use:> > E-mail to administrators: CHEMISTRY-REQUEST- -ccl.net or use> > > =--1377744757-1372404203-1352060508=:29950 > Content-Type: text/html; charset=iso-8859-1 > Content-Transfer-Encoding: quoted-printable > >
Jussi, You have a point here. Let me rephrase my question then:
Can you calculate the Gibbs energy of a system when you are not at a minimum or a TS? In other words, is there a simple way to calculate a potential GIBBS energy surface?
I'm not a specialist on this, but physically having a stretched molecule may only mean being at the geometrical limit of a high vibrationally state. In principle, there should be an equivalent to E+ZPE for each point of the curve of a reaction (as long as it is permitted by > the uncertainty principle). Can someone share some light on this?

Thanks,
Sebastian

face="Arial" size="2">
From: "Jussi Lehtola jussi.lehtola,,helsinki.fi" <owner-chemistry- -ccl.net>
To: "Kozuch, Sebastian " <kozuchs- -yahoo.com>
Sent: Saturday, November 3, 2012 7:10 PM
Subject: CCL: ZPE in non-stationary points

>
Sent to CCL by: Jussi Lehtola [jussi.lehtola]^[helsinki.fi]
On Sat, 3 Nov 2012 16:05:34 -0700 (PDT)
"Sebastian Kozuch kozuchs]~[yahoo.com" <owner-chemistry{:}ccl.net> wrote:
> Dear all,
> Does anyone know of a (simple) method to calculate ZPE and maybe
> Gibbs energies for geometries that are not stationary points (i.e.
> not a stable intermediate or a TS)? How valid is a typical frequency
> calculation for these geometries?

Please elaborate on what you mean.

Zero point vibrations only make sense in cases where the potential can
be expanded locally as a Taylor series as
    V(r) ~ V(r0) + (r-r0)*d2V/dr2*(r-r0)
where d2V/dr2 is the Hessian computed at r0. This means that you must
be in a stationary point, since the first derivative (gradient) needs > to
vanish.

Secondly, any stationary point will not do, since otherwise you will
have a saddle point, meaning that vibrations do not exist in some
directions, instead the system is just unstable: when the system is
pushed in this direction, it will not start to oscillate around the
configuration in the stationary point, instead the perturbation will
just start growing.

To calculate ZPE you need a bound system. This is not the case even for
all stationary points -- and even less for non-stationary points.
--
--------------------------------------------------------
Mr. Jussi Lehtola, M. Sc.        Doctoral Student
jussi.lehtola{:}helsinki.fi        Department of Physics
http://www.helsinki.fi/~jzlehtol  University of Helsinki
Office phone: +358 9 191 50 632  Finland
--------------------------------------------------------
Jussi Lehtola, FM  >               Tohtorikoulutettava
jussi.lehtola{:}helsinki.fi        Fysiikan laitos
http://www.helsinki.fi/~jzlehtol  Helsingin Yliopisto
Työpuhelin: (0)9 191 50 632
--------------------------------------------------------


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