From owner-chemistry@ccl.net Tue Aug 29 10:59:01 2017 From: "Heribert Reis hreis : eie.gr" To: CCL Subject: CCL: Vibrational sublevels along particular coordinate on PES Message-Id: <-52958-170829104323-11031-H5IVQXy0+sYMytU0Ehv1WA!^!server.ccl.net> X-Original-From: Heribert Reis Content-Type: multipart/alternative; boundary="f403045f1aec79e8f00557e56e56" Date: Tue, 29 Aug 2017 17:43:15 +0300 MIME-Version: 1.0 Sent to CCL by: Heribert Reis [hreis~!~eie.gr] --f403045f1aec79e8f00557e56e56 Content-Type: text/plain; charset="UTF-8" Content-Transfer-Encoding: quoted-printable On Fri, Aug 25, 2017 at 10:51 PM, Igors Mihailovs igorsm**cfi.lu.lv < owner-chemistry(_)ccl.net> wrote: > Dear computational chemistry specialists, > > Thank you all for your help and clarifications! Now I think I have an ide= a > about analysing a multidimentional PES, at least from the viewpoint of > statistical mechanics... > > Several minor questions, though: > > 1. > Eric Hermes erichermes+/-gmail.com wrote: > > Second, this approach is only valid if your reaction coordinate is suffic= iently flat that it can > be treated classically. > > How flat is "sufficiently flat" PES? For example, I have barriers of 10 t= o > 20 kcal/mol for going from 10=C2=B0 to 90=C2=B0 torsion (actually this is= called > internal rotation, I think). Is that "sufficiently flat"? Could someone > provide examples for "not sufficiently flat" case (I mean, among well-kno= wn > ones)? Do I understand it correctly that the restriction applies to cases > when tunneling appears, which has also Heribert mentioned (as with proton > transitions)? > > Can I assume that if the PES is "sufficiently flat", then the vibrational > sublevels are close to each other? For the my case of internal rotation, > for instance... > > Only two comments from me here: a) For a very flat torsional energy surface, there will be no vibrations, but (more or less hindered) rotations b) 10-20 kcal/mol is much larger than NkT=3DRT at room temperature, where RT~0.5 kcal/mol, so I assume in your case there will be a not very flat energy surface, and vibrational motions. > 2. > Heribert Reis hreis]|[eie.gr wrote: > > the vibrational wave function of the lowest level (for simplicity) around= that dihedral value > > I am not sure I have understood this. In accord with the following > discussion, does that mean I would need to solve for the one-dimensional > problem with my 1D-PES as the well potential, which would provide me with > vibrational levels, of which some will be located at the vicinity of > torsion angle value NN=C2=B0, some other level at MM=C2=B0, etc., etc.? > > The molecule will 'visit' all torsional values where the wave function of a (populated) level is nonzero. So if there is no tunnelling between two wells, you may have the situation you describe above. That may happen, for example, in the trivial case of a asymmetric two well potential, where the energy minimum of one well lies higher than the lowest vibrational level of the other well. If tunnelling is nonzero for some level, then the wave function of that level will extend over both wells, and the molecule will again visit all torsional values where the wave function is nonzero. Heribert Thank you all again in advance! > > > --f403045f1aec79e8f00557e56e56 Content-Type: text/html; charset="UTF-8" Content-Transfer-Encoding: quoted-printable


On Fri, Aug 25, 2017 at 10:51 PM, Igors Mihailovs igorsm**cfi.lu.lv <owner-chemistry(_)ccl.net> wrote:
=20 =20 =20
Dear computational chemistry specialists,

Thank you all for your help and clarifications! Now I think I have an idea about analysing a multidimentional PES, at least from the viewpoint of statistical mechanics...

Several minor questions, though:

1.
Eric Hermes erichermes+/-gmail.com wrote: 
Second, this approach is only valid if your reaction coordinate is=
 sufficiently flat that it can
be treated classically.
How flat is "sufficiently flat"= ; PES? For example, I have barriers of 10 to 20 kcal/mol for going from 10=C2=B0 to 90=C2=B0 torsion (actually this is called internal rotati= on, I think). Is that "sufficiently flat"? Could someone provide examples for "not sufficiently flat" case (I mean, among well-known ones)? Do I understand it correctly that the restriction applies to cases when tunneling appears, which has also Heribert mentioned (as with proton transitions)?

Can I assume that if the PES is "sufficiently flat", then t= he vibrational sublevels are close to each other? For the my case of internal rotation, for instance...

=C2=A0
Only two comments= from me here:
a) For a very flat torsional energy surface, there= will be no vibrations, but (more or less hindered) rotations
b) = 10-20 kcal/mol is much larger than NkT=3DRT at room temperature, where RT~0= .5 kcal/mol, so I assume in your case there will be a not very flat energy = surface, and vibrational motions.
2.
Heribert Reis hreis]|[eie.gr wrote:
 
the vibrational wave function of the lowest level (for simpl=
icity) around that dihedral value
I am not sure I have understood this. In accord with the following discussion, does that mean I would need to solve for the one-dimensional problem with my 1D-PES as the well potential, which would provide me with vibrational levels, of which some will be located at the vicinity of torsion angle value NN=C2=B0, some other lev= el at MM=C2=B0, etc., etc.?

The molecule will 'visit' all torsi= onal values where the wave function of a (populated) level is nonzero. So i= f there is no tunnelling between two wells, you may have the situation you = describe above. That may happen, for example, in the trivial case of a asym= metric two well potential, where the energy minimum of one well lies higher= than the lowest vibrational level of the other well.
If tunnelli= ng is nonzero for some level, then the wave function of that level will ext= end over both wells, and the molecule will again visit all torsional values= where the wave function is nonzero.

Heribert

Thank you all again in advance!



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