CCL: How to calculate the independent degrees of freedom of a molecule?
- From: Jun Zhang <coolrainbow * yahoo.cn>
- Subject: CCL: How to calculate the independent degrees of freedom
of a molecule?
- Date: Sun, 4 Dec 2011 14:30:11 +0800 (CST)
Dera Cory:
Â
I think you are right -- just what I need! Maybe the "totally symmetric
space" is not curvilinear like internal coordinates should be, but a search
and redundent revoming of all internal coordinates could do it. Thank you!
----------------------------------------------------------------
Jun Zhang (coolrainbow||yahoo.cn)
Computational Chemistry Group
No.94, Weijinlu
Nankai University
Tianjin, China
________________________________
åääï Cory Pye cpye[#]ap.smu.ca
<owner-chemistry||ccl.net>
æääï "Zhang, Jun " <coolrainbow||yahoo.cn>
åéææï 2011å12æ4æ, æææ,
äå 5:39
äé: CCL: How to calculate the independent degrees of freedom of a
molecule?
Sent to CCL by: Cory Pye [cpye++ap.smu.ca]
Jun,
I think that the number of parameters must be the same as the number of totally
symmetric vibrational modes of the molecule. Unfortunately I don't have a proof
for you, but if you take the space spanned by all the totally symmetric
vibrations, then it must be the space spanned by the coordinates as well.
-Cory
On Sat, 3 Dec 2011, Jun Zhang coolrainbow * yahoo.cn wrote:
> Hello everyone:
Â
For a nonlinear N-atom molecule there are 3N-6 internal degrees of freedom, of
course. However, for a point group-constraint molecule, such as C2v H2O,
there are only 2 independent degrees of freedom. So, isÂthere a systematic
way to determine the number and the contents of independent degrees of freedom
of an arbitarily symmetry-constraint molecule? I heard that some knowledge like
Polya theorem are requied, but I am not sure. It will be better if some reviews
can be reccommended.
Â
Thank you in advance. Any suggestions will be appreciated.
Â
Best regards!
Â
----------------------------------------------------------------
Jun Zhang (coolrainbow^-^yahoo.cn)
Computational Chemistry Group
No.94, Weijinlu
Nankai University
Tianjin, China
 *************  ! Dr. Cory C. Pye
***************** ! Associate Professor
*** **  ** ** ! Theoretical and
Computational Chemistry
** * ****    ! Department of
Chemistry, Saint Mary's University
**   * *    ! 923 Robie
Street, Halifax, NS B3H 3C3
**Â Â Â *Â *Â Â Â Â !Â
cpye_-_crux.stmarys.ca http://apwww.stmarys.ca/~cpye
***  * *  ** ! Ph:
(902)-420-5654Â FAX:(902)-496-8104
*****************Â !
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<html><body><div style="color:#000; background-color:#fff;
font-family:times new roman, new york, times,
serif;font-size:12pt"><div><span>Dera
Cory:</span></div><div><span></span> </div><div><span>I
think you are right -- just what I need! Maybe the "totally symmetric
space" is not curvilinear like internal coordinates should be, but a search
and redundent revoming of all internal coordinates could do it. Thank
you!<var
id="yui-ie-cursor"></var></span></div><div></div><div> </div><div>----------------------------------------------------------------<br>Jun
Zhang (coolrainbow||yahoo.cn)<br>Computational Chemistry
Group<br>No.94, Weijinlu<br>Nankai University <br>Tianjin,
China<br></div> <div style="font-family: times new roman,
new york, times, serif; font-size: 12pt;"> <div
style="font-family: times new roman, new york, times, serif; font-size:
12pt;"> <font size="2" face="Arial"> <div
style="margin: 5px 0px; padding: 0px; border: 1px solid
rgb(204, 204, 204); height: 0px; line-height: 0; font-size: 0px;"
class="hr" contentEditable="false"
readonly="true"></div> <b><span
style="font-weight:
bold;">åääï</span></b> Cory Pye
cpye[#]ap.smu.ca <owner-chemistry||ccl.net><br>
<b><span style="font-weight:
bold;">æääï</span></b> "Zhang, Jun
" <coolrainbow||yahoo.cn> <br> <b><span
style="font-weight:
bold;">åéææï</span></b>
2011å12æ4æ, æææ, äå 5:39<br>
<b><span style="font-weight:
bold;">äé:</span></b> CCL: How to calculate the
independent degrees of freedom of a molecule?<br> </font>
<br><br>Sent to CCL by: Cory Pye
[cpye++ap.smu.ca]<br>Jun,<br>I think that the number of parameters
must be the same as the number of totally<br>symmetric vibrational modes
of the molecule. Unfortunately I don't have a proof<br>for you, but if you
take the space spanned by all the totally symmetric<br>vibrations, then it
must be the space spanned by the
coordinates as well.<br>-Cory<br><br>On Sat, 3 Dec 2011, Jun
Zhang coolrainbow * yahoo.cn wrote:<br><br>> Hello
everyone:<br> <br>For a nonlinear N-atom molecule there are
3N-6 internal degrees of freedom, of course. However, for a point
group-constraint molecule, such as C2v H2O, there are only 2 independent degrees
of freedom. So, is there a systematic way to determine the number and
the contents of independent degrees of freedom of an arbitarily
symmetry-constraint molecule? I heard that some knowledge like Polya theorem are
requied, but I am not sure. It will be better if some reviews can be
reccommended.<br> <br>Thank you in advance. Any suggestions
will be appreciated.<br> <br>Best
regards!<br> <br>----------------------------------------------------------------<br>Jun
Zhang (coolrainbow^-^yahoo.cn)<br>Computational Chemistry
Group<br>No.94, Weijinlu<br>Nankai University<br>Tianjin,
China<br><br>
************* ! Dr. Cory C. Pye<br>
***************** ! Associate
Professor<br>*** ** **
** ! Theoretical and Computational
Chemistry<br>** * ****
! Department of Chemistry, Saint Mary's
University<br>** * *
! 923 Robie Street, Halifax, NS B3H
3C3<br>** * *
! cpye_-_crux.stmarys.ca
<a href="http://apwww.stmarys.ca/~cpye";
target="_blank">http://apwww.stmarys.ca/~cpye</a><br>;***
* * ** ! Ph:
(902)-420-5654 FAX:(902)-496-8104<br>
***************** !<br> *************
! Les Hartree-Focks (Apologies to Montreal Canadien
Fans)<br><br><br><br>-= This is automatically added to
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