From owner-chemistry@ccl.net Sat Sep 24 17:49:00 2011 From: "David A Mannock dmannock ~ ualberta.ca" To: CCL Subject: CCL: Fractional to orthonormal converting matrix Message-Id: <-45511-110924171440-4845-kt2YMBDyE0MtFOL8fZ67Ng ~ server.ccl.net> X-Original-From: David A Mannock Content-Type: multipart/alternative; boundary=0016367fb52f5ad1c604adb669af Date: Sat, 24 Sep 2011 15:14:29 -0600 MIME-Version: 1.0 Sent to CCL by: David A Mannock [dmannock]![ualberta.ca] --0016367fb52f5ad1c604adb669af Content-Type: text/plain; charset=ISO-8859-1 Masoud, I am not an expert in maths, but this sounds similar to the shift in the laboratory and reference frames used in NMR spectroscopy. I am not sure in such cases whether the angle between the XY, XZ and YZ axes must be 90 degrees. You may want to look at that possibility before doing lots of hard work starting from the big bang. You may simply be able to expand on what exists in that area to define your own co-ordinate system. Just another crazy idea! David On Sat, Sep 24, 2011 at 4:09 AM, Masoud m_nahali!A!alum.sharif.edu < owner-chemistry-#-ccl.net> wrote: > Dear Herbert > > Thanks for your prompt reply. I fancy calculating the converting matrix > considering no specific preferred direction. I meant if a, b, and c vectors > were in any direction and certainly were not taken in X or XY plane I would > like to calculate the converting matrix in this case. Actually I am writing > a Fortran 90 program in which the a, b, and c vectors (every vectors may > have different angles with respect to X Y Z coordination axes) are as input > file and then the program would calculate converting matrix and it is a key > point since through this matrix any atomic positions (orthonormal or > fractional) could be converted to each other with no limitation on how and > where the vectors or axes are. > > Best Wishes > > Masoud > > > > > > > On Fri, Sep 23, 2011 at 5:54 PM, Herbert Fruchtl herbert.fruchtl.. > st-andrews.ac.uk wrote: > >> >> Sent to CCL by: Herbert Fruchtl [herbert.fruchtl::st-andrews.**ac.uk >> ] >> Fractional coordinates, in connection with lattice parameters (lengths and >> angles rather than lattice vectors), don't contain any information about >> orientation in a Cartesian coordinate system, so you have to choose one. If >> you multiply the transformation matrix described in your link with a >> rotation matrix (rotating your coordinates around any axis by any angle), >> you get another valid transformation matrix. You don't say which orientation >> you want instead of the simplest one. >> >> HTH, >> >> Herbert >> >> >> >> On 23/09/11 15:50, Masoud Nahali m_nahali ~ alum.sharif.edu wrote: >> >>> >>> Sent to CCL by: "Masoud Nahali" [m_nahali=alum.sharif.edu] >>> Dear CCL Friends >>> >>> There is a matrix that converts fractional coordinates to orthonormal >>> ones and certainly the vice versa could be done by an inverted matrix. In >>> the following link you can find this matrix and a brief justification. >>> >>> http://www.angelfire.com/**linux/myp/FracCor/fraccor.html >>> >>> There are 2 limitations in this approach since we have to take one of the >>> vectors on X axis and also another vector must be on X-Y plane. >>> >>> I need a general form of such converting matrix without the 2 >>> limitations. I mean that a, b, and c vectors shouldn't be limited to locate >>> in/on a specific direction (plane) like X-axis or X-Y plane. I appreciate >>> any suggestion in advance to find it. >>> >>> >>> >>> Best Wishes >>> Masoud> >>> >>> >> -- >> Herbert Fruchtl >> Senior Scientific Computing Officer >> School of Chemistry, School of Mathematics and Statistics >> University of St Andrews >> -- >> The University of St Andrews is a charity registered in Scotland: >> No SC013532** >> E-mail to subscribers: CHEMISTRY^^^ccl.net or use: >> http://www.ccl.net/cgi-bin/**ccl/send_ccl_message >> >> E-mail to administrators: CHEMISTRY-REQUEST^^^ccl.net or use >> http://www.ccl.net/cgi-bin/**ccl/send_ccl_message >> **http://www.ccl.net/chemistry/**sub_unsub.shtmlConferences: http://server.ccl.net/** >> chemistry/announcements/**conferences/ >> >> Search Messages: http://www.ccl.net/chemistry/**searchccl/index.shtml >> ** http://www.ccl.net/spammers.**txt >> >> RTFI: http://www.ccl.net/chemistry/**aboutccl/instructions/ >> >> > --0016367fb52f5ad1c604adb669af Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Masoud, I am not an expert in maths, but this sounds similar to the shift i= n the laboratory and reference frames used in NMR spectroscopy. I am not su= re in such cases whether the angle between the XY, XZ and YZ axes must be 9= 0 degrees. You may want to look at that possibility before doing lots of ha= rd work starting from the big bang. You may simply be able to expand on wha= t exists in that area to define your own co-ordinate system. Just another c= razy idea! David

On Sat, Sep 24, 2011 at 4:09 AM, Masoud m_na= hali!A!alum.sharif.edu <owner-chemistry-#-ccl.net= > wrote:
Dear Herbert

Thanks for your prompt reply. I fancy calculating the convertin= g matrix considering no specific=A0preferred direction. I meant if a, b, an= d c vectors were in any direction and certainly were not taken in X or XY p= lane I would like to calculate the converting matrix in this case. Actually= I am writing a Fortran 90 program in which the a, b, and c vectors (every = vectors may have different angles with respect to X Y Z coordination axes) = are as input file and then the program would calculate converting matrix an= d it is a key point since through this matrix any atomic positions (orthono= rmal or fractional) could be converted to each other with no limitation on = how and where the vectors or axes are. =A0=A0=A0=A0

Best Wishes

=A0Masoud



=




On Fri, Sep 23, 2011 at 5:54 PM, Herbert= Fruchtl herbert.fruchtl..st-andrews.ac.uk <owner-chemistry^^^ccl.net>= wrote:

Sent to CCL by: Herbert Fruchtl [herbert.fruchtl::st-andrews.ac.uk]
Fractional coordinates, in connection with lattice parameters (lengths and = angles rather than lattice vectors), don't contain any information abou= t orientation in a Cartesian coordinate system, so you have to choose one. = If you multiply the transformation matrix described in your link with a rot= ation matrix (rotating your coordinates around any axis by any angle), you = get another valid transformation matrix. You don't say which orientatio= n you want instead of the simplest one.

HTH,

=A0 Herbert



On 23/09/11 15:50, Masoud Nahali m_nahali ~ alum.sharif.edu wrote:

Sent to CCL by: "Masoud =A0Nahali" [m_nahali=3Dalum.sharif.edu]
Dear CCL Friends

There is a matrix that converts fractional coordinates to orthonormal ones = and certainly the vice versa could be done by an inverted matrix. In the fo= llowing link you can find this matrix and a brief justification.

http://www.angelfire.com/linux/myp/FracCor/fraccor.html<= /a>

There are 2 limitations in this approach since we have to take one of the v= ectors on X axis and also another vector must be on X-Y plane.

I need a general form of such converting matrix without the 2 limitations. = I mean that a, b, and c vectors shouldn't be limited to locate in/on a = specific direction (plane) like X-axis or X-Y plane. I appreciate any sugge= stion in advance to find it.



Best Wishes
Masoud>


--
Herbert Fruchtl
Senior Scientific Computing Officer
School of Chemistry, School of Mathematics and Statistics
University of St Andrews
--
The University of St Andrews is a charity registered in Scotland:
No SC013532


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