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<DIV><FONT face=Arial size=2>Li Niu:</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Nobody but linear algebra can help you;-) Go to
find a textbook, Gram Schmidt orthogonalization will</FONT></DIV>
<DIV><FONT face=Arial size=2>help you understand the process of vector
orthogonalization. For actual numerical computation, you'd</FONT></DIV>
<DIV><FONT face=Arial size=2>better use Householder transformation in your case
as your 3N vectors are numeric.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Hope this give you a start point.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Huiqun <A
href="mailto:Zhou@Nanjing">Zhou@Nanjing</A> University, China</FONT></DIV>
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<DIV style="FONT: 10pt arial">----- Original Message ----- </DIV>
<DIV
style="BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: black"><B>From:</B>
<A title=niuli1978@yahoo.com.cn href="mailto:niuli1978@yahoo.com.cn">li
niu</A> </DIV>
<DIV style="FONT: 10pt arial"><B>To:</B> <A title=pw_forum@pwscf.org
href="mailto:pw_forum@pwscf.org">pw_forum@pwscf.org</A> </DIV>
<DIV style="FONT: 10pt arial"><B>Sent:</B> Tuesday, July 17, 2007 10:45
AM</DIV>
<DIV style="FONT: 10pt arial"><B>Subject:</B> [Pw_forum] decomoposition of the
atomic contribution to thevibrational spectrum</DIV>
<DIV><BR></DIV>Dear all,<BR> I onced asked this problem but could still
not solved it. My question<BR> is about the projection of
vibrational spectrum. <BR>In order to further decompose the carbon
contribution to the vibrational spectrum, as in the paper "Vibrational
properties of trtrahedral amorphous carbon from first principles"[APL
75,644(1999)], we should define for each bond a "stretching" vector in the
space of the 3N (N is the number of atoms) displacement. The components of
each vector involves the displacement of two atoms in the direction of the
bond and with opposite orientations. We use these vectors as
a<BR> (non-orthonormal) basis of the stretching subspace and define the
bending<BR> subspace as the complement of the stretching
subspace.<BR> My problems:<BR> How can I construct the stretching
subspace and orthorgonalize these<BR> vectors in 3N space?<BR>Which one
code may I use?<BR> <BR> need your help, any help will be
appreciated!<BR> <BR> best regards!<BR> <BR> Niu
Li
<BR> Harbin Institue of
Technology
<BR> People's Republic of China<BR>
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