[Pw_forum] decomoposition of the atomic contribution to thevibrational spectrum

[Huiqun Zhou]

Li Niu:

Nobody but linear algebra can help you;-) Go to find a textbook, Gram Schmidt orthogonalization will
help you understand the process of vector orthogonalization. For actual numerical computation, you'd
better use Householder transformation in your case as your 3N vectors are numeric.

Hope this give you a start point.

Huiqun Zhou at Nanjing University, China
  ----- Original Message ----- 
  From: li niu 
  To: pw_forum at pwscf.org 
  Sent: Tuesday, July 17, 2007 10:45 AM
  Subject: [Pw_forum] decomoposition of the atomic contribution to thevibrational spectrum


  Dear all,
   I onced asked this problem but could still not solved it. My question
   is about the projection of  vibrational spectrum. 
  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
   (non-orthonormal) basis of the stretching subspace and define the bending
   subspace as the complement of the stretching subspace.
   My problems:
   How can I construct the stretching subspace and orthorgonalize these
   vectors in 3N space?
  Which one code may I use?
    
   need your help, any help will be appreciated!
   
   best regards!
   
   Niu Li                        
   Harbin Institue of Technology                     
   People's Republic of China



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