[Pw_forum] decomoposition of the atomic contribution to the vibrational spectrum

[li niu]

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?
 I wonder if someone has written a code for calculating it,and want to share with others?
 
 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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