[Pw_forum] problems with lattice dynamical principle

[luch001]

Dear all,
 
I have read the paper titled ¡°Theory of systematic absence of NaCl-type (¦Â-Sn-type) high pressure phases in covalent (ionic) semiconductors¡± (Phys Rev Lett. 82, 767, 1999). The phonon behaviors are dominated by the competition between the attractive electrostatic Madelung energy ¨CZ2/R (where Z is the excess charge within the atomic sphere) and the repulsive short-range energy. I can not understand well the formula of the force constant given in the last part of page 769, which reads:
 
¦µ¦Á¦Â = nA¦Ä¦Á¦Â/Rn+2-Z2¦Ä¦Á¦Â/R3-¦ËR¦ÁR¦Â/ R5
 
How does it come from? Does it apply to all the systems or just apply to some specific system?  The values of A and ¦Ë are determined by what factors? 
 
The authors claimed that the transverse acoustic mode at X point lowers the repulsive energy and raises the Madelung energy, but why?
 
I have pondered hardly and consulted with others. But I have reached no conclusion. I wrote letter to Alex Zunger, one of the two authors. He did not write back yet.
 
Any reply will be appreciated!
 
With all my best regards!
 
                                                      Yours sincerely
                                                       Jingyun Zhang
 
 
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