[Pw_forum] question about the negative frequency of phonon

[Shaorui Sun]

  Dear all:
     I have calculated the phonon at Gamma point  of ZnO with hexgonal structure under ambient condition.I find some modes with negative frequency as follows:
**************************************************************************
     omega( 1) =      -6.023360 [THz] =    -200.919008 [cm-1]
 ( -0.000260  0.000000 -0.000147  0.000000  0.330600  0.000000 ) 
 (  0.000256  0.000000  0.000145  0.000000  0.330106  0.000000 ) 
 (  0.000292  0.000000  0.000182  0.000000  0.627531  0.000000 ) 
 ( -0.000289  0.000000 -0.000180  0.000000  0.622846  0.000000 ) 
     omega( 2) =      -0.299189 [THz] =      -9.979948 [cm-1]
 ( -0.417072  0.000000 -0.241569  0.000000 -0.000508  0.000000 ) 
 (  0.469981  0.000000  0.271913  0.000000 -0.000476  0.000000 ) 
 (  0.450138  0.000000  0.260507  0.000000 -0.000209  0.000000 ) 
 ( -0.389246  0.000000 -0.225555  0.000000 -0.000180  0.000000 ) 
     omega( 3) =       0.275355 [THz] =       9.184911 [cm-1]
 (  0.237017  0.000000 -0.409752  0.000000  0.000011  0.000000 ) 
 ( -0.276542  0.000000  0.477420  0.000000 -0.000009  0.000000 ) 
 ( -0.264391  0.000000  0.456506  0.000000 -0.000002  0.000000 ) 
 (  0.220039  0.000000 -0.380530  0.000000  0.000001  0.000000 ) 
     omega( 4) =       1.100562 [THz] =      36.711029 [cm-1]
 (  0.279712  0.000000 -0.456681  0.000000 -0.000118  0.000000 ) 
 (  0.237728  0.000000 -0.387807  0.000000  0.000120  0.000000 ) 
 (  0.244071  0.000000 -0.398114  0.000000  0.000013  0.000000 ) 
 (  0.280438  0.000000 -0.457804  0.000000 -0.000013  0.000000 ) 
     omega( 5) =       1.170953 [THz] =      39.059037 [cm-1]
 ( -0.450273  0.000000 -0.275967  0.000000  0.000207  0.000000 ) 
 ( -0.396246  0.000000 -0.242718  0.000000 -0.000272  0.000000 ) 
 ( -0.405025  0.000000 -0.248069  0.000000  0.000257  0.000000 ) 
 ( -0.450841  0.000000 -0.276283  0.000000 -0.000281  0.000000 ) 
     omega( 6) =       6.662384 [THz] =     222.234680 [cm-1]
 ( -0.000176  0.000000  0.000057  0.000000 -0.602850  0.000000 ) 
 ( -0.000171  0.000000  0.000061  0.000000  0.606833  0.000000 ) 
 ( -0.000777  0.000000 -0.000465  0.000000 -0.368226  0.000000 ) 
 ( -0.000772  0.000000 -0.000464  0.000000  0.364325  0.000000 ) 
     omega( 7) =      10.028040 [THz] =     334.501631 [cm-1]
 ( -0.000227  0.000000 -0.000147  0.000000  0.299125  0.000000 ) 
 (  0.000239  0.000000  0.000152  0.000000  0.295094  0.000000 ) 
 ( -0.000184  0.000000 -0.000172  0.000000 -0.645232  0.000000 ) 
 (  0.000136  0.000000  0.000148  0.000000 -0.638059  0.000000 ) 
     omega( 8) =      11.000946 [THz] =     366.954510 [cm-1]
 ( -0.117921  0.000000  0.118231  0.000000 -0.000089  0.000000 ) 
 ( -0.122596  0.000000  0.122893  0.000000  0.000096  0.000000 ) 
 (  0.490765  0.000000 -0.491427  0.000000  0.000517  0.000000 ) 
 (  0.479041  0.000000 -0.479741  0.000000 -0.000537  0.000000 ) 
     omega( 9) =      11.004772 [THz] =     367.082115 [cm-1]
 ( -0.117814  0.000000 -0.117740  0.000000 -0.000393  0.000000 ) 
 ( -0.122545  0.000000 -0.122442  0.000000  0.000417  0.000000 ) 
 (  0.491707  0.000000  0.490773  0.000000  0.001216  0.000000 ) 
 (  0.479808  0.000000  0.478952  0.000000 -0.001280  0.000000 ) 
     omega(10) =      13.060803 [THz] =     435.664405 [cm-1]
 (  0.130505  0.000000  0.094044  0.000000  0.000121  0.000000 ) 
 ( -0.128151  0.000000 -0.092347  0.000000  0.000102  0.000000 ) 
 (  0.550546  0.000000  0.396919  0.000000 -0.000356  0.000000 ) 
 ( -0.566967  0.000000 -0.408750  0.000000 -0.000262  0.000000 ) 
     omega(11) =      13.078335 [THz] =     436.249187 [cm-1]
 (  0.093791  0.000000 -0.130068  0.000000 -0.000002  0.000000 ) 
 ( -0.092121  0.000000  0.127752  0.000000 -0.000005  0.000000 ) 
 (  0.397022  0.000000 -0.550781  0.000000  0.000006  0.000000 ) 
 ( -0.408702  0.000000  0.566970  0.000000  0.000028  0.000000 ) 
     omega(12) =      14.976799 [THz] =     499.575570 [cm-1]
 ( -0.000317  0.000000 -0.000169  0.000000  0.102943  0.000000 ) 
 ( -0.000309  0.000000 -0.000166  0.000000 -0.104318  0.000000 ) 
 (  0.001156  0.000000  0.000475  0.000000 -0.695521  0.000000 ) 
 (  0.001206  0.000000  0.000497  0.000000  0.703397  0.000000 ) 
 **************************************************************************
Who could tell what is the meaning of the negative frequency of the first two modes for the system with stable state?



Best Regards!
                        S. R. Sun
---------------------------------------------
Beijing Synchrotron Radiation Facility
Institute of High Energy Physics
Chinese Academy of Sciences
P. O. Box 918, 100049 Beijing
P. R. China
Tel: 0086+10 88236710
email:sunsr at ihep.ac.cn