Dear CP2K community,<div><br /></div><div>I'm trying to learn how to calculate polarization using CP2K. I'm using 2x2x2 supercell of BaTiO3 to benchmark the polarization values compared to other references and Quantum Espresso. </div><div><br /></div><div>I'm using Berry phase method by setting <font color="#000000"><b>PERIODIC .TRUE. in MOMENTS</b><b> </b></font>as it's periodic system. And the output for the cubic structure looks like:</div><div><font color="#808080"> Dipole vectors are based on the periodic (Berry phase) operator.<br /> They are defined modulo integer multiples of the cell matrix [Debye].<br /> [X] [  38.42563418   0.00000000   0.00000000 ] [i]<br /> [Y]=[   0.00000000   38.42563418   0.00000000 ]*[j]<br /> [Z] [   0.00000000   0.00000000   </font><font color="#008000">38.65618798</font><font color="#808080"> ] [k]<br /> Dipole moment [Debye]<br />  X= -0.1123396E-09 Y= -0.1123351E-09 Z= </font><font color="#008000">-0.1414722E-09</font><font color="#808080">  Total=    0.0000000</font><br /></div><div><br /></div><div>How I have been calculating the polarization value is: 1) As I'm only interested in the polarization in z direction, I combined the two values highlighted in green. And 2) I divide the values by the cell volume. 3) I convert the unit to uC/cm^2. The issue with this method is that the polarization of the cubic phase is not zero. I've been trying to figure this out because the polarization value for cubic phase should be zero or close to zero. And the zero polarization for cubic phase is reproduced by Quantum Espresso:</div><div>   <font color="#808080">             VALUES OF POLARIZATION<br />               ~~~~~~~~~~~~~~~~~~~~~~<br />    The calculation of phases done along the direction of vector 3<br />    of the reciprocal lattice gives the following contribution to<br />    the polarization vector (in different units, and being Omega<br />    the volume of the unit cell):<br />      P =  0.0000000  (mod  30.0953409)  (e/Omega).bohr<br />      P =  0.0000000  (mod  0.0088327)  e/bohr^2<br />      P =  0.0000000  (mod  0.5053585)  C/m^2<br />    The polarization direction is:  ( 0.00000 , 0.00000 , 1.00000 )</font><br /></div><div><br /></div><div><br /></div><div>What I'm confused with is that the difference between the values in the dipole vectors and the dipole moment. Is either of them electronic polarization (from Berry phase) and ionic polarization? Or is the dipole moment in the bottom line calculated from the addition of the electronic polarization (Berry phase) and the ionic polarization? Is there any reference/literature that describes how CP2K operates the Berry phase calculation?</div><div><br /></div><div><br /></div><div>Here's my input script:</div><div><font color="#808080">&GLOBAL<br /> PROJECT BTO<br /> RUN_TYPE CELL_OPT<br /> PRINT_LEVEL MEDIUM<br />&END GLOBAL<br /><br />&FORCE_EVAL<br /> ! This one is used for cell optimization<br /> STRESS_TENSOR ANALYTICAL<br /> METHOD  QS<br /> &SUBSYS<br />  &KIND Ba<br />   ELEMENT  Ba<br />   BASIS_SET DZVP-MOLOPT-PBE-GTH-q10<br />   POTENTIAL GTH-PBE-q10<br />  &END KIND<br />  &KIND Ti<br />   ELEMENT  Ti<br />   BASIS_SET DZVP-MOLOPT-PBE-GTH-q12<br />   POTENTIAL GTH-PBE-q12<br />  &END KIND<br />  &KIND O<br />   ELEMENT  O<br />   BASIS_SET DZVP-MOLOPT-PBE-GTH-q6<br />   POTENTIAL GTH-PBE-q6<br />  &END KIND<br />  &CELL<br />   A   8.000000000   0.000000000   0.000000000<br />   B   0.000000000   8.000000000   0.000000000<br />   C   0.000000000   0.000000000   8.000000000<br />   PERIODIC XYZ<br />  &END CELL<br />  &TOPOLOGY<br />   COORD_FILE_FORMAT pdb<br />   COORD_FILE_NAME BTO.pdb<br />  &END<br /> &END SUBSYS<br /> &DFT<br />  BASIS_SET_FILE_NAME BASIS_MOLOPT_UZH<br />  POTENTIAL_FILE_NAME GTH_POTENTIALS<br />  &QS<br />   METHOD GPW<br />   EPS_DEFAULT 1.0E-12<br />  &END QS<br />  &POISSON<br />   PERIODIC XYZ<br />   PSOLVER PERIODIC<br />  &END<br />  &XC<br />   &XC_FUNCTIONAL<br />     &PBE<br />     &END PBE<br />   &END<br />   &VDW_POTENTIAL<br />     POTENTIAL_TYPE PAIR_POTENTIAL<br />     &PAIR_POTENTIAL<br />      PARAMETER_FILE_NAME ../../dftd3.dat<br />      TYPE DFTD3(BJ)<br />      REFERENCE_FUNCTIONAL PBE<br />     &END<br /></font></div><div><font color="#808080">   &END VDW_POTENTIAL<br />  &END XC<br />  &MGRID<br />   NGRIDS 4<br />   CUTOFF 600<br />  &END MGRID<br />  &SCF<br />   SCF_GUESS ATOMIC<br />   EPS_SCF 1.0E-8<br />   MAX_SCF 300<br />   &MIXING<br />     METHOD BROYDEN_MIXING<br />     ALPHA 0.2<br />     BETA 1.5<br />     NBROYDEN 8<br />   &END MIXING<br />  &END SCF<br />  &PRINT<br />   &MO_CUBES<br />    WRITE_CUBE .FALSE.<br />    NHOMO 1<br />    NLUMO 1<br />   &END MO_CUBES<br />   &MOMENTS MEDIUM<br />    PERIODIC T<br />   &END MOMENTS<br />  &END PRINT<br /> &END DFT<br /> &PRINT<br />  &FORCES ON<br />  &END FORCES<br /> &END PRINT<br />&END FORCE_EVAL<br /><br />&MOTION<br /> &CELL_OPT<br />  TYPE DIRECT_CELL_OPT<br />  MAX_ITER 300<br />  OPTIMIZER BFGS   #Most efficient minimizer, but only for 'small' systems<br /> &END CELL_OPT<br /> &GEO_OPT<br />  MAX_DR 0.003<br />  MAX_FORCE 0.00045<br />  RMS_DR 0.0015<br />  RMS_FORCE 0.0003<br />  MAX_ITER 200<br />  OPTIMIZER BFGS<br />  &BFGS<br />   TRUST_RADIUS 0.25<br />  &END BFGS<br /> &END GEO_OPT<br />&END MOTION</font><br /></div><div><br /></div><div><div>Here's the input structure:</div><div><font color="#808080">CRYST1   8.000   8.000   8.000  90.00  90.00  90.00 P 1      1<br />ATOM    1  Ba  BTO A  1    0.000  0.000  0.000  1.00  0.00      Ba<br />ATOM    2  Ti  BTO A  1    2.000  2.000  2.000  1.00  0.00      Ti<br />ATOM    3  O  BTO A  1    0.000  2.000  2.000  1.00  0.00      O<br />ATOM    4  O  BTO A  1    2.000  0.000  2.000  1.00  0.00      O<br />ATOM    5  O  BTO A  1    2.000  2.000  0.000  1.00  0.00      O<br />ATOM    6  Ba  BTO A  1    0.000  0.000  4.000  1.00  0.00      Ba<br />ATOM    7  Ti  BTO A  1    2.000  2.000  6.000  1.00  0.00      Ti<br />ATOM    8  O  BTO A  1    0.000  2.000  6.000  1.00  0.00      O<br />ATOM    9  O  BTO A  1    2.000  0.000  6.000  1.00  0.00      O<br />ATOM   10  O  BTO A  1    2.000  2.000  4.000  1.00  0.00      O<br />ATOM   11  Ba  BTO A  1    0.000  4.000  0.000  1.00  0.00      Ba<br />ATOM   12  Ti  BTO A  1    2.000  6.000  2.000  1.00  0.00      Ti<br />ATOM   13  O  BTO A  1    0.000  6.000  2.000  1.00  0.00      O<br />ATOM   14  O  BTO A  1    2.000  4.000  2.000  1.00  0.00      O<br />ATOM   15  O  BTO A  1    2.000  6.000  0.000  1.00  0.00      O<br />ATOM   16  Ba  BTO A  1    0.000  4.000  4.000  1.00  0.00      Ba<br />ATOM   17  Ti  BTO A  1    2.000  6.000  6.000  1.00  0.00      Ti<br />ATOM   18  O  BTO A  1    0.000  6.000  6.000  1.00  0.00      O<br />ATOM   19  O  BTO A  1    2.000  4.000  6.000  1.00  0.00      O<br />ATOM   20  O  BTO A  1    2.000  6.000  4.000  1.00  0.00      O<br />ATOM   21  Ba  BTO A  1    4.000  0.000  0.000  1.00  0.00      Ba<br />ATOM   22  Ti  BTO A  1    6.000  2.000  2.000  1.00  0.00      Ti<br />ATOM   23  O  BTO A  1    4.000  2.000  2.000  1.00  0.00      O<br />ATOM   24  O  BTO A  1    6.000  0.000  2.000  1.00  0.00      O<br />ATOM   25  O  BTO A  1    6.000  2.000  0.000  1.00  0.00      O<br />ATOM   26  Ba  BTO A  1    4.000  0.000  4.000  1.00  0.00      Ba<br />ATOM   27  Ti  BTO A  1    6.000  2.000  6.000  1.00  0.00      Ti<br />ATOM   28  O  BTO A  1    4.000  2.000  6.000  1.00  0.00      O<br />ATOM   29  O  BTO A  1    6.000  0.000  6.000  1.00  0.00      O<br />ATOM   30  O  BTO A  1    6.000  2.000  4.000  1.00  0.00      O<br />ATOM   31  Ba  BTO A  1    4.000  4.000  0.000  1.00  0.00      Ba<br />ATOM   32  Ti  BTO A  1    6.000  6.000  2.000  1.00  0.00      Ti<br />ATOM   33  O  BTO A  1    4.000  6.000  2.000  1.00  0.00      O<br />ATOM   34  O  BTO A  1    6.000  4.000  2.000  1.00  0.00      O<br />ATOM   35  O  BTO A  1    6.000  6.000  0.000  1.00  0.00      O<br />ATOM   36  Ba  BTO A  1    4.000  4.000  4.000  1.00  0.00      Ba<br />ATOM   37  Ti  BTO A  1    6.000  6.000  6.000  1.00  0.00      Ti<br />ATOM   38  O  BTO A  1    4.000  6.000  6.000  1.00  0.00      O<br />ATOM   39  O  BTO A  1    6.000  4.000  6.000  1.00  0.00      O<br />ATOM   40  O  BTO A  1    6.000  6.000  4.000  1.00  0.00      O<br />END</font><br /></div><div><br /></div><div><br /></div><div>Any of your inputs would be greatly appreciated. Thank you for your time and consideration in advance.</div><div><br /></div><div>Best, </div><div>Sue</div></div>
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