****************************************************************************** * * * ABINIT tutorial: nonlinear response, Berry phase * * & finite electric fields * * * ****************************************************************************** 1) Parameters used in all calculations -------------------------------------- system AlAs code ABINITv4.4.4 acell theoretical lattice constant computed for the same k-point grid as the corresponding response properties ixc 3 ecut 5 ecutsm 0.5 dilatmx 1.05 nbdbuf 0 nshiftk 4 nband 4 (number of occupied bands) pseudopotentials 13al.pspnc 33as.pspnc 2) Structural optimizations --------------------------- =================================== ngkpt acell ----------------------------------- 6 6 6 10.6395177524329601 8 8 8 10.6396307919372131 10 10 10 10.6396442853730768 12 12 12 10.6397077264277993 14 14 14 10.6396719133078097 16 16 16 10.6396728602652111 =================================== 3) Density functional perturbation theory calculations ------------------------------------------------------ 3A) NGKPT 6 6 6 --------------- Born effective charge of Al: Z* = 2.105999E+00 Nonlinear optical susceptibility (pm/V): d = 32.772254 d chi / d tau (Bohr^-1) of Al = -0.099889084 w_TO (cm^-1) = 3.602635E+02 w_LO (cm^-1) = 3.931598E+02 Electronic dielectric tensor = 9.94846084 Relaxed ion dielectric tensor = 11.84823634 Proper piezoelectric constants(clamped ion)(Unit:c/m^2) = -0.69401363 Proper piezoelectric constants(relaxed ion)(Unit:c/m^2) = -0.04228777 Electronic EO constant (pm/V): -1.324507791 Ionic EO constant (pm/V): 0.533097548 Total EO constant (pm/V): -0.791410242 Faust-Henry coefficient: C = -0.4024874 Raman polarizability (A^2): ato = -8.4222112 alo = -12.418168 Finite difference calculation: d chi / d tau (Bohr^-1) of Al = -0.1066171 4) Ground-state Berry phase calculations ---------------------------------------- Finite differences of the polarization w.r.t. atomic displacements Born effective charge of Al: Z* = 2.1273874 Finite difference calculation of the ddk Born effective charge of Al: Z* = 2.1273577300 Proper piezoelectric constants(clamped ion)(Unit:c/m^2) = -0.69084784 Proper piezoelectric constants(relaxed ion)(Unit:c/m^2) = -0.03251216 Finite differences of the polarization w.r.t. strain Proper piezoelectric constants(clamped ion)(Unit:c/m^2) = -0.6909505 Proper piezoelectric constants(relaxed ion)(Unit:c/m^2) = -0.0326305 5) Finite electric field calculations ------------------------------------- Electronic dielectric constant: 8.72523139872855 Nonlinear optical susceptibility (pm/V): d = 29.7685679334192 Born effective charge of Al: 2.12729059075091 d chi / d tau (Bohr^-1) of Al = -0.0616968881813368 Static dielectric constant: 10.665771361062 Proper piezoelectric constants(clamped ion)(Unit:c/m^2) = -0.690881351221756 Proper piezoelectric constants(relaxed ion)(Unit:c/m^2) = -0.0325937630208201