ttadano
commented
1 year ago Hi,
Sorry for the late response. I guess you calculated the eigenvectors with the band structure mode, and the band structure was computed along G (0,0,0) - X (0,0.5,0). In this case, the polarization vectors of the two TO phonon modes are perpendicular to k=(0, 0.5, 0), so the y-direction components should be zero as you observed. By contrast, the eigenvectors of the LO modes are parallel to k=(0,0.5,0).
Dear Dr. Tadano,
Thanks for your awesome code development. I recently tried to calculate dielectric function of perovskite. I was successful to create effective 2nd order force constants using dfc2 script for calculating bubble self-energy at each temperature. However, when I see the data in PTOcubic.evec, the files are looked as follows:
Eigenvalues and eigenvectors for each phonon modes below:
kpoint 1 : 0.000000e+00 0.000000e+00 0.000000e+00
mode 1 : 1.000000e-30
8.901170e-03 0.000000e+00 7.491646e-02 0.000000e+00 7.636813e-01 0.000000e+00 5.255164e-03 0.000000e+00 4.422995e-02 0.000000e+00 4.508700e-01 0.000000e+00 3.038234e-03 0.000000e+00 2.557122e-02 0.000000e+00 2.606671e-01 0.000000e+00 3.038234e-03 0.000000e+00 2.557122e-02 0.000000e+00 2.606671e-01 0.000000e+00 3.038234e-03 0.000000e+00 2.557122e-02 0.000000e+00 2.606671e-01 0.000000e+00
mode 2 : 1.000000e-30
3.774764e-01 0.000000e+00 -6.653624e-01 0.000000e+00 6.087174e-02 0.000000e+00 2.228584e-01 0.000000e+00 -3.928235e-01 0.000000e+00 3.593808e-02 0.000000e+00 1.288439e-01 0.000000e+00 -2.271080e-01 0.000000e+00 2.077734e-02 0.000000e+00 1.288439e-01 0.000000e+00 -2.271080e-01 0.000000e+00 2.077734e-02 0.000000e+00 1.288439e-01 0.000000e+00 -2.271080e-01 0.000000e+00 2.077734e-02 0.000000e+00
mode 3 : 1.000000e-30
6.680818e-01 -0.000000e+00 3.749417e-01 -0.000000e+00 -4.456835e-02 -0.000000e+00 3.944289e-01 -0.000000e+00 2.213619e-01 -0.000000e+00 -2.631272e-02 -0.000000e+00 2.280362e-01 -0.000000e+00 1.279788e-01 -0.000000e+00 -1.521250e-02 -0.000000e+00 2.280362e-01 -0.000000e+00 1.279788e-01 -0.000000e+00 -1.521250e-02 -0.000000e+00 2.280362e-01 -0.000000e+00 1.279788e-01 -0.000000e+00 -1.521250e-02 -0.000000e+00
mode 4 : 3.808227e-07
2.343478e-03 0.000000e+00 8.423904e-16 0.000000e+00 3.942669e-01 0.000000e+00 1.279352e-03 0.000000e+00 5.123354e-16 0.000000e+00 2.152382e-01 0.000000e+00 -3.374119e-03 0.000000e+00 2.619531e-16 0.000000e+00 -5.676619e-01 0.000000e+00 -3.374119e-03 0.000000e+00 4.390082e-16 0.000000e+00 -3.920597e-01 0.000000e+00 -2.330359e-03 0.000000e+00 3.083278e-17 0.000000e+00 -5.676619e-01 0.000000e+00
mode 5 : 3.808227e-07
-3.942669e-01 0.000000e+00 3.578875e-15 0.000000e+00 2.343478e-03 0.000000e+00 -2.152382e-01 0.000000e+00 1.979970e-15 0.000000e+00 1.279352e-03 0.000000e+00 5.676619e-01 0.000000e+00 1.127290e-15 0.000000e+00 -3.374119e-03 0.000000e+00 5.676619e-01 0.000000e+00 1.103780e-15 0.000000e+00 -2.330359e-03 0.000000e+00 3.920597e-01 0.000000e+00 1.545550e-15 0.000000e+00 -3.374119e-03 0.000000e+00
mode 6 : 2.391416e-06
-6.093217e-15 0.000000e+00 -5.407162e-01 0.000000e+00 -9.124998e-15 0.000000e+00 1.127480e-14 0.000000e+00 8.375125e-01 0.000000e+00 1.553431e-14 0.000000e+00 -3.973184e-16 0.000000e+00 5.233631e-02 0.000000e+00 -3.162952e-16 0.000000e+00 1.378763e-16 0.000000e+00 4.159192e-02 0.000000e+00 2.819295e-16 0.000000e+00 2.504158e-16 0.000000e+00 4.159192e-02 0.000000e+00 -3.211747e-16 0.000000e+00
mode 7 : 2.409540e-06
2.553428e-03 0.000000e+00 9.776298e-15 0.000000e+00 -5.038068e-01 0.000000e+00 -4.375313e-03 0.000000e+00 -1.498545e-14 0.000000e+00 8.632758e-01 0.000000e+00 8.788869e-05 0.000000e+00 -8.940844e-16 0.000000e+00 -1.734097e-02 0.000000e+00 8.788869e-05 0.000000e+00 -6.206520e-16 0.000000e+00 1.750555e-02 0.000000e+00 -8.872280e-05 0.000000e+00 -8.038941e-16 0.000000e+00 -1.734097e-02 0.000000e+00
mode 8 : 2.409540e-06
5.038068e-01 0.000000e+00 -7.093781e-15 0.000000e+00 2.553428e-03 0.000000e+00 -8.632758e-01 0.000000e+00 1.104940e-14 0.000000e+00 -4.375313e-03 0.000000e+00 1.734097e-02 0.000000e+00 6.998247e-16 0.000000e+00 8.788869e-05 0.000000e+00 1.734097e-02 0.000000e+00 3.475531e-16 0.000000e+00 -8.872280e-05 0.000000e+00 -1.750555e-02 0.000000e+00 7.862554e-16 0.000000e+00 8.788869e-05 0.000000e+00
mode 9 : 3.636088e-06
-1.144192e-18 0.000000e+00 7.706186e-17 0.000000e+00 -8.689896e-19 0.000000e+00 -8.094888e-17 0.000000e+00 5.078210e-17 0.000000e+00 -1.159145e-17 0.000000e+00 -4.127205e-03 0.000000e+00 3.151958e-17 0.000000e+00 -7.070793e-01 0.000000e+00 4.127205e-03 0.000000e+00 4.675500e-03 0.000000e+00 6.016873e-17 0.000000e+00 7.434854e-17 0.000000e+00 -4.675500e-03 0.000000e+00 7.070793e-01 0.000000e+00
mode 10 : 3.636088e-06
1.515583e-15 0.000000e+00 5.484634e-16 0.000000e+00 -1.672849e-16 0.000000e+00 -3.723488e-15 0.000000e+00 6.920694e-18 0.000000e+00 3.024897e-16 0.000000e+00 -6.938386e-01 0.000000e+00 1.201874e-16 0.000000e+00 4.950845e-03 0.000000e+00 6.938386e-01 0.000000e+00 1.362476e-01 0.000000e+00 6.598468e-17 0.000000e+00 -3.236404e-16 0.000000e+00 -1.362476e-01 0.000000e+00 -4.950845e-03 0.000000e+00
mode 11 : 3.636088e-06
-2.148579e-16 -0.000000e+00 -4.522865e-16 -0.000000e+00 -2.729378e-16 -0.000000e+00 4.181262e-16 -0.000000e+00 3.852034e-16 -0.000000e+00 -8.361181e-17 -0.000000e+00 1.362751e-01 -0.000000e+00 2.901750e-18 -0.000000e+00 3.792525e-03 -0.000000e+00 -1.362751e-01 -0.000000e+00 6.938406e-01 -0.000000e+00 -1.211333e-17 -0.000000e+00 2.329394e-16 -0.000000e+00 -6.938406e-01 -0.000000e+00 -3.792525e-03 -0.000000e+00
mode 12 : 1.395221e-05
-3.104751e-17 -0.000000e+00 -2.559226e-01 -0.000000e+00 -3.854592e-17 -0.000000e+00 -4.568468e-17 -0.000000e+00 -2.189803e-01 -0.000000e+00 3.998721e-17 -0.000000e+00 -9.973338e-17 -0.000000e+00 -1.788028e-01 -0.000000e+00 -2.078145e-16 -0.000000e+00 -4.503475e-16 -0.000000e+00 6.536745e-01 -0.000000e+00 4.073309e-17 -0.000000e+00 2.276282e-17 -0.000000e+00 6.536745e-01 -0.000000e+00 -2.575802e-17 -0.000000e+00
mode 13 : 2.557073e-05
4.262477e-02 0.000000e+00 7.092121e-17 0.000000e+00 1.602462e-03 0.000000e+00 5.598650e-02 0.000000e+00 -2.760024e-18 0.000000e+00 2.104791e-03 0.000000e+00 3.296723e-01 0.000000e+00 -6.262692e-16 0.000000e+00 1.239390e-02 0.000000e+00 3.296723e-01 0.000000e+00 6.399729e-17 0.000000e+00 -3.312317e-02 0.000000e+00 -8.810617e-01 0.000000e+00 1.272652e-17 0.000000e+00 1.239390e-02 0.000000e+00
mode 14 : 2.557073e-05
-1.602462e-03 0.000000e+00 -8.063793e-18 0.000000e+00 4.262477e-02 0.000000e+00 -2.104791e-03 0.000000e+00 -1.628680e-17 0.000000e+00 5.598650e-02 0.000000e+00 -1.239390e-02 0.000000e+00 5.744580e-18 0.000000e+00 3.296723e-01 0.000000e+00 -1.239390e-02 0.000000e+00 9.193497e-18 0.000000e+00 -8.810617e-01 0.000000e+00 3.312317e-02 0.000000e+00 7.478586e-17 0.000000e+00 3.296723e-01 0.000000e+00
mode 15 : 4.261057e-05
1.778463e-17 0.000000e+00 -2.307135e-01 0.000000e+00 -1.119937e-17 0.000000e+00 3.625774e-17 0.000000e+00 -2.129621e-01 0.000000e+00 4.769906e-17 0.000000e+00 2.487300e-16 0.000000e+00 9.469319e-01 0.000000e+00 2.637773e-17 0.000000e+00 4.749212e-16 0.000000e+00 4.867466e-02 0.000000e+00 -2.534478e-17 0.000000e+00 -6.565641e-16 0.000000e+00 4.867466e-02 0.000000e+00 3.331567e-17 0.000000e+00
When I included NONANALYTIC=2 or NONANALYTIC=3 tag with *.born file, it seems that the real part of eigenvector values in the first-column has a bad pattern. For the Gamma point, the eigenvector of the TO branch (frequency invariant) for each atom differs tens of orders of magnitude in the y-direction from the other two directions, with the y-direction being essentially zero. However, All the results are normal without consideration of LO-TO splitting, the files are looked as follows:
kpoint 1 : 0.000000e+00 0.000000e+00 0.000000e+00
mode 1 : 1.000000e-30
1.829246e-01 0.000000e+00 7.452758e-01 0.000000e+00 1.873427e-03 0.000000e+00 1.079969e-01 0.000000e+00 4.400035e-01 0.000000e+00 1.106053e-03 0.000000e+00 6.243761e-02 0.000000e+00 2.543848e-01 0.000000e+00 6.394562e-04 0.000000e+00 6.243761e-02 0.000000e+00 2.543848e-01 0.000000e+00 6.394562e-04 0.000000e+00 6.243761e-02 0.000000e+00 2.543848e-01 0.000000e+00 6.394562e-04 0.000000e+00
mode 2 : 1.000000e-30
-7.452778e-01 0.000000e+00 1.829223e-01 0.000000e+00 1.122084e-03 0.000000e+00 -4.400047e-01 0.000000e+00 1.079955e-01 0.000000e+00 6.624677e-04 0.000000e+00 -2.543855e-01 0.000000e+00 6.243683e-02 0.000000e+00 3.830008e-04 0.000000e+00 -2.543855e-01 0.000000e+00 6.243683e-02 0.000000e+00 3.830008e-04 0.000000e+00 -2.543855e-01 0.000000e+00 6.243683e-02 0.000000e+00 3.830008e-04 0.000000e+00
mode 3 : 1.000000e-30
-6.431738e-04 0.000000e+00 2.086894e-03 0.000000e+00 -7.673957e-01 0.000000e+00 -3.797235e-04 0.000000e+00 1.232082e-03 0.000000e+00 -4.530629e-01 0.000000e+00 -2.195343e-04 0.000000e+00 7.123191e-04 0.000000e+00 -2.619350e-01 0.000000e+00 -2.195343e-04 0.000000e+00 7.123191e-04 0.000000e+00 -2.619350e-01 0.000000e+00 -2.195343e-04 0.000000e+00 7.123191e-04 0.000000e+00 -2.619350e-01 0.000000e+00
mode 4 : 6.217243e-07
8.339816e-02 0.000000e+00 4.292352e-01 0.000000e+00 -7.826522e-03 0.000000e+00 2.630134e-02 0.000000e+00 1.353682e-01 0.000000e+00 -2.468256e-03 0.000000e+00 -1.075544e-01 0.000000e+00 -3.845559e-01 0.000000e+00 1.009347e-02 0.000000e+00 -1.075544e-01 0.000000e+00 -5.535628e-01 0.000000e+00 7.011857e-03 0.000000e+00 -7.471722e-02 0.000000e+00 -5.535628e-01 0.000000e+00 1.009347e-02 0.000000e+00
mode 5 : 6.217243e-07
-2.975081e-01 -0.000000e+00 5.203712e-02 -0.000000e+00 -3.162917e-01 -0.000000e+00 -9.382534e-02 -0.000000e+00 1.641099e-02 -0.000000e+00 -9.974915e-02 -0.000000e+00 3.836810e-01 -0.000000e+00 -4.662056e-02 -0.000000e+00 4.079053e-01 -0.000000e+00 3.836810e-01 -0.000000e+00 -6.710963e-02 -0.000000e+00 2.833688e-01 -0.000000e+00 2.665404e-01 -0.000000e+00 -6.710963e-02 -0.000000e+00 4.079053e-01 -0.000000e+00
mode 6 : 6.217243e-07
3.095045e-01 0.000000e+00 -6.564028e-02 0.000000e+00 -3.019233e-01 0.000000e+00 9.760867e-02 0.000000e+00 -2.070102e-02 0.000000e+00 -9.521777e-02 0.000000e+00 -3.991522e-01 0.000000e+00 5.880776e-02 0.000000e+00 3.893751e-01 0.000000e+00 -3.991522e-01 0.000000e+00 8.465293e-02 0.000000e+00 2.704960e-01 0.000000e+00 -2.772881e-01 0.000000e+00 8.465293e-02 0.000000e+00 3.893751e-01 0.000000e+00
mode 7 : 2.568010e-06
-4.344268e-01 -0.000000e+00 1.711221e-01 -0.000000e+00 -2.058663e-03 -0.000000e+00 8.177855e-01 -0.000000e+00 -3.221283e-01 -0.000000e+00 3.875325e-03 -0.000000e+00 -6.288435e-02 -0.000000e+00 6.297685e-03 -0.000000e+00 -2.979965e-04 -0.000000e+00 -6.288435e-02 -0.000000e+00 2.477034e-02 -0.000000e+00 -7.576352e-05 -0.000000e+00 -1.598790e-02 -0.000000e+00 2.477034e-02 -0.000000e+00 -2.979965e-04 -0.000000e+00
mode 8 : 2.568010e-06
1.711268e-01 0.000000e+00 4.344291e-01 0.000000e+00 -8.103449e-04 0.000000e+00 -3.221372e-01 0.000000e+00 -8.177898e-01 0.000000e+00 1.525431e-03 0.000000e+00 2.477103e-02 0.000000e+00 1.598799e-02 0.000000e+00 -1.172994e-04 0.000000e+00 2.477103e-02 0.000000e+00 6.288467e-02 0.000000e+00 -2.982255e-05 0.000000e+00 6.297859e-03 0.000000e+00 6.288467e-02 0.000000e+00 -1.172994e-04 0.000000e+00
mode 9 : 2.568010e-06
1.618428e-03 0.000000e+00 -1.508458e-03 0.000000e+00 -4.669141e-01 0.000000e+00 -3.046605e-03 0.000000e+00 2.839592e-03 0.000000e+00 8.789411e-01 0.000000e+00 2.342714e-04 0.000000e+00 -5.551469e-05 0.000000e+00 -6.758696e-02 0.000000e+00 2.342714e-04 0.000000e+00 -2.183529e-04 0.000000e+00 -1.718351e-02 0.000000e+00 5.956185e-05 0.000000e+00 -2.183529e-04 0.000000e+00 -6.758696e-02 0.000000e+00
mode 10 : 3.982987e-06
-1.349208e-16 0.000000e+00 -1.600691e-16 0.000000e+00 2.809676e-17 0.000000e+00 3.868634e-16 0.000000e+00 2.193580e-16 0.000000e+00 -6.526686e-16 0.000000e+00 6.413603e-02 0.000000e+00 1.916194e-16 0.000000e+00 6.736956e-01 0.000000e+00 -6.413603e-02 0.000000e+00 -2.049898e-01 0.000000e+00 -4.315005e-16 0.000000e+00 1.654053e-16 0.000000e+00 2.049898e-01 0.000000e+00 -6.736956e-01 0.000000e+00
mode 11 : 3.982987e-06
7.993499e-17 0.000000e+00 2.899640e-16 0.000000e+00 -7.873890e-18 0.000000e+00 -2.661237e-16 0.000000e+00 -3.586353e-16 0.000000e+00 -2.535794e-16 0.000000e+00 -3.682377e-01 0.000000e+00 3.332347e-16 0.000000e+00 2.075382e-01 0.000000e+00 3.682377e-01 0.000000e+00 5.668588e-01 0.000000e+00 -1.649496e-16 0.000000e+00 5.257117e-17 0.000000e+00 -5.668588e-01 0.000000e+00 -2.075382e-01 0.000000e+00
mode 12 : 3.982987e-06
-1.398920e-16 0.000000e+00 1.288171e-17 0.000000e+00 -1.207701e-16 0.000000e+00 5.018241e-16 0.000000e+00 -2.237290e-16 0.000000e+00 1.582289e-16 0.000000e+00 6.002396e-01 0.000000e+00 5.469128e-16 0.000000e+00 5.533664e-02 0.000000e+00 -6.002396e-01 0.000000e+00 3.696624e-01 0.000000e+00 1.845103e-16 0.000000e+00 -1.393482e-16 0.000000e+00 -3.696624e-01 0.000000e+00 -5.533664e-02 0.000000e+00
mode 13 : 2.625576e-05
3.388846e-02 0.000000e+00 -2.603147e-02 0.000000e+00 1.588373e-17 0.000000e+00 4.454515e-02 0.000000e+00 -3.421742e-02 0.000000e+00 7.475537e-17 0.000000e+00 2.614858e-01 0.000000e+00 5.371714e-01 0.000000e+00 5.215386e-16 0.000000e+00 2.614858e-01 0.000000e+00 -2.008607e-01 0.000000e+00 -1.219728e-15 0.000000e+00 -6.993040e-01 0.000000e+00 -2.008607e-01 0.000000e+00 4.997151e-16 0.000000e+00
mode 14 : 2.625576e-05
-3.376192e-17 0.000000e+00 5.246087e-17 0.000000e+00 4.273248e-02 0.000000e+00 -3.107045e-17 0.000000e+00 6.108159e-17 0.000000e+00 5.617030e-02 0.000000e+00 -2.482157e-16 0.000000e+00 -1.100994e-15 0.000000e+00 3.297269e-01 0.000000e+00 -2.860959e-16 0.000000e+00 3.945893e-16 0.000000e+00 -8.818045e-01 0.000000e+00 7.407238e-16 0.000000e+00 7.087833e-16 0.000000e+00 3.297269e-01 0.000000e+00
mode 15 : 2.625576e-05
-2.603147e-02 -0.000000e+00 -3.388846e-02 -0.000000e+00 -6.118316e-17 -0.000000e+00 -3.421742e-02 -0.000000e+00 -4.454515e-02 -0.000000e+00 3.902541e-17 -0.000000e+00 -2.008607e-01 -0.000000e+00 6.993040e-01 -0.000000e+00 7.343646e-17 -0.000000e+00 -2.008607e-01 -0.000000e+00 -2.614858e-01 -0.000000e+00 -4.180372e-16 -0.000000e+00 5.371714e-01 -0.000000e+00 -2.614858e-01 -0.000000e+00 2.190291e-16 -0.000000e+00 But our physics intuition teaches me that all three dirctions should be the same? Thanks.