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from math import *
# Interface to the HGH pseudopotential parameters.
# See https://arxiv.org/abs/cond-mat/9803286
class Element:
def __init__(self, symbol):
# Get raw data from the table below
global elements
el = elements[symbol]
self.Zion = el[0]
self.rloc = el[1]
self.Cloc = [el[2], el[3], el[4], el[5]]
self.rl = [el[6], el[10], el[14]]
self.h = {}
for l in range(0, 3):
self.h[l] = {}
for i in range(1, 4):
self.h[l][i] = {}
# Only the diagonal h-values are explicitly given
self.h[l][i][i] = el[6 + 4 * l + i]
# Calculate the off-diagonal h-values, see Eqs.(20)-(28)
self.h[0][1][2] = -(1/2) * sqrt( 3/ 5) * self.h[0][2][2]
self.h[0][1][3] = (1/2) * sqrt( 5/ 21) * self.h[0][3][3]
self.h[0][2][3] = -(1/2) * sqrt(100/ 63) * self.h[0][3][3]
self.h[1][1][2] = -(1/2) * sqrt( 5/ 7) * self.h[1][2][2]
self.h[1][1][3] = (1/6) * sqrt( 35/ 11) * self.h[1][3][3]
self.h[1][2][3] = -(1/6) * sqrt(196/ 11) * self.h[1][3][3]
self.h[2][1][2] = -(1/2) * sqrt( 7/ 9) * self.h[2][2][2]
self.h[2][1][3] = (1/2) * sqrt( 63/143) * self.h[2][3][3]
self.h[2][2][3] = -(1/2) * sqrt(324/143) * self.h[2][3][3]
# Mirror around diagonal, see Eq.(29)
for l in range(0, 3):
for i in range(1, 4):
for j in range(1, i):
self.h[l][i][j] = self.h[l][j][i]
# Raw HGH pseudopotential parameters for semiconductor materials.
# See https://arxiv.org/abs/cond-mat/9803286
#
# Indices: Meanings:
# 0 Zion
# 1 2 3 4 5 rloc C1 C2 C3 C4
# 6 7 8 9 r0 h0_1 h0_2 h0_3
# 10 11 12 13 r1 h1_1 h1_2 h1_3
# 14 15 16 17 r2 h2_1 h2_2 h2_3
elements = {
"B" : [3,
0.433930, -5.578642, 0.804251, 0.000000, 0.000000,
0.373843, 6.233928, 0.000000, 0.000000,
0.360393, 0.000000, 0.000000, 0.000000,
0.000000, 0.000000, 0.000000, 0.000000],
"C" : [4,
0.348830, -8.513771, 1.228432, 0.000000, 0.000000,
0.304553, 9.522842, 0.000000, 0.000000,
0.232677, 0.000000, 0.000000, 0.000000,
0.000000, 0.000000, 0.000000, 0.000000],
"N" : [5,
0.289179, -12.234820, 1.766407, 0.000000, 0.000000,
0.256605, 13.552243, 0.000000, 0.000000,
0.270134, 0.000000, 0.000000, 0.000000,
0.000000, 0.000000, 0.000000, 0.000000],
"O" : [6,
0.247621, -16.580318, 2.395701, 0.000000, 0.000000,
0.221786, 18.266917, 0.000000, 0.000000,
0.256829, 0.000000, 0.000000, 0.000000,
0.000000, 0.000000, 0.000000, 0.000000],
"Al" : [3,
0.450000, -8.491351, 0.000000, 0.000000, 0.000000,
0.460104, 5.088340, 2.679700, 0.000000,
0.536744, 2.193438, 0.000000, 0.000000,
0.000000, 0.000000, 0.000000, 0.000000],
"Si" : [4,
0.440000, -7.336103, 0.000000, 0.000000, 0.000000,
0.422738, 5.906928, 3.258196, 0.000000,
0.484278, 2.727013, 0.000000, 0.000000,
0.000000, 0.000000, 0.000000, 0.000000],
"P" : [5,
0.430000, -6.654220, 0.000000, 0.000000, 0.000000,
0.389803, 6.842136, 3.856693, 0.000000,
0.440796, 3.282606, 0.000000, 0.000000,
0.000000, 0.000000, 0.000000, 0.000000],
"S" : [6,
0.420000, -6.554492, 0.000000, 0.000000, 0.000000,
0.361757, 7.905303, 4.471698, 0.000000,
0.405285, 3.866579, 0.000000, 0.000000,
0.000000, 0.000000, 0.000000, 0.000000],
"Zn" : [2,
0.570000, 0.000000, 0.000000, 0.000000, 0.000000,
0.640712, 2.088557, -0.218270, -0.941317,
0.967605, 0.163546, -0.227086, 0.000000,
1.330352, 0.010486, 0.000000, 0.000000],
"Ga" : [3,
0.560000, 0.000000, 0.000000, 0.000000, 0.000000,
0.610791, 2.369325, -0.249015, -0.551796,
0.704596, 0.746305, -0.513132, 0.000000,
0.982580, 0.075437, 0.000000, 0.000000],
"Ge" : [4,
0.540000, 0.000000, 0.000000, 0.000000, 0.000000,
0.493743, 3.826891, 1.100231, -1.344218,
0.601064, 1.362518, -0.627370, 0.000000,
0.788369, 0.191205, 0.000000, 0.000000],
"As" : [5,
0.520000, 0.000000, 0.000000, 0.000000, 0.000000,
0.456400, 4.560761, 1.692389, -1.373804,
0.550562, 1.812247, -0.646727, 0.000000,
0.685283, 0.312373, 0.000000, 0.000000],
"Se" : [6,
0.510000, 0.000000, 0.000000, 0.000000, 0.000000,
0.432531, 5.145131, 2.052009, -1.369203,
0.472473, 2.858806, -0.590671, 0.000000,
0.613420, 0.434829, 0.000000, 0.000000],
"Cd" : [2,
0.625000, -1.796838, 0.000000, 0.000000, 0.000000,
0.828465, 1.485292, -0.424753, -0.407986,
0.972873, 0.469208, -0.448111, 0.000000,
1.240949, 0.065412, 0.000000, 0.000000],
"In" : [3,
0.610000, 2.865777, 0.000000, 0.000000, 0.000000,
0.770602, 1.256194, -0.397255, -0.278329,
0.858132, 0.494459, -0.380789, 0.000000,
1.088691, 0.129208, 0.000000, 0.000000],
"Sn" : [4,
0.605000, 4.610912, 0.000000, 0.000000, 0.000000,
0.663544, 1.648791, -0.141974, -0.576546,
0.745865, 0.769355, -0.445070, 0.000000,
0.944459, 0.225115, 0.000000, 0.000000],
"Sb" : [5,
0.590000, 6.680228, 0.000000, 0.000000, 0.000000,
0.597684, 1.951477, 0.037537, -0.786631,
0.672122, 0.970313, -0.466731, 0.000000,
0.856557, 0.300103, 0.000000, 0.000000],
"Te" : [6,
0.575000, 9.387085, 0.000000, 0.000000, 0.000000,
0.556456, 2.046890, -0.029333, -0.881119,
0.615262, 1.033478, -0.481172, 0.000000,
0.805101, 0.317411, 0.000000, 0.000000],
}
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