# Copyright 2014-2018 The PySCF Developers. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
from functools import reduce
import numpy
[docs]
def rotmatz(ang):
c = numpy.cos(ang)
s = numpy.sin(ang)
return numpy.array((( c, s, 0),
(-s, c, 0),
( 0, 0, 1),))
[docs]
def rotmaty(ang):
c = numpy.cos(ang)
s = numpy.sin(ang)
return numpy.array((( c, 0, s),
( 0, 1, 0),
(-s, 0, c),))
[docs]
def r2edge(ang, r):
return 2*r*numpy.sin(ang/2)
[docs]
def make60(b5, b6):
theta1 = numpy.arccos(1/numpy.sqrt(5))
theta2 = (numpy.pi - theta1) * .5
r = (b5*2+b6)/2/numpy.sin(theta1/2)
rot72 = rotmatz(numpy.pi*2/5)
s2 = numpy.sin(theta2)
c2 = numpy.cos(theta2)
p1 = numpy.array(( s2*b5, 0, r-c2*b5))
p9 = numpy.array((-s2*b5, 0,-r+c2*b5))
p2 = numpy.array(( s2*(b5+b6), 0, r-c2*(b5+b6)))
rot1 = reduce(numpy.dot, (rotmaty(theta1), rot72, rotmaty(-theta1)))
p2s = []
for i in range(5):
p2s.append(p2)
p2 = numpy.dot(p2, rot1)
coord = []
for i in range(5):
coord.append(p1)
p1 = numpy.dot(p1, rot72)
for pj in p2s:
pi = pj
for i in range(5):
coord.append(pi)
pi = numpy.dot(pi, rot72)
for pj in p2s:
pi = pj
for i in range(5):
coord.append(-pi)
pi = numpy.dot(pi, rot72)
for i in range(5):
coord.append(p9)
p9 = numpy.dot(p9, rot72)
return numpy.array(coord)
[docs]
def make12(b):
theta1 = numpy.arccos(1/numpy.sqrt(5))
r = b/2/numpy.sin(theta1/2)
rot72 = rotmatz(numpy.pi*2/5)
s1 = numpy.sin(theta1)
c1 = numpy.cos(theta1)
p1 = numpy.array(( s1*r, 0, c1*r))
p2 = numpy.array((-s1*r, 0, -c1*r))
coord = [( 0, 0, r)]
for i in range(5):
coord.append(p1)
p1 = numpy.dot(p1, rot72)
for i in range(5):
coord.append(p2)
p2 = numpy.dot(p2, rot72)
coord.append(( 0, 0, -r))
return numpy.array(coord)
[docs]
def make20(b):
theta1 = numpy.arccos(numpy.sqrt(5)/3)
theta2 = numpy.arcsin(r2edge(theta1,1)/2/numpy.sin(numpy.pi/5))
r = b/2/numpy.sin(theta1/2)
rot72 = rotmatz(numpy.pi*2/5)
s2 = numpy.sin(theta2)
c2 = numpy.cos(theta2)
s3 = numpy.sin(theta1+theta2)
c3 = numpy.cos(theta1+theta2)
p1 = numpy.array(( s2*r, 0, c2*r))
p2 = numpy.array(( s3*r, 0, c3*r))
p3 = numpy.array((-s3*r, 0, -c3*r))
p4 = numpy.array((-s2*r, 0, -c2*r))
coord = []
for i in range(5):
coord.append(p1)
p1 = numpy.dot(p1, rot72)
for i in range(5):
coord.append(p2)
p2 = numpy.dot(p2, rot72)
for i in range(5):
coord.append(p3)
p3 = numpy.dot(p3, rot72)
for i in range(5):
coord.append(p4)
p4 = numpy.dot(p4, rot72)
return numpy.array(coord)
if __name__ == '__main__':
b5 = 1.46
b6 = 1.38
for c in make60(b5, b6):
print(c)
b = 1.4
for c in make12(b):
print(c)
for c in make20(b):
print(c)
