def nuclear_attraction(gaussian_1, gaussian_2, nuclei):
a_1 = gaussian_1.exponent
a_2 = gaussian_2.exponent
l_1 = gaussian_1.integral_exponents
l_2 = gaussian_2.integral_exponents
r_a = gaussian_1.coordinates
r_b = gaussian_2.coordinates
r_c = nuclei.coordinates
r_p = gaussian_product_coordinate(a_1, r_a, a_2, r_b)
r_ab = coordinate_distance(r_a, r_b)
r_pc = coordinate_distance(r_p, r_c)
r_p_a = vector_minus(r_p, r_a)
r_p_b = vector_minus(r_p, r_b)
r_p_c = vector_minus(r_p, r_c)
g = a_1 + a_2
ans = 0
for l in range(l_1[0] + l_2[0] + 1):
for r in range(int(l / 2) + 1):
for i in range(int((l - 2 * r) / 2) + 1):
out1 = a_function(l, r, i, l_1[0], l_2[0], r_p_a[0], r_p_b[0],
r_p_c[0], g)
for m in range(l_1[1] + l_2[1] + 1):
for s in range(int(m / 2) + 1):
for j in range(int((m - 2 * s) / 2) + 1):
out2 = a_function(m, s, j, l_1[1], l_2[1],
r_p_a[1], r_p_b[1], r_p_c[1], g)
for n in range(l_1[2] + l_2[2] + 1):
for t in range(int(n / 2) + 1):
for k in range(int((n - 2 * t) / 2) + 1):
out3 = a_function(
n, t, k, l_1[2], l_2[2], r_p_a[2],
r_p_b[2], r_p_c[2], g)
v = (l + m +
n) - 2 * (r + s + t) - (i + j + k)
out4 = boys_function(v, g * r_pc**2)
out5 = out1 * out2 * out3 * out4
ans += out5
ans *= ((2 * pi) / g) * exp(-(a_1 * a_2 * r_ab**2) / g)
return ans
def test_input_of_nu_0_and_u_0_returns_1(self):
output = boys_function(0, 0)
testing.assert_approx_equal(output, 1, 6)
def test_input_of_nu_2_and_u_4_4757221852728435_returns_0_0139425(self):
output = boys_function(2, 4.4757221852728435)
testing.assert_approx_equal(output, 0.0139425, 6)
def test_input_of_nu_2_and_4_802164876034457e_minus_31_returns_0_200000(
self):
output = boys_function(2, 4.802164876034457e-31)
testing.assert_approx_equal(output, 0.200000, 6)
def test_input_of_nu_2_and_0_minus_31_returns_0_200000(self):
output = boys_function(2, 0)
testing.assert_approx_equal(output, 0.200000, 6)
def test_input_of_nu_1_and_u_130_80051761256559_returns_0_00029621(self):
output = boys_function(1, 130.80051761256559)
testing.assert_approx_equal(output, 0.000296210, 6)
def test_input_of_nu_1_and_u_12_0769452374367_returns_0_01055(self):
output = boys_function(1, 12.0769452374367)
testing.assert_approx_equal(output, 0.0105576, 6)
def test_input_of_nu_1_and_4_802164876034457e_minus_31_returns_0_333333(
self):
output = boys_function(1, 4.802164876034457e-31)
testing.assert_approx_equal(output, 0.333333, 6)
def test_input_of_nu_0_and_u_130_80051761256559_returns_0_077489(self):
output = boys_function(0, 130.80051761256559)
testing.assert_approx_equal(output, 0.077489, 6)
def test_input_of_nu_1_and_0_minus_31_returns_0_333333(self):
output = boys_function(1, 0)
testing.assert_approx_equal(output, 0.333333, 6)
def test_input_of_nu_0_and_u_12_0769452374367_returns_0_2550(self):
output = boys_function(0, 12.0769452374367)
testing.assert_approx_equal(output, 0.255015, 6)
def test_input_of_nu_0_and_u_4_4757221852728435_returns_0_417742(self):
output = boys_function(0, 4.4757221852728435)
testing.assert_approx_equal(output, 0.417742, 6)
def integrate(self, basis_i, basis_j, basis_k, basis_l):
l_1 = basis_i.integral_exponents
l_2 = basis_j.integral_exponents
l_3 = basis_k.integral_exponents
l_4 = basis_l.integral_exponents
l_total = sum(l_1) + sum(l_2) + sum(l_3) + sum(l_4)
r_1 = basis_i.coordinates
r_2 = basis_j.coordinates
r_3 = basis_k.coordinates
r_4 = basis_l.coordinates
primitives_i = basis_i.primitive_gaussian_array
primitives_j = basis_j.primitive_gaussian_array
primitives_k = basis_k.primitive_gaussian_array
primitives_l = basis_l.primitive_gaussian_array
n_i = basis_i.normalisation
n_j = basis_j.normalisation
n_k = basis_k.normalisation
n_l = basis_l.normalisation
n = n_i * n_j * n_k * n_l
ans = 0.0
for g1, g2, g3, g4 in itertools.product(primitives_i, primitives_j,
primitives_k, primitives_l):
c_1 = g1.contraction
c_2 = g2.contraction
c_3 = g3.contraction
c_4 = g4.contraction
n_1 = g1.normalisation
n_2 = g2.normalisation
n_3 = g3.normalisation
n_4 = g4.normalisation
contraction = c_1 * c_2 * c_3 * c_4 * n_1 * n_2 * n_3 * n_4 * n
a_1 = g1.exponent
a_2 = g2.exponent
a_3 = g3.exponent
a_4 = g4.exponent
a_5 = a_1 + a_2
a_6 = a_3 + a_4
self.a_7 = (a_5 * a_6) / (a_5 + a_6)
r_5 = gaussian_product_coordinate(a_1, r_1, a_2, r_2)
r_6 = gaussian_product_coordinate(a_3, r_3, a_4, r_4)
self.r_7 = gaussian_product_coordinate(a_5, r_5, a_6, r_6)
r_12 = coordinate_distance(r_1, r_2)
r_34 = coordinate_distance(r_3, r_4)
r_56 = coordinate_distance(r_5, r_6)
boys_x = (a_5 * a_6 * r_56**2) / (a_5 + a_6)
boys_out1 = (2 * pi**(5 / 2)) / (a_5 * a_6 * sqrt(a_5 + a_6))
boys_out2 = exp(((-a_1 * a_2 * r_12**2) / a_5) -
((a_3 * a_4 * r_34**2) / a_6))
boys_out3 = boys_function(l_total, boys_x)
self.end_dict = {l_total: boys_out1 * boys_out2 * boys_out3}
m = l_total
while m >= 1:
boys_out3 = boys_function_recursion(m, boys_x, boys_out3)
m -= 1
self.end_dict[m] = boys_out1 * boys_out2 * boys_out3
ans += contraction * self.os_begin(0, g1, g2, g3, g4)
return ans
def test_input_of_nu_2_and_u_12_0769452374367_returns_0_00131107(self):
output = boys_function(2, 12.0769452374367)
testing.assert_approx_equal(output, 0.00131106, 6)
def test_input_of_nu_1_and_u_4_4757221852728435_returns_0_045396(self):
output = boys_function(1, 4.4757221852728435)
testing.assert_approx_equal(output, 0.045396, 6)
def test_input_of_nu_2_and_u_130_80051761256559_returns_3_3969e_minus_6(
self):
output = boys_function(2, 130.80051761256559)
testing.assert_approx_equal(output, 3.39689e-6, 6)
def integrate(self, basis_i, basis_j, basis_k, basis_l):
primitives_i = basis_i.primitive_gaussian_array
primitives_j = basis_j.primitive_gaussian_array
primitives_k = basis_k.primitive_gaussian_array
primitives_l = basis_l.primitive_gaussian_array
l_1 = basis_i.integral_exponents
l_2 = basis_j.integral_exponents
l_3 = basis_k.integral_exponents
l_4 = basis_l.integral_exponents
r_1 = basis_i.coordinates
r_2 = basis_j.coordinates
r_3 = basis_k.coordinates
r_4 = basis_l.coordinates
n_i = basis_i.normalisation
n_j = basis_j.normalisation
n_k = basis_k.normalisation
n_l = basis_l.normalisation
norm = n_i * n_j * n_k * n_l
ans = 0.0
for g1, g2, g3, g4 in itertools.product(primitives_i, primitives_j,
primitives_k, primitives_l):
self.end_dict = {}
c_1 = g1.contraction
c_2 = g2.contraction
c_3 = g3.contraction
c_4 = g4.contraction
n_1 = g1.normalisation
n_2 = g2.normalisation
n_3 = g3.normalisation
n_4 = g4.normalisation
contraction = c_1 * c_2 * c_3 * c_4 * n_1 * n_2 * n_3 * n_4 * norm
g5 = gaussian_product(g1, g2)
g6 = gaussian_product(g3, g4)
a_1 = g1.exponent
a_2 = g2.exponent
a_3 = g3.exponent
a_4 = g4.exponent
a_5 = g5.exponent
a_6 = g6.exponent
r_5 = g5.coordinates
r_6 = g6.coordinates
r_12 = coordinate_distance(r_1, r_2)
r_34 = coordinate_distance(r_3, r_4)
r_56 = coordinate_distance(r_5, r_6)
l_5 = g5.integral_exponents
l_6 = g6.integral_exponents
delta = (1 / (4 * a_5)) + (1 / (4 * a_6))
out_5 = 0
for l in range(l_5[0] + 1):
for r in range(int(l / 2) + 1):
for ll in range(l_6[0] + 1):
for rr in range(int(ll / 2) + 1):
for i in range(
int((l + ll - 2 * r - 2 * rr) / 2) + 1):
out1 = self.b_function(l, ll, r, rr, i, l_1[0],
l_2[0], r_1[0], r_2[0],
r_5[0], a_5, l_3[0],
l_4[0], r_3[0], r_4[0],
r_6[0], a_6)
for m in range(l_5[1] + 1):
for s in range(int(m / 2) + 1):
for mm in range(l_6[1] + 1):
for ss in range(int(mm / 2) + 1):
for j in range(
int((m + mm - 2 * s -
2 * ss) / 2) + 1):
out2 = self.b_function(
m, mm, s, ss, j,
l_1[1], l_2[1], r_1[1],
r_2[1], r_5[1], a_5,
l_3[1], l_4[1], r_3[1],
r_4[1], r_6[1], a_6)
for n in range(l_5[2] + 1):
for t in range(
int(n / 2) +
1):
for nn in range(
l_6[2] +
1):
for tt in range(
int(nn
/ 2
) +
1):
for k in range(
int((
n
+
nn
-
2
*
t
-
2
*
tt
) / 2
)
+
1):
out3 = self.b_function(
n,
nn,
t,
tt,
k,
l_1[2],
l_2[2],
r_1[2],
r_2[2],
r_5[2],
a_5,
l_3[2],
l_4[2],
r_3[2],
r_4[2],
r_6[2],
a_6
)
v = l + ll + m + mm + n + nn - 2 * (
r +
rr
+
s +
ss
+
t +
tt
) - (
i +
j +
k)
if v in self.end_dict:
out4 = self.end_dict[
v]
else:
out4 = boys_function(
v,
(r_56
**
2
/
(4
*
delta
)
)
)
self.end_dict[
v] = out4
out_5 += out1 * out2 * out3 * out4
out_5 *= self.gaussian_product_factor(a_1, a_2, a_3, a_4, a_5, a_6,
r_12, r_34)
ans += contraction * out_5
return ans