def opt_func(exponents):
"""Find the optimal exponents for the hydrogen wave function."""
# print('exponents=', exponents)
hydrogen = Hydrogen(exponents)
hydrogen.variational()
return hydrogen.eigvals[0]
def opt_func(exponents):
"""Find the optimal exponents for the hydrogen wave function."""
# print('exponents=', exponents)
hydrogen = Hydrogen(exponents)
hydrogen.variational()
return hydrogen.eigvals[0]
def fill_arrays(self):
for index in ndindex(self.Q.shape):
alphas = [self.exponents[i] for i in index]
self.Q[index] = self.hartree(*alphas)
Hydrogen.fill_arrays(self)
def __init__(self, exponents):
self.Q = empty([i for i in repeat(len(exponents), 4)])
Hydrogen.__init__(self, exponents)
def coulomb(self, alpha_p, alpha_q):
return 2 * Hydrogen.coulomb(self, alpha_p, alpha_q)
import matplotlib.pyplot as plt
from numpy import array, linspace
from chap3.hydrogen import Hydrogen
exponents = array([13.00773, 1.962079, 0.444529, 0.1219492])
hydrogen = Hydrogen(exponents)
hydrogen.variational()
def print_energies():
for n in range(1, len(exponents)+1):
approx = hydrogen.approx_energy(n)
exact = hydrogen.exact_energy(n)
print('E{0} = {1:+.7e}, {2:.7e}'.format(n, approx, exact))
def plot_groundstate():
r = linspace(0, 3, 100)
n = 1 # Ground state
approx = hydrogen.approx_eigfunc(n, r)
exact = hydrogen.exact_eigfunc(n, r)
if approx[1] * exact[1] < 0:
approx *= -1e0
plt.plot(r, approx, 'r-', label='STO-4G')
plt.plot(r, exact, 'b--', label='STO')
plt.xlabel(r'$r$')
plt.ylabel(r'$\phi_{1s}$')
plt.legend()
plt.title('Ground-state Electronic Eigenfunction of Hydrogen Atom')
# plt.show()
plt.savefig('prob03plot.pdf')
if __name__ == '__main__':
print_energies()
def __init__(self, exponents):
self.Q = empty([i for i in repeat(len(exponents), 4)])
Hydrogen.__init__(self, exponents)
def fill_arrays(self):
for index in ndindex(self.Q.shape):
alphas = [self.exponents[i] for i in index]
self.Q[index] = self.hartree(*alphas)
Hydrogen.fill_arrays(self)
def coulomb(self, alpha_p, alpha_q):
return 2 * Hydrogen.coulomb(self, alpha_p, alpha_q)