def num_grad(elems, coords, basis_set, dr=0.001):
grad = np.zeros_like(coords)
for i_atom in range(len(grad)):
for i_xyz in range(3):
coords[i_atom, i_xyz] += dr
e_p = one_e_qyd.solve_one_e(elems,
coords,
basis_set,
verbose=False)
coords[i_atom, i_xyz] -= dr * 2
e_m = one_e_qyd.solve_one_e(elems,
coords,
basis_set,
verbose=False)
coords[i_atom, i_xyz] += dr
grad[i_atom, i_xyz] = (e_p - e_m) / dr / 2
return grad
def optimize_coords(elems, coords, basis_set, max_iter=100, filename=None):
dr = 0.001
step_length = 0.1
print("--== Optimization start! ==--")
last_e = 0
for i in xrange(max_iter):
print("\n*** Iteration %d ***\n" % i)
e = one_e_qyd.solve_one_e(elems, coords, basis_set, verbose=False)
print("Energy = %13.7f Eh" % e)
grad = num_grad(elems, coords, basis_set)
g_norm = np.sqrt(np.mean(grad**2))
print("Grad norm = %13.7f" % g_norm)
coords -= grad / g_norm * step_length
print("New Coordinates")
print(coords)
if g_norm < 1e-7:
print("Optimization Finished!")
if filename is not None:
one_e_qyd.write_xyz(elems, coords, filename)
return
if e > last_e:
step_length /= 2
last_e = e
print("Optimization not finished in %d steps." % max_iter)
import numpy as np
import one_e_qyd
import matplotlib.pyplot as plt
plt.style.use('ggplot')
elems = ['H', 'H']
coords = np.array([[0, 0, 0], [0, 0, 1.4]])
for basis in ['sto-3g', '3-21g', '6-311g']:
basis_set = one_e_qyd.load_basis(basis)
d_range = np.linspace(0.5, 10.0, num=96)
results = []
for d in d_range:
#print("Dist = %.3f Bohr" % d)
coords[1][-1] = d
energy = one_e_qyd.solve_one_e(elems, coords, basis_set, verbose=False)
#print("Total Energy = %.7f "%energy)
results.append(energy)
plt.plot(d_range, results, lw=1.5, label=basis)
plt.legend()
plt.xlabel("H-H Dist (Bohr)")
plt.ylabel("Total Energy (Eh)")
plt.title("Scan of H2+ PES")
plt.savefig("scan_H2.pdf")
plt.close()
print results