em = f(rc)
R_pv[0, v] += eps
F = -(ep - em) / (2 * eps) * h**3
equal(F, -F_pv[0, v], 1e-9)
# High-level test:
lih = Atoms('LiH')
lih[1].y += 1.64
lih.center(vacuum=3)
pos = lih.cell.sum(axis=0)
print(pos)
pc = PointChargePotential([-1.0], [pos])
lih.calc = GPAW(external=pc, txt='lih-pc.txt')
f1 = lih.get_forces()
fpc1 = pc.get_forces(lih.calc)
print(fpc1)
print(fpc1 + f1.sum(0))
f2 = [[numeric_force(lih, a, v) for v in range(3)] for a in range(2)]
print(f1)
print(f1 - f2)
assert abs(f1 - f2).max() < 2e-3
x = 0.0001
for v in range(3):
pos[v] += x
pc.set_positions([pos])
ep = lih.get_potential_energy()
pos[v] -= 2 * x
pc.set_positions([pos])
calc = GPAW(nbands=1, h=0.2, charge=1, txt='H.txt')
H.set_calculator(calc)
e0 = H.get_potential_energy()
assert abs(e0 + calc.get_reference_energy()) < 0.014
# Test the point charge potential with a smooth cutoff:
pcp = PointChargePotential([-1], rc2=5.5, width=1.5)
calc.set(external=pcp)
E = []
F = []
D = np.linspace(2, 6, 30)
for d in D:
pcp.set_positions([[a / 2, a / 2, a / 2 + d]])
e = H.get_potential_energy() - e0
f1 = H.get_forces()
f2 = pcp.get_forces(calc)
eref = -1 / d * Bohr * Hartree
print(d, e, eref, abs(f1 + f2).max())
if d < 4.0:
error = e + 1 / d * Bohr * Hartree
assert abs(error) < 0.01, error
assert abs(f1 + f2).max() < 0.01
E.append(e)
F.append(f1[0, 2])
E = np.array(E)
FF = (E[2:] - E[:-2]) / (D[2] - D[0]) # numerical force
print(abs(F[1:-1] - FF).max())
assert abs(F[1:-1] - FF).max() < 0.1
if not True: