def get_edensityxc(self, densinfo):
if isinstance(densinfo, ValGrad):
rho = densinfo.value.abs() # safeguarding from nan
return self.a * safepow(rho, self.p)**self.p
else:
return 0.5 * (self.get_edensityxc(densinfo.u * 2) +
self.get_edensityxc(densinfo.d * 2))
def get_edensityxc(self, densinfo):
if isinstance(densinfo, ValGrad): # unpolarized case
rho = densinfo.value.abs()
kf_rho = (3 * np.pi * np.pi)**(1.0 / 3) * safepow(rho, 4.0 / 3)
e_unif = -3.0 / (4 * np.pi) * kf_rho
return e_unif
else: # polarized case
eu = self.get_edensityxc(densinfo.u * 2)
ed = self.get_edensityxc(densinfo.d * 2)
return 0.5 * (eu + ed)
def get_edensityxc(self, densinfo):
if isinstance(densinfo, ValGrad):
rho = densinfo.value.abs()
kf_rho = (3 * np.pi * np.pi)**(1.0 / 3) * safepow(rho, 4.0 / 3)
e_unif = -3.0 / (4 * np.pi) * kf_rho
norm_grad = safenorm(densinfo.grad, dim=-1)
s = norm_grad / (2 * kf_rho)
fx = 1 + self.kappa - self.kappa / (1 +
self.mu * s * s / self.kappa)
return fx * e_unif
else:
return 0.5 * (self.get_edensityxc(densinfo.u * 2) +
self.get_edensityxc(densinfo.d * 2))
def ldac_e_true(rho, xi):
# lda correlation based on PW92
rs = safepow(4 * np.pi * rho / 3.0, -1.0 / 3)
sl = (slice(None, None, None),) + ((None,) * max(rs.ndim, xi.ndim))
a_pp = torch.tensor([1, 1, 1])[sl]
a_a = torch.tensor([0.0310907, 0.01554535, 0.0168869])[sl]
a_alpha1 = torch.tensor([0.21370, 0.20548, 0.11125])[sl]
a_beta1 = torch.tensor([7.5957, 14.1189, 10.357])[sl]
a_beta2 = torch.tensor([3.5876, 6.1977, 3.6231])[sl]
a_beta3 = torch.tensor([1.6382, 3.3662, 0.88026])[sl]
a_beta4 = torch.tensor([0.49294, 0.62517, 0.49671])[sl]
a_fz20 = 1.709920934161365617563962776245
g_aux = a_beta1 * torch.sqrt(rs) + a_beta2 * rs + a_beta3 * rs ** 1.5 + a_beta4 * rs ** (a_pp + 1)
# log1p(x) provides better numerical stability than log(1+x)
g = -2 * a_a * (1 + a_alpha1 * rs) * torch.log1p(1. / (2 * a_a * g_aux))
f_xi = (safepow(1 + xi, 4. / 3) + safepow(1 - xi, 4. / 3) - 2) / (2 ** (4. / 3) - 2)
f_pw = g[0] + xi ** 4 * f_xi * (g[1] - g[0] + g[2] / a_fz20) - f_xi * g[2] / a_fz20
return f_pw * rho
def get_edensityxc(self, densinfo):
if isinstance(densinfo, ValGrad): # unpolarized case
kappa = 0.804
mu = 0.21951
rho = densinfo.value.abs()
kf_rho = (3 * np.pi * np.pi)**(1.0 / 3) * safepow(rho, 4.0 / 3)
e_unif = -3.0 / (4 * np.pi) * kf_rho
norm_grad = safenorm(densinfo.grad, dim=-1)
s = norm_grad / (2 * kf_rho)
fx = 1 + kappa - kappa / (1 + mu * s * s / kappa)
return fx * e_unif
else: # polarized case
eu = self.get_edensityxc(densinfo.u * 2)
ed = self.get_edensityxc(densinfo.d * 2)
return 0.5 * (eu + ed)