def calc_energy(self, coords):
energy = self.shift
for i, qi in enumerate(self.charges):
for j, qj in enumerate(self.charges):
if j >= i: break
scale = self._get_scale(i, j)
if scale==0.0: continue
bond = IC('_internal_ei_bond', [i, j], bond_length)
energy += qi*qj/bond.value(coords)*scale
return energy
def calc_gradient(self, coords):
grad = np.zeros(3*len(self.charges), float)
for i, qi in enumerate(self.charges):
for j, qj in enumerate(self.charges):
if j >= i: break
scale = self._get_scale(i, j)
if scale==0.0: continue
bond = IC('_internal_ei_bond', [i, j], bond_length)
r = bond.value(coords)
grad += -qi*qj/(r**2)*bond.grad(coords)*scale
return grad
def calc_energy(self, coords):
energy = self.shift
for i, qi in enumerate(self.charges):
for j, qj in enumerate(self.charges):
if j >= i: break
scale = self._get_scale(i, j)
if scale==0.0: continue
bond = IC('_internal_ei_bond', [i, j], bond_length)
r = bond.value(coords)
sigma = np.sqrt(self.sigmas[i]**2+self.sigmas[j]**2)
energy += scale*qi*qj/r*math.erf(r/sigma)
return energy
def calc_hessian(self, coords):
hess = np.zeros([3*len(self.charges), 3*len(self.charges)], float)
for i, qi in enumerate(self.charges):
for j, qj in enumerate(self.charges):
if j >= i: break
scale = self._get_scale(i, j)
if scale==0.0: continue
bond = IC('_internal_ei_bond', [i, j], bond_length)
r = bond.value(coords)
qgrad = bond.grad(coords)
hess += qi*qj/(r**2)*(2.0/r*np.outer(qgrad, qgrad) - bond.hess(coords))*scale
return hess
def calc_gradient(self, coords):
grad = np.zeros(3*len(coords), float)
for i, (si, ei) in enumerate(zip(self.sigmas, self.epsilons)):
for j, (sj, ej) in enumerate(zip(self.sigmas, self.epsilons)):
if j >= i: break
scale = self._get_scale(i, j)
if scale==0.0: continue
sigma = 0.5*(si+sj)
epsilon = np.sqrt(ei*ej)
bond = IC('_internal_vdw_bond', [i, j], bond_length)
x = (bond.value(coords)/sigma)
grad += scale*epsilon/sigma*(-2.208e6*np.exp(-12.0*x) + 13.5/x**7)*bond.grad(coords)
return grad
def calc_energy(self, coords):
energy = self.shift
for i, (si, ei) in enumerate(zip(self.sigmas, self.epsilons)):
for j, (sj, ej) in enumerate(zip(self.sigmas, self.epsilons)):
if j >= i: break
scale = self._get_scale(i, j)
if scale==0.0: continue
sigma = 0.5*(si+sj)
epsilon = np.sqrt(ei*ej)
bond = IC('_internal_vdw_bond', [i, j], bond_length)
x = (bond.value(coords)/sigma)
energy += scale*epsilon*(1.84e5*np.exp(-12.0*x) - 2.25/x**6)
return energy
def calc_gradient(self, coords):
grad = np.zeros(3*len(coords), float)
for i, (si, ei) in enumerate(zip(self.sigmas, self.epsilons)):
for j, (sj, ej) in enumerate(zip(self.sigmas, self.epsilons)):
if j >= i: break
scale = self._get_scale(i, j)
if scale==0.0: continue
sigma = 0.5*(si+sj)
epsilon = np.sqrt(ei*ej)
bond = IC('_internal_vdw_bond', [i, j], bond_length)
x = (sigma/bond.value(coords))
grad -= 24.0*epsilon/sigma*(2.0*x**13-x**7)*bond.grad(coords)*scale
return grad
def calc_energy(self, coords):
energy = self.shift
for i, (si, ei) in enumerate(zip(self.sigmas, self.epsilons)):
for j, (sj, ej) in enumerate(zip(self.sigmas, self.epsilons)):
if j >= i: break
scale = self._get_scale(i, j)
if scale==0.0: continue
sigma = 0.5*(si+sj)
epsilon = np.sqrt(ei*ej)
bond = IC('_internal_vdw_bond', [i, j], bond_length)
x = (sigma/bond.value(coords))
energy += 4.0*epsilon*(x**12-x**6)*scale
return energy
def calc_hessian(self, coords):
hess = np.zeros([3*len(coords), 3*len(coords)], float)
for i, (si, ei) in enumerate(zip(self.sigmas, self.epsilons)):
for j, (sj, ej) in enumerate(zip(self.sigmas, self.epsilons)):
if j >= i: break
scale = self._get_scale(i, j)
if scale==0.0: continue
sigma = 0.5*(si+sj)
epsilon = np.sqrt(ei*ej)
bond = IC('_internal_vdw_bond', [i, j], bond_length)
x = (sigma/bond.value(coords))
qgrad = bond.grad(coords)
hess += 24.0*epsilon/sigma**2*(26*x**14-7*x**8)*np.outer(qgrad, qgrad)*scale
hess -= 24.0*epsilon/sigma*(2*x**13-x**7)*bond.hess(coords)*scale
return hess
def calc_hessian(self, coords):
hess = np.zeros([3*len(coords), 3*len(coords)], float)
for i, (si, ei) in enumerate(zip(self.sigmas, self.epsilons)):
for j, (sj, ej) in enumerate(zip(self.sigmas, self.epsilons)):
if j >= i: break
scale = self._get_scale(i, j)
if scale==0.0: continue
sigma = 0.5*(si+sj)
epsilon = np.sqrt(ei*ej)
bond = IC('_internal_vdw_bond', [i, j], bond_length)
x = (bond.value(coords)/sigma)
qgrad = bond.grad(coords)
dVdr = -2.208e6*np.exp(-12.0*x) + 13.5/x**7
d2Vdr2 = 2.6496e7*np.exp(-12.0*x)-94.5/x**8
hess += scale*epsilon/sigma*(d2Vdr2/sigma*np.outer(qgrad, qgrad) + dVdr*bond.hess(coords))
return hess
def calc_gradient(self, coords):
grad = np.zeros(3*len(self.charges), float)
for i, qi in enumerate(self.charges):
for j, qj in enumerate(self.charges):
if j >= i: break
scale = self._get_scale(i, j)
if scale==0.0: continue
bond = IC('_internal_ei_bond', [i, j], bond_length)
r = bond.value(coords)
sigma = np.sqrt(self.sigmas[i]**2+self.sigmas[j]**2)
#intermediate results
erf = math.erf(r/sigma)
exp = np.exp(-(r/sigma)**2)/np.sqrt(np.pi)
#update grad
grad += scale*qi*qj/r*(-erf/r + 2.0*exp/sigma)*bond.grad(coords)
return grad
def calc_hessian(self, coords):
hess = np.zeros([3*len(self.charges), 3*len(self.charges)], float)
for i, qi in enumerate(self.charges):
for j, qj in enumerate(self.charges):
if j >= i: break
scale = self._get_scale(i, j)
if scale==0.0: continue
bond = IC('_internal_ei_bond', [i, j], bond_length)
r = bond.value(coords)
qgrad = bond.grad(coords)
sigma = np.sqrt(self.sigmas[i]**2+self.sigmas[j]**2)
#intermediate results
erf = math.erf(r/sigma)
exp = np.exp(-(r/sigma)**2)/np.sqrt(np.pi)
dVdr = (-erf/r + 2.0/sigma*exp)/r
d2Vdr2 = (erf/r - 2*exp/sigma)/r**2 - 2*exp/sigma**3
#update hessian
hess += scale*qi*qj*(2*d2Vdr2*np.outer(qgrad, qgrad) + dVdr*bond.hess(coords))
return hess