def hess_wuyang(self, x, P_ref, dim, Ne_frag, Ne_env, impJK_sub,
bathJK_sub):
size = dim * (dim + 1) // 2
umat = tools.vec2mat(x, dim)
ops = self.ops
subKin = ops["subKin"]
subVnuc1 = ops["subVnuc1"]
subVnuc2 = ops["subVnuc2"]
subVnuc_bound1 = ops["subVnuc_bound1"]
subVnuc_bound2 = ops["subVnuc_bound2"]
subCoreJK = ops["subCoreJK"]
subTEI = ops["subTEI"]
subOEI1 = subKin + subVnuc1 + subVnuc_bound1 + impJK_sub + umat
subOEI2 = subKin + subVnuc2 + subVnuc_bound2 + subCoreJK + bathJK_sub + umat
FRAG_energy, FRAG_1RDM, mo_coeff_frag, mo_energy_frag, mo_occ_frag = qcwrap.pyscf_rhf.scf_oei(
subOEI1, dim, Ne_frag, self.smear_sigma)
hess_frag = oep_hess(mo_coeff_frag, mo_energy_frag, size, dim,
self.Ne_frag // 2, mo_occ_frag, self.smear_sigma)
ENV_energy, ENV_1RDM, mo_coeff_env, mo_energy_env, mo_occ_env = qcwrap.pyscf_rhf.scf_oei(
subOEI2, dim, Ne_env, self.smear_sigma)
hess_env = oep_hess(mo_coeff_env, mo_energy_env, size, dim,
self.Ne_env // 2, mo_occ_env, self.smear_sigma)
hess = hess_frag + hess_env
return hess
def oep_calc_diffP(self, x, dim, Ne_frag, Ne_env, P_ref, ops):
umat = tools.vec2mat(x, dim)
#print "|umat| = ", np.linalg.norm(umat)
if (self.params.oep_print >= 3):
#print "sum(diag(umat)) = ", np.sum(np.diag(umat))
tools.MatPrint(umat, 'umat')
FRAG_1RDM = np.zeros([dim, dim], dtype=float)
ENV_1RDM = np.zeros([dim, dim], dtype=float)
FRAG_energy = 0.0
ENV_energy = 0.0
frag_mo = np.zeros([dim, dim], dtype=float)
env_mo = np.zeros([dim, dim], dtype=float)
subKin = ops["subKin"]
subVnuc1 = ops["subVnuc1"]
subVnuc2 = ops["subVnuc2"]
subVnuc_bound1 = ops["subVnuc_bound1"]
subVnuc_bound2 = ops["subVnuc_bound2"]
subCoreJK = ops["subCoreJK"]
subTEI = ops["subTEI"]
subOEI1 = subKin + subVnuc1 + subVnuc_bound1 + umat
subOEI2 = subKin + subVnuc2 + subVnuc_bound2 + subCoreJK + umat
if (Ne_frag > 0):
frag_coredm_guess, mo_coeff = tools.fock2onedm(
subOEI1, Ne_frag // 2)
FRAG_energy, FRAG_1RDM, frag_mo = qcwrap.pyscf_rhf.scf(
subOEI1,
subTEI,
dim,
Ne_frag,
frag_coredm_guess,
mf_method=self.mf_method)
if (Ne_env > 0):
env_coredm_guess, mo_coeff = tools.fock2onedm(subOEI2, Ne_env // 2)
ENV_energy, ENV_1RDM, env_mo = qcwrap.pyscf_rhf.scf(
subOEI2,
subTEI,
dim,
Ne_env,
env_coredm_guess,
mf_method=self.mf_method)
self.frag_mo = frag_mo
self.env_mo = env_mo
self.P_imp = FRAG_1RDM
self.P_bath = ENV_1RDM
diffP = FRAG_1RDM + ENV_1RDM - P_ref
grad = tools.mat2vec(diffP, dim)
#print "2-norm (grad), max(grad):"
#print np.linalg.norm(grad), ", ", np.amax(np.absolute(grad))
return grad
def opt_umat_homo_diff(self, umat, gtol=1e-6):
ops = self.ops
Ne_frag = self.Ne_frag
Ne_env = self.Ne_env
dim = self.dim
subTEI = ops["subTEI"]
subOEI1 = ops["subKin"] + ops["subVnuc1"] + ops["subVnuc_bound1"] + umat
subOEI2 = ops["subKin"] + ops["subVnuc2"] + ops[
"subVnuc_bound2"] + ops["subCoreJK"] + umat
coredm = self.core1PDM_ao
ao2sub = self.ao2sub[:, :dim]
#frag_coredm_guess = tools.fock2onedm(subOEI1, Ne_frag//2)[0]
frag_coredm_guess = self.P_imp
mf_frag = qcwrap.qc_scf(Ne_frag,dim,self.mf_method,mol=self.mol,oei=subOEI1,tei=subTEI,\
dm0=frag_coredm_guess,coredm=0.0,ao2sub=ao2sub, smear_sigma = 0.0)
mf_frag.runscf()
#env_coredm_guess = tools.fock2onedm(subOEI2, Ne_env//2)[0]
env_coredm_guess = self.P_bath
mf_env = qcwrap.qc_scf(Ne_env,dim,self.mf_method,mol=self.mol,oei=subOEI2,tei=subTEI,\
dm0=env_coredm_guess,coredm=coredm,ao2sub=ao2sub, smear_sigma = 0.0)
mf_env.runscf()
print(np.linalg.norm(mf_frag.rdm1 - self.P_imp))
print(np.linalg.norm(mf_env.rdm1 - self.P_bath))
diffP = mf_frag.rdm1 + mf_env.rdm1 - self.P_ref
print("|P_frag + P_env - P_ref| = ", np.linalg.norm(diffP))
print("max element of (P_frag + P_env - P_ref) = ",
np.amax(np.absolute(diffP)))
self.P_imp = mf_frag.rdm1
self.P_bath = mf_env.rdm1
#build null space
vint = self.build_null_space(mf_frag, mf_env, Ne_frag, Ne_env, dim)
if vint is None:
return umat
#minimize |ehomo_A-ehomo_B|^2
x0 = tools.mat2vec(umat, dim)
n = vint.shape[-1]
c = np.zeros((n))
res = self.minimize_ehomo_2(c, x0, vint, gtol)
c = res.x
#print '|c| = ', np.linalg.norm(c)
for i in range(n):
x0 += c[i] * vint[:, i]
umat = tools.vec2mat(x0, dim)
#xmat = xmat - np.eye( xmat.shape[ 0 ] ) * np.average( np.diag( xmat ) )
#tools.MatPrint(umat,'umat')
#print '|umat| = ', np.linalg.norm(umat)
return umat
def cost_hess_wuyang(self,
x,
P_ref,
dim,
Ne_frag,
Ne_env,
impJK_sub,
bathJK_sub,
calc_hess=False):
size = dim * (dim + 1) // 2
umat = tools.vec2mat(x, dim)
print("|umat| = ", np.linalg.norm(umat))
#if(self.params.oep_print >= 3):
# print "sum(diag(umat)) = ", np.sum(np.diag(umat))
# tools.MatPrint(umat, 'umat')
FRAG_1RDM = np.zeros([dim, dim], dtype=float)
ENV_1RDM = np.zeros([dim, dim], dtype=float)
FRAG_energy = 0.0
ENV_energy = 0.0
ops = self.ops
subKin = ops["subKin"]
subVnuc1 = ops["subVnuc1"]
subVnuc2 = ops["subVnuc2"]
subVnuc_bound1 = ops["subVnuc_bound1"]
subVnuc_bound2 = ops["subVnuc_bound2"]
subCoreJK = ops["subCoreJK"]
subTEI = ops["subTEI"]
if (impJK_sub is not None):
subOEI1 = subKin + subVnuc1 + subVnuc_bound1 + impJK_sub + umat
subOEI2 = subKin + subVnuc2 + subVnuc_bound2 + subCoreJK + bathJK_sub + umat
FRAG_energy, FRAG_1RDM, frag_mo_coeff, frag_mo_energy, frag_mo_occ = \
qcwrap.pyscf_rhf.scf_oei( subOEI1, dim, Ne_frag, self.smear_sigma)
if (Ne_env > 0):
ENV_energy, ENV_1RDM, env_mo_coeff, env_mo_energy, env_mo_occ =\
qcwrap.pyscf_rhf.scf_oei( subOEI2, dim, Ne_env, self.smear_sigma)
if (calc_hess):
hess_frag = oep_hess(frag_mo_coeff, frag_mo_energy, size, dim,
Ne_frag // 2, frag_mo_occ,
self.smear_sigma)
hess_env = oep_hess(env_mo_coeff, env_mo_energy, size, dim,
Ne_env // 2, env_mo_occ, self.smear_sigma)
hess = hess_frag + hess_env
else:
raise Exception("NYI")
diffP = FRAG_1RDM + ENV_1RDM - P_ref
energy = FRAG_energy + ENV_energy - np.trace(np.dot(P_ref, umat))
grad = tools.mat2vec(diffP, dim)
#grad = tools.mat2vec_hchain(diffP, dim)
grad = -1.0 * grad
print("2-norm (grad), max(grad):")
print(np.linalg.norm(grad), ", ", np.amax(np.absolute(grad)))
f = -energy
print('-W = ', f)
#test
#f = np.linalg.norm(grad)
if (calc_hess):
return (f, grad, hess)
else:
return (f, grad)
def cost_ehomo_2(self, c, x0, vint):
x = x0.copy()
n = len(c)
for i in range(n):
x += c[i] * vint[:, i]
ops = self.ops
Ne_frag = self.Ne_frag
Ne_env = self.Ne_env
dim = self.dim
umat = tools.vec2mat(x, dim)
subTEI = ops["subTEI"]
subOEI1 = ops["subKin"] + ops["subVnuc1"] + ops["subVnuc_bound1"] + umat
subOEI2 = ops["subKin"] + ops["subVnuc2"] + ops[
"subVnuc_bound2"] + ops["subCoreJK"] + umat
coredm = self.core1PDM_ao
ao2sub = self.ao2sub[:, :dim]
frag_coredm_guess = self.P_imp
mf_frag = qcwrap.qc_scf(Ne_frag,dim,self.mf_method,mol=self.mol,oei=subOEI1,tei=subTEI,\
dm0=frag_coredm_guess,coredm=0.0,ao2sub=ao2sub, smear_sigma = 0.0)
mf_frag.runscf()
env_coredm_guess = self.P_bath
mf_env = qcwrap.qc_scf(Ne_env,dim,self.mf_method,mol=self.mol,oei=subOEI2,tei=subTEI,\
dm0=env_coredm_guess,coredm=coredm,ao2sub=ao2sub, smear_sigma = 0.0)
mf_env.runscf()
diffP = mf_frag.rdm1 + mf_env.rdm1 - self.P_ref
#print "|P_frag + P_env - P_ref| = ", np.linalg.norm(diffP)
#print "max element of (P_frag + P_env - P_ref) = ", np.amax(np.absolute(diffP) )
ehomo_A = mf_frag.mo_energy[Ne_frag // 2 - 1]
ehomo_B = mf_env.mo_energy[Ne_env // 2 - 1]
delta_ehomo = ehomo_A - ehomo_B
#print 'ehomo_A=',ehomo_A,' ehomo_B=',ehomo_B, ' delta_ehomo=', delta_ehomo
elumo_A = mf_frag.mo_energy[Ne_frag // 2]
elumo_B = mf_env.mo_energy[Ne_env // 2]
delta_elumo = elumo_A - elumo_B
#print 'elumo_A=',elumo_A,' elumo_B=',elumo_B, ' delta_elumo=', delta_elumo
#objective function
f = delta_ehomo * delta_ehomo + delta_elumo * delta_elumo #+ (elumo_A-ehomo_A-0.3)**2
homo_A = mf_frag.mo_coeff[:, Ne_frag // 2 - 1]
homo_B = mf_env.mo_coeff[:, Ne_env // 2 - 1]
lumo_A = mf_frag.mo_coeff[:, Ne_frag // 2]
lumo_B = mf_env.mo_coeff[:, Ne_env // 2]
#gradient
g = np.zeros((n))
for i in range(n):
tmp = tools.vec2mat(vint[:, i], dim)
EA = np.dot(homo_A, np.dot(tmp, homo_A))
EB = np.dot(homo_B, np.dot(tmp, homo_B))
g[i] = 2.0 * delta_ehomo * (EA - EB)
EA = np.dot(lumo_A, np.dot(tmp, lumo_A))
EB = np.dot(lumo_B, np.dot(tmp, lumo_B))
g[i] += 2.0 * delta_elumo * (EA - EB)
#EB=np.dot(homo_A,np.dot(tmp,homo_A))
#g[i] += 2.0*(elumo_A-ehomo_A-0.3)*(EA-EB)
return (f, g)