def get_bands(self, kpt_band, cell=None, dm_kpts=None, kpts=None): '''Get energy bands at a given (arbitrary) 'band' k-point. Returns: mo_energy : (nao,) ndarray Bands energies E_n(k) mo_coeff : (nao, nao) ndarray Band orbitals psi_n(k) ''' if cell is None: cell = self.cell if dm_kpts is None: dm_kpts = self.make_rdm1() if kpts is None: kpts = self.kpts fock = pbchf.get_hcore(cell, kpt_band) \ + self.get_veff(kpts=kpts, kpt_band=kpt_band) s1e = pbchf.get_ovlp(cell, kpt_band) mo_energy, mo_coeff = pyscf.scf.hf.eig(fock, s1e) return mo_energy, mo_coeff
def get_ovlp(mf, cell, kpts): '''Get the overlap AO matrices at sampled k-points. Args: kpts : (nkpts, 3) ndarray Returns: ovlp_kpts : (nkpts, nao, nao) ndarray ''' nkpts = len(kpts) nao = cell.nao_nr() ovlp_kpts = np.zeros((nkpts,nao,nao), np.complex128) for k in range(nkpts): kpt = kpts[k,:] if mf.analytic_int: ovlp_kpts[k,:,:] = scfint.get_ovlp(cell, kpt) else: ovlp_kpts[k,:,:] = pbchf.get_ovlp(cell, kpt) return ovlp_kpts
def test_components(pseudo=None): # The molecular calculation mol = gto.Mole() mol.unit = 'B' L = 60 mol.atom.extend([['He', (L/2.,L/2.,L/2.)], ]) mol.basis = 'sto-3g' mol.build() m = rks.RKS(mol) m.xc = 'LDA,VWN_RPA' print(m.scf()) # -2.90705411168 dm = m.make_rdm1() # The periodic calculation cell = pbcgto.Cell() cell.unit = 'B' cell.a = np.diag([L,L,L]) cell.gs = np.array([80,80,80]) cell.atom = mol.atom cell.basis = mol.basis cell.pseudo = pseudo cell.build() # These should match reasonably well (roughly with accuracy of normalization) print "Kinetic energy" tao = pbchf.get_t(cell) tao2 = mol.intor_symmetric('cint1e_kin_sph') print np.dot(np.ravel(tao), np.ravel(dm)) # 2.82793077196 print np.dot(np.ravel(tao2), np.ravel(dm)) # 2.82352636524 print "Overlap" sao = pbchf.get_ovlp(cell) print np.dot(np.ravel(sao), np.ravel(dm)) # 1.99981725342 print np.dot(np.ravel(m.get_ovlp()), np.ravel(dm)) # 2.0 # The next two entries should *not* match, since G=0 component is removed print "Coulomb (G!=0)" jao = pbchf.get_j(cell, dm) print np.dot(np.ravel(dm),np.ravel(jao)) # 4.03425518427 print np.dot(np.ravel(dm),np.ravel(m.get_j(dm))) # 4.22285177049 # The next two entries should *not* match, since G=0 component is removed print "Nuc-el (G!=0)" if cell.pseudo: vppao = pbchf.get_pp(cell) print np.dot(np.ravel(dm), np.ravel(vppao)) else: neao = pbchf.get_nuc(cell) print np.dot(np.ravel(dm), np.ravel(neao)) # -6.50203360062 vne = mol.intor_symmetric('cint1e_nuc_sph') print np.dot(np.ravel(dm), np.ravel(vne)) # -6.68702326551 print "Normalization" coords = gen_uniform_grids(cell) aoR = eval_ao(cell, coords) rhoR = eval_rho(cell, aoR, dm) print cell.vol/len(rhoR)*np.sum(rhoR) # 1.99981725342 (should be 2.0) print "(Hartree + vne) * DM" print np.dot(np.ravel(dm),np.ravel(m.get_j(dm)))+np.dot(np.ravel(dm), np.ravel(vne)) if cell.pseudo: print np.einsum("ij,ij", dm, vppao + jao + pbchf.get_jvloc_G0(cell)) else: print np.einsum("ij,ij", dm, neao + jao) ew_cut = (40,40,40) ew_eta = 0.05 for ew_eta in [0.1, 0.5, 1.]: ew = pbchf.ewald(cell, ew_eta, ew_cut) print "Ewald (eta, energy)", ew_eta, ew # should be same for all eta print "Ewald divergent terms summation", ew # These two should now match if the box is reasonably big to # remove images, and ngs is big. print "Total coulomb (analytic) ", print (.5*np.dot(np.ravel(dm), np.ravel(m.get_j(dm))) + np.dot(np.ravel(dm), np.ravel(vne)) ) # -4.57559738004 if not cell.pseudo: print "Total coulomb (fft coul + ewald)", print np.einsum("ij,ij", dm, neao + .5*jao) + ew # -4.57948259115 # Exc cell.ew_eta, cell.ew_cut = ew_eta, ew_cut mf = pbcdft.RKS(cell) mf.xc = 'LDA,VWN_RPA' rks.get_veff(mf, cell, dm) print "Exc", mf._exc # -1.05967570089
def test_components(pseudo=None): # The molecular calculation mol = gto.Mole() mol.unit = 'B' L = 60 mol.atom.extend([ ['He', (L / 2., L / 2., L / 2.)], ]) mol.basis = 'sto-3g' mol.build() m = rks.RKS(mol) m.xc = 'LDA,VWN_RPA' print(m.scf()) # -2.90705411168 dm = m.make_rdm1() # The periodic calculation cell = pbcgto.Cell() cell.unit = 'B' cell.a = np.diag([L, L, L]) cell.gs = np.array([80, 80, 80]) cell.atom = mol.atom cell.basis = mol.basis cell.pseudo = pseudo cell.build() # These should match reasonably well (roughly with accuracy of normalization) print "Kinetic energy" tao = pbchf.get_t(cell) tao2 = mol.intor_symmetric('cint1e_kin_sph') print np.dot(np.ravel(tao), np.ravel(dm)) # 2.82793077196 print np.dot(np.ravel(tao2), np.ravel(dm)) # 2.82352636524 print "Overlap" sao = pbchf.get_ovlp(cell) print np.dot(np.ravel(sao), np.ravel(dm)) # 1.99981725342 print np.dot(np.ravel(m.get_ovlp()), np.ravel(dm)) # 2.0 # The next two entries should *not* match, since G=0 component is removed print "Coulomb (G!=0)" jao = pbchf.get_j(cell, dm) print np.dot(np.ravel(dm), np.ravel(jao)) # 4.03425518427 print np.dot(np.ravel(dm), np.ravel(m.get_j(dm))) # 4.22285177049 # The next two entries should *not* match, since G=0 component is removed print "Nuc-el (G!=0)" if cell.pseudo: vppao = pbchf.get_pp(cell) print np.dot(np.ravel(dm), np.ravel(vppao)) else: neao = pbchf.get_nuc(cell) print np.dot(np.ravel(dm), np.ravel(neao)) # -6.50203360062 vne = mol.intor_symmetric('cint1e_nuc_sph') print np.dot(np.ravel(dm), np.ravel(vne)) # -6.68702326551 print "Normalization" coords = gen_uniform_grids(cell) aoR = eval_ao(cell, coords) rhoR = eval_rho(cell, aoR, dm) print cell.vol / len(rhoR) * np.sum(rhoR) # 1.99981725342 (should be 2.0) print "(Hartree + vne) * DM" print np.dot(np.ravel(dm), np.ravel(m.get_j(dm))) + np.dot( np.ravel(dm), np.ravel(vne)) if cell.pseudo: print np.einsum("ij,ij", dm, vppao + jao + pbchf.get_jvloc_G0(cell)) else: print np.einsum("ij,ij", dm, neao + jao) ew_cut = (40, 40, 40) ew_eta = 0.05 for ew_eta in [0.1, 0.5, 1.]: ew = pbchf.ewald(cell, ew_eta, ew_cut) print "Ewald (eta, energy)", ew_eta, ew # should be same for all eta print "Ewald divergent terms summation", ew # These two should now match if the box is reasonably big to # remove images, and ngs is big. print "Total coulomb (analytic) ", print(.5 * np.dot(np.ravel(dm), np.ravel(m.get_j(dm))) + np.dot(np.ravel(dm), np.ravel(vne))) # -4.57559738004 if not cell.pseudo: print "Total coulomb (fft coul + ewald)", print np.einsum("ij,ij", dm, neao + .5 * jao) + ew # -4.57948259115 # Exc cell.ew_eta, cell.ew_cut = ew_eta, ew_cut mf = pbcdft.RKS(cell) mf.xc = 'LDA,VWN_RPA' rks.get_veff(mf, cell, dm) print "Exc", mf._exc # -1.05967570089
def test_overlap20(self): mol, cell = make_cell2(20, 20) sao = pbchf.get_ovlp(cell) self.assertAlmostEqual(finger(sao), -0.8503588722723614, 9)
def test_ovlp_uniform(self): mol, cell = make_cell2(4, 40) sao = pbchf.get_ovlp(cell) s0 = pscf.scfint.get_ovlp(cell) self.assertAlmostEqual(np.linalg.norm(sao-s0), 0, 9)