def test(): mol = gto.M(atom="Li 0. 0. 0.; Li 0. 0. 1.5", basis="sto-3g", unit="bohr", verbose=0) mf = scf.RHF(mol).run() # Lowdin orthogonalized AO basis. lowdin = lo.orth_ao(mol, "lowdin") # MOs in the Lowdin basis. mo = solve(lowdin, mf.mo_coeff) # make AO to localized orbital coefficients. mfobdm = mf.make_rdm1(mo, mf.mo_occ) ### Test OBDM calculation. nconf = 500 nsteps = 400 obdm_steps = 4 warmup = 15 wf = PySCFSlaterUHF(mol, mf) configs = initial_guess(mol, nconf) energy = EnergyAccumulator(mol) obdm = OBDMAccumulator(mol=mol, orb_coeff=lowdin, nsweeps=1) obdm_up = OBDMAccumulator(mol=mol, orb_coeff=lowdin, nsweeps=1, spin=0) obdm_down = OBDMAccumulator(mol=mol, orb_coeff=lowdin, nsweeps=1, spin=1) df, coords = vmc( wf, configs, nsteps=nsteps, accumulators={ "energy": energy, "obdm": obdm, "obdm_up": obdm_up, "obdm_down": obdm_down, }, ) df = DataFrame(df) obdm_est = {} for k in ["obdm", "obdm_up", "obdm_down"]: avg_norm = np.array(df.loc[warmup:, k + "norm"].values.tolist()).mean(axis=0) avg_obdm = np.array(df.loc[warmup:, k + "value"].values.tolist()).mean(axis=0) obdm_est[k] = normalize_obdm(avg_obdm, avg_norm) print("Average OBDM(orb,orb)", obdm_est["obdm"].diagonal().round(3)) print("mf obdm", mfobdm.diagonal().round(3)) assert np.max(np.abs(obdm_est["obdm"] - mfobdm)) < 0.05 print(obdm_est["obdm_up"].diagonal().round(3)) print(obdm_est["obdm_down"].diagonal().round(3)) assert np.mean( np.abs(obdm_est["obdm_up"] + obdm_est["obdm_down"] - mfobdm)) < 0.05
def test_pbc(li_cubic_ccecp): from pyqmc import supercell import scipy mol, mf = li_cubic_ccecp # S = np.ones((3, 3)) - np.eye(3) S = np.identity(3) mol = supercell.get_supercell(mol, S) kpts = supercell.get_supercell_kpts(mol)[:2] kdiffs = mf.kpts[np.newaxis] - kpts[:, np.newaxis] kinds = np.nonzero(np.linalg.norm(kdiffs, axis=-1) < 1e-12)[1] # Lowdin orthogonalized AO basis. # lowdin = lo.orth_ao(mol, "lowdin") loiao = lo.iao.iao(mol.original_cell, mf.mo_coeff, kpts=kpts) occs = [mf.mo_occ[k] for k in kinds] coefs = [mf.mo_coeff[k] for k in kinds] ovlp = mf.get_ovlp()[kinds] lowdin = [lo.vec_lowdin(l, o) for l, o in zip(loiao, ovlp)] lreps = [np.linalg.multi_dot([l.T, o, c]) for l, o, c in zip(lowdin, ovlp, coefs)] # make AO to localized orbital coefficients. mfobdm = [np.einsum("ij,j,kj->ik", l.conj(), o, l) for l, o in zip(lreps, occs)] ### Test OBDM calculation. nconf = 500 nsteps = 100 warmup = 6 wf = Slater(mol, mf) configs = initial_guess(mol, nconf) obdm_dict = dict(mol=mol, orb_coeff=lowdin, kpts=kpts, nsweeps=4, warmup=10) obdm = OBDMAccumulator(**obdm_dict) df, coords = vmc( wf, configs, nsteps=nsteps, accumulators={"obdm": obdm}, # , "obdm_up": obdm_up, "obdm_down": obdm_down}, verbose=True, ) obdm_est = {} for k in ["obdm"]: # , "obdm_up", "obdm_down"]: avg_norm = np.mean(df[k + "norm"][warmup:], axis=0) avg_obdm = np.mean(df[k + "value"][warmup:], axis=0) obdm_est[k] = normalize_obdm(avg_obdm, avg_norm) mfobdm = scipy.linalg.block_diag(*mfobdm) mae = np.mean(np.abs(obdm_est["obdm"] - mfobdm)) assert mae < 0.05, f"mae {mae}"
def test(): mol = gto.M(atom="Li 0. 0. 0.; Li 0. 0. 1.5", basis="sto-3g", unit="bohr", verbose=0) mf = scf.RHF(mol).run() # Lowdin orthogonalized AO basis. lowdin = lo.orth_ao(mol, "lowdin") # MOs in the Lowdin basis. mo = solve(lowdin, mf.mo_coeff) # make AO to localized orbital coefficients. mfobdm = mf.make_rdm1(mo, mf.mo_occ) ### Test OBDM calculation. nconf = 500 nsteps = 400 warmup = 15 wf = Slater(mol, mf) configs = initial_guess(mol, nconf) obdm_dict = dict(mol=mol, orb_coeff=lowdin, nsweeps=5, warmup=15) obdm = OBDMAccumulator(**obdm_dict) obdm_up = OBDMAccumulator(**obdm_dict, spin=0) obdm_down = OBDMAccumulator(**obdm_dict, spin=1) df, coords = vmc( wf, configs, nsteps=nsteps, accumulators={ "obdm": obdm, "obdm_up": obdm_up, "obdm_down": obdm_down }, ) obdm_est = {} for k in ["obdm", "obdm_up", "obdm_down"]: avg_norm = np.mean(df[k + "norm"][warmup:], axis=0) avg_obdm = np.mean(df[k + "value"][warmup:], axis=0) obdm_est[k] = normalize_obdm(avg_obdm, avg_norm) assert np.mean( np.abs(obdm_est["obdm_up"] + obdm_est["obdm_down"] - mfobdm)) < 0.05
def test(atom="He", total_spin=0, total_charge=0, scf_basis="sto-3g"): mol = gto.M( atom="%s 0. 0. 0.; %s 0. 0. 1.5" % (atom, atom), basis=scf_basis, unit="bohr", verbose=4, spin=total_spin, charge=total_charge, ) mf = scf.UHF(mol).run() # Intrinsic Atomic Orbitals iaos = make_separate_spin_iaos( mol, mf, np.array([i for i in range(mol.natm)]), iao_basis="minao" ) # iaos=make_combined_spin_iaos(mol,mf,np.array([i for i in range(mol.natm)]),iao_basis='minao') # MOs in the IAO basis mo = reps_combined_spin_iaos( iaos, mf, np.einsum("i,j->ji", np.arange(mf.mo_coeff[0].shape[1]), np.array([1, 1])), ) # Mean-field obdm in IAO basis mfobdm = mf.make_rdm1(mo, mf.mo_occ) # Mean-field tbdm in IAO basis mftbdm = singledet_tbdm(mf, mfobdm) ### Test TBDM calculation. # VMC params nconf = 500 n_vmc_steps = 400 vmc_tstep = 0.3 vmc_warmup = 30 # TBDM params tbdm_sweeps = 4 tbdm_tstep = 0.5 wf = PySCFSlater(mol, mf) # Single-Slater (no jastrow) wf configs = initial_guess(mol, nconf) energy = EnergyAccumulator(mol) obdm_up = OBDMAccumulator(mol=mol, orb_coeff=iaos[0], nsweeps=tbdm_sweeps, spin=0) obdm_down = OBDMAccumulator(mol=mol, orb_coeff=iaos[1], nsweeps=tbdm_sweeps, spin=1) tbdm_upup = TBDMAccumulator( mol=mol, orb_coeff=iaos, nsweeps=tbdm_sweeps, tstep=tbdm_tstep, spin=(0, 0) ) tbdm_updown = TBDMAccumulator( mol=mol, orb_coeff=iaos, nsweeps=tbdm_sweeps, tstep=tbdm_tstep, spin=(0, 1) ) tbdm_downup = TBDMAccumulator( mol=mol, orb_coeff=iaos, nsweeps=tbdm_sweeps, tstep=tbdm_tstep, spin=(1, 0) ) tbdm_downdown = TBDMAccumulator( mol=mol, orb_coeff=iaos, nsweeps=tbdm_sweeps, tstep=tbdm_tstep, spin=(1, 1) ) print("VMC...") df, coords = vmc( wf, configs, nsteps=n_vmc_steps, tstep=vmc_tstep, accumulators={ "energy": energy, "obdm_up": obdm_up, "obdm_down": obdm_down, "tbdm_upup": tbdm_upup, "tbdm_updown": tbdm_updown, "tbdm_downup": tbdm_downup, "tbdm_downdown": tbdm_downdown, }, verbose=True, ) # Compares obdm from QMC and MF obdm_est = {} for k in ["obdm_up", "obdm_down"]: avg_norm = np.mean(df[k + "norm"][vmc_warmup:], axis=0) avg_obdm = np.mean(df[k + "value"][vmc_warmup:], axis=0) obdm_est[k] = normalize_obdm(avg_obdm, avg_norm) qmcobdm = np.array([obdm_est["obdm_up"], obdm_est["obdm_down"]]) print("\nComparing QMC and MF obdm:") for s in [0, 1]: # print('QMC obdm[%d]:\n'%s,qmcobdm[s]) # print('MF obdm[%d]:\n'%s,mfobdm[s]) print("diff[%d]:\n" % s, qmcobdm[s] - mfobdm[s]) # Compares tbdm from QMC and MF avg_norm = {} avg_tbdm = {} tbdm_est = {} for t in ["tbdm_upup", "tbdm_updown", "tbdm_downup", "tbdm_downdown"]: for k in df.keys(): if k.startswith(t + "norm_"): avg_norm[k.split("_")[-1]] = np.mean(df[k][vmc_warmup:], axis=0) if k.startswith(t + "value"): avg_tbdm[k.split("_")[-1]] = np.mean(df[k][vmc_warmup:], axis=0) for k in avg_tbdm: tbdm_est[k] = normalize_tbdm( avg_tbdm[k].reshape(2, 2, 2, 2), avg_norm["a"], avg_norm["b"] ) qmctbdm = np.array( [ [tbdm_est["upupvalue"], tbdm_est["updownvalue"]], [tbdm_est["downupvalue"], tbdm_est["downdownvalue"]], ] ) print("\nComparing QMC and MF tbdm:") for sa, sb in [[0, 0], [0, 1], [1, 0], [1, 1]]: # print('QMC tbdm[%d,%d]:\n'%(sa,sb),qmctbdm[sa,sb]) # print('MF tbdm[%d,%d]:\n'%(sa,sb),mftbdm[sa,sb]) diff = qmctbdm[sa, sb] - mftbdm[sa, sb] print("diff[%d,%d]:\n" % (sa, sb), diff) assert np.max(np.abs(diff)) < 0.05
def test_pbc(): from pyscf.pbc import gto, scf from pyqmc import PySCFSlaterUHF, PySCFSlaterPBC from pyqmc import slaterpbc import scipy lvecs = (np.ones((3, 3)) - np.eye(3)) * 2.0 mol = gto.M( atom="H 0. 0. -{0}; H 0. 0. {0}".format(0.7), basis="sto-3g", unit="bohr", verbose=0, a=lvecs, ) mf = scf.KRHF(mol, kpts=mol.make_kpts((2, 2, 2))) mf = mf.run() S = np.ones((3, 3)) - 2 * np.eye(3) mol = slaterpbc.get_supercell(mol, S) kpts = slaterpbc.get_supercell_kpts(mol)[:2] kdiffs = mf.kpts[np.newaxis] - kpts[:, np.newaxis] kinds = np.nonzero(np.linalg.norm(kdiffs, axis=-1) < 1e-12)[1] # Lowdin orthogonalized AO basis. # lowdin = lo.orth_ao(mol, "lowdin") loiao = lo.iao.iao(mol.original_cell, mf.mo_coeff, kpts=kpts) occs = [mf.mo_occ[k] for k in kinds] coefs = [mf.mo_coeff[k] for k in kinds] ovlp = mf.get_ovlp()[kinds] lowdin = [lo.vec_lowdin(l, o) for l, o in zip(loiao, ovlp)] lreps = [np.linalg.multi_dot([l.T, o, c]) for l, o, c in zip(lowdin, ovlp, coefs)] # make AO to localized orbital coefficients. mfobdm = [np.einsum("ij,j,kj->ik", l.conj(), o, l) for l, o in zip(lreps, occs)] ### Test OBDM calculation. nconf = 800 nsteps = 50 warmup = 6 wf = PySCFSlaterPBC(mol, mf) configs = initial_guess(mol, nconf) obdm_dict = dict(mol=mol, orb_coeff=lowdin, kpts=kpts, nsweeps=4, warmup=10) obdm = OBDMAccumulator(**obdm_dict) obdm_up = OBDMAccumulator(**obdm_dict, spin=0) obdm_down = OBDMAccumulator(**obdm_dict, spin=1) df, coords = vmc( wf, configs, nsteps=nsteps, accumulators={"obdm": obdm, "obdm_up": obdm_up, "obdm_down": obdm_down}, verbose=True, ) df = DataFrame(df) obdm_est = {} for k in ["obdm", "obdm_up", "obdm_down"]: avg_norm = np.array(df.loc[warmup:, k + "norm"].values.tolist()).mean(axis=0) avg_obdm = np.array(df.loc[warmup:, k + "value"].values.tolist()).mean(axis=0) obdm_est[k] = normalize_obdm(avg_obdm, avg_norm) print("Average OBDM(orb,orb)", obdm_est["obdm"].round(3)) mfobdm = scipy.linalg.block_diag(*mfobdm) print("mf obdm", mfobdm.round(3)) max_abs_err = np.max(np.abs(obdm_est["obdm"] - mfobdm)) assert max_abs_err < 0.05, "max abs err {0}".format(max_abs_err) print(obdm_est["obdm_up"].diagonal().round(3)) print(obdm_est["obdm_down"].diagonal().round(3)) mae = np.mean(np.abs(obdm_est["obdm_up"] + obdm_est["obdm_down"] - mfobdm)) maup = np.mean(np.abs(obdm_est["obdm_up"])) madn = np.mean(np.abs(obdm_est["obdm_down"])) mamf = np.mean(np.abs(mfobdm)) assert mae < 0.05, "mae {0}\n maup {1}\n madn {2}\n mamf {3}".format( mae, maup, madn, mamf )