Browsing by Author "Bulik, Ireneusz W."
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Item Blind test of density-functional-based methods on intermolecular interaction energies(AIP Publishing LLC., 2016) Taylor, DeCarlos E.; Ángyán, János G.; Galli, Giulia; Zhang, Cui; Gygi, Francois; Hirao, Kimihiko; Song, Jong Won; Rahul, Kar; von Lilienfeld, O. Anatole; Podeszwa, Rafał; Bulik, Ireneusz W.; Henderson, Thomas M.; Scuseria, Gustavo E.; Toulouse, Julien; PIn the past decade, a number of approaches have been developed to fix the failure of (semi)local density-functional theory (DFT) in describing intermolecular interactions. The performance of several such approaches with respect to highly accurate benchmarks is compared here on a set of separation-dependent interaction energies for ten dimers. Since the benchmarks were unknown before the DFT-based results were collected, this comparison constitutes a blind test of these methods.Item Density matrix embedding from broken symmetry lattice mean fields(American Physical Society, 2014) Bulik, Ireneusz W.; Scuseria, Gustavo E.; Dukelsky, JorgeSeveral variants of the recently proposed density matrix embedding theory (DMET) [G. Knizia and G. K-L. Chan, Phys. Rev. Lett. 109, 186404 (2012)] are formulated and tested. We show that spin symmetry breaking of the lattice mean-field allows precise control of the lattice and fragment filling while providing very good agreement between predicted properties and exact results. We present a rigorous proof that at convergence this method is guaranteed to preserve lattice and fragment filling. Differences arising from fitting the fragment one-particle density matrix alone versus fitting fragment plus bath are scrutinized. We argue that it is important to restrict the density matrix fitting to solely the fragment. Furthermore, in the proposed broken symmetry formalism, it is possible to substantially simplify the embedding procedure without sacrificing its accuracy by resorting to density instead of density matrix fitting. This simplified density embedding theory (DET) greatly improves the convergence properties of the algorithm.Item Electron correlation in solids via density embedding theory(AIP Publishing, 2014) Bulik, Ireneusz W.; Chen, Weibing; Scuseria, Gustavo E.Density matrix embeddingﾠtheoryﾠ[G. Knizia and G. K.-L. Chan,ﾠPhys. Rev. Lett.109, 186404 (2012)] and density embeddingﾠtheoryﾠ[I. W. Bulik, G. E. Scuseria, and J. Dukelsky,ﾠPhys. Rev. Bﾠ89, 035140 (2014)] have recently been introduced for model lattice Hamiltonians and molecular systems. In the present work, the formalism is extended to theﾠab initioﾠdescription of infinite systems. An appropriate definition of the impurity Hamiltonian for such systems is presented and demonstrated in cases of 1, 2, and 3 dimensions, usingﾠcoupled clusterﾠtheoryﾠas the impurity solver. Additionally, we discuss the challenges related to disentanglement of fragment and bath states. The current approach yields results comparable toﾠcoupled clusterﾠcalculations of infinite systems even when using a single unit cell as the fragment. Theﾠtheoryﾠis formulated in the basis of Wannier functions but it does not require separate localization of unoccupied bands. The embedding scheme presented here is a promising way of employing highly accurate electronic structure methods for extended systems at a fraction of their original computational cost.Item Noncollinear density functional theory having proper invariance and local torque properties(American Physical Society, 2013) Bulik, Ireneusz W.; Scalmani, Giovanni; Frisch, Michael J.Noncollinear spins are among the most interesting features of magnetic materials, and their accurate description is a central goal of density functional theory applied to periodic solids. However, these calculations typically yield a magnetization vector that is everywhere parallel to the exchange-correlation magnetic field. No meaningful description of spin dynamics can emerge from a functional constrained to have vanishing local magnetic torque. In this contribution we present a generalization to periodic systems of the extension of exchange-correlation functionals to the noncollinear regime, proposed by Scalmani and Frisch [J. Chem. Theory Comput. 8, 2193 (2012)]. This extension does afford a nonvanishing local magnetic torque and is free of numerical instabilities. As illustrative examples, we discuss frustrated triangular and kagome lattices evaluated with various density functionals, including screened hybrid functionals.Item Pair extended coupled cluster doubles(AIP Publishing LLC., 2015) Henderson, Thomas M.; Bulik, Ireneusz W.; Scuseria, Gustavo E.The accurate and efficient description of strongly correlated systems remains an important challenge for computational methods. Doubly occupied configuration interaction (DOCI), in which all electrons are paired and no correlations which break these pairs are permitted, can in many cases provide an accurate account of strong correlations, albeit at combinatorial computational cost. Recently, there has been significant interest in a method we refer to as pair coupled cluster doubles (pCCD), a variant of coupled cluster doubles in which the electrons are paired. This is simply because pCCD provides energies nearly identical to those of DOCI, but at mean-field computational cost (disregarding the cost of the two-electron integral transformation). Here, we introduce the more complete pair extended coupled cluster doubles (pECCD) approach which, like pCCD, has mean-field cost and reproduces DOCI energetically. We show that unlike pCCD, pECCD also reproduces the DOCI wave function with high accuracy. Moreover, pECCD yields sensible albeit inexact results even for attractive interactions where pCCD breaks down.Item Particle-particle and quasiparticle random phase approximations: Connections to coupled cluster theory(American Institute of Physics, 2013) Scuseria, Gustavo E.; Henderson, Thomas M.; Bulik, Ireneusz W.We establish a formal connection between the particle-particle (pp) random phase approximation (RPA) and the ladder channel of the coupled cluster doubles (CCD) equations. The relationship between RPA and CCD is best understood within a Bogoliubov quasiparticle (qp) RPA formalism. This work is a follow-up to our previous formal proof on the connection between particle-hole (ph) RPA and ring-CCD. Whereas RPA is a quasibosonic approximation, CC theory is a “correct bosonization” in the sense that the wavefunction and Hilbert space are exactly fermionic, yet the amplitude equations can be interpreted as adding different quasibosonic RPA channels together. Coupled cluster theory achieves this goal by interacting the ph (ring) and pp (ladder) diagrams via a third channel that we here call “crossed-ring” whose presence allows for full fermionic antisymmetry. Additionally, coupled cluster incorporates what we call “mosaic” terms which can be absorbed into defining a new effective one-body Hamiltonian. The inclusion of these mosaic terms seems to be quite important. The pp-RPA and qp-RPA equations are textbook material in nuclear structure physics but are largely unknown in quantum chemistry, where particle number fluctuations and Bogoliubov determinants are rarely used. We believe that the ideas and connections discussed in this paper may help design improved ways of incorporating RPA correlation into density functionals based on a CC perspective.Item Proper and improper zero energy modes in Hartree-Fock theory and their relevance for symmetry breaking and restoration(American Institute of Physics, 2013) Cui, Yao; Bulik, Ireneusz W.; Jiménez-Hoyos, Carlos A.; Henderson, Thomas M.; Scuseria, Gustavo E.We study the spectra of the molecular orbital Hessian (stability matrix) and random-phase approximation (RPA) Hamiltonian of broken-symmetry Hartree-Fock solutions, focusing on zero eigenvalue modes. After all negative eigenvalues are removed from the Hessian by following their eigenvectors downhill, one is left with only positive and zero eigenvalues. Zero modes correspond to orbital rotations with no restoring force. These rotations determine states in the Goldstone manifold, which originates from a spontaneously broken continuous symmetry in the wave function. Zero modes can be classified as improper or proper according to their different mathematical and physical properties. Improper modes arise from symmetry breaking and their restoration always lowers the energy. Proper modes, on the other hand, correspond to degeneracies of the wave function, and their symmetry restoration does not necessarily lower the energy. We discuss how the RPA Hamiltonian distinguishes between proper and improper modes by doubling the number of zero eigenvalues associated with the latter. Proper modes in the Hessian always appear in pairs which do not double in RPA. We present several pedagogical cases exemplifying the above statements. The relevance of these results for projected Hartree-Fock methods is also addressed.Item Semilocal exchange hole with an application to range-separated density functionals(American Physical Society, 2017) Tao, Jianmin; Bulik, Ireneusz W.; Scuseria, Gustavo E.The exchange-correlation hole is a central concept in density functional theory. It not only provides justification for an exchange-correlation energy functional but also serves as a local ingredient for nonlocal range-separated density functionals. However, due to the nonlocal nature, modeling the conventional exact exchange hole presents a great challenge to density functional theory. In this work, we propose a semilocal exchange hole underlying the Tao-Perdew-Staroverov-Scuseria (TPSS) meta-generalized gradient approximation functional. Our model is distinct from previous ones not only at small separation between an electron and the hole around the electron but also in the way it interpolates between rapidly varying and slowly varying densities. Here the interpolation is determined by the wave-vector analysis on the infinite-barrier model for a jellium surface. Numerical tests show that our exchange-hole model mimics the conventional exact one quite well for atoms. As a simple application, we apply the hole model to construct a TPSS-based range-separated functional. We find that this range-separated functional can substantially improve the band gaps and barrier heights of TPSS, without losing much accuracy for atomization energies.Item Seniority-based coupled cluster theory(AIP Publishing, 2014) Henderson, Thomas M.; Bulik, Ireneusz W.; Stein, Tamar; Scuseria, Gustavo E.Doubly occupied configuration interaction (DOCI) with optimized orbitals often accurately describes strong correlations while working in a Hilbert space much smaller than that needed for full configuration interaction. However, the scaling of such calculations remains combinatorial with system size. Pair coupled cluster doubles (pCCD) is very successful in reproducing DOCI energetically, but can do so with low polynomial scaling (N3, disregarding the two-electron integral transformation from atomic to molecular orbitals). We show here several examples illustrating the success of pCCD in reproducing both the DOCI energy and wave function and show how this success frequently comes about. What DOCI and pCCD lack are an effective treatment of dynamic correlations, which we here add by including higher-seniority cluster amplitudes which are excluded from pCCD. This frozen pair coupled cluster approach is comparable in cost to traditional closed-shell coupled cluster methods with results that are competitive for weakly correlated systems and often superior for the description of strongly correlated systems.Item Solutions of the Two-Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms(American Physical Society, 2015) LeBlanc, J.P.F.; Antipov, Andrey E.; Becca, Federico; Bulik, Ireneusz W.; Chan, Garnet Kin-Lic; Chung, Chia-Min; Deng, Youjin; Ferrero, Michel; Henderson, Thomas M.; Jiménez-Hoyos, Carlos A.; Kozik, E.; Liu, Xuan-Wen; Millis, Andrew J.; Prokof’ev, N.V.; Qin, Mingpu; Scuseria, Gustavo E.; Shi, Hao; Svistunov, B.V.; Tocchio, Luca F.; Tupitsyn, I.S.; White, Steven R.; Zhang, Shiwei; Zheng, Bo-Xiao; Zhu, Zhenyue; Gull, Emanuel; Simons Collaboration on the Many-Electron ProblemNumerical results for ground-state and excited-state properties (energies, double occupancies, and Matsubara-axis self-energies) of the single-orbital Hubbard model on a two-dimensional square lattice are presented, in order to provide an assessment of our ability to compute accurate results in the thermodynamic limit. Many methods are employed, including auxiliary-field quantum Monte Carlo, bare and bold-line diagrammatic Monte Carlo, method of dual fermions, density matrix embedding theory, density matrix renormalization group, dynamical cluster approximation, diffusion Monte Carlo within a fixed-node approximation, unrestricted coupled cluster theory, and multireference projected Hartree-Fock methods. Comparison of results obtained by different methods allows for the identification of uncertainties and systematic errors. The importance of extrapolation to converged thermodynamic-limit values is emphasized. Cases where agreement between different methods is obtained establish benchmark results that may be useful in the validation of new approaches and the improvement of existing methods.Item Structural phase transitions of the metal oxide perovskites SrTiO3, LaAlO3, and LaTiO3 studied with a screened hybrid functional(American Physical Society, 2013) El-Mellouhi, Fedwa; Brothers, Edward N.; Lucerno, Melissa J.; Bulik, Ireneusz W.; Scuseria, Gustavo E.We have investigated the structural phase transitions of the transition metal oxide perovskites SrTiO3, LaAlO3, and LaTiO3 using the screened hybrid density functional of Heyd, Scuseria, and Ernzerhof (HSE06). We show that HSE06-computed lattice parameters, octahedral tilts, and rotations, as well as electronic properties, are significantly improved over semilocal functionals. We predict the crystal-field splitting (ΔCF) resulting from the structural phase transition in SrTiO3 and LaAlO3 to be 3 meV and 10 meV, respectively, in excellent agreement with experimental results. HSE06 identifies correctly LaTiO3 in the magnetic states as a Mott insulator. Also, it predicts that the GdFeO3-type distortion in nonmagnetic LaTiO3 will induce a large ΔCF of 410 meV. This large crystal-field splitting associated with the large magnetic moment found in the G-type antiferromagnetic state suggests that LaTiO3 has an induced orbital order, which is confirmed by the visualization of the highest occupied orbitals. These results strongly indicate that HSE06 is capable of efficiently and accurately modeling perovskite oxides and promises to efficiently capture the physics at their heterointerfaces.Item Synergy between pair coupled cluster doubles and pair density functional theory(AIP Publishing, 2015) Garza, Alejandro J.; Bulik, Ireneusz W.; Henderson, Thomas M.; Scuseria, Gustavo E.Pair coupled cluster doubles (pCCD) has been recently studied as a method capable of accounting for static correlation with low polynomial cost. We present three combinations of pCCD with Kohn–Sham functionals of the density and on-top pair density (the probability of finding two electrons on top of each other) to add dynamic correlation to pCCD without double counting. With a negligible increase in computational cost, these pCCD+DFT blends greatly improve upon pCCD in the description of typical problems where static and dynamic correlations are both important. We argue that—as a black-box method with low scaling, size-extensivity, size-consistency, and a simple quasidiagonal two-particle density matrix—pCCD is an excellent match for pair density functionals in this type of fusion of multireference wavefunctions with DFT.