Pair extended coupled cluster doubles

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. Moreoever, pECCD yields sensible albeit inexact results even for attractive interactions where pCCD breaks down.Comment: submitted manuscrip

Electron correlation in solids via density embedding theory

Density matrix embedding theory (Phys. Rev. Lett. 109, 186404 (2012)) and density embedding theory ((Phys. Rev. B 89, 035140 (2014)) have recently been introduced for model lattice Hamiltonians and molecular systems. In the present work, the formalism is extended to the ab initio description 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, using coupled cluster theory as the impurity solver. Additionally, we discuss the challenges related to disentanglement of fragment and bath states. The current approach yields results comparable to coupled cluster calculations of infinite systems even when using a single unit cell as the fragment. The theory is 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

Semilocal exchange hole with an application to range-separated density functionals

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

Density matrix embedding from broken symmetry lattice mean fields

12 pags. ; 7 figs. ; 3 tabs. ; App. ; PACS number(s): 71.10.Fd, 71.27.+a, 71.30.+hSeveral variants of the recently proposed density matrix embedding theory (DMET) [G. Knizia and G. K-L. Chan, Phys. Rev. Lett. 109, 186404 (2012)PRLTAO0031-900710.1103/PhysRevLett.109.186404] 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. © 2014 American Physical Society.This work was supported by the Department of Energy, Office of Basic Energy Sciences, Heavy Element Chemistry program, under Grant No. DE-FG02-04ER15523. G.E.S. is a Welch Foundation Chair (C-0036). J.D. acknowledges support from the Spanish Ministry of Economy and Competitiveness under Grant FIS2012-34479.Peer Reviewe

Noncollinear density functional theory having proper invariance and local torque properties

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

Particle-particle and quasiparticle random phase approximations: Connections to coupled cluster theory

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. 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 an d 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

Structural Phase Transitions of the Metal Oxide Perovskites SrTiO3, LaAlO3 and LaTiO3 Studied with a Screened Hybrid Functional

We have investigated the structural phase transitions of the transition metal oxide perovskites SrTiO$_{3}$, LaAlO$_{3}$ and LaTiO$_{3}$ 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 ($\Delta_{CF}$) resulting from the structural phase transition in SrTiO$_{3}$ and LaAlO$_{3}$ to be 3 meV and 10 meV, respectively, in excellent agreement with experimental results. HSE06 identifies correctly LaTiO$_{3}$ in the magnetic sates as a Mott insulator. Also, it predicts that the GdFeO$_{3}$-type distortion in non-magnetic LaTiO$_{3}$ will induce a large $\Delta_{CF}$ of 410 meV. This large crystal-field splitting associated with the large magnetic moment found in the G-type antiferromagnetic state suggest that LaTiO$_{3}$ has an induced orbital order, which is confirmed by the visualisation 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