arXiv subjects

Gustavo E. Scuseria

Publications and source records attributed to Gustavo E. Scuseria.

At least 109 records · Page 6Linked to original sources

arXiv2013

Density Functionals that Recognize Covalent, Metallic, and Weak Bonds

Computationally-efficient semilocal approximations of density functional theory at the level of the local spin density approximation (LSDA) or generalized gradient approximation (GGA) poorly describe weak interactions. We show improved descriptions for weak bonds (without loss of accuracy for strong ones) from a newly-developed semilocal meta-GGA (MGGA), by applying it to molecules, surfaces, and solids. We argue that this improvement comes from using the right MGGA dimensionless ingredient to recognize all types of orbital overlap.

cond-mat.mtrl-sci↗

arXiv2013

On pair functions for strong correlations

The UHF wave function may be written as a spin-contaminated \textit{pair} wave function of the APSG form, and the overlap of the alpha and beta corresponding orbitals of the UHF solution can be taken as a proxy for the strength of the correlation captured by breaking symmetry. We demonstrate this with calculations on one- and two-dimensional hydrogen clusters and make contact with the well studied Hubbard model. The UHF corresponding orbitals pair in a manner that allows a smooth evolution from doubly occupied orbitals at small distance to one in which wave function breaks symmetry, segregating the $α$ and $β$ electrons onto distinct sublattices at large distances. By performing spin projection on these UHF solutions, we address strong correlations that are difficult to capture at intermediate distances using a single determinant. Approved for public release: LA-UR-13-22691.

cond-mat.str-el↗

arXiv2013

Renormalized Second-order Perturbation Theory for The Electron Correlation Energy: Concept, Implementation, and Benchmarks

We present a renormalized second-order perturbation theory (rPT2), based on a Kohn-Sham (KS) reference state, for the electron correlation energy that includes the random-phase approximation (RPA), second-order screened exchange (SOSEX), and renormalized single excitations (rSE). These three terms all involve a summation of certain types of diagrams to infinite order, and can be viewed as "renormalization" of the 2nd-order direct, exchange, and single excitation (SE) terms of Rayleigh-Schrödinger perturbation theory based on an KS reference. In this work we establish the concept of rPT2 and present the numerical details of our SOSEX and rSE implementations. A preliminary version of rPT2, in which the renormalized SE (rSE) contribution was treated approximately, has already been benchmarked for molecular atomization energies and chemical reaction barrier heights and shows a well balanced performance [Paier et al, New J. Phys. 14, 043002 (2012)]. In this work, we present a refined version of rPT2, in which we evaluate the rSE series of diagrams rigorously. We then extend the benchmark studies to non-covalent interactions, including the rare-gas dimers, and the S22 and S66 test sets. Despite some remaining shortcomings, we conclude that rPT2 gives an overall satisfactory performance across different chemical environments, and is a promising step towards a generally applicable electronic structure approach.

cond-mat.other↗

arXiv2013

Semilocal and Hybrid Meta-Generalized Gradient Approximations Based on the Understanding of the Kinetic-Energy-Density Dependence

We present a global hybrid meta-generalized gradient approximation (meta-GGA) with three empirical parameters, as well as its underlying semilocal meta-GGA and a meta-GGA with only one empirical parameter. All of them are based on the new meta-GGA resulting from the understanding of kinetic-energy-density dependence [J. Chem. Phys. 137, 051101 (2012)]. The obtained functionals show robust performances on the considered molecular systems for the properties of heats of formation, barrier heights, and noncovalent interactions. The pair-wise additive dispersion corrections to the functionals are also presented.

physics.chem-ph↗

arXiv2012

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 ($Δ_{CF}$) 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 $Δ_{CF}$ 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.

cond-mat.str-el↗

arXiv2012

N-electron Slater determinants from non-unitary canonical transformations of fermion operators

Mean-field methods such as Hartree-Fock (HF) or Hartree-Fock-Bogoliubov (HFB) constitute the building blocks upon which more elaborate many-body theories are based on. The HF and HFB wavefunctions are built out of independent quasi-particles resulting from a unitary linear canonical transformation of the elementary fermion operators. Here, we discuss the possibility of allowing the HF transformation to become non-unitary. The properties of such HF vacua are discussed, as well as the evaluation of matrix elements among such states. We use a simple ansatz to demonstrate that a non-unitary transformation brings additional flexibility that can be exploited in variational approximations to many-fermion wavefunctions. The action of projection operators on non-unitary based HF states is also discussed and applied to the one-dimensional Hubbard model with periodic boundary conditions.

cond-mat.str-el↗

arXiv2012

Symmetry-projected variational approach for ground and excited states of the two-dimensional Hubbard model

We present a symmetry-projected configuration mixing scheme to describe ground and excited states, with well defined quantum numbers, of the two-dimensional Hubbard model with nearestneighbor hopping and periodic boundary conditions. Results for the half-filled 2{\times}4, 4{\times}4, and 6{\times}6 lattices, as well as doped 4 {\times} 4 systems, compare well with available results, both exact and from other state-of-the-art approximations. We report spectral functions and density of states obtained from a well-controlled ansatz for the (Ne {\pm} 1)-electron system. Symmetry projected methods have been widely used for the many-body nuclear physics problem but have received little attention in the solid state community. Given their relatively low (mean-field) computational cost and the high quality of results here reported, we believe that they deserve further scrutiny.

cond-mat.str-el↗

arXiv2012

Assessment of correlation energies based on the random-phase approximation

The random-phase approximation to the ground state correlation energy (RPA) in combination with exact exchange (EX) has brought Kohn-Sham (KS) density functional theory one step closer towards a universal, "general purpose first principles method". In an effort to systematically assess the influence of several correlation energy contributions beyond RPA, this work presents dissociation energies of small molecules and solids, activation energies for hydrogen transfer and non-hydrogen transfer reactions, as well as reaction energies for a number of common test sets. We benchmark EX+RPA and several flavors of energy functionals going beyond it: second-order screened exchange (SOSEX), single excitation (SE) corrections, renormalized single excitation (rSE) corrections, as well as their combinations. Both the single excitation correction as well as the SOSEX contribution to the correlation energy significantly improve upon the notorious tendency of EX+RPA to underbind. Surprisingly, activation energies obtained using EX+RPA based on a KS reference alone are remarkably accurate. RPA+SOSEX+rSE provides an equal level of accuracy for reaction as well as activation energies and overall gives the most balanced performance, which makes it applicable to a wide range of systems and chemical reactions.

cond-mat.mtrl-sci↗

arXiv2012

Projected Hartree-Fock Theory

Projected Hartree-Fock theory (PHF) has a long history in quantum chemistry. PHF is here understood as the variational determination of an N-electron broken symmetry Slater determinant that minimizes the energy of a projected state with the correct quantum numbers. The method was actively pursued for several decades but seems to have been abandoned. We here derive and implement a "variation after projection" PHF theory using techniques different from those previously employed in quantum chemistry. Our PHF methodology has modest mean-field computational cost, yields relatively simple expressions, can be applied to both collinear and non-collinear spin cases, and can be used in conjunction with deliberate symmetry breaking and restoration of other molecular symmetries like complex conjugation and point group. We present several benchmark applications to dissociation curves and singlet-triplet energy splittings, showing that the resulting PHF wavefunctions are of high quality multireference character. We also provide numerical evidence that in the thermodynamic limit, the energy in PHF is not lower than that of broken-symmetry HF, a simple consequence of the lack of size consistency and extensivity of PHF.

cond-mat.str-el↗

arXiv2011

Improved Semiconductor Lattice Parameters and Band Gaps from a Middle-Range Screened Hybrid Functional

We show that the middle-range exchange-correlation hybrid of Henderson, Izmaylov, Scuseria and Savin (HISS) performs extremely well for elemental and binary semiconductors with narrow or visible spectrum band gaps, as well as some wider gap or more ionic systems used commercially. The lattice parameters are superior to those predicted by the screened hybrid functional of Heyd, Scuseria and Ernzerhof (HSE), and provide a significant improvement over geometries predicted by semilocal functionals. HISS also yields band gaps superior to those produced by functionals developed specifically for the solid state. Timings indicate that HISS is more computationally efficient than HSE, implying that the high quality lattice constants coupled with improved optical band gap predictions render HISS a useful adjunct to HSE in the modeling of geometry-sensitive semiconductors.

cond-mat.mtrl-sci↗

arXiv2011

Projected Quasiparticle Theory for Molecular Electronic Structure

We derive and implement symmetry-projected Hartree-Fock-Bogoliubov (HFB) equations and apply them to the molecular electronic structure problem. All symmetries (particle number, spin, spatial, and complex conjugation) are deliberately broken and restored in a self-consistent variation-after-projection approach. We show that the resulting method yields a comprehensive black-box treatment of strong correlations with effective one-electron (mean-field) computational cost. The ensuing wave function is of multireference character and permeates the entire Hilbert space of the problem. The energy expression is different from regular HFB theory but remains a functional of an independent quasiparticle density matrix. All reduced density matrices are expressible as an integration of transition density matrices over a gauge grid. We present several proof-of-principle examples demonstrating the compelling power of projected quasiparticle theory for electronic structure theory.

cond-mat.str-el↗

arXiv2011

Computing the energy of a water molecule using MultiDeterminants: A simple, efficient algorithm

Quantum Monte Carlo (QMC) methods such as variational Monte Carlo and fixed node diffusion Monte Carlo depend heavily on the quality of the trial wave function. Although Slater-Jastrow wave functions are the most commonly used variational ansatz in electronic structure, more sophisticated wave-functions are critical to ascertaining new physics. One such wave function is the multiSlater-Jastrow wave function which consists of a Jastrow function multiplied by the sum of Slater determinants. In this paper we describe a method for working with these wavefunctions in QMC codes that is easy to implement, efficient both in computational speed as well as memory, and easily parallelized. The computational cost scales quadratically with particle number making this scaling no worse than the single determinant case and linear with the total number of excitations. Additionally we implement this method and use it to compute the ground state energy of a water molecule.

cond-mat.mtrl-sci↗

arXiv2011

Accurate Modeling of the Cubic and Antiferrodistortive Phases of SrTiO3 with Screened Hybrid Density Functional Theory

We have calculated the properties of SrTiO3 (STO) using a wide array of density functionals ranging from standard semi-local functionals to modern range-separated hybrids, combined with several basis sets of varying size/quality. We show how these combination's predictive ability varies significantly, both for STO's cubic and antiferrodistortive (AFD) phases, with the greatest variation in functional/basis set efficacy seen in modeling the AFD phase. The screened hybrid functionals we utilized predict the structural properties of both phases in very good agreement with experiment, especially if used with large (but still computationally tractable) basis sets. The most accurate results presented in this study, namely those from HSE06/modified-def2-TZVP, stand as the most accurate modeling of STO to date when compared to the literature; these results agree well with experimental structural and electronic properties as well as providing insight into the band structure alteration during the phase transition.

physics.comp-ph↗

arXiv2010

Constrained-Pairing Mean-Field Theory. IV. Inclusion of corresponding pair constraints and connection to unrestricted Hartree-Fock theory

Our previously developed Constrained-Pairing Mean-Field Theory (CPMFT) is shown to map onto an Unrestricted Hartree-Fock (UHF) type method if one imposes a corresponding pair constraint to the correlation problem that forces occupation numbers to occur in pairs adding to 1. In this new version, CPMFT has all the advantages of standard independent particle models (orbitals and orbital energies, to mention a few), yet unlike UHF, it can dissociate polyatomic molecules to the correct ground-state restricted open-shell Hartree-Fock atoms or fragments.

cond-mat.str-el↗

arXiv2010

ROHF Theory Made Simple

Restricted open-shell Hartree-Fock (ROHF) theory is formulated as a projected self-consistent unrestricted HF (UHF) model by mathematically constraining spin density eigenvalues. The resulting constrained UHF (CUHF) wave function is identical to that obtained from Roothaan's effective Fock operator. Our $α$ and $β$ CUHF Fock operators are parameter-free and have canonical orbitals and orbital energies that are physically meaningful as in UHF, except for eliminating spin contamination. The present approach removes ambiguities in ROHF orbital energies and the non-uniqueness of methods that build upon them. We present benchmarks to demonstrate CUHF physical correctness and good agreement with experimental results.

cond-mat.str-el↗

arXiv2009

Accurate Hartree-Fock energy of extended systems using large Gaussian basis sets

Calculating highly accurate thermochemical properties of condensed matter via wave function-based approaches (such as e.g. Hartree-Fock or hybrid functionals) has recently attracted much interest. We here present two strategies providing accurate Hartree-Fock energies for solid LiH in a large Gaussian basis set and applying periodic boundary conditions. The total energies were obtained using two different approaches, namely a supercell evaluation of Hartree-Fock exchange using a truncated Coulomb operator and an extrapolation toward the full-range Hartree-Fock limit of a Padé fit to a series of short-range screened Hartree-Fock calculations. These two techniques agreed to significant precision. We also present the Hartree-Fock cohesive energy of LiH (converged to within sub-meV) at the experimental equilibrium volume as well as the Hartree-Fock equilibrium lattice constant and bulk modulus.

cond-mat.mtrl-sci↗

arXiv2009

Strong correlations via constrained-pairing mean-field theory

We present a mean-field approach for accurately describing strong correlations via electron number fluctuations and pairings constrained to an active space. Electron number conservation is broken and correct only on average but both spin and spatial symmetries are preserved. Optimized natural orbitals and occupations are determined by diagonalization of a mean-field Hamiltonian. This constrained-pairing mean-field theory (CPMFT) yields a two-particle density matrix ansatz that exclusively describe strong correlations. We demonstrate CPMFT accuracy with applications to the metal-insulator transition of large hydrogen clusters and molecular dissociation curves.

cond-mat.mtrl-sci↗

arXiv2009

Electromechanical properties of suspended Graphene Nanoribbons

Graphene nanoribbons present diverse electronic properties ranging from semiconducting to half-metallic, depending on their geometry, dimensions and chemical composition. Here we present a route to control these properties via externally applied mechanical deformations. Using state-of-the-art density functional theory calculations combined with classical elasticity theory considerations, we find a remarkable Young's modulus value of ~7 TPa for ultra-narrow graphene strips and a pronounced electromechanical response towards bending and torsional deformations. Given the current advances in the synthesis of nanoscale graphene derivatives, our predictions can be experimentally verified opening the way to the design and fabrication of miniature electromechanical sensors and devices based on ultra-narrow graphene nanoribbons.

cond-mat.mes-hall↗