Gustavo E. Scuseria

Hybrid functionals based on a screened Coulomb potential

Hybrid density functionals are very successful in describing a wide range of molecular properties accurately. In large molecules and solids, however, calculating the exact (Hartree–Fock) exchange is computationally expensive, especially for systems with metallic characteristics. In the present work, we develop a new hybrid density functional based on a screened Coulomb potential for the exchange interaction which circumvents this bottleneck. The results obtained for structural and thermodynamic properties of molecules are comparable in quality to the most widely used hybrid functionals. In addition, we present results of periodic boundary condition calculations for both semiconducting and metallic single wall carbon nanotubes. Using a screened Coulomb potential for Hartree–Fock exchange enables fast and accurate hybrid calculations, even of usually difficult metallic systems. The high accuracy of the new screened Coulomb potential hybrid, combined with its computational advantages, makes it widely applica...

Crystalline Ropes of Metallic Carbon Nanotubes

Fullerene single-wall nanotubes (SWNTs) were produced in yields of more than 70 percent by condensation of a laser-vaporized carbon-nickel-cobalt mixture at 1200°C. X-ray diffraction and electron microscopy showed that these SWNTs are nearly uniform in diameter and that they self-organize into “ropes,” which consist of 100 to 500 SWNTs in a two-dimensional triangular lattice with a lattice constant of 17 angstroms. The x-ray form factor is consistent with that of uniformly charged cylinders 13.8 ± 0.2 angstroms in diameter. The ropes were metallic, with a single-rope resistivity of <10−4 ohm-centimeters at 300 kelvin. The uniformity of SWNT diameter is attributed to the efficient annealing of an initial fullerene tubelet kept open by a few metal atoms; the optimum diameter is determined by competition between the strain energy of curvature of the graphene sheet and the dangling-bond energy of the open edge, where growth occurs. These factors strongly favor the metallic (10,10) tube with C5v symmetry and an open edge stabilized by triple bonds.

An efficient implementation of time-dependent density-functional theory for the calculation of excitation energies of large molecules

Time-dependent density-functional (TDDFT) methods are applied within the adiabatic approximation to a series of molecules including C70. Our implementation provides an efficient approach for treating frequency-dependent response properties and electronic excitation spectra of large molecules. We also present a new algorithm for the diagonalization of large non-Hermitian matrices which is needed for hybrid functionals and is also faster than the widely used Davidson algorithm when employed for the Hermitian case appearing in excited energy calculations. Results for a few selected molecules using local, gradient-corrected, and hybrid functionals are discussed. We find that for molecules with low lying excited states TDDFT constitutes a considerable improvement over Hartree–Fock based methods (like the random phase approximation) which require comparable computational effort.

Restoring the density-gradient expansion for exchange in solids and surfaces.

Popular modern generalized gradient approximations are biased toward the description of free-atom energies. Restoration of the first-principles gradient expansion for exchange over a wide range of density gradients eliminates this bias. We introduce a revised Perdew-Burke-Ernzerhof generalized gradient approximation that improves equilibrium properties of densely packed solids and their surfaces.Successful modern generalized gradient approximations (GGAs) are biased toward atomic energies. Restoration of the first-principles gradient expansion for the exchange energy over a wide range of density gradients eliminates this bias. With many collaborators, I introduce PBEsol, a revised Perdew-Burke-Ernzerhof GGA that improves equilibrium properties of densely-packed solids and their surfaces.

Assessment of the Perdew–Burke–Ernzerhof exchange-correlation functional

In order to discriminate between approximations to the exchange-correlation energy EXC[ρ↑,ρ↓], we employ the criterion of whether the functional is fitted to a certain experimental data set or if it is constructed to satisfy physical constraints. We present extensive test calculations for atoms and molecules, with the nonempirical local spin-density (LSD) and the Perdew–Burke–Ernzerhof (PBE) functional and compare our results with results obtained with more empirical functionals. For the atomization energies of the G2 set, we find that the PBE functional shows systematic errors larger than those of commonly used empirical functionals. The PBE ionization potentials, electron affinities, and bond lengths are of accuracy similar to those obtained from empirical functionals. Furthermore, a recently proposed hybrid scheme using exact exchange together with PBE exchange and correlation is investigated. For all properties studied here, the PBE hybrid gives an accuracy comparable to the frequently used empirical ...

Influence of the exchange screening parameter on the performance of screened hybrid functionals

This work reexamines the effect of the exchange screening parameter omega on the performance of the Heyd-Scuseria-Ernzerhof (HSE) screened hybrid functional. We show that variation of the screening parameter influences solid band gaps the most. Other properties such as molecular thermochemistry or lattice constants of solids change little with omega. We recommend a new version of HSE with the screening parameter omega=0.11 bohr(-1) for further use. Compared to the original implementation, the new parametrization yields better thermochemical results and preserves the good accuracy for band gaps and lattice constants in solids.

An efficient reformulation of the closed‐shell coupled cluster single and double excitation (CCSD) equations

The closed‐shell CCSD equations are reformulated in order to achieve superior computational efficiency. Using a spin adaptation scheme based on the unitary group approach (UGA), we have obtained a new set of equations that greatly improves our previous formulation. Based on this scheme we have also derived equations for the closed‐shell configuration interaction including all single and double excitations (CISD) case. Both methods have been implemented and tested. For a range of test cases the new CCSD method is more efficient than the earlier CCSD method. The new closed‐shell CISD procedure is faster than the shape‐driven (SD)GUGA algorithm and the new CCSD scheme is less than two times more computation intensive than SDGUGA CISD per iteration.

Assessment of a long-range corrected hybrid functional

Common approximate exchange-correlation functionals suffer from self-interaction error, and as a result, their corresponding potentials have incorrect asymptotic behavior. The exact asymptote can be imposed by introducing range separation into the exchange component and replacing the long-range portion of the approximate exchange by the Hartree-Fock counterpart. The authors show that this long-range correction works particularly well in combination with the short-range variant of the Perdew-Burke-Ernzerhof (PBE) exchange functional. This long-range-corrected hybrid, here denoted LC-omegaPBE, is remarkably accurate for a broad range of molecular properties, such as thermochemistry, barrier heights of chemical reactions, bond lengths, and most notably, description of processes involving long-range charge transfer.

Comparative assessment of a new nonempirical density functional: Molecules and hydrogen-bonded complexes

A comprehensive study is undertaken to assess the nonempirical meta-generalized gradient approximation (MGGA) of Tao, Perdew, Staroverov, and Scuseria (TPSS) against 14 common exchange-correlation energy functionals. Principal results are presented in the form of statistical summaries of deviations from experiment for the G3/99 test set (223 enthalpies of formation, 86 ionization potentials, 58 electron affinities, 8 proton affinities) and three additional test sets involving 96 bond lengths, 82 harmonic vibrational frequencies, and 10 hydrogen-bonded complexes, all computed using the 6-311++G(3df,3pd) basis. The TPSS functional matches, or exceeds in accuracy all prior nonempirical constructions and, unlike semiempirical functionals, consistently provides a high-quality description of diverse systems and properties. The computational cost of self-consistent MGGA is comparable to that of ordinary GGA, and exact exchange (unavailable in some codes) is not required. A one-parameter global hybrid version of ...

Efficient hybrid density functional calculations in solids: Assessment of the Heyd–Scuseria–Ernzerhof screened Coulomb hybrid functional

The present work introduces an efficient screening technique to take advantage of the fast spatial decay of the short range Hartree-Fock (HF) exchange used in the Heyd-Scuseria-Ernzerhof (HSE) screened Coulomb hybrid density functional. The screened HF exchange decay properties and screening efficiency are compared with traditional hybrid functional calculations on solids. The HSE functional is then assessed using 21 metallic, semiconducting, and insulating solids. The examined properties include lattice constants, bulk moduli, and band gaps. The results obtained with HSE exhibit significantly smaller errors than pure density functional theory (DFT) calculations. For structural properties, the errors produced by HSE are up to 50% smaller than the errors of the local density approximation, PBE, and TPSS functionals used for comparison. When predicting band gaps of semiconductors, we found smaller errors with HSE, resulting in a mean absolute error of 0.2 eV (1.3 eV error for all pure DFT functionals). In addition, we present timing results which show the computational time requirements of HSE to be only a factor of 2-4 higher than pure DFT functionals. These results make HSE an attractive choice for calculations of all types of solids.