Simple Modifications of the SCAN Meta-Generalized Gradient Approximation Functional.

We analyzed various possibilities to improve upon the SCAN meta-generalized gradient approximation density functional obeying all known properties of the exact functional that can be satisfied at this level of approximation. We examined the necessity of locally satisfying a strongly tightened lower bound for the exchange energy density in single-orbital regions, the nature of the error cancellation between the exchange and correlation parts in two-electron regions, and the effect of the fourth-order term in the gradient expansion of the correlation energy density. We have concluded that the functional can be modified to separately reproduce the exchange and correlation energies of the helium atom by locally releasing the strongly tightened lower bound for the exchange energy density in single-orbital regions, but this leads to an unbalanced improvement in the single-orbital electron densities.

Electron Density Errors and Density-Driven Exchange-Correlation Energy Errors in Approximate Density Functional Calculations.

Since its formal introduction, density functional theory has achieved many successes in the fields of molecular and solid-state chemistry. According to its central theorems, the ground state of a many-electron system is fully described by its electron density, and the exact functional minimizes the energy at the exact electron density. For many years of density functional development, it was assumed that the improvements in the energy are accompanied by the improvements in the density, and the approximations approach the exact functional.

Construction of a Spin-Component Scaled Dual-Hybrid Random Phase Approximation.

Recently, we have constructed a dual-hybrid direct random phase approximation method, called dRPA75, and demonstrated its good performance on reaction energies, barrier heights, and noncovalent interactions of main-group elements. However, this method has also shown significant but quite systematic errors in the computed atomization energies. In this paper, we suggest a constrained spin-component scaling formalism for the dRPA75 method (SCS-dRPA75) in order to overcome the large error in the computed atomization energies, preserving the good performance of this method on spin-unpolarized systems at the same time.

Application of a Dual-Hybrid Direct Random Phase Approximation to Water Clusters.

In water clusters, there is a delicate balance of van der Waals interactions and hydrogen bonds. Although semilocal and nonlocal density functional approximations have been recently routinely applied to water in various phases, the accurate description of hydrogen bonds remains a challenge. The most popular density functional approaches fail to predict the correct ordering of the energies of water clusters.

Accurate Diels-Alder reaction energies from efficient density functional calculations.

We assess the performance of the semilocal PBE functional; its global hybrid variants; the highly parametrized empirical M06-2X and M08-SO; the range separated rCAM-B3LYP and MCY3; the atom-pairwise or nonlocal dispersion corrected semilocal PBE and TPSS; the dispersion corrected range-separated ωB97X-D; the dispersion corrected double hybrids such as PWPB95-D3; the direct random phase approximation, dRPA, with Hartree-Fock, Perdew-Burke-Ernzerhof, and Perdew-Burke-Ernzerhof hybrid reference orbitals and the RPAX2 method based on a Perdew-Burke-Ernzerhof exchange reference orbitals for the Diels-Alder, DARC; and self-interaction error sensitive, SIE11, reaction energy test sets with large, augmented correlation consistent valence basis sets. The dRPA energies for the DARC test set are extrapolated to the complete basis set limit. CCSD(T)/CBS energies were used as a reference.

Accurate Complete Basis Set Extrapolation of Direct Random Phase Correlation Energies.

The direct random phase approximation (dRPA) is a promising way to obtain improvements upon the standard semilocal density functional results in many aspects of computational chemistry. In this paper, we address the slow convergence of the calculated dRPA correlation energy with the increase of the quality and size of the popular Gaussian-type Dunning's correlation consistent aug-cc-pVXZ split valence atomic basis set family. The cardinal number X controls the size of the basis set, and we use X = 3-6 in this study.

Construction and application of a new dual-hybrid random phase approximation.

The direct random phase approximation (dRPA) combined with Kohn-Sham reference orbitals is among the most promising tools in computational chemistry and applicable in many areas of chemistry and physics. The reason for this is that it scales as N(4) with the system size, which is a considerable advantage over the accurate ab initio wave function methods like standard coupled-cluster. dRPA also yields a considerably more accurate description of thermodynamic and electronic properties than standard density-functional theory methods.

Accurate, precise, and efficient theoretical methods to calculate anion-π interaction energies in model structures.

A correct description of the anion-π interaction is essential for the design of selective anion receptors and channels and important for advances in the field of supramolecular chemistry. However, it is challenging to do accurate, precise, and efficient calculations of this interaction, which are lacking in the literature. In this article, by testing sets of 20 binary anion-π complexes of fluoride, chloride, bromide, nitrate, or carbonate ions with hexafluorobenzene, 1,3,5-trifluorobenzene, 2,4,6-trifluoro-1,3,5-triazine, or 1,3,5-triazine and 30 ternary π-anion-π' sandwich complexes composed from the same monomers, we suggest domain-based local-pair natural orbital coupled cluster energies extrapolated to the complete basis-set limit as reference values.

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.

Van der waals coefficients for nanostructures: fullerenes defy conventional wisdom.

The van der Waals coefficients between quasispherical nanostructures can be modeled accurately and analytically by those of classical solid spheres (for nanoclusters) or spherical shells (for fullerenes) of uniform valence electron density, with the true static dipole polarizability. Here, we derive analytically and confirm numerically from this model the size dependencies of the van der Waals coefficients of all orders, showing, for example, that the asymptotic dependence for C(6) is the expected n(2) for pairs of nanoclusters A(n)-A(n), each containing n atoms, but n(2.75) for pairs of single-walled fullerenes C(n)-C(n).

Performance of meta-GGA Functionals on General Main Group Thermochemistry, Kinetics, and Noncovalent Interactions.

Among the computationally efficient semilocal density functionals for the exchange-correlation energy, meta-generalized-gradient approximations (meta-GGAs) are potentially the most accurate. Here, we assess the performance of three new meta-GGAs (revised Tao-Perdew-Staroverov-Scuseria or revTPSS, regularized revTPSS or regTPSS, and meta-GGA made simple or MGGA_MS), within and beyond their "comfort zones," on Grimme's big test set of main-group molecular energetics (thermochemistry, kinetics, and noncovalent interactions). We compare them against the standard Perdew-Burke-Ernzerhof (PBE) GGA, TPSS, and Minnesota M06L meta-GGAs, and Becke-3-Lee-Yang-Parr (B3LYP) hybrid of GGA with exact exchange.

Spherical-shell model for the van der Waals coefficients between fullerenes and/or nearly spherical nanoclusters.

Fullerene molecules such as C(60) are large nearly spherical shells of carbon atoms. Pairs of such molecules have a strong long-range van der Waals attraction that can produce scattering or binding into molecular crystals. A simplified classical-electrodynamics model for a fullerene is a spherical metal shell, with uniform electron density confined between outer and inner radii (just as a simplified model for a nearly spherical metallic nanocluster is a solid metal sphere or filled shell).

A meta-GGA Made Free of the Order of Limits Anomaly.

We have improved the revised Tao-Perdew-Staroverov-Scuseria (revTPSS) meta-generalized gradient approximation (GGA) in order to remove the order of limits anomaly in its exchange energy. The revTPSS meta-GGA recovers the second-order gradient expansion for a wide range of densities and therefore provides excellent atomization energies and lattice constants. For other properties of materials, however, even the revTPSS does not give the desired accuracy.

Conformational analysis of cellobiose by electronic structure theories.

Adiabatic Φ/ψ maps for cellobiose were prepared with B3LYP density functional theory. A mixed basis set was used for minimization, followed with 6-31+G(d) single-point calculations, with and without SMD continuum solvation. Different arrangements of the exocyclic groups (38 starting geometries) were considered for each Φ/ψ point.

Accurate Conformational Energy Differences of Carbohydrates: A Complete Basis Set Extrapolation.

Correlated ab initio wave function calculations have been performed, using nonrelativistic frozen core MP2 complete basis set extrapolation model chemistry. The calculations have been made for three test sets of gas-phase saccharide conformations to provide reference values for their relative energies. The remaining correlation effects are estimated from frozen core coupled-cluster singles and doubles [CCSD(T)] calculations.

A simple but fully nonlocal correction to the random phase approximation.

The random phase approximation (RPA) stands on the top rung of the ladder of ground-state density functional approximations. The simple or direct RPA has been found to predict accurately many isoelectronic energy differences. A nonempirical local or semilocal correction to this direct RPA leaves isoelectronic energy differences almost unchanged, while improving total energies, ionization energies, etc.

The RPA Atomization Energy Puzzle.

There is current interest in the random phase approximation (RPA), a "fifth-rung" density functional for the exchange-correlation energy. RPA has full exact exchange and constructs the correlation with the help of the unoccupied Kohn-Sham orbitals. In many cases (uniform electron gas, jellium surface, and free atom), the correction to RPA is a short-ranged effect that is captured by a local spin density approximation (LSDA) or a generalized gradient approximation (GGA).

Comparison of different force fields for the study of disaccharides.

Eighteen empirical force fields and the semi-empirical quantum method PM3CARB-1 were compared for studying beta-cellobiose, alpha-maltose, and alpha-galabiose [alpha-D-Galp-(1-->4)-alpha-D-Galp]. For each disaccharide, the energies of 54 conformers with differing hydroxymethyl, hydroxyl, and glycosidic linkage orientations were minimized by the different methods, some at two dielectric constants. By comparing these results and the available crystal structure data and/or higher level density functional theory results, it was concluded that the newer parameterizations for force fields (GROMOS, GLYCAM06, OPLS-2005 and CSFF) give results that are reasonably similar to each other, whereas the older parameterizations for Amber, CHARMM or OPLS were more divergent.

Workhorse semilocal density functional for condensed matter physics and quantum chemistry.

Semilocal density functionals for the exchange-correlation energy are needed for large electronic systems. The Tao-Perdew-Staroverov-Scuseria (TPSS) meta-generalized gradient approximation (meta-GGA) is semilocal and usefully accurate, but predicts too-long lattice constants. Recent "GGA's for solids" yield good lattice constants but poor atomization energies of molecules.

Some Fundamental Issues in Ground-State Density Functional Theory: A Guide for the Perplexed.

Some fundamental issues in ground-state density functional theory are discussed without equations: (1) The standard Hohenberg-Kohn and Kohn-Sham theorems were proven for a Hamiltonian that is not quite exact for real atoms, molecules, and solids. (2) The density functional for the exchange-correlation energy, which must be approximated, arises from the tendency of electrons to avoid one another as they move through the electron density. (3) In the absence of a magnetic field, either spin densities or total electron density can be used, although the former choice is better for approximations.

Regularized Gradient Expansion for Atoms, Molecules, and Solids.

A new, regularized gradient expansion (RGE) approximation density functional (i.e., a generalized gradient approximation or GGA that recovers the second-order gradient expansion for exchange in the slowly varying limit) was designed in an attempt to obtain good solid-state and molecular properties at the same time from a single GGA.

Evaluation of Density Functionals and Basis Sets for Carbohydrates.

Correlated ab initio wave function calculations using MP2/aug-cc-pVTZ model chemistry have been performed for three test sets of gas phase saccharide conformations to provide reference values for their relative energies. The test sets consist of 15 conformers of α- and β-d-allopyranose, 15 of 3,6-anhydro-4-O-methyl-d-galactitol, and four of β-d-glucopyranose. For each set, conformational energies varied by about 7 kcal/mol.

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.

Improved Description of Stereoelectronic Effects in Hydrocarbons Using Semilocal Density Functional Theory.

Serious and systematic errors with popular density functionals occur for isodesmic stabilization energies of n-alkanes, isomerization, and dimerization energies of hydrocarbons and geometries of sterically overcrowded aromatic systems. These functionals are too biased toward the correct description of free atoms. Changing two parameters within the Perdew-Burke-Ernzerhof approximation leads to a new nonempirical functional, PBEsol, that improves the description of large organic systems.