We compare the ability of four popular hybrid density functionals (B3LYP, B3PW91, HSE, and PBE0) for predicting band gaps of semiconductors and insulators over a large benchmark set using a consistent methodology. We observe no significant statistical difference in their overall performance, although the screened hybrid HSE is more accurate for typical semiconductors. HSE can improve its accuracy for large band gap materials—without affecting that of semiconductors—by including a larger portion of Hartree–Fock exchange in its short-range. Given that screened hybrids are computationally much less expensive than their global counterparts, we conclude that they are a better option for the black box prediction of band gaps.

Pair coupled cluster doubles (pCCD) is a size-consistent, size-extensive, low-cost simplification of CCD that has been shown to be able to describe static correlation without breaking symmetry. We combine pCCD with Kohn–Sham functionals of the density and the local pair density in order to incorporate dynamic correlation in pCCD while maintaining its low cost. Double counting is eliminated by splitting the (interelectron) Coulomb operator into complementary short- and long-range parts, and evaluating the two-body energy with pCCD in the long-range and with density functionals in the short-range. This simultaneously suppresses self-interaction in the Hartree-exchange term of the functionals. Generalizations including a fraction of wavefunction two-body energy in the short-range are also derived and studied. The improvement of our pCCD+DFT hybrids over pCCD is demonstrated in calculations on benchmarks where both types of correlation are important.

Long-range corrected hybrid density functionals (LC-DFT), with range separation parameters optimally tuned to obey Koopmans’ theorem, are used to calculate the first-order hyperpolarizabilities of prototypical charge-transfer compounds p-nitroaniline (PNA) and dimethylamino nitrostilbene (DANS) in the gas phase and various solvents. It is shown that LC-DFT methods with default range separation parameters tend to underestimate hyperpolarizabilities (most notably in solution) and that the tuning scheme can sharply improve results, especially in the cases when the standard LC-DFT errors are largest. Nonetheless, we also identify pathological cases (two pyrrole derivatives) for which LC-DFT underestimates the hyperpolarizabilities, regardless of tuning. It is noted that such pathological cases do not follow the usual inverse relation between the hyperpolarizability and amount of exact exchange, and thus this behavior may serve as a diagnostic tool for the adequacy of LC-DFT.

The hyperpolarizabilities of five prototypical and four recently synthesized long-range charge-transfer (CT) organic compounds are calculated using short- and middle-range (SR and MR) hybrid functionals. These results are compared with data from MP2 and other DFT methods including GGAs, global hybrids, long-range corrected functionals (LC-DFT), and optimally tuned LC-DFT. Although it is commonly believed that the overestimation of hyperpolarizabilities associated with CT excitations by GGA and global hybrid functionals is the result of their wrong asymptotic exchange potential, and that LC-DFT heals this issue, we show here that SR and MR functionals yield results similar to those from LC-DFT. Hence, the long-range correction per se does not appear to be the key element in the well-known improved description of hyperpolarizabilities by LC-DFT. Rather, we argue that the inclusion of substantial amounts of Hartree–Fock exchange, which reduces the many-electron self-interaction error, is responsible for the relatively good results afforded by range separated hybrids. Additionally, we evaluate the effects of solvent and frequency on hyperpolarizabilities computed by SR and MR hybrids and compare these predictions with other DFT methods and available experimental data.

•The hyperpolarizability of chromophore p-nitroaniline is calculated.•Results are compared to experimental data.•Traditional DFT methods are inadequate for predicting hyperpolarizabilities.•Long-range corrected functionals provide good agreement with experiment.We calculate the hyperpolarizability of the prototypical chromophore p  -nitroaniline in gas phase using different long-range corrected Density Functional Theory (LC-DFT) methods and compare it with experimental data. While traditional DFT methods are inadequate for predicting hyperpolarizabilities, LC-DFT functionals provide very good agreement with experiment (less than 10% error) for this archetypal organic molecule with large nonlinear optical (NLO) susceptibility. Additionally, we use the LC-ωωPBE functional to calculate the structures and predict the hyperpolarizabilities of two recently synthesized potential organic NLO materials. The structures are compared with experimental measurements and found to be in excellent agreement.

•Fulgides are important photochromic materials.•That have interesting NLO properties.•We predict their properties using long-range corrected functionals.•We obtain excellent agreement with experiment.The photochromic and nonlinear optical (NLO) properties of three isomers of the fulgide dicyclopropyl-methylene-(2,5-dimethyl-3-furylethylidene)-succinic anhydride (1-Z, 1-E and 1-C) were studied using hybrid and range separated density functional theory (DFT) methods. Theoretical spectroscopic data (λmaxλmax) is compared to experiment; the DFT calculations are capable of qualitatively, but not quantitatively, predicting the photochromic properties of 1-E. Large changes in the λmaxλmax of 1-E upon irradiation of light are also predicted to be accompanied by a substantial increase in hyperpolarizability.Graphical abstract

The gas phase properties of the Z- and E-isomers of 4-(p-N,N-dimethyl-aminophenylmethylene)-2-phenyl-5-oxazolone (DPO) and 4-(2,5-dimethoxyphenylmethylene)-2-phenyl-5-oxazolone (DMPO) are studied using traditional hybrid and long-range-corrected density functional theories (LC-DFT). Excellent agreement is found between the optimized molecular geometries and the experimental crystal structures. Our calculations predict both DPO and DMPO to have significant nonlinear optical (NLO) susceptibilities. These results are compared with data for the prototypical NLO chromophore p-nitroaniline, and the effect of the range separation parameter on LC-DFT hyperpolarizabilities is also analyzed.

Coupled binuclear copper oxide cores are present in the active sites of some of the very common metalloenzymes found in most living organisms. The correct theoretical description of the interconversion between the two dominant structural isomers of this core, namely, side-on μ-η2:η2-peroxodicopper(II) and bis(μ-oxo)-dicopper(III), is challenging since it requires a method that can provide a balanced description of static and dynamic correlations. We investigate this problem using our recently developed projected Hartree–Fock method (PHF). Here, the spin and complex conjugation symmetries of the trial wave function are deliberately broken and restored in a variation-after-projection scheme. The projected wave function carries good quantum numbers, has multireference character, and accounts for static and some dynamic correlation. Most importantly, the calculations are done at a mean-field computational cost allowing us to address large systems at a modest expense. The interconversion is studied here for the bare [Cu2O2]2+ core using a variety of projection methods (SUHF, SGHF, KSUHF, KSGHF). The results seem to be on par with much more demanding traditional multireference methods.

Over the last several years, low-dimensional graphene derivatives, such as carbon nanotubes and graphene nanoribbons, have played a central role in the pursuit of a plausible carbon-based nanotechnology. Their electronic properties can be either metallic or semiconducting depending purely on morphology, but predicting their electronic behavior has proven challenging. The combination of experimental efforts with modeling of these nanometer-scale structures has been instrumental in gaining insight into their physical and chemical properties and the processes involved at these scales. Particularly, approximations based on density functional theory have emerged as a successful computational tool for predicting the electronic structure of these materials. In this Account, we review our efforts in modeling graphitic nanostructures from first principles with hybrid density functionals, namely the Heyd−Scuseria−Ernzerhof (HSE) screened exchange hybrid and the hybrid meta-generalized functional of Tao, Perdew, Staroverov, and Scuseria (TPSSh).These functionals provide a powerful tool for quantitatively studying structure−property relations and the effects of external perturbations such as chemical substitutions, electric and magnetic fields, and mechanical deformations on the electronic and magnetic properties of these low-dimensional carbon materials. We show how HSE and TPSSh successfully predict the electronic properties of these materials, providing a good description of their band structure and density of states, their work function, and their magnetic ordering in the cases in which magnetism arises. Moreover, these approximations are capable of successfully predicting optical transitions (first and higher order) in both metallic and semiconducting single-walled carbon nanotubes of various chiralities and diameters with impressive accuracy. This versatility includes the correct prediction of the trigonal warping splitting in metallic nanotubes.The results predicted by HSE and TPSSh provide excellent agreement with existing photoluminescence and Rayleigh scattering spectroscopy experiments and Green's function-based methods for carbon nanotubes. This same methodology was utilized to predict the properties of other carbon nanomaterials, such as graphene nanoribbons. Graphene nanoribbons may be viewed as unrolled (and passivated) carbon nanotubes. However, the emergence of edges has a crucial impact on the electronic properties of graphene nanoribbons. Our calculations have shown that armchair nanoribbons are predicted to be nonmagnetic semiconductors with a band gap that oscillates with their width. In contrast, zigzag graphene nanoribbons are semiconducting with an electronic ground state that exhibits spin polarization localized at the edges of the carbon nanoribbon. The spatial symmetry of these magnetic states in graphene nanoribbons can give rise to a half-metallic behavior when a transverse external electric field is applied. Our work shows that these properties are enhanced upon different types of oxidation of the edges. We also discuss the properties of rectangular graphene flakes, which present spin polarization localized at the zigzag edges.

An electronic structure method is said to be size-consistent if the energy of noninteracting fragments is the same when the fragments are treated in a supermolecule approach or are treated in isolation. Size consistency is often violated by Hartree–Fock when symmetries of the exact wave function are imposed on the Hartree–Fock determinant. Relaxing the requirement that the Hartree–Fock wave function be a spin eigenfunction leads to unrestricted Hartree–Fock, which is often (but not always) size-consistent. In this Perspective, we discuss the usually forgotten fact that imposing none of the exact symmetries in what is known as generalized Hartree–Fock allows Hartree–Fock to always be size-consistent and allows size extensive correlated methods such as coupled cluster theory to also be size-consistent. Furthermore, with all symmetries broken, dissociation curves connect the molecule to the fragments better than with symmetries imposed, although the curves are not smooth and show derivative discontinuities akin to unphysical phase transitions. In many cases, correlated dissociation curves based on this generalized Hartree–Fock reference are discontinuous.

Homogeneous catalysis by transition metal complexes is challenging to model with electronic structure theory. This is due to the large system sizes encountered, the wide range of bonding motifs, and the need for accurate treatments of reaction kinetics. Range-separated hybrid density functionals have been shown to accurately predict a variety of properties in (organic) main group chemistry. Here we benchmark representative range-separated hybrids for geometric and energetic properties of transition metal complexes. Results from conventional semilocal and global hybrid approaches are included for comparison. The range-separated hybrids’ performance, combined with their demonstrated accuracy for main group kinetics, makes them promising for applications to homogeneous catalysis. Our results also point to the importance of the correlation functional in range-separated hybrids.

While hybrid functionals are largely responsible for the utility of modern Kohn−Sham density functional theory, they are not without their weaknesses. In the solid state, the slow decay of their nonlocal Hartree−Fock-type exchange makes hybrids computationally demanding and can introduce unphysical effects. Both problems can be remedied by a screened hybrid which uses exact exchange only at short-range. Many molecular properties, in contrast, benefit from the inclusion of long-range exact exchange. Recently, the authors reconciled these two seemingly contradictory requirements by introducing the HISS functional [ J. Chem. Phys. 2007, 127, 221103], which uses exact exchange only in the middle range. In this paper, we expand upon our previous work, benchmarking the performance of the HISS functional for several simple properties and applying it to the dissociation of homonuclear diatomic cations and to the polarizability of linear H2 chains to determine the importance of middle-range exact exchange for these systems, which are expected to be sensitive to the asymptotic exchange potential.

We present an assessment of different density functionals, with emphasis on range-separated hybrids, for the prediction of fundamental and harmonic vibrational frequencies, infrared intensities, and Raman activities. Additionally, we discuss the basis set convergence of vibrational properties of H2O with long-range corrected hybrids. Our results show that B3LYP is the best functional for predicting vibrational frequencies (both fundamental and harmonic); the screened-PBE hybrid (HSE) density functional works best for infrared intensities, and the long-range corrected PBE (LC-ωPBE), M06-HF, and M06-L density functionals are almost as good as MP2 for predicting Raman activities. We show the predicted Raman spectrum of adenine as an example of a medium-size molecule where a DFT/Sadlej pVTZ calculation is affordable and compare our results against the experimental spectrum.

Kohn−Sham density functional theory has become a standard method for modeling energetic, spectroscopic, and chemical reactivity properties of large molecules and solids. Density functional theory provides a rigorous theoretical framework for modeling the many-body exchange-correlation effects that dominate the computational cost of traditional wave function approaches. The advent of hybrid exchange-correlation functionals which incorporate a fraction of nonlocal exact exchange has solidified the prominence of density functional theory within computational chemistry. Hybrids provide accurate treatments of properties such as thermochemistry and molecular geometry. But they also exhibit some rather spectacular failures, and often contain multiple empirical parameters. This article reviews our work on developing novel exchange-correlation functionals that build upon the successes of global hybrids. We focus on more flexible functional forms, including local and range-separated hybrid functionals, constructed to obey known exact constraints and (ideally) to incorporate a minimum of empirical parametrization. The article places our work within the context of some other new approximate density functionals and discusses prospects for future work.

We present an assessment of different density functionals, with emphasis on range-separated hybrids, for the prediction of fundamental and harmonic vibrational frequencies, infrared intensities, and Raman activities. Additionally, we discuss the basis set convergence of vibrational properties of H2O with long-range corrected hybrids. Our results show that B3LYP is the best functional for predicting vibrational frequencies (both fundamental and harmonic); the screened-PBE hybrid (HSE) density functional works best for infrared intensities, and the long-range corrected PBE (LC-ωPBE), M06-HF, and M06-L density functionals are almost as good as MP2 for predicting Raman activities. We show the predicted Raman spectrum of adenine as an example of a medium-size molecule where a DFT/Sadlej pVTZ calculation is affordable and compare our results against the experimental spectrum.

Pair coupled cluster doubles (pCCD) is a size-consistent, size-extensive, low-cost simplification of CCD that has been shown to be able to describe static correlation without breaking symmetry. We combine pCCD with Kohn–Sham functionals of the density and the local pair density in order to incorporate dynamic correlation in pCCD while maintaining its low cost. Double counting is eliminated by splitting the (interelectron) Coulomb operator into complementary short- and long-range parts, and evaluating the two-body energy with pCCD in the long-range and with density functionals in the short-range. This simultaneously suppresses self-interaction in the Hartree-exchange term of the functionals. Generalizations including a fraction of wavefunction two-body energy in the short-range are also derived and studied. The improvement of our pCCD+DFT hybrids over pCCD is demonstrated in calculations on benchmarks where both types of correlation are important.