Based on constraints from reported experimental observations and density functional theory simulations, we propose a mechanism for the reduction of CO 2 to C 2 products on copper electrodes. To model the effects of an applied potential bias on the reactions, calculations are carried out with a variable, fractional number of electrons on the unit cell, which is optimized so that the Fermi level matches the actual chemical potential of electrons (i.e., the applied bias); an implicit electrolyte model allows for compensation of the surface charge, so that neutrality is maintained in the overall simulation cell. Our mechanism explains the presence of the seven C 2 species that

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 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.Introduction. Band structure calculations are an important application of electronic structure methods in materials science. Due to the cost of computing electronic properties for extended solids, density functional theory (DFT) methods are most often used for such calculations. However, local and semilocal density functional approximations-the most affordable type of Kohn-Sham functionals for solids-badly underestimate the band gaps of semiconductors (the materials of principal interest in practical applications) and insulators due to self-interaction error [1,2]. Hybrid functionals that incorporate a fraction of nonlocal Hartree-Fock (HF) exchange overcome this issue; however, computing HF exchange in solids is considerably more expensive than evaluating a semilocal density functional. Methods based on the GW approximation can also be used to compute band gaps more accurately, but these techniques are even more expensive than hybrids. A good compromise between cost and accuracy is provided by short-range screened hybrids: functionals that include HF exchange only for the short-range part of the electron-electron interaction, which significantly reduces the cost of evaluating the nonlocal HF part of the exchange as compared to standard hybrids [3]. This type of functionals have been shown to provide reasonably accurate band gaps for semiconductors, and variants of the Heyd-Scuseria-Ernzerhof [3][4][5][6][7] (HSE) short-range hybrid have been widely used for the calculation of semiconductor band gaps for many years [8].

A major challenge in the modeling of electrochemical phenomena is the accurate description of the interface between an electrolyte and a charged conductor. Polarizable continuum models (PCM) have been gaining popularity because they offer a computationally inexpensive method of modeling the electrolyte. In this Perspective, we discuss challenges from using one such model which treats the ions using a linearized Poisson−Boltzmann (LPB) distribution. From a physical perspective, this model places charge unphysically close to the surface and adsorbates, and it includes excessively steep ramping of the dielectric constant from the surface to the bulk solvent. Both of these issues can be somewhat mitigated by adjusting parameters built into the model, but in doing so, the resultant capacitance deviates from experimental values. Likewise, hybrid explicit-implicit approaches to the solvent may offer a more realistic description of hydrogen bonding and solvation to reaction intermediates, but the corresponding capacitances also deviate from experimental values. These deviations highlight the need for a careful adjustment of parameters in order to reproduce not only solvation energies but also other physical properties of solid− liquid interfaces. Continuum approaches alone also necessarily do not capture local variations in the electric field from cations at the interface, which can affect the energetics of intermediates with substantial dipoles or polarizability. Finally, since the doublelayer charge can be varied continuously, LPB/PCM models provide a way to determine electrochemical barriers at constant potential. However, double-layer charging and the atomic motion associated with reaction events occur on significantly different timescales. We suggest that more detailed approaches, such as the modified Poisson−Boltzmann model and/or the addition of a Stern layer, may be able to mitigate some but not all of the challenges discussed.

It has recently been proposed that subsurface oxygen is crucial for the adsorption and subsequent electroreduction of CO on copper. Using density functional theory, we have studied the stability and diffusion of subsurface oxygen in single crystals of copper exposing (111) and (100) facets. Oxygen is at least 1.5 eV more stable on the surface than beneath it for both crystal orientations; interstitial sites are too small to accommodate oxygen. The rate of atomic oxygen diffusion from one layer below a Cu(111) surface to the surface is 5 × 10 s. Oxygen can survive longer in deeper layers, but it does not promote CO adsorption there. Diffusion of subsurface oxygen is easier to the less-dense Cu(100) surface, even from lower layers (rate ≈ 1 × 10 s). Once the applied voltage and dispersion forces are properly modeled, we find that subsurface oxygen is unnecessary for CO adsorption on copper.

The entropies of molecules in solution are routinely calculated using gas phase formulae. It is assumed that, because implicit solvation models are fitted to reproduce free energies, this is sufficient for modeling reactions in solution. However, this procedure exaggerates entropic effects in processes that change molecularity. Here, computationally efficient (i.e., having similar cost as gas phase entropy calculations) approximations for determining solvation entropy are proposed to address this issue. The S ω , S , and S α models are nonempirical and rely only on physical arguments and elementary properties of the medium (e.g., density and relative permittivity). For all three methods, average errors as compared to experiment are within chemical accuracy for 110 solvation entropies, 11 activation entropies in solution, and 32 vaporization enthalpies. The models also make predictions regarding microscopic and bulk properties of liquids which prove to be accurate. These results imply that ∆H sol and ∆S sol can be described separately and with less reliance on parametrization by a combination of the methods presented here with existing, reparametrized implicit solvation models.

The recently proposed ADIIS and LIST methods for accelerating self-consistent field (SCF) convergence are compared to the previously proposed energy-DIIS (EDIIS) + DIIS technique. We here show mathematically that the ADIIS functional is identical to EDIIS for Hartree-Fock wavefunctions. Convergence failures of EDIIS + DIIS reported in the literature are not reproduced with our codes. We also show that when correctly implemented, the EDIIS + DIIS method is generally better than the LIST methods, at least for the cases previously examined in the literature. We conclude that, among the family of DIIS methods, EDIIS + DIIS remains the method of choice for SCF convergence acceleration.

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 firstorder hyperpolarizabilities of prototypical charge-transfer compounds p-nitroaniline (PNA) and dimethylamino nitrostilbene (DANS) in gas phase and various solvents.It is shown that LC-DFT methods with default range separation parameters tend to * To whom correspondence should be addressed between the hyperpolarizability and amount of exact exchange, and thus this behavior may serve as a diagnostic tool for the adequacy of LC-DFT.