Heterogenized Pyridine-Substituted Cobalt(II) Phthalocyanine Yields Reduction of CO2 by Tuning the Electron Affinity of the Co Center.

Conversion of CO2 to reduced products is a promising route to alleviate irreversible climate change. Here we report the synthesis of a Co-based phthalocyanine with pyridine moieties (CoPc-Pyr), which is supported on a carbon electrode and shows Faradaic efficiency ∼90% for CO at 490 mV of overpotential (-0.6 V vs reversible hydrogen electrode (RHE)). In addition, its catalytic activity at -0.7 V versus RHE surpasses other Co-based molecular and metal-organic framework catalysts for CO2 reduction at this bias. Density functional theory calculations show that pyridine moieties enhance CO2 adsorption and electron affinity of the Co center by an inductive effect, thus lowering the overpotential necessary for CO2 conversion. Our study shows that CoPc-Pyr reduces CO2 at lower overpotential and with higher activity than noble metal electrodes, such as silver.

Solvation Entropy Made Simple.

The entropies of molecules in solution are often calculated using gas phase formulas. 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 Sω, Sϵ, and S ϵα 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 Δ Hsol and Δ Ssol can be described separately and with less reliance on parametrization by a combination of the methods presented here with existing, reparametrized, implicit solvation models.

Explaining the Incorporation of Oxygen Derived from Solvent Water into the Oxygenated Products of CO Reduction over Cu.

The electrochemical reduction of CO and CO2 over Cu produces a variety of multicarbon products. Interestingly, recent isotope experiments have suggested that the oxygen atoms contained in the multicarbon alcohols produced over Cu are derived from solvent water. This observation has brought into question many of the proposed reaction mechanisms by which these multicarbon alcohols are produced over Cu. However, these surprising experimental observations are likely the result of isotopic scrambling between transiently produced carbonyl-containing intermediate reaction products, such as acetaldehyde, with solvent water and not another mechanism. The existence of such carbonyl-containing intermediate reaction products is supported by both experimental and theoretical studies. Furthermore, theoretical calculations support the notion that the reversible hydration of these carbonyl-containing species is facile in the vicinity of the Cu surface.

Reaction mechanism of the selective reduction of CO2 to CO by a tetraaza [CoIIN4H]2+ complex in the presence of protons.

The tetraaza [CoIIN4H]2+ complex (1) is remarkable for its ability to selectively reduce CO2 to CO with 45% Faradaic efficiency and a CO to H2 ratio of 3 : 2. We employ density functional theory (DFT) to determine the reasons behind the unusual catalytic properties of 1 and the most likely mechanism for CO2 reduction. The selectivity for CO2 over proton reduction is explained by analyzing the catalyst's affinity for the possible ligands present under typical reaction conditions: acetonitrile, water, CO2, and bicarbonate. After reduction of the catalyst by two electrons, formation of [CoIN4H]+-CO2- is strongly favored. Based on thermodynamic and kinetic data, we establish that the only likely route for producing CO from here consists of a protonation step to yield [CoIN4H]+-CO2H, followed by reaction with CO2 to form [CoIIN4H]2+-CO and bicarbonate. This conclusion corroborates the idea of a direct role of CO2 as a Lewis acid to assist in C-O bond dissociation, a conjecture put forward by other authors to explain recent experimental observations. The pathway to formic acid is predicted to be forbidden by high activation barriers, in accordance with the products that are known to be generated by 1. Calculated physical observables such as standard reduction potentials and the turnover frequency for our proposed catalytic cycle are in agreement with available experimental data reported in the literature. The mechanism also makes a prediction that may be experimentally verified: that the rate of CO formation should increase linearly with the partial pressure of CO2.

Nonempirical Meta-Generalized Gradient Approximations for Modeling Chemisorption at Metal Surfaces.

We assess the accuracy of popular nonempirical GGAs (PBE, PBEsol, RPBE) and meta-GGAs (TPSS, revTPSS, and SCAN) for describing chemisorption reactions at metal surfaces. Except for RPBE, all the functionals tend to overbind the adsorbate significantly. We then propose a nonempirical meta-GGA, denoted as RTPSS, that is based on RPBE in the same way that TPSS is based on PBE. The RTPSS functional remedies the overbinding problem and improves the description of chemisorption energies. As an example of an application of RTPSS, we study the adsorption of CO on Cu surfaces (a notably difficult problem for semilocal functionals) and find that RTPSS is the only tested functional that predicts accurate chemisorption energies and the preferred adsorption site of CO. Although RTPSS gives an accurate description of chemisorption, nonlocal correlation may be necessary to describe physisorption if long-range van der Waals interactions are involved (however, this is true for semilocal functionals in general). We suggest that RTPSS can be a useful meta-GGA for studying chemisorption processes and mechanisms of heterogeneous catalysis.

Is Subsurface Oxygen Necessary for the Electrochemical Reduction of CO2 on Copper?

It has recently been proposed that subsurface oxygen is crucial for the adsorption and subsequent electroreduction of CO2 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 × 103 s-1. Oxygen can survive longer in deeper layers, but it does not promote CO2 adsorption there. Diffusion of subsurface oxygen is easier to the less-dense Cu(100) surface, even from lower layers (rate ≈ 1 × 107 s-1). Once the applied voltage and dispersion forces are properly modeled, we find that subsurface oxygen is unnecessary for CO2 adsorption on copper.

Electronic Structure and Properties of Berkelium Iodates.

The reaction of 249Bk(OH)4 with iodate under hydrothermal conditions results in the formation of Bk(IO3)3 as the major product with trace amounts of Bk(IO3)4 also crystallizing from the reaction mixture. The structure of Bk(IO3)3 consists of nine-coordinate BkIII cations that are bridged by iodate anions to yield layers that are isomorphous with those found for AmIII, CfIII, and with lanthanides that possess similar ionic radii. Bk(IO3)4 was expected to adopt the same structure as M(IO3)4 (M = Ce, Np, Pu), but instead parallels the structural chemistry of the smaller ZrIV cation. BkIII-O and BkIV-O bond lengths are shorter than anticipated and provide further support for a postcurium break in the actinide series. Photoluminescence and absorption spectra collected from single crystals of Bk(IO3)4 show evidence for doping with BkIII in these crystals. In addition to luminescence from BkIII in the Bk(IO3)4 crystals, a broad-band absorption feature is initially present that is similar to features observed in systems with intervalence charge transfer. However, the high-specific activity of 249Bk (t1/2 = 320 d) causes oxidation of BkIII and only BkIV is present after a few days with concomitant loss of both the BkIII luminescence and the broadband feature. The electronic structure of Bk(IO3)3 and Bk(IO3)4 were examined using a range of computational methods that include density functional theory both on clusters and on periodic structures, relativistic ab initio wave function calculations that incorporate spin-orbit coupling (CASSCF), and by a full-model Hamiltonian with spin-orbit coupling and Slater-Condon parameters (CONDON). Some of these methods provide evidence for an asymmetric ground state present in BkIV that does not strictly adhere to Russel-Saunders coupling and Hund's Rule even though it possesses a half-filled 5f 7 shell. Multiple factors contribute to the asymmetry that include 5f electrons being present in microstates that are not solely spin up, spin-orbit coupling induced mixing of low-lying excited states with the ground state, and covalency in the BkIV-O bonds that distributes the 5f electrons onto the ligands. These factors are absent or diminished in other f7 ions such as GdIII or CmIII.

Predicting Band Gaps with Hybrid Density Functionals.

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.

Range separated hybrids of pair coupled cluster doubles and density functionals.

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.

On the equivalence of LIST and DIIS methods for convergence acceleration.

Self-consistent field extrapolation methods play a pivotal role in quantum chemistry and electronic structure theory. We, here, demonstrate the mathematical equivalence between the recently proposed family of LIST methods [Wang et al., J. Chem. Phys. 134, 241103 (2011); Y. K. Chen and Y. A. Wang, J. Chem. Theory Comput. 7, 3045 (2011)] and the general form of Pulay's DIIS [Chem. Phys. Lett. 73, 393 (1980); J. Comput. Chem. 3, 556 (1982)] with specific error vectors. Our results also explain the differences in performance among the various LIST methods.

Synergy between pair coupled cluster doubles and pair density functional theory.

Pair coupled cluster doubles (pCCD) has been recently studied as a method capable of accounting for static correlation with low polynomial cost. We present three combinations of pCCD with Kohn-Sham functionals of the density and on-top pair density (the probability of finding two electrons on top of each other) to add dynamic correlation to pCCD without double counting. With a negligible increase in computational cost, these pCCD+DFT blends greatly improve upon pCCD in the description of typical problems where static and dynamic correlations are both important. We argue that-as a black-box method with low scaling, size-extensivity, size-consistency, and a simple quasidiagonal two-particle density matrix-pCCD is an excellent match for pair density functionals in this type of fusion of multireference wavefunctions with DFT.

Actinide chemistry using singlet-paired coupled cluster and its combinations with density functionals.

Singlet-paired coupled cluster doubles (CCD0) is a simplification of CCD that relinquishes a fraction of dynamic correlation in order to be able to describe static correlation. Combinations of CCD0 with density functionals that recover specifically the dynamic correlation missing in the former have also been developed recently. Here, we assess the accuracy of CCD0 and CCD0+DFT (and variants of these using Brueckner orbitals) as compared to well-established quantum chemical methods for describing ground-state properties of singlet actinide molecules. The f(0) actinyl series (UO2(2+), NpO2(3+), PuO2(4+)), the isoelectronic NUN, and thorium (ThO, ThO(2+)) and nobelium (NoO, NoO2) oxides are studied.

Can gap tuning schemes of long-range corrected hybrid functionals improve the description of hyperpolarizabilities?

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.

Can short- and middle-range hybrids describe the hyperpolarizabilities of long-range charge-transfer compounds?

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.

Electronic correlation without double counting via a combination of spin projected Hartree-Fock and density functional theories.

Several schemes to avoid the double counting of correlations in methods that merge multireference wavefunctions with density functional theory (DFT) are studied and here adapted to a combination of spin-projected Hartree-Fock (SUHF) and DFT. The advantages and limitations of the new method, denoted SUHF+fcDFT, are explored through calculations on benchmark sets in which the accounting of correlations is challenging for pure SUHF or DFT. It is shown that SUHF+fcDFT can greatly improve the description of certain molecular properties (e.g., singlet-triplet energy gaps) which are not improved by simple addition of DFT dynamical correlation to SUHF. However, SUHF+fcDFT is also shown to have difficulties dissociating certain types of bonds and describing highly charged ions with static correlation. Possible improvements to the current SUHF+fcDFT scheme are discussed in light of these results.

Capturing static and dynamic correlations by a combination of projected Hartree-Fock and density functional theories.

This paper explores the possibility of combining projected Hartree-Fock and density functional theories for treating static and dynamic correlations in molecular systems with mean-field computational cost. The combination of spin-projected unrestricted Hartree-Fock (SUHF) with the TPSS correlation functional (SUHF+TPSS) yields excellent results for non-metallic molecular dissociations and singlet-triplet splittings. However, SUHF+TPSS fails to provide the qualitatively correct dissociation curve for the notoriously difficult case of the chromium dimer. By tuning the TPSS correlation parameters and adding complex conjugation symmetry breaking and restoration to SUHF, the right curve shape for Cr2 can be obtained; unfortunately, such a combination is found to lead to overcorrelation in the general case.

Comparison of self-consistent field convergence acceleration techniques.

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.

Conformational preferences of trans-1,2- and cis-1,3-cyclohexanedicarboxylic acids in water and dimethyl sulfoxide as a function of the ionization state as determined from NMR spectroscopy and density functional theory quantum mechanical calculations.

The populations of diaxial (aa) and diequatorial (ee) conformers of trans-1,2- and cis-1,3-cyclohexanedicarboxylic acids (CDCAs; 1 and 2, respectively) and their salts were determined in water and dimethyl sulfoxide (DMSO) solutions from vicinal proton-proton NMR J couplings ((3)J(HH)). Optimized geometries and free energies for these compounds were obtained at the M06-2X/cc-pVTZ(-f)++ level. Although carboxylic acid groups in cyclohexane rings are generally believed to be far more stable (~2 kcal/mol) in equatorial than axial positions, this investigation demonstrated that an aa conformation (normally assumed to be completely insignificant for these compounds) can be favored depending on the medium and ionization state: strong ee preferences (>90%) were observed in water and DMSO for both diacids and their salts, except for the dianion of 1 in DMSO, which was found to be substantially aa (~57%). The possibility of intramolecular hydrogen bonding (H-bonding) was also investigated; the ratios of the ionization constants (K(1)/K(2)) indicated an absence of intramolecular H-bonding because K(1)/K(2) ≪ 10(4) (a standard criterion for non-H-bonding in dicarboxylic acids) for both 1 and 2 in water and also for 2 in DMSO. For 1, K(1)/K(2) increased drastically in DMSO (K(1)/K(2) = 4 × 10(6)), where (3)J(HH) and the ratio K(1)/K(E) = 10, K(E) being the acidity constant of the monomethyl ester of 1, indicated the formation of an intramolecular H-bond for the monoanion in this solvent. An explanation for the observation of compact dianions in solution in terms of the generalized Born equation is also provided.