A self-consistent scheme for determining the optimal fraction of exact exchange for full-range hybrid functionals is presented and applied to the calculation of band gaps and dielectric constants of solids. The exchange-correlation functional is defined in a similar manner to the PBE0 functional, but the mixing parameter is set equal to the inverse macroscopic dielectric function and it is determined self-consistently by computing the optimal dielectric screening. We found excellent agreement with experiments for the properties of a broad class of systems, with band gaps ranging between 0.7 and 21.7 eV and dielectric constants within 1.23 and 15.9. We propose that the eigenvalues and eigenfunctions obtained with the present self-consistent hybrid scheme may be excellent inputs for G$_0$W$_0$ calculations.Comment: Reprint of PRB articl

The vibronic couplings for the phenoxyl/phenol and the benzyl/toluene self-exchange reactions are calculated with a semiclassical approach, in which all electrons and the transferring hydrogen nucleus are treated quantum mechanically. In this formulation, the vibronic coupling is the Hamiltonian matrix element between the reactant and product mixed electronic-proton vibrational wavefunctions. The magnitude of the vibronic coupling and its dependence on the proton donor-acceptor distance can significantly impact the rates and kinetic isotope effects, as well as the temperature dependences, of proton-coupled electron transfer reactions. Both of these self-exchange reactions are vibronically nonadiabatic with respect to a solvent environment at room temperature, but the proton tunneling is electronically nonadiabatic for the phenoxyl/phenol reaction and electronically adiabatic for the benzyl/toluene reaction. For the phenoxyl/phenol system, the electrons are unable to rearrange fast enough to follow the proton motion on the electronically adiabatic ground state, and the excited electronic state is involved in the reaction. For the benzyl/toluene system, the electrons can respond virtually instantaneously to the proton motion, and the proton moves on the electronically adiabatic ground state. For both systems, the vibronic coupling decreases exponentially with the proton donor-acceptor distance for the range of distances studied. When the transferring hydrogen is replaced with deuterium, the magnitude of the vibronic coupling decreases and the exponential decay with distance becomes faster. Previous studies designated the phenoxyl/phenol reaction as proton-coupled electron transfer and the benzyl/toluene reaction as hydrogen atom transfer. In addition to providing insights into the fundamental physical differences between these two types of reactions, the present analysis provides a new diagnostic for differentiating between the conventionally defined hydrogen atom transfer and proton-coupled electron transfer reactions.

Dielectric-dependent hybrid (DDH) functionals were recently shown to yield accurate energy gaps and dielectric constants for a wide variety of solids, at a computational cost considerably less than that of GW calculations. The fraction of exact exchange included in the definition of DDH functionals depends (self-consistently) on the dielectric constant of the material. Here we introduce a range-separated (RS) version of DDH functionals where short and long-range components are matched using system dependent, non-empirical parameters. We show that RS DDHs yield accurate electronic properties of inorganic and organic solids, including energy gaps and absolute ionization potentials. Furthermore we show that these functionals may be generalized to finite systems.

We present a simple approach for the calculation of accurate pKa values in water and acetonitrile based on the straightforward calculation of the gas-phase absolute free energies of the acid and conjugate base with use of only a continuum solvation model to obtain the corresponding solution-phase free energies. Most of the error in such an approach arises from inaccurate differential solvation free energies of the acid and conjugate base which is removed in our approach using a correction based on the realization that the gas-phase acidities have only a small systematic error relative to the dominant systematic error in the differential solvation. The methodology is outlined in the context of the calculation of a set of neutral acids with water as the solvent for a reasonably accurate electronic structure level of theory (DFT), basis set, and implicit solvation model. It is then applied to the comparison of results for three different hybrid density functionals to illustrate the insensitivity to the functional. Finally, the approach is applied to the comparison of results for sets of neutral acids and protonated amine cationic acids in both aqueous (water) and nonaqueous (acetonitrile) solvents. The methodology is shown to generally predict the pKa values for all the cases investigated to within 1 pH unit so long as the differential solvation error is larger than the systematic error in the gas-phase acidity calculations. Such an approach is rather general and does not have additional complications that would arise in a cluster-continuum method, thus giving it strength as a simple high-throughput means to calculate absolute pKa values. This article is part of a Special Issue entitled: Metals in Bioenergetics and Biomimetics Systems.

The Lewis acidity of metal-organic frameworks (MOFs) has attracted much research interest in recent years. We report here the development of two quantitative methods for determining the Lewis acidity of MOFs-based on electron paramagnetic resonance (EPR) spectroscopy of MOF-bound superoxide (O) and fluorescence spectroscopy of MOF-bound N-methylacridone (NMA)-and a simple strategy that significantly enhances MOF Lewis acidity through ligand perfluorination. Two new perfluorinated MOFs, Zr-fBDC and Zr-fBPDC, where HfBDC is 2,3,5,6-tetrafluoro-1,4-benzenedicarboxylic acid and HfBPDC is 2,2',3,3',5,5',6,6'-octafluoro-4,4'-biphenyldicarboxylic acid, were shown to be significantly more Lewis acidic than nonsubstituted UiO-66 and UiO-67 as well as the nitrated MOFs Zr-BDC-NO and Zr-BPDC-(NO). Zr-fBDC was shown to be a highly active single-site solid Lewis acid catalyst for Diels-Alder and arene C-H iodination reactions. Thus, this work establishes the important role of ligand perfluorination in enhancing MOF Lewis acidity and the potential of designing highly Lewis acidic MOFs for fine chemical synthesis.

We present a combined computational and experimental study of the photoelectron spectrum of a simple aqueous solution of NaCl. Measurements were conducted on microjets, and first-principles calculations were performed using hybrid functionals and many-body perturbation theory at the G0W0 level, starting with wave functions computed in ab initio molecular dynamics simulations. We show excellent agreement between theory and experiments for the positions of both the solute and solvent excitation energies on an absolute energy scale and for peak intensities. The best comparison was obtained using wave functions obtained with dielectric-dependent self-consistent and range-separated hybrid functionals. Our computational protocol opens the way to accurate, predictive calculations of the electronic properties of electrolytes, of interest to a variety of energy problems.

Theoretical studies of proton-coupled electron transfer (PCET) reactions for model systems provide insight into fundamental concepts relevant to bioenergetics. A dynamical theoretical formulation for vibronically nonadiabatic PCET reactions has been developed. This theory enables the calculation of rates and kinetic isotope effects, as well as the pH and temperature dependences, of PCET reactions. Methods for calculating the vibronic couplings for PCET systems have also been developed and implemented. These theoretical approaches have been applied to a wide range of PCET reactions, including tyrosyl radical generation in a tyrosine-bound rhenium polypyridyl complex, phenoxyl/ phenol and benzyl/toluene self-exchange reactions, and hydrogen abstraction catalyzed by the enzyme lipoxygenase. These applications have elucidated some of the key underlying physical principles of PCET reactions. The tools and concepts derived from these theoretical studies provide the foundation for future theoretical studies of PCET in more complex bioenergetic systems such as Photosystem II.

The nuclear-electronic orbital nonorthogonal configuration interaction (NEO-NOCI) approach is presented. In this framework, the hydrogen nuclei are treated quantum mechanically on the same level as the electrons, and a mixed nuclear-electronic time-independent Schrodinger equation is solved with molecular orbital techniques. For hydrogen transfer systems, the transferring hydrogen is represented by two basis function centers to allow delocalization of the nuclear wave function. In the two-state NEO-NOCI approach, the ground and excited state delocalized nuclear-electronic wave functions are expressed as linear combinations of two nonorthogonal localized nuclear-electronic wave functions obtained at the NEO-Hartree-Fock level. The advantages of the NEO-NOCI approach are the removal of the adiabatic separation between the electrons and the quantum nuclei, the computational efficiency, the potential for systematic improvement by enhancing the basis sets and number of configurations, and the applicability to a broad range of chemical systems. The tunneling splitting is determined by the energy difference between the two delocalized vibronic states. The hydrogen tunneling splittings calculated with the NEO-NOCI approach for the [He-H-He]+ model system with a range of fixed He-He distances are in excellent agreement with NEO-full CI and Fourier grid calculations. These benchmarking calculations indicate that NEO-NOCI is a promising approach for the calculation of delocalized, bilobal hydrogen wave functions and the corresponding hydrogen tunneling splittings.