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Using a hydrogen molecule as a test system we demonstrate how to compute the effective potential according to the formalism of the new density functional theory (DFT), in which the basic variable is the set of spherically averaged densities instead of the total density, used in the traditional DFT. The effective potential together the external potential, nuclear Coulomb potential, can be substituted in the Schrodinger like differential equation to obtain the spherically averaged electron density of the system. In the new method instead of one three-dimensional low symmetry equation one has to solve as many spherically symmetric equations as there are atoms in the system.
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The toolbox for imaging molecules is well-equipped today. Some techniques visualize the geometrical structure, others the electron density or electron orbitals. Molecules are many-body systems for which the correlation between the constituents is decisive and the spatial and the momentum distribution of one electron depends on those of the other electrons and the nuclei. Such correlations have escaped direct observation by imaging techniques so far. Here, we implement an imaging scheme which visualizes correlations between electrons by coincident detection of the reaction fragments after high energy photofragmentation. With this technique, we examine the H2 two-electron wave function in which electron-electron correlation beyond the mean-field level is prominent. We visualize the dependence of the wave function on the internuclear distance. High energy photoelectrons are shown to be a powerful tool for molecular imaging. Our study paves the way for future time resolved correlation imaging at FELs and laser based X-ray sources.
Analysis of the electron density distribution in clusters composed of hydrogen fluoride, water, and ammonia molecules, especially within the hydrogen-bond domains, reveals the existence of both sigma- and pi-binding between molecules. The sigma-kind density distribution determines the mutual orientation of molecules. A pi-system may be delocalized conjugated, which provides additional stabilization of molecular clusters. In those clusters where the sequence of hydrogen bonds is not planar, a peculiar kind of pi-conjugation exists. HF anion and H5O2 cation are characterized by quasi-triple bonds between the electronegative atoms. The most long-lived species stabilized by delocalized pi-binding are rings and open or closed hoops composed of fused rings. It is conjugated pi-system that determines cooperativity phenomenon.
Advanced oxidation processes that utilize highly oxidative radicals are widely used in water reuse treatment. In recent years, the application of sulfate radical (SO$_4cdot^-$) as a promising oxidant for water treatment has gained increasing attention. To understand the efficiency of SO$_4cdot^-$ in the degradation of organic contaminants in wastewater effluent, it is important to be able to predict the reaction kinetics of various SO$_4cdot^-$-driven oxidation reactions. In this study, we utilize density functional theory (DFT) and high-level wavefunction-based methods (including computationally-intensive coupled cluster methods), to explore the activation energies and kinetic rates of SO$_4cdot^-$-driven oxidation reactions on a series of benzene-derived contaminants. These high-level calculations encompassed a wide set of reactions including 110 forward/reverse reactions and 5 different computational methods in total. Based on the high-level coupled-cluster quantum calculations, we find that the popular M06-2X DFT functional is significantly more accurate for HO-additions than for SO$_4cdot^-$ reactions. Most importantly, we highlight some of the limitations and deficiencies of other computational methods, and we recommend the use of high-level quantum calculations to spot-check environmental chemistry reactions that may lie outside the training set of the M06-2X functional, particularly for water oxidation reactions that involve SO$_4cdot^-$ and other inorganic species.
The homogeneous electron gas (HEG) is a key ingredient in the construction of most exchange-correlation functionals of density-functional theory. Often, the energy of the HEG is parameterized as a function of its spin density $n$, leading to the local density approximation (LDA) for inhomogeneous systems. However, the connection between the electron density and kinetic energy density of the HEG can be used to generalize the LDA by evaluating it on a weighted geometric average of the local spin density and the spin density of a HEG that has the local kinetic energy density of the inhomogeneous system, with a mixing ratio $x$. This leads to a new family of functionals that we term meta-local density approximations (meta-LDAs), which are still exact for the HEG, which are derived only from properties of the HEG, and which form a new rung of Jacobs ladder of density functionals. The first functional of this ladder, the local $tau$ approximation (LTA) of Ernzerhof and Scuseria that corresponds to $x=1$ is unfortunately not stable enough to be used in self-consistent field calculations, because it leads to divergent potentials as we show in this work. However, a geometric averaging of the LDA and LTA densities with smaller values of $x$ not only leads to numerical stability of the resulting functional, but also yields more accurate exchange energies in atomic calculations than the LDA, the LTA, or the tLDA functional ($x=1/4$) of Eich and Hellgren. We choose $x=0.50$ as it gives the best total energy in self-consistent exchange-only calculations for the argon atom. Atomization energy benchmarks confirm that the choice $x=0.50$ also yields improved energetics in combination with correlation functionals in molecules, almost eliminating the well-known overbinding of the LDA and reducing its error by two thirds.
The treatment of atomic anions with Kohn-Sham density functional theory (DFT) has long been controversial since the highest occupied molecular orbital (HOMO) energy, $E_{HOMO}$, is often calculated to be positive with most approximate density functionals. We assess the accuracy of orbital energies and electron affinities for all three rows of elements in the periodic table (H-Ar) using a variety of theoretical approaches and customized basis sets. Among all of the theoretical methods studied here, we find that a non-empirically tuned range-separated approach (constructed to satisfy DFT-Koopmans theorem for the anionic electron system) provides the best accuracy for a variety of basis sets - even for small basis sets where most functionals typically fail. Previous approaches to solve this conundrum of positive $E_{HOMO}$ values have utilized non-self-consistent methods; however electronic properties, such as electronic couplings/gradients (which require a self-consistent potential and energy), become ill-defined with these approaches. In contrast, the non-empirically tuned range-separated procedure used here yields well-defined electronic couplings/gradients and correct $E_{HOMO}$ values since both the potential and resulting electronic energy are computed self-consistently. Orbital energies and electron affinities are further analyzed in the context of the electronic energy as a function of electronic number (including fractional numbers of electrons) to provide a stringent assessment of self-interaction errors for these complex anion systems.
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