Reliable Prediction of Charge Transfer Excitations in Molecular Complexes Using Time-Dependent Density Functional Theory

Reliable Prediction of Charge Transfer Excitations in Molecular Complexes Using Time-Dependent Density Functional Theor

Curvature and Frontier Orbital Energies in Density Functional Theory

Perdew et al. discovered two different properties of exact Kohn–Sham density functional theory (DFT): (i) The exact total energy versus particle number is a series of linear segments between integer electron points. (ii) Across an integer number of electrons, the exchange-correlation potential “jumps” by a constant, known as the derivative discontinuity (DD). Here we show analytically that in both the original and the generalized Kohn–Sham formulation of DFT the two properties are two sides of the same coin. The absence of a DD dictates deviation from piecewise linearity, but the latter, appearing as curvature, can be used to correct for the former, thereby restoring the physical meaning of orbital energies. A simple correction scheme for any semilocal and hybrid functional, even Hartree–Fock theory, is shown to be effective on a set of small molecules, suggesting a practical correction for the infamous DFT gap problem. We show that optimally tuned range-separated hybrid functionals can inherently minimize <i>both</i> DD and curvature, thus requiring no correction, and that this can be used as a sound theoretical basis for novel tuning strategies

Probing Ionic Complexes of Ethylene and Acetylene with Vacuum-Ultraviolet Radiation

Mixed complexes of acetylene–ethylene are studied using vacuum-ultraviolet (VUV) photoionization mass spectrometry and theoretical calculations. These complexes are produced and ionized at different distances from the exit of a continuous nozzle followed by reflectron time-of-flight mass spectrometry detection. Acetylene, with a higher ionization energy (11.4 eV) than ethylene (10.6 eV), allows for tuning the VUV energy and initializing reactions either from a C₂H₂⁺ or a C₂H₄⁺ cation. Pure acetylene and ethylene expansions are separately carried out to compare, contrast, and hence identify products from the mixed expansion: these are C₃H₃⁺ (<i>m</i>/<i>z</i> = 39), C₄H₅⁺ (<i>m</i>/<i>z</i> = 53), and C₅H₅⁺ (<i>m</i>/<i>z</i> = 65). Intensity distributions of C₂H₂, C₂H₄, their dimers and reactions products are plotted as a function of ionization distance. These distributions suggest that association mechanisms play a crucial role in product formation closer to the nozzle. Photoionization efficiency (PIE) curves of the mixed complexes demonstrate rising edges closer to both ethylene and acetylene ionization energies. We use density functional theory (ωB97X-V/aug-cc-pVTZ) to study the structures of the neutral and ionized dimers, calculate their adiabatic and vertical ionization energies, as well as the energetics of different isomers on the potential energy surface (PES). Upon ionization, vibrationally excited clusters can use the extra energy to access different isomers on the PES. At farther ionization distances from the nozzle, where the number densities are lower, unimolecular decay is expected to be the dominant mechanism. We discuss the possible decay pathways from the different isomers on the PES and examine the ones that are energetically accessible