Self-Interaction Corrected Functional Calculations of a Dipole-Bound Molecular Anion

Orbital-optimized density functional calculations of molecular Rydberg excited states with real space grid representation and self-interaction correction

Density functional calculations of Rydberg excited states up to high energy are carried out for several molecules using an approach where the orbitals are variationally optimized by converging on saddle points on the electronic energy surface within a real space grid representation. Remarkably good agreement with experimental estimates of the excitation energy is obtained using the generalized gradient approximation (GGA) functional of Perdew, Burke, and Ernzerhof (PBE) when Perdew-Zunger self-interaction correction is applied in combination with complex-valued orbitals. Even without the correction, the PBE functional gives quite good results despite the fact that corresponding Rydberg virtual orbitals have positive energy in the ground state calculation. Results obtained using the Tao, Perdew, Staroverov, and Scuseria (TPSS) and r2SCAN meta-GGA functionals are also presented, but they do not provide a systematic improvement over the results from the uncorrected PBE functional. The grid representation combined with the projector augmented-wave approach gives a simpler and better representation of diffuse Rydberg orbitals than a linear combination of atomic orbitals with commonly used basis sets, the latter leading to an overestimation of the excitation energy due to confinement of the excited states.

Use of FLOSIC for understanding anion-solvent interactions

An Achille's heel of lower-rung density-functional approximations is that the highest-occupied-molecular-orbital energy levels of anions, known to be stable or metastable in nature, are often found to be positive in the worst case or above the lowest-unoccupied-molecular-orbital levels on neighboring complexes that are not expected to accept charge. A trianionic example, [Cr(C2O4)3]3-, is of interest for constraining models linking Cr isotope ratios in rock samples to oxygen levels in Earth's atmosphere over geological timescales. Here we describe how crowd sourcing can be used to carry out self-consistent Fermi-Löwdin-Orbital-Self-Interaction corrected calculations (FLOSIC) on this trianion in solution. The calculations give a physically correct description of the electronic structure of the trianion and water. In contrast, uncorrected local density approximation (LDA) calculations result in approximately half of the anion charge being transferred to the water bath due to the effects of self-interaction error. Use of group-theory and the intrinsic sparsity of the theory enables calculations roughly 125 times faster than our initial implementation in the large N limit reached here. By integrating charge density densities and Coulomb potentials over regions of space and analyzing core-level shifts of the Cr and O atoms as a function of position and functional, we unambiguously show that FLOSIC, relative to LDA, reverses incorrect solute-solvent charge transfer in the trianion-water complex. In comparison to other functionals investigated herein, including Hartree-Fock and the local density approximation, the FLOSIC Cr 1s eigenvalues provide the best agreement with experimental core ionization energies.

Probing Dipole-Bound States Using Photodetachment Spectroscopy and Resonant Photoelectron Imaging of Cryogenically Cooled Anions

Molecular anions with polar neutral cores can support highly diffuse dipole-bound states below their detachment thresholds due to the long-range charge-dipole interaction. Such nonvalence states constitute a special class of excited electronic states for anions and were observed in early photodetachment experiments to measure the electron affinities of organic radicals. Recent experimental advances, in particular, the ability to create cold anions using a cryogenically cooled Paul trap, have allowed the investigation of dipole-bound excited states at a new level. For the first time, the zero-point level of dipole-bound excited states can be observed via resonant two-photon detachment, and resonant photoelectron spectroscopy can be performed via the above-threshold vibrational levels (Feshbach resonances) of the dipole-bound states. This Perspective describes recent progress in the investigation of dipole-bound states in the authors' lab using an electrospray photoelectron spectroscopy apparatus equipped with a cryogenically cooled Paul trap and high-resolution photoelectron imaging.

How Accurately Can DFT Describe Non-valence Anions?

Weakly bound non-valence anions are molecular systems where the excess electron stabilizes in a very diffuse orbital whose size, shape, and binding energy (∼1-100 meV) are governed by the long-range electrostatic potential of the molecule. Its binding energy comes mainly from charge-dipole or charge-multipole interactions or dispersion forces. While highly correlated methods, like coupled cluster methods, are considered to be the state of the art for describing anionic systems, especially when the electron lies in a very diffuse orbital, we consider here the possibility to use DFT-based calculations. In such molecular anions, the outer electron experiences long-range exchange and correlation interactions. We show that DFT can describe long-range bound states provided that a correct asymptotic exchange and correlation potential is used, namely, that from a range-separated hybrid functional. This opens an alternative to the computationally demanding highly correlated method calculations. It is also suggested that the study of weakly bound anions could help in the construction of new DFT potentials to study systems where nonlocal effects are significant.

Ultrafast Imaging of the Jahn-Teller Topography in Carbon Tetrachloride

We report the direct time-domain observation of ultrafast dynamics driven by the Jahn-Teller effect. Using time-resolved photoelectron spectroscopy with a vacuum-ultraviolet femtosecond source to prepare high-lying Rydberg states of carbon tetrachloride, our measurements reveal the local topography of a Jahn-Teller conical intersection. The pump pulse prepares a configurationally mixed superposition of the degenerate ¹T₂ 4p-Rydberg states, which then distorts through spontaneous symmetry breaking that we identify to follow the t₂ bending motion. Photoionization of these states to three cationic states ²T₁, ²T₂, and ²E reveals a shift in the center-of-mass of the photoelectron peaks associated with the ²T_n states which reveals the local topography of the Jahn-Teller conical intersection region prepared by the pump pulse. Time-dependent density functional theory calculations confirm that the dominant nuclear motion observed in the spectrum is the CCl₄ t₂ bending mode. The large density of states in the VUV spectral region at 9.33 eV of carbon tetrachloride and strong vibronic coupling result in ultrafast decay of the excited-state signal with a time constant of 75(4) fs.

Variational calculations of excited states via direct optimization of the orbitals in DFT

A direct optimization method for obtaining excited electronic states using density functionals is presented.