Stark Ionization of Atoms and Molecules within Density Functional Resonance Theory

Abstract

ABSTRACT:We show that the energetics and lifetimes of resonances of finite systems under an external electric field can be captured by Kohn-Sham density functional theory (DFT) within the formalism of uniform complex scaling. Properties of resonances are calculated self-consistently in terms of complex densities, potentials and wavefunctions using adapted versions of the known algorithms from DFT. We illustrate this new formalism by calculating ionization rates using the complex-scaled local density approximation and exact exchange. We consider a variety of atoms (H, He, Li and Be) as well as the H 2 molecule. Extensions are briefly discussed. SECTION: Spectroscopy, Photochemistry, and Excited States KEYWORDS: Resonances, Tunneling, Spectroscopy, Lasers, Excitations, Complex scaling, Open quantum systems.This document is the unedited Author's version of a Submitted Work that was subsequently accepted for publication in J.Phys.Chem.Lett., copyright c American Chemical Society after peer review. To access the final edited and published work see http://pubs.acs.org/doi/abs/10.1021/jz401110h. T he description of metastable compounds has been elusive to first-principles calculations due to the lack of a variational principle. The concepts of metastability and long-lived resonances (or tunneling processes) are closely related, and in the end we are facing the description of the lifetime of a given open quantum system. One approach to such calculations is the complex-scaling method, pioneered by Aguilar, Balslev and Combes. 1,2 Within this formalism, resonances appear as the result of a complex scaling r → re iθ of the real-space coordinates in the Hamiltonian. The method has been used to calculate resonance energies and lifetimes of negative ions of atoms, 3 as well as resonances induced by static electric fields. 4,5 Applications have however generally been limited to small systems or systems with reduced dimensionality due to the computational difficulty of solving many-particle problems. A different approach must be taken to accommodate realistic systems with many electrons. Recently it has been proven that the low-lying metastable states of a given system can be described within a density functional framework once we allow for complex densities. 6 An analog of the Hohenberg-Kohn theorem then allows for the calculation of the lowest-energy resonance of a system. Based on this, the first Kohn-Sham density functional resonance theory (DFRT) calculations have since been published, although limited to 1D systems with one or two electrons. 7,8 A notable ongoing development, termed complex DFT (CODFT), is based on complex absorbing potentials. 9,10 This method relies on the definition of an absorption zone outside the system boundary to calculate lifetimes based on how wavefunctions extend into the absorbing region. Another method is exterior complex scaling, where a complex coordinate scaling is applied outside of a certain radius. 11 The method presented in this Letter is based on uniform complex scaling, where all reg...

Real-space grids and the Octopus code as tools for the development of new simulation approaches for electronic systems

“…Note that no complex conjugation is performed on the left component in matrix elements such as the density or kinetic energy. In order to define the complex-scaled xc potential, it is necessary to perform an analytic continuation procedure [111]. In standard DFT, the KS equations are obtained by taking the functional derivative of the energy functional with respect to the density.…”

Isoquinoline-substituted triazole and pyran derivatives: synthesis and computational studies

“…The geometry optimizations of all the structures leading to energy minima were performed by the application of density functional theory (DFT) 59,60 at the level of B3LYP/6-31G(d,p) with no symmetry restrictions. The exchange term of B3LYP consists of hybrid Hartree-Fock and local spin density (LSD) exchange functions with…”

<strong>Isoquinoline-substituted hybrid compounds: synthesis and computational studies</strong>

“…The geometry optimizations of all the structures leading to energy minima were performed by the application of the density functional theory (DFT) 59,60 at the level of B3LYP/6-31G(d,p) with no symmetry restrictions. The exchange term of B3LYP…”