Proceedings - Interdisciplinary Center for Nanotoxicity

140
Conference on Current Trends in Computational Chemistry 2009
Empirical methods for Electronically Metastable Anions
Becky Weber and Thomas Sommerfeld
Southeastern Louisiana University, Department of Chemistry and Physics, SLU 10878
Hammond, LA 70402 USA
Most closed‐shell molecules have a negative vertical attachment energy. In other words,
when an electron is attached to a closed‐shell molecule at its equilibrium geometry, as a rule,
the energy goes up, and the radial anion that is formed is a short‐lived metastable species, an
anion that is unstable with respect to decaying back into a neutral molecule and a free electron.
In contrast to electronically stable states, metastable states, also referred to as
resonances, have finite lifetimes, and are embedded into a continuum of neutral‐plus‐free‐
electron states. Owing to their continuum nature these states cannot be described by square‐
integrable wavefunctions, but for an ab initio treatment one needs to use explicit, or at least
implicit, scattering approaches. Examples for explicit scattering methods are the R‐matrix and
the Complex‐Kohn method, examples for implicit scattering methods are the complex scaling,
the absorbing potential, and the stabilization methods. Needless to say that both explicit and
implicit scattering methods are computationally far more expensive than bound‐state
calculations for systems of similar size, and these approaches are thus limited to fairly small
molecules.
π* LUMO of furan. This orbital is only well‐defined
using a minimal basis set. It can still be computed with
larger basis sets, however, only if the basis set contains
no diffuse functions [3]. When basis sets with diffuse
functions are used the π* orbital will mix with orbitals
describing the neutral and a free electron, and in the
complete basis set limit the π* orbital will completely
“dissolve” in the neutral‐plus‐free‐electron continuum.
Due to the large computational effort associated with ab initio treatments of metastable
anions several empirical methods have been developed to compute the energy, though not the
lifetime, of certain classes of metastable radical anion. The most economical method is to
empirical scale the LUMO energy [1,2]. For this type of approach it is crucial to use a pure
valence basis sets without any diffuse function as the use of diffuse functions gives LUMOs with
too much continuum character [1,2,3], and for a set of hydrocarbons Dunning's double‐zeta set
(without any polarization or diffuse functions) turned out to yield the best correlation between
the experimentally determined attachment energy and the computed LUMO energy. More
recently it has been shown that for a larger class of compounds density functional calculations
for the lowest‐energy attachment state can also yield energies close to experiment [4,5]. Again,
the basis set, or artificial confinement, play the role of an empirical parameter, as calculations
at the basis set limit will yield attachment energies of 0 (for long‐range corrected functions) or
negative infinity (for self‐interaction uncorrected functional such as B3LYP).
Here we investigate the performance of empirical schemes for classes of metastable
states not in their fitting (or basis set selection) procedure, consider alternative empirical
schemes that do not rely on scaling the correlation‐energy contributions to the attachment