J. Phys. B: At. Mol. Opt. Phys. 31 (1998) 4107–4122. Printed in the UK PII: S0953-4075(98)92102-2 Temporary anions—calculation of energy and lifetime by absorbing potentials: the N − 2 2 Π g resonance T Sommerfeld†§, U V Riss†, H-D Meyer†, L S Cederbaum†, B Engels‡ and H U Suter‡ † Theroretische Chemie, Physikalisch-Chemisches Institut, Universit¨ at Heidelberg, Im Neuenheimer Feld 253, 69120 Heidelberg, Germany ‡ Institut f¨ ur Physikalische und Theoretische Chemie, Universit¨ at Bonn, Wegelerstraße 12, 53115 Bonn, Germany Received 2 March 1998, in final form 15 June 1998 Abstract. The calculation of energies and lifetimes of metastable molecules requires the treatment of both the continuum and correlation effects. We describe the complex absorbing potential approach incorporated within a configuration-interaction framework. The absorbing potential method allows a very efficient solution of the continuum problem, making possible a detailed study of the correlation effects that turn out to be surprisingly strong. The famous N − 2 2  g resonance is studied as a test case and much attention is paid to an internally balanced treatment of the metastable state. Our findings are rationalized within a simple model that is then used to understand the results of various previous studies. 1. Introduction Negative ionic states which lie energetically above the ground state of the corresponding neutral species can decay by electron autodetachment. Such states are called anionic resonances or temporary anions. Their lifetime can, in general, be found in a range of 10 −13 –10 −15 s. The structural and spectroscopic properties of such states are similar to those of bound states and this is the reason why these systems are of particular interest to the physical chemist. In fact, resonance states can be understood as discrete states coupled to the continuum. They represent a particularly challenging problem to the quantum chemist because one has to treat a continuum problem, i.e. electron–molecule scattering, and the electron correlation simultaneously. In particular, the latter effect plays a crucial role in most temporary anions. To be more precise, resonance states are embedded into one or more continua so that the Rayleigh–Ritz variational method, which is the standard approach for the computation of correlated bound states, cannot be applied directly. Turning to the scattering problem, one finds that scattering calculations beyond the one-particle (i.e. static-exchange) level are difficult. Moreover, using a scattering approach the resonance parameters must be extracted from a cross section or phase shift, and it is thus difficult to interpret the results in terms of chemical concepts. This has led to a considerable interest in approaches that allow the description of temporary anionic states in a similar way to bound states. Historically the direct access to resonance states began with the treatment of the radioactive decay of nuclei by Gamow [1] and later by Siegert [2]. Instead of extracting § Present address: Physical and Theoretical Chemistry Laboratory, South Parks Road, Oxford OX1 3QZ, UK. 0953-4075/98/184107+16$19.50 c  1998 IOP Publishing Ltd 4107