The spectral properties of Hamilton operators perturbed by a complex absorbing potential (CAP) are studied. For a wide class of CAPS proper eigenvalues of the perturbed Hamilton operator converge to Siegert resonance eigenvalues of the unperturbed Hamiltonian with decreasing CAP strength. The errors in the calculation of complex resonance energies caused by the additional CAP and by finite basis set representation are examined. In order to minimize these errors a scheme of approximations is provided. The application of this method allows for the use of real L2 basis sets. The feasibility and accuracy of the proposed method is demonstrated by calculations of resonance energies of a model potential and of the 2 Pi g shape resonance of N2.

The reflection and transmission properties of different complex absorbing potentials (CAPs) are studied using WKB and scaling procedures which make the results transferable to any mass and kinetic energy. Explicit formulas are obtained which describe the reflection and transmission properties of monomial CAPs −iηxn with high accuracy. These properties are now well understood. The approximate results are compared to exact analytical results available for quadratic CAPs, and to numerical results obtained by wave packet propagation followed by an energy resolved analysis. The approximate, but accurate, description of the action of the CAP is finally used to determine optimal CAP parameters. CAP length, strength, and order can now be chosen in such a way that the sum of reflection and transmission is minimized. Optimal parameters are compiled for different energies and energy intervals.

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.

The reflection properties of complex absorbing potentials (CAPs) are examined. Completely reflection-free CAPs are constructed by the introduction of small additional potential terms that remove the residual reflections. In order to simplify the computation of these additional terms several approximations are presented and discussed leading to reflection-reduced CAPs (RCAPs). As an alternative approach a transformative CAP (TCAP) method is introduced that uses a modified kinetic energy operator. By the TCAP method reflections can be avoided even more efficiently. The different effects that are responsible for the reflections are discussed in detail. Similarities and differences to the method of complex scaling are discussed. The feasibility and superiority of the methods to usual CAP methods is demonstrated by calculations of resonance energies for a model potential.

The derivation of the transformative complex absorbing potential (TCAP) method and its performance are discussed. This approach was developed in a previous paper (1995 J. Phys. B: At. Mol. Opt. Phys. 28 1475 and illustrates the relation between complex absorbing potentials (CAPs) and the smooth exterior scaling (SES) method. Starting from an energy-dependent CAP one arrives at an SES-like Hamiltonian via an elementary similarity transformation. Developing this idea further leads to the so-called TCAP equation. It differs from the SES Schrödinger equation in two respects. Firstly, the potential is not transformed and, secondly, an additional correction term appears. Neglecting this rather small term leads to a Hamilton operator that is easy to apply to time-dependent as well as time-independent problems. This Hamiltonian can be extended order by order ending up in the full SES Hamiltonian. By numerical application it is demonstrated that the TCAP approach is very efficient and can easily be generalized to the multi-dimensional case for which formulae are provided.

Information systems (IS) increasingly expand actor-to-actor networks beyond their temporal, organizational, and spatial boundaries. In such networks and through digital technology, IS enable distributed economic and social actors to not only exchange but also integrate their resources in materializing value co-creation processes. To account for such IS-enabled value co-creation processes in multi-actor settings, this research gives rise to the phenomenon of digital value co-creation networks (DVNs). In designing DVNs, it is not only necessary to consider underpinning value co-creation processes, but also the characteristics of the business environments in which DVNs evolve. To this end, our study guides the design of DVNs through employing servicedominant logic, a theoretical lens that conceptualizes value co-creation as well as business environments. Through an iterative research process, this study derives design requirements and design principles for DVNs, and eventually discusses how these design principles can be illustrated by expository design features for DVNs.Drawing on and integrating into extant value co-creation and S-D logic research, we give rise to the phenomenon of DVNs, briefly synthesize DVNs' conceptual constituents (i.e., digital infrastructure, value co-creation, and actor-to-actor networks), and introduce S-D logic as employed kernel theory. Digital value co-creation networksStill, little light has been shed on how actors engage in contexts of dyadic and physical resource integration (Breidbach

A metastable molecular dianion C 22 2 in a closed-shell 1 S 1 g state has been found. Using a complex absorbing potential in conjunction with a multireference configuration interaction wave function, the resonance position and width are calculated and their dependence on the nuclear charge Z is examined. Based on our findings the interpretation of a recent scattering experiment is questioned and an alternative experiment is proposed. [S0031-9007 (97)03848-9] PACS numbers: 31.25.Nj, 34.80.Kw, 36.40.Wa Dianionic species as small as O 22 or SO 22 4 are very common in solid state and solution chemistry, but it has only recently been shown that small doubly negative charged systems may exist as isolated entities [1,2]. In fact the smallest dianions which have been observed in a mass spectrometer (implying lifetimes of at least 10 25 sec) are C 22 7 [3] and S 2 O 22 6 [4]. Based on ab initio calculations many smaller systems have been predicted to form long-lived dianions [1], which consist typically of a central metal atom and three to eight fluorine or chlorine ligands. The smallest dianion predicted to be long-lived is LiF 22 3[5]. However, even if small solid-state dianions are unstable in the gas phase, they may nevertheless exist as shortlived metastable species. It is not possible to detect such temporary dianions directly in a mass spectrometer, but one may observe them as resonance structures in electron scattering from the associated monoanion. Reports on electron scattering from monoanions, especially in the energy region of only a few eV are rare, but recently the electron impact detachment cross section of the three anions H 2 , O 2 , and C 2 2 has been measured [6-9]. Both the detachment cross sections of H 2 and O 2 are smooth functions of energy and show no resonance structure. In contrast, in scattering from C 2 2 the detachment cross section exhibits a broad feature at an energy of about 10 eV, which has been interpreted in terms of a closedshell C 22 2 resonance state [9]. From a theoretical point of view the treatment of a resonance state is far more involved than the description of bound states and so far only calculations on metastable states of atomic dianions have been reported [10,11]. In this Letter we present evidence for a resonance state of C 22 2 which is to our best knowledge the first theoretical examination of a metastable molecular dianion in the literature. Specifically we investigate the closed-shell 1 S 1 g state of C 22 2 which is isoelectronic with the neutral N 2 molecule exhibiting the electron configuration ͑core͒ 4 ͑1s g ͒ 2 ͑1s u ͒ 2 ͑1p u ͒ 4 ͑2s g ͒ 2 .We emphasize that a metastable closed-shell state cannot be classified by one of the schemes developed for monoanionic resonances [12], since all monoanions possessing rare-gas-like electronic structures are bound.We begin with a brief description of the C 2 2 and C 2 states relevant in the present context. It is a well known fact that the target anion C 2 2 possesses three bound electronic states [13][14][15]. The electronic...

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