Resonances and pseudoresonances in a potential with attractive coulomb tail: A study using analytic‐continuation techniques

Abstract

AbstractThe performance of the complex absorbing potential (CAP) and the complex scaling (CS) methods in the detection and calculation of complex Siegert energies is studied using a 1‐D long‐range attractive model potential. This potential is constructed to mimic molecular properties, in particular an attractive Coulombic term, to allow one to draw conclusions on molecular ab initio studies. Analyzing the spectrum of the model potential, one compact bound state embedded in the manifold of Rydberg states is found that shows artificial resonance characteristics when applying the CAP and the CS methods. This pseudoresonance problem is less pronounced in the calculation using the CS method than in that using the CAP method. Despite this deficiency, the CAP method is shown to possess advantages over CS when dealing with physical resonances under conditions that simulate the application of standard basis sets in ab initio calculations. The accuracy of the Siegert energy is shown to be maintained when applying a subspace projection technique to the CAP method. This technique reduces the computational demand significantly and leads to an important improvement of the CAP method, which should be of particular significance in molecular applications. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003