On the possibility of analytically continuing stabilization graphs to determine resonance positions and widths accurately

Stabilizing potentials in bound state analytic continuation methods for electronic resonances in polyatomic molecules

“…Scattering methods [5][6][7][8][9][10] treat the continuum with explicit use of scattering boundary conditions in order to compute observables like the crosssection. Stabilization methods 11,12 and associated analytic continuation methods, [13][14][15] use continuum eigenvalues from bound state calculations to extract resonance a) Electronic mail: mhg@cchem.berkeley.edu b) Electronic mail: cwmccurdy@ucdavis.edu parameters. Complex coordinate methods 4,[16][17][18][19][20][21] compute the Siegert energy as an eigenvalue of a transformed, non-Hermitian, Hamiltonian operator.…”

Approximate calculation of lifetimes of resonance states in the continuum from real stabilization graphs

“…According to (6), the branching point of the E function occurs for D = kiV, and this implies that the branching point is closer to the real axis than the optimum 7 values, as stressed by McCurdy and McNutt [4]. Since the functions considered here are all analytic, we have no problem with the branching points.…”

“…In [4] pointed out that the energy curves belong to a multivalued algebraic function with branching points in the complex plane and that it is impossible to carry out the necessary analytic continuations from the real axis, across these branching points, to reach the complex resonance energies; instead they suggested that one should analytically continue the coefficients entering the characteristic polynomial. …”

Atomic and Molecular Complex Resonances from Real Eigenvalues Using Standard (Hermitian) Electronic Structure Calculations

“…In our approach a single real eigenvalue obtained from standard stabilization calculations is analytically continued into the complex plane. This idea is not new and it faced criticism in the past since the whole eigenvalue plot is not an analytical function of the scaling parameter [17]. The transition from a stabilization plot into the complex plane and the search for a stationary resonance state goes through a singularity point, known as a branch point (BP) [18].…”

“…Under this approach the resonance complex energy is obtained by analytically continuing a single eigenvalue into the complex plane, to this end the whole stabilization curve is used. However, as McCurdy and McNutt [17] multi-eigenvalue method is indeed pursued until today [28,29] and it relies on the correct description of the avoided crossings. Nevertheless, in this paper we show that under easy to fulfill conditions, resonances can be calculated from a single stabilization root, similar to Thompson and Truhlar [26].…”