Correlated complex independent particle potential for calculating electronic resonances

Abstract

We have formulated and applied an analytic continuation method for the recently formulated correlated independent particle potential [A. Beste and R. J. Bartlett J. Chem. Phys. 120, 8395 (2004)] derived from Fock space multireference coupled cluster theory. The technique developed is an advanced ab initio tool for calculating the properties of resonances in the low-energy electron-molecule collision problem. The proposed method quantitatively describes elastic electron-molecule scattering below the first electronically inelastic threshold. A complex absorbing potential is utilized to define the analytic continuation for the potential. A separate treatment of electron correlation and relaxation effects for the projectile-target system and the analytic continuation using the complex absorbing potential is possible, when an approximated form of the correlated complex independent particle potential is used. The method, which is referred to as complex absorbing potential-based correlated independent particle (CAP-CIP), is tested by application to the well-known (2)Pi(g) shape resonance of e-N(2) and the (2)B(2g) shape resonance of e-C(2)H(4) (ethylene) with highly satisfactory results.

Analytically continued Fock space multi-reference coupled-cluster theory: Application to the shape resonance

“…FSMRCC has been used to calculate the shape resonances in electron-atoms/molecule collisions [7][8][9]. In shape resonances, where the trapping of the projectile electron occurs in the potential well created by an angular momentum barrier and the attractive polarization forces at small distances of the molecule, target electrons are affected both statically and dynamically.…”

“…This is the method we adopt in the CAP-FSMRCC approach [8]. As shown in our previous publications, the treatment here is quite general [8,9]. In this approach the electron correlation, relaxation and the analytic continuation are treated together.…”

“…Recent years have witnessed advances in ab initio quantum chemical techniques using the analytical continuation methods for probing the electronic resonances in atoms and molecules [1][2][3][4][5][6][7][8][9][10]. The advantage of analytical continuation of the Hamiltonian in the complex plane giving the direct access to the resonances parameters is that they can be represented by using L 2 wavefunction [1].…”

“…The analytically continued effective Hamiltonian [8,9,23] in both the methods, which yields the exact wavefunction and complex energies -when operating on the model space, are obtained by solving the Bloch equation [24]. In principle, the analytically continued effective Hamiltonian can be constructed in a brute-force manner as in the conventional FSMRCC methods by solving the non-linear amplitude equations iteratively.…”

“…The accuracy of the effective oneparticle based approximations in the case of an electron scattering resonance depends on the extent to which the electron correlation is important in the description of particular states. CAP potentials have been applied to the molecular resonances in the context of configuration interaction [CI] [6] and electron propagator theories [3,4] and coupled-cluster based methods [7][8][9]. In these calculations, the resonance energies and width are calculated from the difference between the ground state total energies of the [N ± 1] and the neutral target.…”