Use of bound state methods to calculate partial and total widths of shape resonances.

In this work we study the 2Π resonances of a two-site model system designed to mimic a smooth transition from the 2Πg temporary anion of N2 to the 2Π temporary anion of CO. The model system possesses the advantage that scattering and bound state (L2) methods can be directly compared without obfuscating electron-correlation effects. Specifically, we compare resonance parameters obtained with the complex Kohn variational (CKV) method with those from stabilization, complex absorbing potential, and regularized analytical continuation calculations. The CKV calculations provide p-wave and d-wave widths, the sum of which provides a good approximation of the total width. Then we demonstrate that the width obtained with modified bound state methods depends on the basis set employed: It can be the total width, a partial width, or an ill-defined sum of partial widths. Provided the basis set is chosen appropriately, widths from bound state methods agree well with the CKV results.

Role of Overlap between the Discrete State and Pseudocontinuum States in Stabilization Calculations of Metastable States.

In a diabatic picture metastable states subject to decay by electron detachment can be viewed as arising from the coupling between a discrete state and a continuum. In treating such states with bound-state quantum chemical methods, the continuum is discretized. In this study, we elucidate the role of overlap in this interaction in the application of the stabilization method to temporary anion states. This is accomplished by use of a minimalist stabilization calculation on the lowest energy l=2 (D) resonance of the finite spherical well potential using two basis functions, one describing the diabatic discrete state and the other a diabatic discretized continuum state. We show that even such a simple treatment predicts a complex resonance energy in good agreement with the exact result. If the energy of the discrete state is assumed to be constant, which is tantamount to orthogonalizing the discretized continuum state to the discrete state, it is demonstrated that the square of the off-diagonal coupling has a maximum close to the crossing point of the orthogonalized diabatic curves and that the curvature in the coupling is responsible for the complex stationary point associated with the resonance. Moreover, this curvature is a consequence of the overlap between the two diabatic states.

A Fresh Look at the Role of the Coupling of a Discrete State with a Pseudocontinuum State in the Stabilization Method for Characterizing Metastable States.

The stabilization method is widely used to theoretically characterize temporary anions and other systems displaying resonances. In this approach, information about a metastable state is encoded in the interaction of a diabatic discrete state and discretized continuum solutions, the energy of which are varied by scaling the extent of the basis set. In this work, we identify the aspects of the coupling between the discrete state and the discretized continuum states that encode information about the existence of complex stationary points and, hence, complex resonance energies in stabilization graphs. This allows us to design a simple two-level model for extracting complex resonance energies from stabilization graphs. The resulting model is applied to the 2Πg anion state of N2.

Prediction of a Non-Valence Temporary Anion State of (NaCl)2.

The equation-of-motion coupled cluster method is used to characterize the low-lying anion states of (NaCl)2 in its rhombic structure. This species is known to possess a non-valence bound anion of Ag symmetry. Our calculations also demonstrate that it has a non-valence temporary anion of B2u symmetry, about 14 meV above threshold. The potential energy curves of the two anion states and of the ground state of the neutral molecule are reported as a function of distortion along the symmetric stretch normal coordinate. Implications for experimental detection of the temporary anion state are discussed. The sensitivity of the results to the inclusion of high-order correlation effects and of core correlation is examined.

Prediction of a Nonvalence Temporary Anion Shape Resonance for a Model (H2O)4 System.

Ab initio calculations are used to demonstrate the existence of a nonvalence temporary anion shape resonance for a model (H2O)4 cluster system with no net dipole moment. The cluster is composed of two water dimers, the distance between which is varied. Each dimer possesses a weakly bound nonvalence anion state. For large separations of the dimer subunits, there are two bound nonvalence anion states (of Ag and B2u symmetry) corresponding to the symmetric and asymmetric combinations of the nonvalence anion states of the two dimer subunits. As the separation between the dimer subunits is decreased, the B2u anion increases in energy and becomes a temporary anion shape resonance. The real part of the resonance energy is determined as a function of the distance between the dimers and is found to increase monotonically from just above threshold to 28 meV for the range of geometries considered. Over this same range of geometries, the resonance half-width varies from 0 to 21 meV. The B2u anion, both when bound and when temporary, has a very diffuse charge distribution. The effective radial potential for the interaction of the excess electron with the cluster has a barrier at large distance arising from the electron-quadrupole interaction in combination with the repulsive angular momentum ( l = 1) contribution. This barrier impacts both the resonance energy and its lifetime.

Ab initio calculation of the cross sections for electron impact vibrational excitation of CO via the (2)Π shape resonance.

The stabilization method is used to calculate the complex potential energy curve of the (2)Π state of CO(-) as a function of bond length, with the refinement that separate potentials are determined for p-wave and d-wave attachment and detachment of the excess electron. Using the resulting complex potentials, absolute vibrational excitation cross sections are calculated as a function of electron energy and scattering angle. The calculated cross sections agree well with experiment.

Assessment of various electronic structure methods for characterizing temporary anion states: application to the ground state anions of N2, C2H2, C2H4, and C6H6.

The theoretical characterization of temporary anions is an especially challenging problem. In the present study we assess the performance of several electronic structure methods when used in conjunction with the stabilization method to characterize temporary anion states. The ground state anions of N2, C2H2, C2H4, and C6H6 are used as the test systems, with the most extensive testing being done for N2. For the (2)Πg anion state of N2(-) the ADC(2), EOM-MP2, and EOM-CCSD methods give values of the resonance parameters in excellent agreement with the results of prior high-level calculations. For the hydrocarbon systems, the EOM-MP2 method consistently provides excellent agreement with the EOM-CCSD results for the test systems, whereas the ADC(2) considerably underestimates the widths for ethylene and benzene. Several density functional theory (DFT) approaches are tested and, although none performs as well as the EOM-MP2 method, it is found that inclusion of Hartree-Fock exchange greatly improves the results. Of the DFT-based methods, time-dependent DFT with standard correlation functionals and use of Hartree-Fock exchange provides the best performance for N2(-) over the range of bond lengths considered and is also found to give reasonable values of the resonance parameters of the three hydrocarbon molecules.