A spherical-box approach to resonances

Vibronic Correlations in Molecular Strong-Field Dynamics

We investigate the ultrafast vibronic dynamics triggered by intense femtosecond infrared pulses in small molecules. Our study is based on numerical simulations performed with 2D model molecules and analyzed in the perspective of the renowned Lochfrass and bond-softening models. We give a new interpretation of the observed nuclear wave packet dynamics with a focus on the phase of the bond oscillations. Our simulations also reveal intricate features in the field-induced nuclear motion that are not accounted for by existing models. Our analyses assign these features to strong dynamical correlations between the active electron and the nuclei, which significantly depend on the carrier envelope phase of the pulse, even for relatively "long" pulses, which should make them experimentally observable.

Projected Complex Absorbing Potential Multireference Configuration Interaction Approach for Shape and Feshbach Resonances

Anion resonances are formed as metastable intermediates in low-energy electron-induced reactions. Due to the finite lifetimes of resonances, applying standard Hermitian formalism for their characterization presents a vexing problem for computational chemists. Numerous modifications to conventional quantum chemical methods have enabled satisfactory characterization of resonances, but specific issues remain, especially in describing two-particle one-hole (2p-1h) resonances. An accurate description of these resonances and their coupling with single-particle resonances requires a multireference approach. We propose a projected complex absorbing potential (CAP) implementation within the multireference configuration interaction (MRCI) framework to characterize single-particle and 2p-1h resonances. As a first application, we use the projected-CAP-MRCI approach to characterize and benchmark the ²Π_g shape resonance in N₂^-. We test its performance as a function of the size of the subspace and other parameters, and we compute the complex potential energy surface of the ²Π_g shape resonance to show that a smooth curve is obtained. One key benefit of MRCI is that it can describe Feshbach resonances (most common examples of 2p-1h resonances) at the same footing as shape resonances. Therefore, it is uniquely positioned to describe mixing between the different channels. To test these additional capabilities, we compute Feshbach resonances in H₂O^- and anions of dicyanoethylene isomers. We find that CAP-MRCI can efficiently capture the mixing between the Feshbach and shape resonances in dicyanoethylene isomers, which has significant consequences for their lifetimes.

Variational Solutions for Resonances by a Finite-Difference Grid Method

We demonstrate that the finite difference grid method (FDM) can be simply modified to satisfy the variational principle and enable calculations of both real and complex poles of the scattering matrix. These complex poles are known as resonances and provide the energies and inverse lifetimes of the system under study (e.g., molecules) in metastable states. This approach allows incorporating finite grid methods in the study of resonance phenomena in chemistry. Possible applications include the calculation of electronic autoionization resonances which occur when ionization takes place as the bond lengths of the molecule are varied. Alternatively, the method can be applied to calculate nuclear predissociation resonances which are associated with activated complexes with finite lifetimes.

Predissociation spectra of the 35Cl-(H2) complex and its isotopologue 35Cl-(D2)

The predissociation spectra of the 35Cl-(H2) and 35Cl-(D2) complexes are determined within an accurate quantum approach and compared to those recently measured in an ionic trap at 8 K and 22 K. The calculations are performed using an existing three-dimensional potential energy surface. A variational approach is used for the accurate quantum calculations of the rovibrational bound states. Several methods are compared for the search and the characterization of the resonant states. A good agreement between the calculated and measured spectra is obtained, despite a slight shift to the red of the calculated spectra. The comparison shows that only the ortho or para contribution is observed in the measured 35Cl-(H2) or 35Cl-(D2) spectrum, respectively. Quantum numbers are assigned to the rovibrational resonant states. It demonstrates that the main features observed in the measured predissociation spectra correspond to a progression in the intermonomer vibrational stretching mode.

Interatomic and Intermolecular Coulombic Decay

Interatomic or intermolecular Coulombic decay (ICD) is a nonlocal electronic decay mechanism occurring in weakly bound matter. In an ICD process, energy released by electronic relaxation of an excited atom or molecule leads to ionization of a neighboring one via Coulombic electron interactions. ICD has been predicted theoretically in the mid nineties of the last century, and its existence has been confirmed experimentally approximately ten years later. Since then, a number of fundamental and applied aspects have been studied in this quickly growing field of research. This review provides an introduction to ICD and draws the connection to related energy transfer and ionization processes. The theoretical approaches for the description of ICD as well as the experimental techniques developed and employed for its investigation are described. The existing body of literature on experimental and theoretical studies of ICD processes in different atomic and molecular systems is reviewed.

Laser-induced blurring of molecular structure information in high harmonic spectroscopy

High harmonic spectroscopy gives access to molecular structure with Angström resolution. Such information is encoded in the destructive interferences occurring between the harmonic emissions from the different parts of the molecule. By solving the time-dependent Schrödinger equation, either numerically or with the molecular strong-field approximation, we show that the electron dynamics in the emission process generally results in a strong spectral smoothing of the interferences, blurring the structural information. However we identify specific generation conditions where they are unaffected. These findings have important consequences for molecular imaging and orbital tomography using high harmonic spectroscopy.

Resonance Energies and Lifetimes from the Analytic Continuation of the Coupling Constant Method: Robust Algorithms and a Critical Analysis

The energy of a metastable state can be computed by adding an artificial stabilizing potential to the Hamiltonian, increasing the stabilization until the metastable state is turned into a bound one, and then further increasing the stabilization until enough bound-state data have been collected so that these can be extrapolated back to vanishing stabilization. The lifetime of the metastable state can be obtained from the same data, but only if the extrapolation is performed by analytic continuation. This extrapolation method is called analytic continuation of the coupling constant (ACCC). Here we introduce preconditioning schemes for two of the three established extrapolation algorithms and critically compare results from all three extrapolation schemes in a variety of situations: As examples for resonance states serve the π* temporary anions of ethylene and formaldehyde as well as a model potential, which provides a case where input data with full numeric precision are available. In the data collection step, three different stabilizing potentials are employed, a Coulomb potential, a short-range Coulomb potential, and a soft-box Voronoi potential. Effects of different orders of the extrapolating Padé approximant are investigated, and last, the energy range of input data for the extrapolation is studied. Moreover, all ACCC results are compared to resonance parameters that have been independently obtained with the same theoretical method, but with a different continuum approach-complex scaling for the model and complex absorbing potentials for the temporary anions.

Empirical correlation methods for temporary anions

A temporary anion is a short-lived radical anion that decays through electron autodetachment into a neutral molecule and a free electron. The energies of these metastable species are often predicted using empirical correlation methods because ab initio predictions are computationally very expensive. Empirical correlation methods can be justified in the framework of Weisskopf-Fano-Feshbach theory but tend to work well only within closely related families of molecules or within a restricted energy range. The reason for this behavior can be understood using an alternative theoretical justification in the framework of the Hazi-Taylor stabilization method, which suggests that the empirical parameters do not so much correct for the coupling of the computed state to the continuum but for electron correlation effects and that therefore empirical correlation methods can be improved by using more accurate electronic structure methods to compute the energy of the confined electron. This idea is tested by choosing a heterogeneous reference set of temporary states and comparing empirical correlation schemes based on Hartree-Fock orbital energies, Kohn-Sham orbital energies, and attachment energies computed with the equation-of-motion coupled-cluster method. The results show that using more reliable energies for the confined electron indeed enhances the predictive power of empirical correlation schemes and that useful correlations can be established beyond closely related families of molecules. Certain types of σ* states are still problematic, and the reasons for this behavior are analyzed. On the other hand, preliminary results suggest that the new scheme can even be useful for predicting energies of bound anions at a fraction of the computational cost of reliable ab initio calculations. It is then used to make predictions for bound and temporary states of the furantrione and croconic acid radical anions.

Accurate quantum calculation of the bound and resonant rovibrational states of Li−(H2)

In a recent paper [B. Poirier, Chem. Phys. 308, 305 (2005)] a full-dimensional quantum method for computing the rovibrational dynamics of triatomic systems was presented, incorporating three key features: (1) exact analytical treatment of Coriolis coupling, (2) three-body "effective potential," and (3) a single bend angle basis for all rotational states. In this paper, these ideas are applied to the Li-(H2) electrostatic complex, to compute all of the rovibrational bound state energies, and a number of resonance energies and widths, to very high accuracy (thousandths of a wave number). This application is very challenging, owing to the long-range nature of the interaction and to narrow level spacings near dissociation. Nevertheless, by combining the present method with a G4 symmetry-adapted phase-space-optimized representation, only modest basis sizes are required for which the matrices are amenable to direct diagonalization. Several new bound levels are reported, as compared with a previous calculation [D. T. Chang, G. Surratt, G. Ristroff, and G. I. Gellene, J. Chem. Phys. 116, 9188 (2002)]. The resonances exhibit a clear-cut separation into shape and Feshbach varieties, with the latter characterized by extremely long lifetimes (microseconds or longer).

Extrapolating bound state data of anions into the metastable domain

Computing energies of electronically metastable resonance states is still a great challenge. Both scattering techniques and quantum chemistry based L2 methods are very time consuming. Here we investigate two more economical extrapolation methods. Extrapolating bound states energies into the metastable region using increased nuclear charges has been suggested almost 20 years ago. We critically evaluate this attractive technique employing our complex absorbing potential/Green's function method that allows us to follow a bound state into the continuum. Using the (2)Pi(g) resonance of N2- and the (2)Pi(u) resonance of CO2- as examples, we found that the extrapolation works suprisingly well. The second extrapolation method involves increasing of bond lengths until the sought resonance becomes stable. The keystone is to extrapolate the attachment energy and not the total energy of the system. This method has the great advantage that the whole potential energy curve is obtained with quite good accuracy by the extrapolation. Limitations of the two techniques are discussed.