CAP/EA-ADC method for metastable anions: Computational aspects and application to π* resonances of norbornadiene and 1,4-cyclohexadiene

Complex potential energy surfaces with projected CAP technique: Vibrational excitation of N2

The projected complex absorbing potential (CAP) technique is one of the methods that allow one to extend the bound state methods for computing resonances' energies and widths. Here, we explore the accuracy of the potential energy curves generated with different electronic structure theory methods in combination with the projected CAP technique by considering resonant vibrational excitation (RVE) of N2 by electron impact as a model process. We report RVE cross sections computed using the boomerang model with potential energy curves obtained with CAP-based extended multistate complete active space perturbation theory (XMS-CASPT2) and equation of motion coupled-cluster method for electron attachment with single and double substitution (EOM-EA-CCSD) methods. We also compare potential energy curves computed with several electronic structure methods, including XMS-CASPT2, EOM-EA-CCSD, multireference configuration interaction with singles (MR-CIS) and singles and doubles (MR-CISD). A good agreement is observed between the experiment and simulated RVE cross sections obtained with the potential energy curves generated with XMS-CASPT2 and EOM-EA-CCSD methods, thus highlighting the potential of the projected CAP technique combined with accurate electronic structure methods for dynamical simulations of the processes that proceed through metastable electronic states.

Taming Negative Ion Resonances Using Nonlocal Exchange-Correlation Functionals

The characterization of negative ion resonances poses a fundamental challenge to density functional methods due to the unbound nature of resonances. To overcome this challenge, we propose one-particle nonlocal exchange-correlation (xc) potentials combining the exact-exchange (EXX) and the random phase approximation (RPA) correlation potentials. The negative ion resonances are identified by perturbing the real Hermitian nonlocal xc potentials using complex absorbing local potentials. Our studies show that the nonlocal EXX+RPA potential significantly enhances the description of positions and widths of negative ion resonance states compared to potentials that exclude dynamic polarization in RPA or include only EXX. The use of low-scaling algorithms simplifies the computation of the RPA potential, thereby providing a practical solution for resonance-state characterization within the density functional framework. A theoretical framework and the underlying assumptions required for combining real Hermitian nonlocal xc potentials with complex local potentials are discussed.

A New Strategy to Optimize Complex Absorbing Potentials for the Computation of Resonance Energies and Widths

Complex absorbing potentials (CAPs) are artificial potentials added to electronic Hamiltonians to make the wave function of metastable electronic states square-integrable. This makes the electronic-structure theory of resonances comparable to that of bound states, thus reducing the complexity of the problem. However, the most often used box and Voronoi CAPs depend on several parameters that have a substantial impact on the numerical results. Among these parameters are the CAP strength and a set of spatial parameters that define the onset of the CAP. It has been a common practice to minimize the perturbation of the resonance states due to the CAP by optimizing the strength parameter while fixing the onset parameters, although the performance of this approach strongly depends on the chosen onset. Here, we introduce a more general approach that allows one to optimize not only the CAP strength but also the spatial parameters. We show that fixing the CAP strength and optimizing the spatial parameters is a reliable way to minimize CAP perturbations. We illustrate the performance of this new approach by computing resonance energies and widths of the temporary anions of dinitrogen, ethylene, and formic acid. This is done at the Hartree-Fock and equation-of-motion coupled-cluster singles and doubles levels of theory using full and projected box and Voronoi CAPs.

Algebraic Diagrammatic Construction Schemes Employing the Intermediate State Formalism: Theory, Capabilities, and Interpretation

Algebraic diagrammatic construction (ADC) schemes represent a family of ab initio methods for the calculation of excited electronic states and electron-detached and -attached states. All ADC methods have been demonstrated to possess great potential for molecular applications, e.g., for the calculation of absorption or photoelectron spectra or electron attachment processes. ADC originates from Green's function or propagator theory; however, most recent ADC developments heavily rely on the intermediate state representation or effective Liouvillian formalisms, which comprise new ADC methods and computational schemes for high-order properties. The different approaches for the calculation of excitation energies, ionization potentials, and electron affinities are intimately related, and they provide a coherent description of these quantities at equivalent levels of theory and with comparable errors. Most quantum chemical program packages contain ADC methods; however, the most complete ADC suite of methods can be found in the recent release of Q-Chem.

Recent Advances in the Study of Negative-Ion Resonances Using Multiconfigurational Propagator and a Complex Absorbing Potential

The transient resonances are a challenge to bound state quantum mechanics. These states lie in the continuum part of the spectrum of the Hamiltonian. For this, one has to treat a continuum problem due to electron-molecule scattering and the many-electron correlation problem simultaneously. Moreover, the description of a resonance requires a wavefunction that bridges the part that resembles a bound state with another that resembles a continuum state such that the continuity of the wavefunction and its first derivative with respect to the distance between the incoming projectile and the target is maintained. A review of the recent advances in the theoretical investigation of the negative-ion resonances (NIR) is presented. The NIRs are ubiquitous in nature. They result from the scattering of electrons off of an atomic or molecular target. They are important for numerous chemical processes in upper atmosphere, space and even biological systems. A contextual background of the existing theoretical methods as well as the newly-developed multiconfigurational propagator tools based on a complex absorbing potential are discussed.

A high-efficiency decomposition method for mono and dimethylmercury induced by low-energy electron attachment (<≈7 eV): A computational insight into the decomposition mechanism of extremely toxic mercury compounds

Dimethylmercury (DMM) and monomethylmercury (MMM) are extremely toxic and dangerous environmental contaminants. Unfortunately, there is no effective way to remove these substances from the environment. This study looks into the efficient decomposition of DMM and MMM by low-energy electrons. The calculated quantum scattering properties reveal the presence of metastable electronic states in both molecules. An examination of the spatial features of the electronic resonances, as well as the computation and characterization of the vibrational normal modes, suggests possible bond break pathways of the metastable electronic states. Most electronic resonances result in the release of Hg(0), which is easily transported to the gas phase due to its low solubility in water and high volatility.

Ab Initio Molecular Dynamics of Temporary Anions Using Complex Absorbing Potentials

Dissociative electron attachment, that is, the cleavage of chemical bonds induced by low-energy electrons, is difficult to model with standard quantum-chemical methods because the involved anions are not bound but subject to autodetachment. We present here a new computational development for simulating the dynamics of temporary anions on complex-valued potential energy surfaces. The imaginary part of these surfaces describes electron loss, whereas the gradient of the real part represents the force on the nuclei. In our method, the forces are computed analytically based on Hartree-Fock theory with a complex absorbing potential. Ab initio molecular dynamics simulations for the temporary anions of dinitrogen, ethylene, chloroethane, and the five mono- to tetrachlorinated ethylenes show qualitative agreement with experiments and offer mechanistic insights into dissociative electron attachments. The results also demonstrate how our method evenhandedly deals with molecules that may undergo dissociation upon electron attachment and those which only undergo autodetachment.

Application of Box and Voronoi CAPs for Metastable Electronic States in Molecular Clusters

The complex absorbing potential (CAP) approach offers a practical tool for characterization of energies and lifetimes of metastable electronic states, such as temporary anions and core ionized states. Here, we present an implementation of the smooth Voronoi CAP combined with the equation-of-motion coupled cluster with single and double substitutions method for metastable states. The performances of the smooth Voronoi CAP and box CAP are compared for different classes of systems: resonances in isolated molecules and localized and delocalized resonances in molecular clusters. The benchmark calculations show that the Voronoi CAP is generally more robust when applied to molecular clusters, but box CAPs are equally reliable for localized resonances or in the cases when the resonance does not exhibit significant electron density delocalization into the intramolecular region. As such, the choice of the CAP shape and onset should be guided by the character of the metastable states.

Investigation of negative-ion resonances using a subspace-projected multiconfigurational electron propagator perturbed with a complex absorbing potential

The transient negative-ion resonances found in scattering experiments are important intermediates in many chemical processes. These metastable states correspond to the continuum part of the Hamiltonian of the projectile-target composite system. Usual bound-state electronic structure methods are not applicable for these. In this work, we develop a subspace-projection method in connection with an electron propagator (EP) defined in terms of a complete-active-space self-consistent-field initial state. The target Hamiltonian (Ĥ) is perturbed by a complex absorbing potential (CAP) for the analytical continuation of the spectrum of Ĥ to complex eigenvalues associated with the continuum states. The resonance is identified as a pole of the EP, which is stable with respect to variations in the strength of the CAP. The projection into a small subspace reduces the size of the complex matrices to be diagonalized, minimizes the computational cost, and affords some insight into the orbitals that are likely to play some role in the capture of the projectile. Two molecular (Πg2N₂ ^- and ²Π CO^-) and an atomic shaperesonance (²P Be^-) are investigated using this method. The position and width of the resonances are in good agreement with the previously reported values.

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.

Theory of electronic resonances: fundamental aspects and recent advances

Electronic resonances are states that are unstable towards loss of electrons. They play critical roles in high-energy environments across chemistry, physics, and biology but are also relevant to processes under ambient conditions that involve unbound electrons. This feature article focuses on complex-variable techniques such as complex scaling and complex absorbing potentials that afford a treatment of electronic resonances in terms of discrete square-integrable eigenstates of non-Hermitian Hamiltonians with complex energy. Fundamental aspects of these techniques as well as their integration into molecular electronic-structure theory are discussed and an overview of some recent developments is given: analytic gradient theory for electronic resonances, the application of rank-reduction techniques and quantum embedding to them, as well as approaches for evaluating partial decay widths.