Assessment of Various Electronic Structure Methods for Characterizing Temporary Anion States: Application to the Ground State Anions of N2, C2H2, C2H4, and C6H6

Novel Approach for Predicting Vertical Electron Attachment Energies in Bulk-Solvated Molecules

When low-energy electrons interact with molecules, they can give rise to transient anion states commonly known as resonances. These states are formed through vertical electron attachment processes and have the potential to induce various forms of DNA lesions, including base damage, single- and double-strand breaks, cross-links, and clustered lesions that are challenging to repair. So far, most experimental and theoretical studies have investigated the formation of resonances of (bio)molecules in the gas phase or in microsolvated environments. Since cellular environments are mainly composed of water molecules, it is crucial to understand how bulk water affects the resonances of (bio)molecules. Given the existing gap in studies on resonances of bulk-solvated molecules, we propose a novel theoretical-computational approach to address this void. Our approach combines the multibasis-set (time-dependent-)density functional theory and self-consistent sequential quantum mechanics/molecular mechanics polarizable electrostatic embedding methods. We apply this combined methodology to predict the vertical electron attachment energies of 1-methyl-5-nitroimidazole (1M5NI), a well-known radiosensitizer model, in bulk water. In addition, we analyze the rapid mutual polarization between the resonances (both shape- and core-excited) of 1M5NI and the surrounding bulk water environment. For comparison, we also studied the isolated and microsolvated 1M5NI. Overall, while the polarization of the environment is clearly sensitive to the solute charge, causing a significant impact on the vertical electron affinity and consequently on the attachment electron energies, it does not have a significant impact on the excitation energies of the anion.

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.

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.

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.

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.

Multi-Basis-Set (TD-)DFT Methods for Predicting Electron Attachment Energies

The interaction of low-energy electron collisions with molecules may lead to temporary anions via resonant processes. While experimental measurements, e.g., electron transmission spectroscopy or dissociation electron attachment spectroscopy, are efficient to characterize the temporary anions, simulating the electron attachment is still very challenging. Here, we propose a methodology to calculate the resonance energies of the electron attachment using ab initio (TD)-DFT calculations together with two different basis sets: a large basis set with diffuse functions to compute the vertical electron affinity and a smaller one to calculate the excitation energy of the anion. To demonstrate the capabilities and the reliability of this computational approach, 53 resonance energies from 18 molecules are calculated and compared to experimental data.

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.

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 ²Π_g anion state of N₂.

Temporary anion states of fluorine substituted benzenes probed by charge transfer in O2 -·C6H6-xFx (x = 0-5) ion-molecule complexes

The broadband photoelectron source realized by detaching O₂ ^-·X (X = neutral unsaturated molecule) complexes offers a unique opportunity to probe temporary anion states of the unsaturated species. Detachment of the ion molecule complex typically accesses a dissociative portion of the neutral potential, creating a continuum electron source that can undergo scattering with X. We present the application of this new approach to electron-neutral scattering toward a study of the series of fluorinated benzenes via photoelectron spectroscopy of O₂ ^-·C₆H_6-xF_x (x = 0-6) measured with several photon energies. We compare these spectra to the reference O₂ ^-·hexane spectrum and observe evidence of temporary anion states of C₆H_6-xF_x for species with x = 0-5 in the form of enhanced signal intensity at electron kinetic energies coinciding with the energies of the temporary anions. Furthermore, we observe autodetachment features in the x = 3, 5 spectra. Results of calculations on the isolated symmetric isomer of C₆H₃F₃ suggest that the molecule cannot support a weakly-bound non-valence state that could be associated with the observed autodetachment. However, C₆HF₅ ^- is predicted to support a valence bound state, which, if produced by charge transfer from O₂ ^- with sufficient vibrational energy, may undergo autodetachment. Finally, the [O₂·C₆F₆]^- spectrum is unique insofar as the spectrum is substantially higher in binding energy and qualitatively different from the x = 0-5 spectra. This result suggests much stronger interactions and charge delocalization between O₂ ^- and C₆F₆.

Combination of a Voronoi-Type Complex Absorbing Potential with the XMS-CASPT2 Method and Pilot Applications

Electronic resonances are metastable (N + 1) electron states, in other words, discrete states embedded in an electronic continuum. While great progress has been made for certain types of resonances-for example, temporary anions created by attaching one excess electron to a closed shell neutral-resonances in general remain a great challenge of quantum chemistry because a successful description of the decay requires a balanced description of the bound and continuum aspect of the resonance. Here, a smoothed Voronoi complex absorbing potential (CAP) is combined with the XMS-CASPT2 method, which enables us to address the balance challenge by appropriate choice of the CAS space. To reduce the computational cost, the method is implemented in the projected scheme. In this pilot application, three temporary anions serve as benchmarks: the π* resonance state of formaldehyde; the π* and σ* resonance states of chloroethene as functions of the C-Cl bond dissociation coordinate; and the ⁴Π_u and ²Π_u resonance states of N₂^-. The convergence of the CAP/XMS-CASPT2 results has been systematically examined with respect to the size of the active space. Resonance parameters predicted by the CAP/XMS-CASPT2 method agree well with CAP/SAC-CI results (deviations of about 0.15 eV); however, as expected, CAP/XMS-CASPT2 has clear advantages in the bond dissociation region. The advantages of CAP/XMS-CASPT2 are further demonstrated in the calculations of ⁴Π_u and ²Π_u resonance states of N₂^- including their ³Σ_u⁺ and ³Δ_u parent states. Three of the involved states (²Π_u, ³Σ_u⁺, and ³Δ_u) possess multireference character, and CAP/XMS-CASPT2 can easily describe these states with a relatively modest active space.

Vibrationally Mediated Stabilization of Electrons in Nonpolar Matter

We explore solvation of electrons in nonpolar matter, here represented by butadiene clusters. Isolated butadiene supports only the existence of transient anions (resonances). Two-dimensional electron energy loss spectroscopy shows that the resonances lead to an efficient vibrational excitation of butadiene, which can result into the almost complete loss of energy of the interacting electron. Cluster-beam experiments show that molecular clusters of butadiene form stable anions, however only at sizes of more than 9 molecular units. We have calculated the distribution of electron affinities of clusters using classical and path integral molecular dynamics simulations. There is almost a continuous transition from the resonant to the bound anions with an increase in cluster size. The comparison of the classical and quantum dynamics reveals that the electron binding is strongly supported by molecular vibrations, brought about by nuclear zero-point motion and thermal agitation. We also inspected the structure of the solvated electron, finding it well localized.

Photoelectron spectroscopic study of I-·ICF3: a frontside attack SN2 pre-reaction complex

Photodetachment and 2D photoelectron spectra of the mass-selected I-·CF3I complex are presented together with electronic structure calculations. Calculations show that the I- is located at the iodine side of CF3I. Vertical and adiabatic detachment energies were measured at 4.03 and approximately 3.8 eV, respectively. The photoelectron spectra and molecular orbitals show a significant covalent bonding character in the cluster. The presence of electronic excited states is observed. Below threshold, iodide is generated which can be assigned to the photoexcitation of degenerate charge-transfer bands from the off-axis p-orbitals localised on iodide. Near the onset of two spin-orbit thresholds, bright excited states are seen in the experiment and calculations. Excitation of these leads to the formation of slow electrons. The spectroscopy of I-·CF3I is compared to the well-studied I-·CH3I cluster, a pre-reaction complex in the text-book I- + CH3I SN2 reaction. Despite the reversed stereodynamics (i.e. inversion of the CX3 between X = H and F) of the SN2 reaction, striking similarities are seen. Both complexes possess charge transfer excited states near their respective vertical detachment energies and exhibit vibrational structure in their photoelectron spectra. The strong binding is consistent with observations in crossed molecular beam studies and molecular dynamics simulations that suggest that iodine as a leaving group in an SN2 reaction affects the reaction dynamics.

Concluding remarks for advances in ion spectroscopy Faraday Discussion

Because the Introductory Lecture of this Faraday Discussion emphasized the recent history and exciting developments in the fields of experimental methods and applications of gaseous ion spectroscopy, these Concluding Remarks are, by design, directed somewhat more toward the roles played by theory. In discussing both the experimental and theoretical studies of gaseous ions, it is important to recognize and appreciate the delicate balance workers in the field are pursuing in terms of methodological/tool development and applications to current-day pressing problems in chemistry, physics, materials science, and biology. Without both components of modern research in this field, progress will not be efficient. Substantial discussion is included about the reductive approach that is commonly used to attempt to connect studies of ions in the gas phase (i.e., as isolated species) with properties of these ions as they exist in nature. Issues of how small a model system can be, to what extent surroundings/solvation can be addressed, and how our experimental or theoretical tools might limit us are all discussed in some detail. The current ability of theory to assist in the interpretation of experimental spectral data on gaseous ions is discussed, as are several of the most pressing limitations of theory on this front. Finally, the author offers his thoughts about what advances/improvements in theory are needed and the outlook for when they might be expected, and urges the experimental community to remain in close contact with theory groups developing new methods so that progress can be optimized.

Dependence on the Initial Configuration of Strong Field-Driven Isomerization of C2H2 Cations and Anions

We have investigated the femtosecond laser-induced fragmentation of C₂H₂ ^q ion beam targets in various initial configurations, including acetylene (linear HCCH), vinylidene (H₂CC), and cis/ trans. The initial configuration is shown to have a tremendous impact on the branching ratio of acetylene-like (CH ^q₁ + CH ^q₂) and vinylidene-like (C ^q₁' + CH₂ ^q₂') dissociation of a specific C₂H₂ ^q molecular ion. In particular, whereas C₂H₂⁺ generated from C₂H₂, a linear HCCH target, exhibits comparable levels of acetylene-like and vinylidene-like fragmentation, vinylidene or cis/ trans configuration ion beams preferably undergo vinylidene-like fragmentation, with an acetylene branching ratio ranging from 13.9% to zero.

Quantum Effects in Cold Molecular Collisions from Spatial Polarization of Electronic Wave Function

The quantum phenomena of electronic and nuclear resonances are associated with structures in measured cross sections. Such structures were recently reported in a cold chemistry experiment of ground-state hydrogen isotopologues (H₂/HD) colliding with helium atoms in the excited triplet P-state (He(2³P)) [Shagam et al. Nature Chem. 2015, 7, 921], but a theoretical explanation of their appearance was not given. This work presents a quantum explanation and simulation of this experiment, which are strictly based on ab initio calculations. We incorporate complex potential energy surfaces into adiabatic variational theory, thereby reducing the multidimensional scattering process to a series of uncoupled 1D scattering "gedanken experiments". Our theoretical result, which is in remarkable agreement with the experimental data, manifests that the structures in the observed reaction rate coefficient are due to the spatial arrangement of the excited He p-orbitals with respect to the interaction axis, consequently changing the system from a normal two-rotor model to a three-rotor one. This theoretical scheme can be applied to explain and predict cross sections or reaction rate coefficients for any resonance-related phenomenon.

Core-excited and shape resonances of uracil

Attachment of an electron to nucleobases leads to metastable anion states called resonances. There are two types of electronic resonances present in the nucleobases. Shape resonances occur when the electron is attached to one of the previously unoccupied π* orbitals of the base. An electron can also be attached to an electronically excited state leading to core-excited or Feshbach resonances. In this work we present both types of resonances of uracil, a nucleobase present in RNA. Both the positions and widths of the resonances have been calculated using a stabilization method coupled with high level electronic structure methods. Core-excited resonances which are accessed with electrons of energy >4.6 eV are expected to play an important role in the dissociative electron attachment of uracil. Mixing between configurations corresponding to shape and core-excited resonances is also present which complicates the theoretical treatment of this system and necessitates multiconfigurational approaches for a proper description.

Unravelling the dissociation pathways of acetic acid upon electron transfer in potassium collisions: experimental and theoretical studies

Electron transfer in alkali-molecule collisions with gas phase acetic acid and its deuterated analogues resulting in OH^- formation requires considerable internal rearrangement in the temporary negative ion. At a collision energy well above the threshold of negative ion formation, electron transfer from potassium to CH₃COOH/CH₃COOD and CD₃COOH results not only in H transfer from CH₃ to COOH/COOD, but also in H release from COOH and subsequent rearrangement to eliminate OH^-. These processes are also investigated by theoretical post-Hartree-Fock and DFT calculations. The combination of both studies reveals that the most favourable intermediate mechanism occurs via diol formation. Such intramolecular H transfer is reported here for the first time in the context of electron transfer induced dissociation experiments in alkali-molecule collisions. A comprehensive fragmentation study is presented and dissociation mechanisms are suggested.

Chemical pathways for poly-anionic isomerisation in the metastable anions of tetra-deprotonated naphthalene: an intra-molecular inter-ring proton-transfer

An intra-molecular proton-transfer between the two different aromatic rings of naphthalene in the metastable isomeric tetra-anionic species of naphthalene is revealed by this computational work.

Mechanisms of H and CO loss from the uracil nucleobase following low energy electron irradiation

Uracil anion fragments into 1-IM-, H and CO when an electron is attached to the D2 anionic state in a concerted mechanism.

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.