Structure Optimization of Temporary Anions

Signatures of s-wave scattering in bound electronic states

We compute EOM-EA-CCSD and EOM-EA-CCSDT potential energy curves and one-electron properties of several anions at bond lengths close to where these states become unbound. We compare the anions of HCl and pyrrole, which are associated with s-wave scattering, with N2 and H2, which correspond to resonances. For HCl and pyrrole, we observe, on inclusion of diffuse basis functions, a pronounced bending effect in the anionic potential energy curves near the crossing points with their corresponding neutral molecules. Additionally, we observe that the Dyson orbital and second moment of the electron density become extremely large in this region; for HCl, the size of the latter becomes 5 orders of magnitude larger over a range of 5 pm. This behaviour is not observed in H2 or N2. Our work thus shows that bound state electronic-structure methods can distinguish between anions that turn into electronic resonances and those associated with s-wave scattering states.

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.

Analytic Evaluation of Nonadiabatic Couplings within the Complex Absorbing Potential Equation-of-Motion Coupled-Cluster Method

We present the theory for the evaluation of nonadiabatic couplings (NACs) involving resonance states within the complex absorbing potential equation-of-motion coupled-cluster (CAP-EOM-CC) framework implemented within the singles and doubles approximation. Resonance states are embedded in the continuum and undergo rapid decay through autodetachment. In addition, nuclear motion can facilitate transitions between different resonances and between resonances and bound states. These nonadiabatic transitions affect the chemical fate of resonances and have distinct spectroscopic signatures. The NAC vector is a central quantity needed to model such effects. In the CAP-EOM-CC framework, resonance states are treated on the same footing as bound states. Using the example of fumaronitrile, which supports a bound radical anion and several anionic resonances, we analyze the NAC between bound states and pseudocontinuum states, between bound states and resonances, and between two resonances. We find that the NAC between a bound state and a resonance is nearly independent of the CAP strength and thus straightforward to evaluate, whereas the NAC between two resonance states or between a bound state and a pseudocontinuum state is more difficult to evaluate.

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.

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.

Software for the frontiers of quantum chemistry: An overview of developments in the Q-Chem 5 package

This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange-correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear-electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an "open teamware" model and an increasingly modular design.

Selective bond breaking of halothane induced by electron transfer in potassium collisions

We present novel experimental results of negative ion formation of halothane (C₂HBrClF₃) upon electron transfer from hyperthermal neutral potassium atoms (K°) in the collision energy range of 8-1000 eV. The experiments were performed in a crossed molecular beam setup allowing a comprehensive analysis of the time-of-flight (TOF) mass negative ions fragmentation pattern and a detailed knowledge of the collision dynamics in the energy range investigated. Such TOF mass spectra data show that the only negative ions formed are Br^-, Cl^- and F^-, with a strong energy dependence in the low-energy collision region, with the bromine anion being the most abundant and sole fragment at the lowest collision energy probed. In addition, potassium cation (K⁺) energy loss spectra in the forward scattering direction were obtained in a hemispherical energy analyser at different K° impact energies. In order to support our experimental findings, ab initio quantum chemical calculations have been performed to help interpret the role of the electronic structure of halothane. Potential energy curves were obtained along the C-X (X = Br, Cl) coordinate to lend support to the dissociation processes yielding anion formation.

Approximate equation-of-motion coupled-cluster methods for electron affinities of closed-shell molecules

We investigate performance of the equation-of-motion coupled-cluster method at the single and doubles level (EOM-CCSD) and a series of approximate methods based on EOM-CCSD on electron affinities (EA) of closed-shell cations and neutral molecules with positive and negative EAs in this work. Our results confirm that P-EOM-MBPT2 can provide reasonable EAs when molecules with significant multireference character are not considered and its mean absolute error on EAs of these molecules is around or less than 0.2 eV. Its accuracy is comparable to that of the more expensive EOM-CCSD(2) method. Results of EOM-CCSD(2), P-EOM-MBPT2, and CIS(D_∞) indicate that the [[H, a_c ⁺], T₂] term in the 1h2p-1h block is more important on EAs than the term neglected in the 1h2p-1h2p block in P-EOM-MBPT2. We proposed an economical method where EAs from CIS(D_∞) are corrected by treating this [[H, a_c ⁺], T₂] term in the 1h2p-1h block perturbatively [corr-CIS(D_∞)]. EAs with corr-CIS(D_∞) agree very well with those of P-EOM-MBPT2 with a difference of less than 0.02 eV. Computational scaling of this method is N⁴ for the iterative part and N⁵ for some non-iterative steps. Its storage requirement is only of OV³. Corr-CIS(D_∞) is an economical and reliable method on EAs, and it can be applied to EAs of large molecules.

EOM-CC guide to Fock-space travel: the C2 edition

Electronic structure calculations for C₂, C₂⁻, and C₂²⁻ using the CC/EOM-CC family of methods. Results illustrate that EOM-CCSD provides an attractive alternative to MR approaches.

Locating Exceptional Points on Multidimensional Complex-Valued Potential Energy Surfaces

We present a method for locating non-Hermitian degeneracies, called exceptional points (EPs), and minimum-energy EPs between molecular resonances using the complex absorbing potential equation-of-motion coupled-cluster (CAP-EOM-CC) method. EPs are the complex-valued analogue of conical intersections (CIs) and have a similar impact on nonadiabatic processes between resonances as CIs have on nonradiative transitions between bound states. We demonstrate that the CAP-EOM-CC method in the singles and doubles approximation (CAP-EOM-CCSD) yields crossings of the correct dimensionality. The use of analytic gradients enables applications to multidimensional problems. Results are presented for hydrogen cyanide and chloroethylene, for which the location of the crossings of anionic resonances is crucial for understanding the dissociative electron attachment process.

Real and Imaginary Excitons: Making Sense of Resonance Wave Functions by Using Reduced State and Transition Density Matrices

Within non-Hermitian quantum mechanics, metastable electronic states can be represented by isolated L²-integrable complex-valued wave functions with complex energies. An analysis scheme of the real and imaginary parts of resonance wave functions by using reduced transition density matrices and natural transition orbitals is presented. While the real parts of excitons describe changes in the electron density corresponding to the bound part of the resonance, the imaginary excitons can be interpreted as virtual states facilitating one-electron decay into the continuum. The different nature of real and imaginary excitons is revealed by exciton descriptors, in particular hole-particle separation and their correlation. Singular values and respective participation ratios quantify the extent of collectivity of the excitation and a number of distinct decay channels. The utility of the new tool is illustrated by the analysis of bound and metastable excited states of cyanopolyyne anions.