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6 nm super-resolution optical transmission and scattering spectroscopic imaging of carbon nanotubes using a nanometer-scale white light source

Abstract Optical transmission and scattering spectroscopic microscopy at the visible and adjacent wavelengths denote one of the most informative and inclusive characterization methods in material research. Unfortunately, restricted by the diffraction limit of light, it cannot resolve the nanoscale variation in light absorption and scattering, diagnostics of the local inhomogeneity in material structure and properties. Moreover, a large quantity of nanomaterials has anisotropic optical properties that are appealing yet hard to characterize through conventional optical methods. There is an increasing demand to extend the optical hyperspectral imaging into the nanometer length scale. In this work, we report a super-resolution hyperspectral imaging technique that uses a nanoscale white light source generated by superfocusing the light from a tungsten-halogen lamp to simultaneously obtain optical transmission and scattering spectroscopic images. A 6-nm spatial resolution in the visible to near-infrared wavelength regime (415–980 nm) is demonstrated on an individual single-walled carbon nanotube (SW-CNT). Both the longitudinal and transverse optical electronic transitions are measured, and the SW-CNT chiral indices can be identified. The band structure modulation in a SW-CNT through strain engineering is mapped.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Scattering Processes from Quantum Simulation Algorithms for Scalar Field Theories

We provide practical simulation methods for scalar field theories on a quantum computer that yield improved asymptotics as well as concrete gate estimates for the simulation and physical qubit estimates using the surface code. We achieve these improvements through two optimizations. First, we consider a finite volume approach for estimating the elements of the S-matrix. This approach is appropriate in general for 1+1D and for certain low-energy elastic collisions in higher dimensions. Second, we implement our approach using a series of different fault-tolerant simulation algorithms for Hamiltonians formulated both in the field occupation basis and field amplitude basis. Our algorithms are based on either second-order Trotterization or qubitization. The cost of Trotterization in occupation basis scales as O ( λ N 7 | Ω | 3 / ( M 5 / 2 ϵ 3 / 2 ) ) where λ is the coupling strength, N is the occupation cutoff, | Ω | is the volume of the spatial lattice, M is the mass of the particles and ϵ is the uncertainty in the energy calculation used for the S -matrix determination. Qubitization in the field basis scales as O ( | Ω | 2 ( k 2 Λ + k M 2 ) / ϵ ) , where k is the cutoff in the field and Λ is a scaled coupling constant. We find in both cases that the bounds suggest physically meaningful simulations can be performed using on the order of 4 × 10 6 physical qubits and 10 12 T -gates which corresponds to roughly one day on a superconducting quantum computer with surface code and a cycle time of 100 ns. This places the simulation of scalar field theory within striking distance of the gate counts for the best available chemistry simulation results.

Hardy, Andrew [Toronto U.] (ORCID:0000000235817382↗

Guanosine Dianions Hydrated by One to Four Water Molecules

Intermolecular interactions as those present in molecule…water complexes may profoundly influence the physico-chemical properties of molecules. Here, we carried out an experimentally-computational study on the doubly-deprotonated guanosine monophosphate…water clusters, [dGMP-2H] 2- •nH 2 O (n=1–4), using a combination of negative anion photoelectron spectroscopy (NIPES) with molecular dynamics (MD) and quantum chemical (QM) calculations. Successive addition of water molecules to [dGMP-2H] 2- increases the experimental adiabatic detachment (ADE) and vertical detachment energy (VDE) by 0.5 to 0.1 eV, depending on the cluster size. In order to choose the representative conformations, we combined MD simulations with a clustering procedure to identify low energy geometries for which ADEs and VDEs were computed at the CAM-B3LYP/6-31++G(d,p) level. Our results demonstrate that the assumed approach lead to the sound geometries and energetics of the studied micro-solvates since the calculated ADEs and VDEs are in pretty good agreement with the experimental characteristics. The evolution of hydrogen bonding with cluster size indicates possibility of the occurrence of proton transfer for clusters comprising a larger number of water molecules.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

K 2 CuX 3 (X = Cl, Br): All-Inorganic Lead-Free Blue Emitters with Near-Unity Photoluminescence Quantum Yield

Recently, copper(I) halides have been gaining increased attention as highly luminescent nontoxic alternatives to lead halide perovskites for optoelectronic applications. In this paper, we report preparation of blue emitting, lead free, all-inorganic halides K 2 CuX 3 (X = Cl, Br) through five synthetic methods including traditional solid-state and solution methods. The photoluminescence (PL) emission spectra of K 2 CuCl 3 and K 2 CuBr 3 exhibit narrow peaks centered at 392 and 388 nm with full widths at half-maximum (fwhm) values of ~54 nm. The visible bright blue emission is corroborated by the remarkably high photoluminescence quantum yield (PLQY) values up to ~97%. Furthermore, radioluminescence measurements on K 2 CuCl 3 yield a bright peak at 404 nm under irradiation with X-rays at 200 kVp and 20 mA, which is optimal for use with PMTs and Si photomultipliers, suggesting a strong potential of this family for radiation detection applications. Based on our combined experimental and computational investigations, the origin of the efficient luminescence in K 2 CuX 3 is attributed to the high stability self-trapped excitons (STE) formed in the one-dimensional anionic ∞ 1 [CuX 3 ] 2– chains. Advantageously, K 2 CuX 3 demonstrate improved air- and photostability compared to the previously reported copper(I) halides. The discovery of highly efficient and high stability light emitters based on earth-abundant copper(I) halides paves the way for their potential practical applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Empirically Optimized One-Electron Pseudopotential for the Hydrated Electron: A Proof-of-Concept Study

Mixed quantum-classical molecular dynamics simulations have been important tools for studying the hydrated electron. They generally use a one-electron pseudopotential to describe the interactions of an electron with the water molecules. Furthermore, this approximation shows both the strength and weakness of the approach. On the one hand, it enables extensive statistical sampling and large system sizes that are not possible with more accurate ab initio molecular dynamics methods. On the other hand, there has (justifiably) been much debate about the ability of pseudopotentials to accurately and quantitatively describe the hydrated electron properties. These pseudopotentials have largely been derived by fitting them to ab initio calculations of an electron interacting with a single water molecule. In this paper, we present a proof-of-concept demonstration of an alternative approach in which the pseudopotential parameters are determined by optimizing them to reproduce key experimental properties. Specifically, we develop a new pseudopotential, using the existing TBOpt model as a starting point, which correctly describes the hydrated electron vertical detachment energy and radius of gyration. In addition to these properties, this empirically optimized model displays a significantly modified solvation structure, which improves, for example, the prediction of the partial molar volume.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

A matrix completion algorithm for efficient calculation of quantum and variational effects in chemical reactions

This work examines the viability of matrix completion methods as cost-effective alternatives to full nuclear Hessians for calculating quantum and variational effects in chemical reactions. The harmonic variety-based matrix completion (HVMC) algorithm, developed in a previous study (https://doi.org/10.1063/5.0018326), exploits the low-rank character of the polynomial expansion of potential energy to recover, using a small sample, vibrational frequencies (square roots of nuclear Hessian eigenvalues) constituting the reaction path. Furthermore, these frequencies are essential for calculating rate coefficients using variational transition state theory with multidimensional tunneling (VTST-MT). HVMC performance is examined for four SN2 reactions and five hydrogen transfer reactions, with each H-transfer reaction consisting of at least one vibrational mode strongly coupled to the reaction coordinate. HVMC is robust and captures zero-point energies, vibrational free energies, zero-curvature tunneling, and adiabatic ground state and free energy barriers as well as their positions on the reaction coordinate. For medium to large reactions involving H-transfer, with the exception of the most complex Ir catalysis system, less than 35% of total eigenvalue information is necessary for accurate recovery of key VTST-MT observables.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Nature of polariton transport in a Fabry-Perot cavity

Fabry-Perot microcavities can strongly enhance interactions between light and molecules, leading to the formation of hybrid light-matter states known as polaritons. Polaritons possess much smaller effective masses and much larger group velocities when the molecules are resonant with cavity modes that have finite (nonzero) in-plane wave vectors, giving rise to the possibilities of long-range and ultrafast ballistic transport. In this paper, we present the results of numerical simulations of the ultrafast ballistic transport phenomenon in real space and time during and after initialization with a short, spatially localized pulse. Here, we address this problem with two approaches: the standard transfer-matrix method (TMM) for planar structures and a second simulation based on the numerical solution of the Maxwell-Bloch equations that can be used for general configurations (complex metasurfaces, for instance) and excitation modes. The agreement between the TMM and the full numerical calculation with the Maxwell-Bloch equations when applied to multilayer planar configurations provides proof of the validity of both approaches for the present analyses. Overall, we find that the transport of the molecular excitons inside the cavity synchronize with the evolution of the enhanced electromagnetic field inside the cavity. Moreover, the synchronized transport rate is in good agreement with the group velocities predicted from a calculated dispersion relation across a wide range of frequencies. Finally, we relate the group velocity to the Hopfield coefficient obtained from quantum modeling and suggest that the dependence of light-matter coupling on the in-plane wave vector can be an important but overlooked factor for understanding the transport behavior of polaritons. These simulations provide an intuitive tool for understanding the collective motion of light and excitons and helps us to better understand how experimental observations of polaritons should be interpreted.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Subspace recursive Fermi-operator expansion strategies for large-scale DFT eigenvalue problems on HPC architectures

Quantum mechanical calculations for material modeling using Kohn–Sham density functional theory (DFT) involve the solution of a nonlinear eigenvalue problem for N smallest eigenvector-eigenvalue pairs, with N proportional to the number of electrons in the material system. Here, these calculations are computationally demanding and have asymptotic cubic scaling complexity with the number of electrons. Large-scale matrix eigenvalue problems arising from the discretization of the Kohn–Sham DFT equations employing a systematically convergent basis traditionally rely on iterative orthogonal projection methods, which are shown to be computationally efficient and scalable on massively parallel computing architectures. However, as the size of the material system increases, these methods are known to incur dominant computational costs through the Rayleigh–Ritz projection step of the discretized Kohn–Sham Hamiltonian matrix and the subsequent subspace diagonalization of the projected matrix. This work explores the potential of polynomial expansion approaches based on recursive Fermi-operator expansion as an alternative to the subspace diagonalization of the projected Hamiltonian matrix to reduce the computational cost. Subsequently, we perform a detailed comparison of various recursive polynomial expansion approaches to the traditional approach of explicit diagonalization on both multi-node central processing unit and graphics processing unit architectures and assess their relative performance in terms of accuracy, computational efficiency, scaling behavior, and energy efficiency.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Robust, Accurate, and Efficient: Quantum Embedding Using the Huzinaga Level-Shift Projection Operator for Complex Systems

Using wave function (WF) in density functional theory (DFT) embedding methods provides a framework for performing localized, high-accuracy WF calculations on a system, while not incurring the full computational cost of the WF calculation on the full system. To effectively partition a system into localized WF and DFT subsystems, we utilize the Huzinaga level-shift projection operator within an absolutely localized basis. In this work, we study the ability of the absolutely localized Huzinaga level-shift projection operator method to study complex WF and DFT partitions, including partitions between multiple covalent bonds, a double bond, and transition-metal–ligand bonds. We find that our methodology can accurately describe all of these complex partitions. Additionally, we study the robustness of this method with respect to the WF method, specifically where the embedded systems were described using a multiconfigurational WF method. We found that the method is systematically improvable with respect to both the number of atoms in the WF region and the size of the basis set used, with energy errors less than 1 kcal/mol. Additionally, we calculated the adsorption energy of H2 to a model of an iron metal–organic framework (Fe-MOF-74) to within 1 kcal/mol compared to CASPT2 calculations performed on the full model while incurring only a small fraction of the full computational cost. In conclusion, this work demonstrates that the absolutely localized Huzinaga level-shift projection operator method is applicable to very complex systems with difficult electronic structures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A Sensitive Electrochemical Cholinesterase-Inhibiting Biosensor for Organophosphorus Pesticides Based on Ti 3 C 2 TX MXene Quantum Dots

Organophosphorus pesticides (OPs) pose significant environmental and health risks due to their widespread use and toxicity, primarily by inhibiting acetylcholinesterase. Traditional detection methods are often slow and costly, highlighting the urgent need for advanced, sensitive, and accessible technologies. This study developed a highly sensitive electrochemical cholinesterase-inhibiting biosensor for OP pesticides, utilizing Ti 3 C 2 T x MXene Quantum Dots (MQDs), which was synthesized via a hydrothermal method. The biosensor’s performance was characterized using electrochemical impedance spectroscopy, differential pulse voltammetry (DPV), and cyclic voltammetry. DPV proved to be the optimal technique, exhibiting an ultralow detection limit of 1 × 10 −17 M and a wide linear range (10 −14 –10 −8 M) for chlorpyrifos (a model OP) with an estimated inhibition constant of 62 nM. The biosensor demonstrated high selectivity for OPs (chlorpyrifos, acephate, glyphosate) over a non-target pyrethroid (permethrin), confirmed by distinct electrochemical signatures and compared to in vitro cholinergic activity assays in bean beetle homogenates. The enhanced performance is attributed to the high surface-to-volume ratio, quantum confinement effects, and superior conductivity of the MQDs, as well as the robust enzyme immobilization facilitated by glutaraldehyde cross-linking and a chitosan matrix. This work presents a promising platform for rapid, sensitive, and selective detection of OP pesticides, with potential applications in environmental monitoring and public health protection.

Chemistry↗

The ANI-1ccx and ANI-1x data sets, coupled-cluster and density functional theory properties for molecules

Abstract Maximum diversification of data is a central theme in building generalized and accurate machine learning (ML) models. In chemistry, ML has been used to develop models for predicting molecular properties, for example quantum mechanics (QM) calculated potential energy surfaces and atomic charge models. The ANI-1x and ANI-1ccx ML-based general-purpose potentials for organic molecules were developed through active learning; an automated data diversification process. Here, we describe the ANI-1x and ANI-1ccx data sets. To demonstrate data diversity, we visualize it with a dimensionality reduction scheme, and contrast against existing data sets. The ANI-1x data set contains multiple QM properties from 5 M density functional theory calculations, while the ANI-1ccx data set contains 500 k data points obtained with an accurate CCSD(T)/CBS extrapolation. Approximately 14 million CPU core-hours were expended to generate this data. Multiple QM calculated properties for the chemical elements C, H, N, and O are provided: energies, atomic forces, multipole moments, atomic charges, etc. We provide this data to the community to aid research and development of ML models for chemistry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A spectroscopic, structural, and computational study of Ag–oxo interactions in Ag + /UO 2 2+ complexes

For this work, twelve novel Ag + /UO 2 2+ heterometallic complexes have been prepared and characterized via structural, spectroscopic, and computational methods to probe the effects of Ag–oxo interactions on bonding and photophysical properties of the uranyl cation. Structural characterization reveals Ag–oxo interaction distances ranging from 2.475(3) Å to 4.287(4) Å. These interactions were probed using luminescence and Raman spectroscopy which displayed little effect on the luminescence intensity and the energy of the Raman active U═O symmetric stretch peak as compared to previously reported Pb–oxo interactions. Computational efforts via density functional theory-based natural bond orbital analysis revealed that the highest stabilization energy associated with the Ag–oxo interaction had a value of only 11.03 kcal mol –1 and that all other energy values fell at 7.05 kcal mol –1 or below indicating weaker interactions relative to those previously reported for Pb 2+ /UO 2 2+ heterometallic compounds. In contrast, quantum theory of atoms in molecules analysis of bond critical point electron density values indicated higher electron density in Ag–oxo interactions as compared to Pb–oxo interactions which suggests more covalent character with the Ag + . Overall, this data indicates that Ag + has a less significant effect on UO 2 2+ bonding and photophysical properties as compared to other Pb 2+ , likely due to the high polarizability of the cation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Development of neural network force fields for corrosion studies

To fully understand the chemistry and physics of corrosion, novel methods of simulation must be developed. One approach is designing machine learning (ML) algorithms integrated with density functional theory to develop adaptive force fields to gain insight into corrosion behavior namely at the surface of metal oxides. Current methods of modeling corrosion are slow due to the computational cost of resolving both reaction mechanics and mass transport processes. Machine learning methods can be implemented to obtain structure-activity relationships at both the molecular and bulk scale while still retaining the accuracy of density functional theory (DFT) and significantly decreasing the time needed for simulations of complex chemical processes in the various environments of corrosion. Multiscale models are needed for corrosion studies to fully understand its processes not only at the atomic length scale (chemical bonding, energies, and forces), but also at the nano and meso length scales (solid-state physics and material science processes). Current methods of study include DFT, molecular dynamics, and Monte Carlo. The limitation of DFT is that only a small number of atoms or molecules can be simulated at that level of theory. Density functional theory is used to study the electronic structure of atoms and molecules, and calculate the force component of each atom. However, these calculations are limited to about 1000 atoms. Custom periodic boundary conditions (PBC) can be used to describe the various environments and defects that affect the atomic forces to produce a large data set from which a training set can be derived. Machine learning can be utilized to overcome the barrier of modeling macroscopic and multi-scale processes from ab initio calculations through the development of adaptive force fields. Local environments determine the atomic forces of a given system, therefore adaptive force fields must be created to produce reliable quantum mechanical calculations. This can be achieved by developing a learning algorithm that uses the mapped atomic forces or fingerprint as an input to produce energies and magnetic moments as output. A systematic approach was used to begin to build a data set in order to accurately describe the atomic forces in various environments. In Figure 4 below, a simple PBC cell of Fe{sub 2}O{sub 3} was first optimized. A surface optimization was performed next, followed by a hydroxylated surface optimization. Once this calculation has converged, the adsorption of halide species to the hydroxylated surface will be investigated. TensorFlow is an open source platform for machine learning developed by Google. Using a high level application program interface (API) such as Keras allows for building and training ML models easily in a number of different environments and languages. For this project, a neural network was developed within Anaconda in Python. Future Work: Further development of reference data set; Refining neural network and learning algorithm; Fingerprinting atomic environment to enable mapping of atomic force components; Choosing appropriate training set from reference data; Learning from training set and enabling non-linear mapping of training set fingerprints and the atomic forces; Estimation of uncertainty to identify ranges of outside applicability; Testing and analysis of molecular dynamic simulations.

36 MATERIALS SCIENCE↗

Efficient simulation of open quantum systems coupled to a reservoir through multiple channels

It is challenging to simulate open quantum systems that are connected to a reservoir through multiple channels. For example, vibrations may induce fluctuations in both energy gaps and electronic couplings, which represent two independent channels of system–bath couplings. Systems of this kind are ubiquitous in the processes of excited state radiationless decay. Combined with density matrix renormalization group (DMRG) and matrix product states (MPS) methods, we develop an interaction-picture chain mapping strategy for vibrational reservoirs to simulate the dynamics of these open systems, resulting in time-dependent spatially local system–bath couplings in the chain-mapped Hamiltonian. This transformation causes the entanglement generated by the system–bath interactions to be restricted within a narrow frequency window of vibrational modes, enabling efficient DMRG/MPS dynamical simulations. We demonstrate the utility of this approach by simulating singlet fission dynamics using a generalized spin-boson Hamiltonian with both diagonal and off-diagonal system–bath couplings. This approach generalizes an earlier interaction-picture chain mapping scheme, allowing for efficient and exact simulation of systems with multi-channel system–bath couplings using matrix product states, which may further our understanding of nonlocal exciton–phonon couplings in exciton transport and the non-Condon effect in energy and electron transfer.

Chemistry↗

Magnetosynthesis Effect on the Structure and Ground State of Cu 2+ -Based Antiferromagnets

Synthetic variables can have an outsized influence on the crystal structure and magnetic properties of a material, particularly those of quantum materials. In this work, we investigate the impact of synthesis under a magnetic field (magnetosynthesis) on the crystal structure and magnetic properties of several Cu 2+ (S = 1/2)-based materials with antiferromagnetic interactions and varying levels of magnetic frustration, from simple antiferromagnets to a quantum spin liquid. Here, we develop methods to apply small (0.09–0.37 T) magnetic fields during low-temperature hydrothermal, evaporative, and rehydration syntheses of the simple antiferromagnet CuCl 2 ·2H 2 O, the canted antiferromagnet (Cu,Zn) 3 Cl 4 (OH) 2 ·2H 2 O, the frustrated and canted antiferromagnet atacamite Cu 2 (OH) 3 Cl, and the highly frustrated quantum spin liquid herbertsmithite Cu 3 Zn(OH) 6 Cl 2 . We report the first single-crystal X-ray structural determination of the Cu 3 Cl 4 (OH) 2 ·2H 2 O structure type and probe the stability of this phase both experimentally and computationally. Atacamite Cu 2 (OH) 3 Cl synthesized under a 0.19 T field experiences a 0.15 K (∼3%) decrease in its Néel transition temperature. This result suggests that magnetosynthesis with small applied fields may have a very subtle influence upon the magnetic properties of moderately magnetically frustrated 3 d materials.

36 MATERIALS SCIENCE↗

Study of Self-Interaction Errors in Density Functional Calculations of Magnetic Exchange Coupling Constants Using Three Self-Interaction Correction Methods

We examine the role of self-interaction errors (SIE) removal on the evaluation of magnetic exchange coupling constants. In particular we analyze the effect of scaling down the self-interaction-correction (SIC) for three non-empirical density functional approximations (DFAs) namely, the local spin density approximation, the Perdew-Burke-Ernzerhof generalized gradient approximation, and recent SCAN family of meta-GGA functionals. To this end, we employ three one-electron SIC methods: Perdew-Zunger [Perdew, J. P.; Zunger, A. Phys. Rev. B, 1981, 23, 5048] SIC, the orbitalwise scaled SIC method [Vydrov, O. A. et al., J. Chem. Phys. 2006, 124, 094108], and the recent local scaling method [Zope, R. R. et al., J. Chem. Phys. 2019, 151, 214108]. We compute the magnetic exchange coupling constants using the spin projection and non projection approaches for sets of molecules composed of dinuclear and polynuclear H-He models, organic radical molecules, and chlorocuprate, and compare these results against accurate theories and experiment. Our results show that for the systems that mainly consist of single electron regions, PZSIC performs well but for more complex organic systems and the chlorcuprates, an overcorrecting tendency of PZSIC combined with the DFAs utilized in this work is more pronounced, and in such cases LSIC with kinetic energy density ratio performs better than PZSIC. Furthermore, analysis of the results in terms of SIC corrections to the density and to the total energy shows that both density and energy correction are required to obtain an improved prediction of magnetic exchange couplings.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Study of self-interaction-errors in barrier heights using locally scaled and Perdew-Zunger self-interaction methods

We study the effect of self-interaction errors on the barrier heights of chemical reactions. For this purpose we use the well-known Perdew-Zunger [J. P. Perdew and A. Zunger, Phys. Rev. B,23, 5048 (1981)] self-interaction-correction(PZSIC), as well two variations of the recently developed, locally scaled self-interaction correction (LSIC) [Zope et al.,J. Chem. Phys.151, 214108 (2019)] to study the barrier heights of the BH76 benchmark dataset. Our results show that both PZSIC and especially the LSIC methods improve the barrier heights relative to the local density approximation(LDA). The version of LSIC that uses the iso-orbital indicator z as a scaling factor gives a more consistent improvement than an alternative version that uses an orbital-dependent factor based on the ratio of orbital densities to the total electron density. We show that LDA energies evaluated using the self-consistent and self-interaction-free PZSIC densities can be used to assess density-driven errors. Furthermore, the LDA reaction barrier errors for the BH76 set are found to contain significant density-driven errors for all types of reactions contained in the set, but the corrections due to adding SIC to the functional are much larger than those stemming from the density for the hydrogen transfer reactions and of roughy equal size for the non-hydrogen transfer reactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Competing ionization and dissociation: Extension of the energy-dependent frame transformation to the gerade symmetry of H 2

This article solves two major tasks that frequently arise in the theory of electron collisions with a target molecular cation. First, it extends the energy-dependent frame transformation (EDFT) treatment, which is needed to map fixed-nuclei electron-molecule scattering matrices into an energy-dependent laboratory-frame scattering matrix with vibrational channel indices. The EDFT mapping can now be carried out even when the target molecule possesses multiple low-energy potential curves, significantly transcending previous applications. Second, it implements a method to extract the rest of the full laboratory-frame scattering matrix, i.e., the columns and rows describing input and/or output dissociation channels. The treatment is benchmarked in this article against the essentially exact solution of a refined two-dimensional model of the singlet gerade Σ symmetry of H 2 . Our tests demonstrate that the theory accurately maps fixed-nuclei scattering information, of the type provided by existing electron-molecule computer codes, into a laboratory-frame scattering matrix that includes both ionization and dissociation. Furthermore, this treatment can provide a general framework applicable to a broad class of electron collision processes involving diatomic target ions, suitable for an accurate description of challenging processes such as dissociative recombination.

74 ATOMIC AND MOLECULAR PHYSICS↗