Static-exchange Approximation Research Articles

Electron-Affinity Time-Dependent Density Functional Theory: Formalism and Applications to Core-Excited States.

The lack of particle-hole attraction and orbital relaxation within time-dependent density functional theory (TDDFT) lead to extreme errors in the prediction of K-edge X-ray absorption spectra (XAS). We derive a linear-response formalism that uses optimized orbitals of the n - 1-electron system as the reference, building orbital relaxation and a proper hole into the initial density. Our approach is an exact generalization of the static-exchange approximation that ameliorates the particle-hole interaction error associated with the adiabatic approximation and reduces errors in TDDFT XAS by orders of magnitude. With a statistical performance of just 0.5 eV root-mean-square error and the same computational scaling as TDDFT under the core-valence separation approximation, we anticipate that this approach will be of great utility in XAS calculations of large systems.

Joint experimental and theoretical study on low-energy elastic electron scattering by gaseous alkynes: Differential cross sections, shape resonances, and methylation effects

A detailed comparison of experimental and theoretical elastic cross sections for low-energy electron scattering by ethyne (${\mathrm{C}}_{2}{\mathrm{H}}_{2}$), taken earlier in our group by Gauf et al. [Phys. Rev. A 87, 012710 (2013)], and some of its methylated derivatives, propyne (${\mathrm{C}}_{3}{\mathrm{H}}_{4}$), and the isomers 1-butyne and 2-butyne ($n\ensuremath{-}{\mathrm{C}}_{4}{\mathrm{H}}_{6}, n=1,2$), taken here, are presented. The present differential cross sections were measured at incident electron energies ranging from 1 eV to 30 eV and for scattering angles from ${5}^{\ensuremath{\circ}}$ to ${130}^{\ensuremath{\circ}}$ using the relative flow method with an aperture gas source. Our earlier work was taken over a larger energy range of up to $100\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$. The theoretical calculations were carried out for impact energies up to $30\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$, employing the Schwinger multichannel method with pseudopotentials in the static-exchange plus polarization approximation. In addition to the differential cross sections, we present the integral and momentum transfer cross sections with which we discuss the shape resonances present in these systems and other physical phenomena, such as the presence of Ramsauer-Townsend minimum. We also compare our theoretical and experimental results with previous data that are available in the literature.

Elastic and electronically inelastic electron collisions by the thiophene molecule

Differential and integral cross sections for elastic and electronically inelastic scattering of electrons by the thiophene molecule were determined by means of the Schwinger multichannel method within the static-exchange plus polarization approximation in the energy range from 3.41 to 50 eV. We investigated the influence of multichannel coupling effects by calculating the cross sections according to different schemes of channel coupling that range from 1 to 61 open channels along with polarization effects, depending on the energy considered. The comparison of these results shows that the inclusion of more channels in the scattering calculations leads to a significant decrease in the magnitude of the cross sections. Present results corresponding to our best level of channel coupling at a given energy, both for elastic and electronically inelastic electron scattering by thiophene, display an overall good agreement with the data available in the literature.

Elastic electron scattering with formamide-(H2O) n complexes (n = 1, 2): Influence of microsolvation on the π * and σ * resonances* *Project supported by the National Natural Science Foundation of China (Grant Nos. U1504109 and 11604085) and the Program for Science and Technology Innovation Talents in the Universities of Henan Province, China (Grant No. 19HASTIT018).

We report elastic cross sections for low-energy electron scattering with formamide-(H2O) n complexes (n = 1, 2) in the energy region of 0.01–8 eV. The scattering calculations are performed using the R-matrix method in the static-exchange (SE) approximation. We consider three structures of formamide–H2O and six structures of formamide–(H2O)2 in the present work. Our purpose is to investigate effects of water molecules hydrogen-bonding to formamide. We focus on the influence of microsolvation on the π * and σ * resonances of formamide. The scattering result for complexes shows that the position of π * resonance appears at lower or higher energies in the cluster than in the isolated formamide depending on the complex structure and the water role in the hydrogen bonding. We explain this behavior according to the net charge of the solute. It is found that the microsolvation environment has a substantial effect on the width of π * resonance. Our results indicate that surrounding water molecules may affect the lifetime of the resonances, and hence the process is driven by the anion state, such as the dissociative electron attachment.

Validity of the static-exchange approximation for inner-shell photoionization of polyatomic molecules

Author(s): Marante, CA; Greenman, L; Trevisan, CS; Rescigno, TN; McCurdy, CW; Lucchese, RR | Abstract: The simple single-channel static-exchange approximation completely ignores correlation between the continuum and molecular ion electrons. In molecular systems with symmetry equivalent atoms, the single-channel approximation can seriously fail in core ionization when using delocalized orbitals to represent the core hole states. We present cross sections and molecular frame photoelectron angular distributions with both localized and delocalized core orbitals in CF4 F (1s) ionization. We show that only a full coupled-channel calculation can recover an accurate description of the physics of inner-shell photoionization when using delocalized orbitals, whereas nearly the same result can be obtained from independent single-channel static-exchange calculations when localized core orbitals are used. A grid-based variational method described here makes such single-channel calculations possible on larger systems without local-exchange approximations. Illustrative calculations on the core ionization of SF6 are presented to illustrate the power of the grid-based method.

Elastic-electron-scattering from 1,2-ethylenediamine and dimethyldiazene

We present elastic integral, differential and momentum transfer cross sections for scattering of electrons by 1,2-ethylenediamine (NH2C2H4NH2) and by dimethyldiazene (CH3N2CH3). The cross sections were computed with the Schwinger multichannel method implemented with norm-conserving pseudopotentials. The calculations were carried out in the static-exchange and static-exchange plus polarization approximations for energies up to 20 eV. We found the presence of a Ramsauer–Townsend minimum at around 0.38 eV in the integral cross section of 1,2-ethylenediamide and a π* shape resonance at around 1.0 eV in the integral cross section of dimethyldiazene, both cross sections computed in the static-exchange plus polarization approximation. In the static-exchange approximation the resonance is located at 3.5 eV. For dimethyldiazene we also employed an empirical scaling relation to estimate the vertical attachment energy and the value of 1.1 eV agree well with the position of the resonance of 1.0 eV obtained through the scattering calculation. We compare our results with recent calculations [G. L. C. de Souza, J. Electron Spectrosc. Relat. Phenom. 234, 64 (2019)] and found in general a very good agreement in the shape of the cross sections, but there are some discrepancies regarding their magnitude.

Elastic electron scattering by SnCl4 in the low-energy regime

We report integral, differential, and momentum-transfer cross sections for elastic scattering of electrons by tin tetrachloride (SnCl4). The scattering cross sections were calculated with the Schwinger multichannel method implemented with norm-conserving pseudopotentials, in the static-exchange and static-exchange plus polarization levels of approximation, for energies ranging from 0.01 eV to 30 eV. Our calculations show the presence of two resonant structures in the integral cross section located at 3.3 eV and 7.5 eV in the static-exchange approximation, while in the static exchange plus polarization approximation, these structures are centered around 1.2 eV and 5.6 eV. The symmetry decomposition of the integral cross section in both C2v and Td groups along with the analysis of the eigenvalues of the scattering Hamiltonian supports that the first resonance belongs to the T2 symmetry and the second to the E symmetry. Our results also support that the ground state of the negative ion SnCl4− is stable, in agreement with the results of previous studies. The low-energy behavior of the s-wave cross section and the s-wave eigenphase support the presence of a Ramsauer–Townsend minimum at 0.1027 eV. The present integral, differential, and momentum-transfer cross sections in the static exchange approximation are in good agreement with the previous results reported by Joucoski and Bettega [J. Phys. B: At. Mol. Opt. Phys. 35, 4953 (2002)]. In the static exchange plus polarization approximation, our integral cross section shows a good qualitative agreement with the measured grand-total cross section of Możejko et al. [J. Chem. Phys. 151, 064305 (2019)].

Solvent effects on the π* shape resonances of uracil

We have investigated the effect of microsolvation on the π* shape resonances of uracil, referred to as π1 * and π2 * in the order of increasing energy. Our study considered uracil-water aggregates with six solvent molecules obtained from Monte Carlo simulations in the liquid phase. To explore the ensemble statistics, we combined scattering calculations, performed in the static exchange and static exchange plus polarization approximations, with linear regressions of virtual orbital energies to the scattering results. In general, the solvent molecules stabilize the anion states, and the lower lying π1 * resonance becomes a bound state in most of the solute-water clusters. We also discuss how the strength of the H bonds can affect the energies of the anion states, in addition to the number and donor/acceptor characters of those bonds. The thermal distributions for the vertical attachment energies, obtained from 133 statistically uncorrelated solute-solvent clusters, are significantly broad in the energy scale of the autoionization widths. The distributions for the π1 * and π2 * anion states slightly overlap, thus giving rise to a quasi-continuum of attachment energies below ≲2.5 eV, in contrast to the gas phase picture of electron attachment to well separated resonances below the electronic excitation threshold. Both the stabilization of the anion states and the spread of attachment energies could be expected to favor the dissociative electron attachment processes believed to underlie the electron-induced damage to biomolecules.

Generalized single excitation configuration interaction: an investigation into the impact of the inclusion of non-orthogonality on the calculation of core-excited states.

In this paper, we investigate different non-orthogonal generalizations of the configuration interaction with single substitutions (CIS) method for the calculation of core-excited states. Fully non-orthogonal CIS (NOCIS) has been described previously for species with singlet and doublet ground states, and this paper reports the extension to molecules in their triplet ground state. In addition to NOCIS, we present a novel method, one-center NOCIS (1C-NOCIS), for open-shell molecules which is intermediate between NOCIS and the computationally less demanding static exchange approximation (STEX). We explore this hierarchy of spin-pure methods for core excitations of molecules with singlet, doublet, and triplet ground states. We conclude that, while NOCIS provides the best results and preserves the spatial symmetry of the wavefunction, 1C-NOCIS retains much of the accuracy of NOCIS at a dramatically reduced cost. For molecules with closed-shell ground states, STEX and 1C-NOCIS are identical.

Vibrationally-resolved excitation and dissociation collision strengths of AlO+ by electron-impact using the R-matrix method

The electron-impact calculations are reported for excitation and dissociation of AlO+ ion using the R-matrix method. Calculations are performed in the static-exchange (SE) and close-coupling (CC) approximation. Each target state in CC approximation is represented by a configuration interaction (CI) wavefunction that takes into account the correlation and polarisation effects. In CC approximation 14-target states are included in the trial wavefunction of the entire scattering system. Potential energy curves (PECs) for the first four low-lying states are generated using the basis functions 6-311G* wherein we obtain X1Σ+ as the ground state contrary to a3Π as stated elsewhere in literature. Scattering calculations are then performed to yield vibrationally-resolved electronic excitation collision strengths to the first three lowest excited states a3Π, A1Π and b3Σ+. Using more accurate PECs we calculated the Franck–Condon factors which were then employed to get the vibrationally-resolved electronic excitations and dissociation collision strengths for the fragment channel Al++O of the lowest three excited states a3Π, A1Π and b3Σ+. All scattering calculations are performed at the experimental bond length 1.6178 A of AlO+. Rotational excitation cross sections (0→j, j = 1, 2 … 5) have also been calculated and the corresponding rate coefficients have been evaluated for excitation and de-excitation by using the Maxwellian distribution function for electron temperature upto 5000 K. There are many Feshbach resonances detected in this work. We have analysed only the low-lying resonances below the excitation threshold of A1Π excited state. Beyond this threshold the resonance structure is too complex to analyse due to many overlapping resonances.

An ab initio investigation for elastic and electronically inelastic electron scattering from para-benzoquinone.

We report the results of ab initio calculations for elastic scattering and also for excitation of individual electronic states of para-benzoquinone (pBQ) by the impact of low-energy electrons. The calculations for elastic scattering were performed with the Schwinger multichannel method implemented with pseudopotentials (SMCPP) in the static-exchange (SE) plus polarization (SEP) approximation for energies up to 50 eV. The assignments for the resonance spectrum obtained in this study are, in general, in good agreement with previous results available in the literature. For electronic excitation by electron impact, the SMCPP method with N energetically open electronic states (N open ), at either the static-exchange (N open ch-SE) or the static-exchange-plus-polarisation (N open ch-SEP) approximation, was employed to calculate the scattering amplitudes using a channel coupling scheme that ranges from the 1ch-SEP up to the 89ch-SE level of approximation, depending on the energy of interest. Integral cross sections (ICSs) and differential cross sections (DCSs) were obtained for incident electron energies lying between 15 eV and 50 eV. The study focuses on the influence of multichannel coupling effects for electronically inelastic processes, more specifically, on how the number of excited states included in the open-channel space impacts upon the convergence of the cross sections at intermediate and higher energies. In particular, we found that the magnitude of DCS and ICS results for electronic excitation decreases as more channels are included in the calculations. To the best of our knowledge, there are no other experimental or theoretical ICS or DCS results for excitation into individual electronic states of pBQ available in the literature between 15 and 50 eV against which we might compare the present calculations.

Low-energy electron elastic scattering from ethylene oxide and thiirane

We present elastic integral cross sections for electron collisions with ethylene oxide and thiirane. The calculations were performed with R-matrix method in the static-exchange and static exchange polarization approximations for electron energies ranging from 0.01 to 15 eV. We found two shape resonances in the 2B1 and 2B2 symmetry in each molecule. We also detected one shape resonance in the 2A1 symmetry for thiirane. The positions of the resonances agree well with available results. We shed some light on the nature of the resonances of these two compounds together with molecular orbital calculations. The similarities and differences among the resonances are discussed.

Low-energy electron collisions with proline and pyrrolidine: A comparative study.

We present a comparative study on the calculated cross sections obtained for the elastic collisions of low-energy electrons with the amino acid proline (C5H9NO2) and its building block pyrrolidine (C4H9N). We employed the Schwinger multichannel method implemented with pseudopotentials to compute integral, differential, and momentum transfer cross sections in the static-exchange plus polarization approximation, for energies up to 15 eV. We report three shape resonances for proline at around 1.7 eV, 6.8 eV, and 10 eV and two shape resonances for pyrrolidine centered at 7 eV and 10.2 eV. The present resonance energies are compared with available experimental data on vertical attachment energies and dissociative electron attachment, where a good agreement is found. From the comparison of the present results with available calculated cross sections for the simplest carboxylic acid, formic acid (HCOOH), and from electronic structure calculations, we found that the first resonance of proline, at 1.7 eV, is due the presence of the carboxylic group, whereas the other two structures, at 6.8 eV and 10 eV, clearly arise from the pyrrolidine ring. A comparison between the differential cross sections for proline and pyrrolidine at some selected energies of the incident electron is also reported in this paper.

Variational treatment of electron–polyatomic-molecule scattering calculations using adaptive overset grids

The Complex Kohn variational method for electron-polyatomic molecule scattering is formulated using an overset grid representation of the scattering wave function. The overset grid consists of a central grid and multiple dense, atom-centered subgrids that allow the simultaneous spherical expansions of the wave function about multiple centers. Scattering boundary conditions are enforced by using a basis formed by the repeated application of the free particle Green's function and potential, $\hat{G}^+_0\hat{V}$ on the overset grid in a "Born-Arnoldi" solution of the working equations. The theory is shown to be equivalent to a specific Pad\'e approximant to the $T$-matrix, and has rapid convergence properties, both in the number of numerical basis functions employed and the number of partial waves employed in the spherical expansions. The method is demonstrated in calculations on methane and CF$_4$ in the static-exchange approximation, and compared in detail with calculations performed with the numerical Schwinger variational approach based on single center expansions. An efficient procedure for operating with the free-particle Green's function and exchange operators (to which no approximation is made) is also described.

Low energy electron-impact study of AlO using the R-matrix method

This comprehensive study reports the electron-impact on the open shell AlO molecule at low energy (less than 10 eV) using the R-matrix method. We present the elastic (integrated and differential), momentum-transfer, electronic excitation and ionisation cross sections; along with effective collision frequency over a wide electron temperature range (1000–100 000 K). Correlations via a configuration interaction technique are used to represent the target states. Calculations are performed in the static-exchange and 24-target states close-coupling approximation at the experimental bond length of 1.6178 A. We have used different basis sets 6-311G*, double zeta, polarization (DZP), cc-pCVTZ to represent our target states. We have chosen the Gaussian Type Orbitals (GTOs) basis set DZP to represent the atomic orbitals which gave the best one-electron properties of the molecule. The calculated dipole moment (1.713 au), rotational constant (0.641399 cm-1) and the vertical excitation energies are in concurrence with the best available data. The continuum electron is also represented by GTOs and is placed at the center of mass of the molecule. Resonance analysis is carried out to assign the resonance parameters and the parentage of detected resonances by fitting the eigenphase sums to the Breit–Wigner profile. Our study has detected three core-excited shape resonances in the 24-state model. We detect a stable bound state of AlO- of 1 A 1 symmetry having configuration 1σ 2 … 7σ 21π 42π 4 with a vertical electronic affinity value of 2.59 eV which is in good accord with the experimental value of 2.6 ± (0.01) eV. The ionisation cross sections are calculated using the Binary-Encounter-Bethe Model in which Hartree–Fock molecular orbitals at self-consistent level are used to calculate kinetic and binding energies of the occupied molecular orbitals. We include partial waves up to g-wave beyond which Born closure method is employed to obtain converged cross sections.

Calculation of photoionization differential cross sections using complex Gauss-type orbitals.

Accurate theoretical calculation of photoelectron angular distributions for general molecules is becoming an important tool to image various chemical reactions in real time. We show in this article that not only photoionization total cross sections but also photoelectron angular distributions can be accurately calculated using complex Gauss-type orbital (cGTO) basis functions. Our method can be easily combined with existing quantum chemistry techniques including electron correlation effects, and applied to various molecules. The so-called two-potential formula is applied to represent the transition dipole moment from an initial bound state to a final continuum state in the molecular coordinate frame. The two required continuum functions, the zeroth-order final continuum state and the first-order wave function induced by the photon field, have been variationally obtained using the complex basis function method with a mixture of appropriate cGTOs and conventional real Gauss-type orbitals (GTOs) to represent the continuum orbitals as well as the remaining bound orbitals. The complex orbital exponents of the cGTOs are optimized by fitting to the outgoing Coulomb functions. The efficiency of the current method is demonstrated through the calculations of the asymmetry parameters and molecular-frame photoelectron angular distributions of H2+ and H2. In the calculations of H2, the static exchange and random phase approximations are employed, and the dependence of the results on the basis functions is discussed. © 2017 Wiley Periodicals, Inc.

Transient negative ion spectrum of the cytosine-guanine pair

We employed elastic scattering calculations, performed in the static exchange approximation, to investigate the π ∗ transient anion states of cytosine, guanine and the cytosine-guanine pair. Our results for the isolated monomers, also obtained in the static-exchange plus polarization approximation, are in good agreement with the available calculations and electron transmission data. Virtual orbital analysis for the lower-lying π ∗ anion states, with pure shape resonance character, indicates that electron attachment to the cytosine-guanine pair gives rise to resonances located on either monomer (the orbitals do not delocalize over the pair). The π ∗ shape resonances of the pair localized on the cytosine unit have lower energies in comparison with those of the isolated base, with the opposite trend for the guanine unit. The underlying mechanism would be the net positive charge transfer to the cytosine unit, as the guanine monomer acts as a proton donor in two out of the three hydrogen bonds formed in the pair. Even though the calculations were performed in the static-exchange approximation (due to the size of the system), the conclusions drawn were also corroborated by empirical estimates of the vertical attachment energies. The results for the cytosine-guanine pair are compared to those previously obtained for the formic acid-formamide complex, having two hydrogen bonds with opposite donor/acceptor characters and negligible charge transfer.

Theoretical study of low-energy electron scattering with GeH2

We present a comprehensive study of electron collisions with germylene (GeH2 using the UK molecular R-matrix codes for electron energies ranging from 0.01 to 10 eV. The calculations are performed within the static-exchange, static-exchange-polarization, and 17-state close-coupling approximations. The elastic integral, differential, momentum transfer cross sections and the excitation cross sections from the ground state to the six low-lying electron excited states are presented. We found three Feshbach resonances and one Core-excited resonance. These resonances reveal the probability of anion formation by an electron attachment process and further decay to neutral and negative ion fragments. The electronic and rotational excitation cross sections for e-GeH2 scattering are reported for the first time. The cross-section dataset obtained from the present calculations are expected to be sufficiently accurate and comprehensive for most current modeling applications involving neutral GeH2.

Electron scattering studies of NO2 radical using R-matrix method

Nitrogen dioxide molecule plays an important role in modeling atmospheric process. It is a toxic gas and considered as an atmospheric pollutant due to its involvement in reactions that produce ground-level ozone. The electron scattering of NO2 molecule has been extensively studied, specifically at intermediate and high energies. The discrepancies between previous theoretical studies and experimental data at low impact energies (below 4 eV) suggest that the in-depth research should be carried out. The target optimized equilibrium geometry is computed at the highly accurate coupled cluster singles, doubles and perturbative triples[CCSD(T)] level in this study. The ab initio R-matrix method is employed to study the integral and momentum transfer cross sections of low-energy electron scattering from NO2 radical up to 10 eV. Two models including static-exchange and close-coupling approximation are used to reveal the dynamic interaction. The electronic excitation cross sections are computed from ground state to seven electronically allowed excited states. All target states whose vertical excitation energies are below 20 eV are included in the close-coupling expansions of the scattering system. In our CC model, six electrons are in the core orbitals 1a1, 2a1 and 1b2, and the remaining 17 electrons are free to occupy the 4a1, 5a1, 6a1, 7a1, 1b1, 2b1, 3b2, 4b2, and 1a2 orbitals. The aug-cc-pVTZ dunning basis sets are used to optimize the target structure and electron scattering. A Born closure procedure is used to account for the contribution of partial waves higher than l=4 to obtain cross sections. Two shape resonances found at 0.76 eV and 1.82 eV in this study are lower than previous theoretical calculations, but the comparisons with other theoretical calculations and experimental data show that the present R-matrix study not only agrees well with the experiments but also corrects the overestimations of total cross sections of some other theoretical data in the very low energy regions. To study the influence of electron correlations, 21, 82 and 107 target electronic configurations are used in the close coupling model calculations, respectively. The comparisons of integrated cross sections indicate that it is very important to include more target electronic configurations to obtain the converged scattering cross sections, which reveals the importance of electron correlations.

Positron and electron scattering by glycine and alanine: Shape resonances and methylation effect.

We report integral cross sections (ICSs) for both positron and electron scattering by glycine and alanine amino acids. These molecules differ only by a methyl group. We computed the scattering cross sections using the Schwinger multichannel method for both glycine and alanine in different levels of approximation for both projectiles. The alanine ICSs are greater in magnitude than the glycine ICSs for both positron and electron scattering, probably due to the larger size of the molecule. In electron scattering calculations, we found two resonances for each molecule. Glycine presents one at 1.8 eV, and another centered at around 8.5 eV, in the static-exchange plus polarization (SEP) approximation. The ICS for alanine shows one resonance at 2.5 eV and another at around 9.5 eV, also in SEP approximation. The results are in good agreement with most of the data present in the literature. The comparison of the electron scattering ICSs for both molecules indicates that the methylation of glycine destabilizes the resonances, shifting them to higher energies.