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Electron-impact high-lying N 2 − resonant states
Abstract
Quasibound states of the nitrogen molecular anion are studied by electron scattering from N 2 using ab initio R -matrix theory and a close-coupling model. Scattering calculations are performed using both cc-pVTZ and cc-pVQZ target basis sets involving up to 26 low-lying target states in a complete active space configuration-interaction representation. Complex resonance potential energy curves are characterized as a function of internuclear separation for all eight N 2 − states identified, including the well-known X 2 Π g shape resonance, one 1 2 Σ + g Feshbach resonance, as well as six core-excited resonances involving 1 2 Δ g , 1 2 Π u , 2 2 Π u , 3 2 Π u , 1 2 Σ + u , and 1 2 Σ − u . The 2 Δ g and 2 Σ − u resonant states are identified and characterized. Comparisons are made with the very different resonance structure in the isoelectronic CO − anion. The present resonance analysis provides a starting point for studies of the vibrational excitation, electron-impact dissociation, and other resonance-driven phenomena in N 2 .
... XMS-CASPT2 8.35 eV De is quite close to the R-matrix MCSCF value of 8.22 34 and to the R-matrix MR-CISD results of 8.36 eV. 77 The computed vibrational frequencies (Table II) vary quite substantially and are much smaller than the values for the neutral. 30 ∼2.173 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ R-matrix method (MCSCF/cc-pVQZ) 34 2.23 8.22 ⋅ ⋅ ⋅ R-matrix method (MR-CISD/aug-cc-pVQZ) 77 ⋅ ⋅ ⋅ 8.36 ⋅ ⋅ ⋅ 34 ⋅ ⋅ ⋅ 2.657 5.132 R-matrix method (MR-CISD/aug-cc-pVQZ) 77 ⋅ ⋅ ⋅ 2.823 4.316 ...
... 77 The computed vibrational frequencies (Table II) vary quite substantially and are much smaller than the values for the neutral. 30 ∼2.173 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ R-matrix method (MCSCF/cc-pVQZ) 34 2.23 8.22 ⋅ ⋅ ⋅ R-matrix method (MR-CISD/aug-cc-pVQZ) 77 ⋅ ⋅ ⋅ 8.36 ⋅ ⋅ ⋅ 34 ⋅ ⋅ ⋅ 2.657 5.132 R-matrix method (MR-CISD/aug-cc-pVQZ) 77 ⋅ ⋅ ⋅ 2.823 4.316 ...
... 77 The computed vibrational frequencies (Table II) vary quite substantially and are much smaller than the values for the neutral. 30 ∼2.173 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ R-matrix method (MCSCF/cc-pVQZ) 34 2.23 8.22 ⋅ ⋅ ⋅ R-matrix method (MR-CISD/aug-cc-pVQZ) 77 ⋅ ⋅ ⋅ 8.36 ⋅ ⋅ ⋅ 34 ⋅ ⋅ ⋅ 2.657 5.132 R-matrix method (MR-CISD/aug-cc-pVQZ) 77 ⋅ ⋅ ⋅ 2.823 4.316 ...
The projected complex absorbing potential (CAP) technique is one of the methods that allow one to extend the bound state methods for computing resonances’ energies and widths. Here, we explore the accuracy of the potential energy curves generated with different electronic structure theory methods in combination with the projected CAP technique by considering resonant vibrational excitation (RVE) of N2 by electron impact as a model process. We report RVE cross sections computed using the boomerang model with potential energy curves obtained with CAP-based extended multistate complete active space perturbation theory (XMS-CASPT2) and equation of motion coupled-cluster method for electron attachment with single and double substitution (EOM-EA-CCSD) methods. We also compare potential energy curves computed with several electronic structure methods, including XMS-CASPT2, EOM-EA-CCSD, multireference configuration interaction with singles (MR-CIS) and singles and doubles (MR-CISD). A good agreement is observed between the experiment and simulated RVE cross sections obtained with the potential energy curves generated with XMS-CASPT2 and EOM-EA-CCSD methods, thus highlighting the potential of the projected CAP technique combined with accurate electronic structure methods for dynamical simulations of the processes that proceed through metastable electronic states.
... To describe the avoided crossings more clearly, the adiabatic PECs, diabatic PECs, and NACTs for avoided crossings are shown in figure 2. It shows that the non-zero NACTs are found at the crossings, and the diabatic representations of the PECs (dashed lines) are smoothed through the matrix transformation in equation (10). Table 2 presents the potential wells, equilibrium distances, and vertical excitation energies of selected N 2 electronic states, compared to the available experimental data [68][69][70]. For the X 1 Σ + g and A 3 Σ + u states relating to the N( 4 S)-N( 4 S) dissociation limit, the differences of the potential wells D e between the present calculation and the experimental data [68] are 0.007 eV and 0.013 eV, respectively. ...
... Moreover, the differences of vertical excitation energies E ve (excitation energies from the X 1 Σ + g electronic ground state) are smaller than 0.05 eV for all excited states compared to the experimental data [69]. It is noted that this is a better agreement than the result in [70] where the cc-pVQZ basis set is employed. Furthermore, the calculated energy separation between N( 4 S) and N( 2 D) is 2.392 eV and that between N( 4 S) and N( 2 P) is 3.589 eV while the experimental data are found to be 2.383 eV and 3.575 eV, respectively [68,71]. ...
The current work presents the collision integral data for N( ⁴ S )-N( ⁴ S , ² D, ² P) and O( ³ P, ¹ D, ¹ S)-O( ³ P, ¹ D, ¹ S) interactions in the temperature range of 500–50,000K. The collision integrals are calculated based on high-quality potential energy curves (PECs) obtained from fitting the high-level ab initio calculation data in a wide energy range to the Neural Network (NN) functions. In the construction of PECs, the diabatic PECs are adopted when avoided crossings exist because the diabatic paths are much more likely to be followed for such situations. Moreover, the nonadiabatic transition effects are estimated to be negligible for PECs crossings. The accuracy of traditional analytical formulas to fit PECs are also examined. It is found that the collision integral calculations are sensitive to the accuracy of PECs and the NN based PECs overwhelm the others. The contribution of inelastic excitation exchange processes to the diffusion collision integrals are also computed by using an accurate evaluation of the differences of PECs for gerade and ungerade pairs of excited atoms. Finally, based on the new collision integral data, we calibrate the collision model parameters suitable for the widely used particle simulation methods. The collision integrals and collision models developed in this work can be used to support high-confidence simulations of weakly ionized air plasma problems.
... Among recent theoretical approaches, we mention R-matrix calculations by Gillan et al. 81 and by Tashiro and Morokuma 82 and the Schwinger multichannel calculations by Da Costa and Lima. 83 Recently, Su et al. 84,85 used the UK molecular R-matrix codes to perform a comprehensive study of electronic excitation from the ground state as well as the metastable A 3 Σ + u and a 1 Πu excited states of the molecule to the eight lowest electronic states: ...
... To our knowledge, no experiments on TCSs of metastable states of N 2 have been performed. Recently, Su et al. 85 using the R-matrix method (UKRMol+/QEC codes 74,75 ) calculated integral elastic cross sections for electron scattering on N 2 being in the A 3 Σ + u and a 1 Πg states for energies 0-10 eV. The integral elastic cross section for scattering on N 2 in the ground X 1 Σ + g state was also computed. ...
Electron collision cross section data are complied from the literature for electron collisions with the nitrogen molecules, N2, N2+, and N2*. Cross sections are collected and reviewed for total scattering, elastic scattering, momentum transfer, rotational excitation, vibrational excitation, electronic excitation, dissociative processes, and ionization. The literature has been surveyed up to the end of 2021. For each of these processes, the recommended values of the cross sections are presented.
... For the well-studied 2 P g valence anion of N 2 , bound state 16,17,20,29,[32][33][34] and scattering calculations carried out with high level treatment of electron correlation 14 have been found to give similar resonance parameters. Yet, as will be discussed below, this is not necessarily the case for the resonance widths for heteronuclear diatomic molecules or large organic molecules such as anthracene for which multiple partial waves contribute to the various TA resonances. ...
In this work we study the ² Π resonances of a two-site model system designed to mimic a smooth transition from the ² Π g temporary anion of N 2 to the ² Π temporary...
Electron–molecule collisions drive many natural phenomena and are playing an increasing role in modern technologies. Over recent years, studies of the collision processes have become increasingly driven by quantum mechanical calculations rather than experiments. This tutorial surveys important issues underlying the physics and theoretical methods used to study electron–molecule collisions. It is aimed at nonspecialists with suitable references for further reading for those interested and pointers to software for those wanting to perform actual calculations.
Interhalogen compounds such as iodine chloride play a crucial role in the earth’s atmosphere. The R-matrix
method is used to perform electron collision calculations for ICl with different scattering models. The results
are presented for static exchange (SE), static exchange plus polarization (SEP) and 12-state close-coupling
(CC) model up to 10 eV including virtual orbitals. A 2Σ+ bound state for ICl− is predicted from the potential
energy curve. Three resonances are detected, one with 2Σ+ and two with 2Π symmetry. The variation of
eigenphase sums with inclusion of polarization and correlation effects is reported. Differential cross section
are calculated as a function energy and scattering angle for a 12-state CC model. ICl ionization cross sections
are computed for the first time using the Binary Encounter Bethe (BEB) model. An estimate of the dissociative
electron attachment cross section is reported; we predict that the dominant product is Cl+I− arising from the
2Σ+ resonance state of ICl−. The results will be useful in the studies of the Earth’s atmosphere and provide
input for modeling of ICl-containing plasmas.
We discuss peculiar features of electron scattering on the N 2 molecule and the N 2 ⁺ ion, that are important for modeling plasmas, Earth’s and other planets’ atmospheres. These features are, among others: the resonant enhancement of the vibrational excitation in the region of the shape resonance around 2.4 eV, the resonant character of some of electronic excitation channels (and high values of these cross sections, both for triplet and singlet states), high cross section for the dissociation into neutrals, high cross sections for elastic scattering (and electronic transitions) on metastable states. For the N 2 ⁺ ion we discuss both dissociation and the dissociative ionization, leading to the formation of atoms in excited states, and dissociative recombination which depends strongly on the initial vibrational state of the ion. We conclude that the theory became an indispensable completion of experiments, predicting many of partial cross sections and their physical features. We hope that the data presented will serve to improve models of nitrogen plasmas and atmospheres.
Graphical abstract
Low energy electron collisions with hydrogen cyanide and hydrogen isocyanide molecules are studied using the R-matrix method. Scattering calculations are carried out using static exchange (SE), static exchange plus polarization (SEP) and close-coupling (CC) models. Electronic excitation cross sections are reported for HCN in our best 24-state close-coupling model with 17 virtual orbitals and for HNC using 25-state close-coupling model in which 18 virtual orbitals are included to account for polarization and correlation effects. These effects are necessary to obtain accurate results and also responsible for shift in the positions of 2Π shape resonance (in both HCN and HNC) to lower energy compared to previous studies. These resonances are dissociative in nature. Complex resonance potential energy curves are produced for HCN and found to give narrower widths than previous theoretical results. Ionization cross section computed using Binary Encounter Bethe (BEB) method. Differential cross section (DCS) at 2, 4, 6, 8 and 10 eV and momentum transfer cross sections (MTCS) are also reported using 2-state CC model for HCN. The results obtained are useful for various research fields including plasma modelling and astrophysics.
In this second part of a two part paper (first part: Zawadzki et al (2020 J. Phys. B: At. Mol. Opt. Phys. 53 165201)) we present differential scattering cross sections for excitation of several Rydberg electronic states of carbon monoxide by electron impact. The first part concerned the low-lying valence states of CO. In the present study cross sections are obtained experimentally using low-energy electron energy-loss spectroscopy and theoretically using the R-matrix method. Incident electron energies range from near-threshold of 12.5 eV to 20 eV while the scattering angles range from 20° to 120°. The R-matrix calculations use three distinct close-coupling models and their results are compared to available experimental and theoretical cross sections. The overall comparison leads to significantly improved description of the excitation cross sections for this target.
A comprehensive study of electron collisions with the X1Σg+ ground state as well as the metastable A3Σu+ and a1Πg excited states of the N2 molecule is reported using the fixed-nucleus R-matrix method. Integral elastic scattering and electronic excitation cross sections from the X1Σg+ ground state to the eight lowest electronic states, A3Σu+, B3Πg, W3Δu, B'3Σu−, a1Πg, a'1Σu−, w1Δu and C3Πu, overall agree well with the available experimental and theoretical results although updates of some recommended values are suggested. Accurate electron impact electronic transition cross sections starting from the A3Σu+ and a1Πg metastable excited states are reported. The total summed electronic transition cross sections from the a1Πg state is dominant: an order of magnitude higher than those of the X1Σg+ ground state. The de-excitation cross sections generally show a downward trend with increasing incident electron energy, which is different from the elastic and electronic excitation cross sections which generally increase with collision energy. There is a prominent 2Πu symmetry resonance peak at 2.8 eV for electronic de-excitation scattering of a1Πg → B3Πg, which significantly contributes to the total summed cross sections from the a1Πg excited state. The present results provide a new insight which will aid understanding of electron spectra in the atmosphere of the Earth and Titan.
Cross section data for electron impact electronic excitation of electronically excited states of H2 are computed using fixed-nuclear R-matrix calculations. Specifically, there is a focus on transitions from the quasi-metastable excited states a 3 Σ+ g and c 3 Πu. Data are compared with known theoretical data where available. Our calculations suggest that the published cross sections are generally too large in the low energy (<20 eV) collision region. The effect of shifting the electronic excitation thresholds to those given by essentially exact calculations is tested.
Collisions of low energy electrons with molecules are important for understanding many aspects of the environment and technologies. Understanding the processes that occur in these types of collisions can give insights into plasma etching processes, edge effects in fusion plasmas, radiation damage to biological tissues and more. A radical update of the previous expert system for computing observables relevant to these processes, Quantemol-N, is presented. The new Quantemol Electron Collision (QEC) expert system simplifyies the user experience, improving reliability and implements new features. The QEC graphical user interface (GUI) interfaces the Molpro quantum chemistry package for molecular target setups, and the sophisticated UKRmol+ codes to generate accurate and reliable cross-sections. These include elastic cross-sections, super elastic cross-sections between excited states, electron impact dissociation, scattering reaction rates, dissociative electron attachment, differential cross-sections, momentum transfer cross-sections, ionization cross sections, and high energy electron scattering cross-sections. With this new interface we will be implementing dissociative recombination estimations, vibrational excitations for neutrals and ions, and effective core potentials in the near future.
Resonance energies and widths of eight long-lived metastable electronic states of the CO− anion are obtained using the R-matrix method as a function of bond distance. High-level ab initio scattering calculations are performed for a large number (above 150) of fixed-nuclear geometries using the large cc-pV6Z Gaussian basis set and a close-coupling model involving 27 low-lying target states. Potential curves for narrow resonances, three 2Σ+, four 2Π and one 2Δ, in the 10–14 eV region are reported, along with the data on the low-lying 2Π shape resonance. These curves provide a starting point for performing nuclear dynamics and hence studies of dissociative attachment via these states.
Differential scattering cross sections for electron excitation of the three lowest excited electron states of carbon monoxide are obtained experimentally using low-energy electron energy-loss spectroscopy and theoretically using the R-matrix method. The incident electron energies range from near-threshold of 6.3 eV to 20 eV. Experimental scattering angles range from 20° to 120°. The normalization of the experimental cross sections is made to available experimental elastic scattering data (Gibson et al 1996 J. Phys. B: At. Mol. Opt. Phys. 29 3197). The R-matrix calculations use three distinct close-coupling models and their results are compared to available experimental and theoretical cross sections. The overall comparison leads to significantly improved description of the excitation cross sections for this target.
Succeeding our previous finding about coherent interference of the resonant
states of CO^- formed by the low-energy electron attachment [Phys. Rev. A 88,
012708 (2013)], here we provide more evidences of the coherent interference, in
particular, we find the state configuration change in the interference with the
increase of electron attachment energy by measuring the completely backward
distributions of the O^- fragment ion of the temporary CO^- in an energy range
11.3-12.6 eV. Therefore, different pure states, namely, coherent resonances,
can be formed when the close-lying resonant states are coherently superposed by
a broad-band electron pulse.
Articles you may be interested in Geometries and electronic structures of the ground and low-lying excited states of FeCO: An ab initio study J. Chem. Phys. 137, 244303 (2012); 10.1063/1.4769283 Accurate ab initio ro-vibronic spectroscopy of the X ̃ 2 Π CCN radical using explicitly correlated methods J. Chem. Phys. 135, 144309 (2011); 10.1063/1.3647311 An ab initio study of the hyperfine structure in the X 2 Π electronic state of CCCH J. Chem. Phys. 121, 2636 (2004); 10.1063/1.1768162 Electronic structure of isolated PtX 6 2− (X = F,Cl,Br) dianions J. Chem. Phys. 118, 1747 (2003); 10.1063/1.1529678 Ab initio configuration interaction study of the predissociation of the (4s), (4pσ) 1,3 Π, and (4pπ) 3 Σ + Rydberg states of HCl and DCl J. Chem The electronic structure of the X 2 + , A 2 , and B 2 + states of aluminum monoxide (AlO) are studied via ab initio multi-reference configuration interaction calculations. Core correlation correc-tions, several basis sets, and active space choices are considered. Angular momentum and spin-orbit coupling terms are obtained at different levels of theory. The resulting ab initio curves are used to solve the associated rovibronic problem for the total angular momentum J up to 112.5 and then also refined by fitting to the experimental wavenumbers available in the literature, reproducing them with the root-mean-square error of 0.07 cm −1 . Theoretical rovibronic energy levels of AlO in its X 2 + , A 2 , and B 2 + electronic states are presented including those from the X − B blue-green system. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4897484]
A systematic calculation of the positions and widths of the resonances converging on the first two excited states of N (A and B ) is presented. A closely-spaced grid of geometries is used to give continuous resonance curves without the need for curve fitting. Three methods, fitting the eigenphase sum, the time-delay method and the R-matrix specific QB method, are tested. Fits to the longest three time-delays are found to give the most reliable and complete determination of the resonance parameters. The low excitation energies of the A and B ion states results in complex resonance features with many avoided crossings leading to pronounced structures in both the resonance curves and the associated widths. The resonance curves likely to be important for dissociative recombination are identified. Their positions generally agree well with the calculations of Guberman, although in some cases their widths are narrower. Full data on all curves is provided.
Resonant vibrational excitation cross sections and the corresponding rate
coefficients for electron-N collisions occurring through the
N resonant state are reviewed. New calculations are
performed using accurate potential energies curves for the N electronic
ground state, taken from literature, and for the N resonant state,
obtained from R-matrix calculations. The calculations are extended also to
the resonant excitation processes involving the N ground state vibrational
continuum, leading to dissociation. Electron impact dissociation is found to be
significant from higher vibrational levels. Accurate analytical fits for the
complete set of the rate coefficients are provided. The behavior of the
dissociative cross sections is investigated for rotationally excited N
molecules, with J=50,100 and 150 and for different vibrational levels.
Dissociative electron attachment to carbon monoxide, e− + CO → C + O−, at 9.5, 10.0, and 10.6 eV is investigated by using the anion velocity time-sliced map imaging technique. The completely backward scattering distributions of the fast O− fragment are observed at 10.0 and 10.6 eV. The single electron-molecule resonance model fails in interpretation to these unusual angular distributions, while a quantum interference model including two (at 10.0 eV) or three (at 10.6 eV) dissociative outgoing waves is consequently proposed and provides the satisfying results about the experimental data fittings. Moreover, coherent interference among the 2Π, 2Δ, and 2Φ resonant states of CO− at 10.6 eV could be further established, based on the fact that the sum of the phase-shift fitting values equals π rad.
Ab initio R-matrix scattering calculations are presented for electron - as a function of bond length. It is found that and resonances in the 10 eV region appear to be associated with multiple `parent' target states and that the resonances can swap parents as a function of internuclear separation. It is shown how these phenomena provide an explanation for the inconsistencies in previous assignments of resonances in this region and other anomalies such as pronounced isotopic effects. It is suggested that this parent swapping behaviour is likely to be a common feature of electron-impact excitation of other molecules and is particularly important for any models that include nuclear motion.
A method is presented for constructing configuration-interaction (CI) Hamiltonians for electron - molecule collision calculations based on close-coupling expansions. This method utilizes the structure of the wavefunction used in scattering calculations to greatly reduce the computational cost compared to conventional procedures. In particular, CI target configurations are treated only at the prototype configuration state function stage of the calculation. Only then are these prototype configurations expanded over all scattering functions using an improved version of a previous algorithm by Morgan and Tennyson. This new algorithm has been implemented as part of the UK R-matrix codes. Test calculations show that it leads to a large reduction in both the number of integrals and matrix elements which need to be explicitly constructed and evaluated. Use of this new program should allow significantly more sophisticated target wavefunctions to be employed in future scattering calculations.
Resonances in low-energy electron- collisions are studied using the R-matrix method for eight total symmetries: , over a range of bond lengths from 0.8 to . A rich and complicated structure of resonances is apparent. Where possible, the resonances are fitted using the more appropriate of the eigenphase sum and time-delay methods. Positions and widths are tabulated. Potential curves of individual resonant states are derived and used for nuclear motion calculations. Excellent agreement with experiment has allowed the explanation and assignment of all the resonances below 13 eV where previously there had been confusion and contradiction among different experiments and theory.
Electron-impact vibrational-excitation cross sections, involving rovibrationally excited N2 and NO molecules, are calculated for collisions occurring through the nitrogen resonant electronic state , and the three resonant states of nitric oxide NO⁻(³Σ⁻, ¹Δ, ¹Σ⁺). Complete sets of cross sections have been obtained for all possible transitions involving 68 vibrational levels of and 55 levels of NO(X ²Π), for incident electron energy between 0.1 and 10 eV. In order to study the rotational motion in the resonant processes, cross sections have also been computed for rotationally elastic transitions characterized by the rotational quantum number J running from 0 to 150. The calculations are performed within the framework of the local complex potential model, using potential energies and widths optimized to reproduce the experimental cross sections available in the literature. Rate coefficients are calculated for transitions between all vibrational levels by assuming a Maxwellian electron energy distribution function in the temperature range from 0.1 to 100 eV.
All numerical data are available at http://users.ba.cnr.it/imip/cscpal38/phys4entry/database.html
Ab initio calculations are performed on the e--N2 scattering system, at low impact energies, using the R-matrix technique. The X 1Σ+g ground state and the lowest seven valence excited states, A 3Σ+u, B 3Πg, W 3Δu, B′ 3Σ-u, a′ 1Σ-u, a 1Πg and w 1Δu, of N2 are included in the close coupling expansion with each state being represented by a configuration interaction wavefunction in a hybrid orbital set. Various approximations for the representation of the correlation between the target and the incident electron are investigated. Integrated and differential scattering cross sections are presented, and compared to experiment, for excitation from the ground level to optically forbidden levels. The results compare favourably with recent experiments in this energy region and remove a number of problems with our previous work.
The semi-empirical permanent electric dipole-moment function (DMF) for the ground state of the CO molecule has been reconstructed analytically in the entire range of the inter-nuclear distance r∈[0,+∞) by means of the simultaneous non-linear least-squares fitting (NLLSF) of the selected experimental intensities for the main 12C16O isotopologue (including those with sub-percent uncertainties) and the ab initio permanent dipole moment. The ab initio DMFs were evaluated using single-reference coupled cluster (SR-CCSD(T)) and multi-reference averaged coupled-pair functional (MR-ACPF) methods. The ab initio data were involved in the NLLSF procedure to propagating smoothly the semi-empirical DMF outside the local region covered by the experimental intensities for the lowest vibrational v′≤11 levels. The derived mass-invariant DMF possesses the physically correct asymptotic behavior in both the united-atom and dissociation limits as well as reproduces the vast majority of the measured intensities in v″=0→v′∈[0,6] and v″=1→v′=4,5 bands within their experimental uncertainties. The resulting DMF and the mass-corrected potential-energy function of Meshkov et al. (2018) were used to upgrade line lists for all CO isotopologues in the wide range of vibrational and rotational quantum numbers v∈[0,41],Δv∈[0,6], J∈[0,150] (J∈[0,200] for the 0-0 and 1-0 bands). The predicted intensities are compared with their experimental counterparts, which were not involved in the present NLLSF, to highlight presumable random and systematic errors in the measured data; in particular, the intensities in the “abnormal” 0→5 band of the 12C16O isotopologue and some other bands of minor isotopologues should be revisited experimentally. The resultant line list should be considered superior to previous efforts in terms of accuracy.
Vibrationally resolved photoemission spectra of the electronic-state transitions C³Πu → B³Πg of N2 and b³Σ⁺ → a³Π of CO following low-energy electron impacts are measured with a crossed-beam experimental arrangement. The absolute cross sections of C³Πu (ν′) → B³Πg (ν″) of N2 are presented for the vibrational state-to-state transitions (ν′,ν″) = (0,0), (0,1), (1,0), (1,2), and (2,1). The excitation cross sections of the metastable state C³Πu of N2 show the maxima at the electron-impact energies 14.10 (ν′ = 0) eV and 14.50 (ν′ = 1) eV, which are potentially related to the core-excited vibrational Feshbach resonant state ²Σu⁺ of N2⁻ formed by electron attachment. The absolute cross sections of b³Σ⁺ (ν′ = 0) → a³Π (ν″ = 0, 1, 2, 3, 4) of CO are given by the calibrations with those of N2 measured in this work. Besides the maximum excitation cross section 5.85 × 10⁻¹⁸ cm² at 10.74 eV of the CO b³Σ⁺ (ν′ = 0) state, some fine structures on the excitation function profile are attributed to different shapes and Feshbach resonant states of CO⁻ formed by electron attachment, while the others arise from the direct electron-impact excitation. Some discrepancies, particularly for N2, between the present data and the results available in the literature studies arise from different experimental techniques and data-processing procedures. Furthermore, contributions of physical processes such as wave-packet evolution and non-Franck–Condon dynamics are highlighted here.
Molpro is a general purpose quantum chemistry software package with a long development history. It was originally focused on accurate wavefunction calculations for small molecules but now has many additional distinctive capabilities that include, inter alia, local correlation approximations combined with explicit correlation, highly efficient implementations of single-reference correlation methods, robust and efficient multireference methods for large molecules, projection embedding, and anharmonic vibrational spectra. In addition to conventional input-file specification of calculations, Molpro calculations can now be specified and analyzed via a new graphical user interface and through a Python framework.
UKRmol+ is a new implementation of the time-independent UK R-matrix electron–molecule scattering code. Key features of the implementation are the use of quantum chemistry codes such as Molpro to provide target molecular orbitals; the optional use of mixed Gaussian — B-spline basis functions to represent the continuum and improved configuration and Hamiltonian generation. The code is described, and examples covering electron collisions from a range of targets, positron collisions and photoionization are presented. The codes are freely available as a tarball from Zenodo.
Absolute grand total cross sections for electron scattering from N2 are obtained in the energy range from 20 eV down to 5 meV with very narrow electron energy width of 9 meV using the threshold-photoelectron source. Total cross sections obtained in the present study are compared with the previous experimentally obtained results. At the very-low energy region below 50 meV, the present total cross sections are somewhat smaller than those reported by the Aarhus group [S.V. Hoffmann et al., Rev. Sci. Instrum. 73, 4157 (2002)], which has been the only experimental work that provided the total cross sections in the very-low energy region. The energy positions of the peaks in the total cross sections due to the ²Π g shape resonance are obtained with higher accuracy, due to the improved uncertainty of the energy position in the present measurement compared to the previous works. The resonance structure in the total cross sections due to the Feshbach resonances of N2 at around 11.5 eV are also observed. Analysis of the resonant structure was carried out in order to determine the values of resonance width of Feshbach resonances of N2.
Graphical abstract
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AbstractR-matrix calculations on electron collisions with CO are reported whose aim is to identify any higher-lying resonances above the well-reported and lowest 2Π resonance at about 1.6 eV. Extensive tests with respect to basis sets, target models and scattering models are performed. The final results are reported for the larger cc-pVTZ basis set using a 50 state close-coupling (CC) calculation. The Breit-Wigner eigenphase sum and the time-delay methods are used to detect and fit any resonances. Both these methods find a very narrow 2Σ+ symmetry Feshbach-type resonance very close to the target excitation threshold of the b 3Σ+ state which lies at 12.9 eV in the calculations. This resonance is seen in the CC calculation using cc-pVTZ basis set while a CC calculation using the cc-pVDZ basis set does not produce this feature. The electronic structure of CO− is analysed in the asymptotic region; 45 molecular states are found to correlate with states dissociating to an anion and an atom. Electronic structure calculations are used to study the behaviour of these states at large internuclear separation. Quantitative results for the total, elastic and electronic excitation cross sections are also presented. The significance of these results for models of the observed dissociative electron attachment of CO in the 10 eV region is discussed. Graphical abstract
Dissociative electron attachment to CO leading to the formation of O− is studied using the velocity
slice imaging technique. The angular distributions we obtained for the C(3P) and the C(1D) limits are found to be
considerably different from a recent set of measurements [Tian et al., Phys. Rev. A
88, 012708 (2013); Wang et al., J. Chem. Phys. 143, 066101
(2015)] using a similar technique. The analysis of our results indicate incoherent
contributions from states of Σ and Π symmetries to both these dissociation channels
and rules out the need to invoke coherent excitation of several resonances, in contrast to
what has been done in the above publications. We try to correlate these resonances to
those observed in inelastic scattering and transmission experiments. We also confirm the
presence of a third dissociation channel leading to C(1S) limit.
Graphical abstract
Complete dissociation dynamics in electron attachment to carbon monoxide (CO) have been studied using the newly developed velocity slice imaging (VSI) technique. Both kinetic energy and angular distributions of O− ions formed by dissociative electron attachment (DEA) to CO molecules have been measured for 9, 9.5, 10, 10.5, 11, and 11.5 eV incident electron energies around the resonance. Detailed observations conclusively show that two separate DEA reactions lead to the formation of O− ions in the ground 2P state along with the neutral C atoms in the ground 3P state and the first excited 1D state, respectively. Within the axial recoil approximation and involving four partial waves, our angular distribution results clearly indicate that the two reactions leading to O− formation proceed through the specific resonant state(s). For the first process, more than one intermediate state is involved. On the other hand, for the second process, only one state is involved. The observed forward–backward asymmetry is explained in terms of the interference between the different partial waves that are involved in the processes.
A sharp and isolated resonance of the ``helium‐window'' type has been discovered in electron transmission measurements in N2 at 11.48 eV (believed accurate to within 0.05 eV). Additional resonance structure is observed at 11.75 and 11.87 eV. The E3Σg+ state is coincident in energy with the 11.87‐eV structure and is found to exhibit an excitation probability sharply peaked near threshold. The series of resonances, previously known to exist between 1.8 and 3.5 eV as a consequence of an N2− state with vibrational structure, has been studied with improved resolution and by different procedures.
An attempt has been made to observe the thermal dissociation of N2 in order to choose between the two values, 7.385 ev and 9.765 ev, for the dissociation energy of N2. At the highest available temperatures no dissociation could be observed, and a lower limit of 8.80 ev is set for D(N2).
Using common finite basis sets we have compared the equation of motion and the polarization propagator method, both through second order. Calculations
The resonant electron impact quenching of metastable molecules might be important for understanding the phenomena in the upper atmosphere. In order to obtain information about the relative importance of this scattering event the resonant cross sections for electron scattering by metastable nitrogen in the state were calculated using the “boomerang” model and quenching rates for this state were evaluated for the altitudes of 130,170 and 210km. The obtained quenching rates are small (≲5 × 10−3 s−1), even with respect to the radiative transition rate showing that under the considered conditions this process is unimportant for population of nitrogen state in the Earth's thermosphere.
Excitation spectra of CO have been obtained at low electron impact energy in the 10.600–13.400 eV energy loss range for scattering angles from 10 to 120°, with a 35 meV experimental resolution. The angular behaviour of the observed peaks is used to discriminate singlet-singlet and singlet-triplet transitions. Previously calculated Rydberg states are observed, in particular the triplet analogue of the F1Σ+ state. A new high energy valence triplet state is identified; the first observed vibrational level is at 11.595 eV and the vibrational spacing is 90 meV. Upper levels are strongly affected by predissociation.
In this review we present the energies, configuration, and other properties of resonances (also called "compound states" and "temporary negative ions") in diatomic molecules. Much of the information is presented in the form of tables and energy level diagrams. Vibrational, rotational, and electronic excitation are discussed whenever these processes have given information on resonances; often these excitation processes proceed via resonances. The paper is divided according to molecular species (H2, N2, CO, NO, O2), but the main conclusions are discussed by the nature of the processes involved.
A transmission experiment is used to observe the structure in the total electron-impact cross section in CO and O2. The structure in the cross sections is enhanced by measuring directly the derivative of the transmitted current. An isolated resonance in CO is observed at an electron energy of 10.04+/-0.03 eV. In O2, structure is observed which correlates well with the absorption spectra in the energy range 8-10 eV. In addition, two very sharp resonances (30-meV width) are observed at 8.02+/-0.03 and at 8.25+/-0.03 eV.
A combined experimental and theoretical investigation of the dissociative-electron-attachment (DEA) dynamics in methanol are presented for the Feshbach resonance at 6.5-eV incident electron energy. Highly differential laboratory-frame momentum distributions have been measured for each fragmentation channel using a DEA reaction microscope. These measurements are combined with calculations of the molecular-frame electron attachment probability in order to investigate the dynamics of the dissociating methanol transient negative anion. In contrast to previous comparisons between water and methanol [Curtis and Walker, J. Chem. Soc., Faraday Trans. 88, 2805 (1992); Prabhudesai, Nandi, Kelkar, and Krishnakumar, J. Chem. Phys. 128, 154309 (2008)], we find subtle differences in the dissociation dynamics of the two fragment channels that are direct evidence of planar symmetry-breaking of warm methanol in its electronic ground state. We also find that the DEA fragmentation does not strictly follow the axial recoil approximation and we describe the dynamics that enable an accurate prediction of the fragment angular distributions.
A high-resolution and high-sensitivity electron transmission spectrometer is used to study sharp structures in the total scattering cross section of H2, D2, O2, NO, N2, and CO. Many new resonances are found, some of which form bands which consist of progressions of negative-ion vibronic states. The existence of bands makes the identification of temporary negative-ion states easier, since the spacing and the magnitudes of the structure can be compared with the appropriate parameters of various positive-ion cores. The most prominent features observed consist of two Rydberg electrons attached to a particular positive-ion core.
The lifetime and level width of the metastable 2Πg state of N2- are
calculated using restricted Hartree-Fock theory.(AIP)
The excitation of carbon monoxide by electron impact has been studied in the energy range from 8 to 17 eV using an optical method. The excitation of several states has been detected in the emission spectral range between 180 and 550 nm. Excitation functions for the A and a′ states have been measured in the near-threshold energy region and are compared with recent experimental and theoretical results.
A dissociative attachment process has been observed in both N2 and NO which yields N- ions in their unstable ground state (3P). An electron impact spectrometer has been used to detect the N- ions by collecting the electrons emitted when this ion decays to the 4S ground state of atomic nitrogen. The 3P state of N- is found to be located at an energy of 0.07+or-0.02 eV above the ground state of N and its natural width is determined to be 16+or-5 meV.
Cross sections for the excitation of vibrational levels up to nu =19 in N2 have been calculated for electron impact energies in the range 1-7 eV. The R-matrix method is used to describe both the electronic and nuclear motions. Polarisation effects are included in a non-empirical manner and no adjustable parameters are included in any aspect of the model. The results are compared with recent experimental data and are found to be in excellent qualitative agreement.
For pt. I see ibid., vol.6, 862 of 1973. The study of the excitation function of the E state vibrational levels shows a strong threshold excitation, several bumps and extra structure. An angular analysis of these phenomena leads to the determination of the configuration and symmetry of four transient N2- states.
Polarised pseudostates representing the long-range polarisation potential are included in a new e-N2 scattering calculation. The results remove an earlier disagreement in the total cross section between theory and experiment at energies below 1.5 eV and reduce the position and width of the 2 Pi g resonance.
High-resolution electron impact has been used to measure the excitation functions of the metastable states in CO and N2. A low work function detector has been used and this has enabled the lowest metastable states of CO and N2, a 3 Pi and A 3 Sigma u+ respectively, to be included in the measurements. This ability to observe the lowest-lying metastable states and the high sensitivity of the measurements has allowed much new structure to be observed in the metastable excitation functions of these molecules. The modified Rydberg formula has been used to obtain tentative classifications of the higher-lying resonances. The measurements also provide information about the shape of the total metastable cross sections in CO and N2.
The energy dependences of the vibrational excitation of up to nu =17 by electron impact in N2 are reported from threshold to approximately 5 eV. The resulting relative differential cross sections are normalised to the absolute integral value of Jung et al. (1982) at 2.25 eV. The curve shapes are compared with published theoretical results where available. The direct process near threshold of the first three vibrational levels is also investigated and the nu =1 results are compared with the results of electron drift experiments.
An electron impact spectrometer has been employed to study resonance phenomena associated with the 10.04 eV Feshbach resonance of CO. The 2 Sigma + symmetry of this resonant state is confirmed and strong evidence indicates the b3 Sigma + and B1 Sigma + states as parents. A 2 Sigma + resonance at threshold and two shape resonances are observed in the b3 Sigma + nu '=0 level excitation cross section at 10.7 eV and 11.2 eV, the 10.7 eV resonance is shown to have 2 Pi symmetry. Other Feshbach resonances are detected at 11.3 eV and 12.2 eV.
For pt.I see ibid., vol.15, no.12, p.1929-37 (1982). An electron impact spectrometer incorporating a position-sensitive multidetector has been used to study the excited electronic states carbon monoxide in the energy region 11 to 20 eV. A series of peaks previously assigned to one vibrational progression have been resolved into two progressions, one of which has been assigned to a transition to a previously unobserved state. At high impact energy and small scattering angle the spectra observed are in good agreement with previous photoabsorption data. At high scattering angle members of Rydberg series resulting from spin-forbidden transitions have been observed in the energy region below the first ionisation potential. At higher excitation energies several new spectral features have been observed, some of which have been assigned to Rydberg series.
Differential cross sections for the electron scattering processes: X1 Sigma + to X1 Sigma +, a3 Pi , a'3 Sigma +, (d3 Delta i+e3 Sigma -+I1 Sigma -+D1 Delta ), A1 Pi , b3 Sigma +, B1 Sigma +, j3 Sigma +, (C1 Sigma ++c3 Pi ) and E1 Pi in CO have been determined for incident electron energies 20, 30, 40 and 50 eV. These differential cross sections were obtained for the scattered electron angle range 10-90 degrees by analysing electron-energy-loss spectra in CO at a number of fixed scattering angles within that range. To the best of the authors' knowledge the present study represents the first comprehensive investigation of electron impact excitation of the electronic states of CO to be thus far reported in the literature.
Studies have been made of resonant scattering of electrons from N2 in the energy region 11 eV to 13 eV. By measuring cross sections for scattering leaving the target molecule in vibrational levels of the ground state the potential curve of a state of N2- has been determined. The symmetry of this state appears to be 2 Sigma g+ and an estimate has been obtained of its width. Additional structure has been observed in the elastic channel and this is discussed.
The -matrix method is an embedding procedure which is based on the division of space into an inner region where the physics is complicated and an outer region for which greatly simplified equations can be solved. The method developed out of nuclear physics, where the effects of the inner region were simply parametrized, into atomic and molecular physics, where the full problem can be formulated and hopefully solved ab initio. In atomic physics -matrix based procedures are the method of choice for the ab initio calculation of electron collision parameters. There has been a number of -matrix procedures developed to treat the low-energy electron–molecule collision problem or particular aspects of this problem. These methods have been extended to both positron physics and the -matrix treatment of vibrational motion.
GTOBAS is a program for fitting Gaussian-type orbitals (GTOs) to Bessel and Coulomb functions over a finite range. The exponents of the GTOs are optimized using the method of Nestmann and Peyerimhoff [J. Phys. B 23 (1990) L773]. The appended module NUMCBAS provides the numerical Bessel and Coulomb functions required as input for the program. The use of GTO continuum basis sets is particularly important in electron–molecule scattering calculations when polyatomic targets are involved. Sample results for such calculations are also discussed.
The relative differential cross-sections for electron impact excitation of v=0, 1 and 2 vibrational levels of the C state of the nitrogen molecule have been measured for incident energies from threshold to 17 eV and for 0° scattering angle. By considering a number of possible angular distributions for this excitation a range of differential and integral vibrational cross-sections and the total cross-section for excitation of the C state are determined. These are used in a comparison with previous results where there are considerable discrepancies. Resonant structures in excitation functions of all three vibrational levels are observed and their locations are compared with resonances obtained in different decay channels, from the literature.
Using two different experimental setups with energy widths of about 6 and 13 meV, we obtained significantly improved results for the energy dependence of angle-differential (10°–180°) elastic and vibrationally inelastic cross sections for electron scattering from N₂ molecules in the energy range around the narrow N⁻₂(R²Σ⁺g) resonance. The energy location and the natural width of this resonance are determined as 11.497(2) eV and 1.3(2) meV, respectively. Ab initio potential energy curves are obtained from CCSD(T) calculations for the neutral N₂(X¹Σ⁺g) and N*₂(E³Σ⁺g) states as well as for the N⁻₂(R²Σ⁺g) resonance state. They corroborate quite accurately the measured resonance energy and provide accurate energy spacings and overlap integrals for the pertinent vibrational states. A detailed analysis of resonance line shapes for selected scattering angles is performed by applying a model for the interference of resonant and nonresonant scattering processes. It provides a link between the resonance width to absolute DCS and describes elastic and vibrational excitation processes on a common basis. Through both their size and sign, vibrational overlap integrals are shown to determine the observed Fano-type line shapes and account for the opposite asymmetries and intensity changes of adjacent vibrational resonance peaks. Fine-tuning of the fits to the observed shapes is achieved by proper parametrization of the nonresonant amplitudes. A highly resolved excitation function for the formation of the metastable N*₂(E³Σ⁺g) level from threshold (near 11.88 eV) to 13.4 eV is also presented.