Potential energy curves for electronically excited states of molecular nitrogen are calculated using three different ab initio procedures. The most comprehensive of these involves the use of scattering calculations, performed at negative energy using the UK molecular R-matrix method. Such calculations are used to characterize all the Rydberg states of N2 with n ⩽ 6 and ℓ ⩽ 4 as well as many higher states including some Rydberg states associated with the first excited A 2Πu state of N. Many of these states are previously unknown. The calculations are performed at a dense grid of internuclear separations allowing the many avoided crossings present in the system to be mapped out in detail. Extensive comparisons are made with the previously available data for excited states of N2.
Resonant vibrational excitation cross sections and the corresponding rate coefficients for electron-N 2 collisions occurring through the N − 2 (X 2 Π g ) resonant state are reviewed. New calculations are performed using accurate potential energies curves for the N 2 electronic ground state, taken from literature, and for the N − 2 resonant state, obtained from R-matrix calculations. The calculations are extended to resonant excitation processes involving the N 2 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 2 molecules, with J = 50, 100 and 150 and for different vibrational levels.
Cross sections for the dissociative recombination of N + 2 for v + i = 0-3 are computed using multichannel quantum defect theory with molecular data generated using the R-matrix method. The calculation is completely ab initio and includes three electronic cores of the ion. Extensive comparisons are made with previous experimental and theoretical studies. Our cross section is in excellent agreement with experimental results and other theoretical results. Cross sections and isotropic rate coefficients are provided for all computed vibrational levels.
A systematic calculation of the positions and widths of the resonances converging on the first two excited states of N + 2 (A 2 u and B 2 + u ) 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.
We compute molecular continuum orbitals in the single center expansion scheme. We then employ these orbitals to obtain molecular Auger rates and single-photon ionization cross sections to study the interaction of N 2 with Free-Electron-Laser (FEL) pulses. The nuclei are kept fixed. We formulate rate equations for the energetically allowed molecular and atomic transitions and we account for dissociation through additional terms in the rate equations. Solving these equations for different parameters of the FEL pulse, allows us to identify the most efficient parameters of the FEL pulse for obtaining the highest contribution of double core hole states (DCH) in the final atomic ion fragments. Finally we identify the contribution of DCH states in the electron spectra and show that the DCH state contribution is more easily identified in the photo-ionization rather than the Auger transitions.
Cross sections are presented for dissociative recombination and electron-impact vibrational excitation of the ArH + molecular ion at electron energies appropriate for the interstellar environment. The R-matrix method is employed to determine the molecular structure data, i.e. the position and width of the resonance states. The cross sections and the corresponding Maxwellian rate coefficients are computed using a method based on the Multichannel Quantum Defect Theory. The main result of the paper is the very low dissociative recombination rate found at temperatures below 1000K. This is in agreement with the previous upper limit measurement in merged beams and offers a realistic explanation to the presence of ArH + in exotic interstellar conditions.
Random forests are among the most popular classification and regression methods used in industrial applications. To be effective, the parameters of random forests must be carefully tuned. This is usually done by choosing values that minimize the prediction error on a held out dataset. We argue that error reduction is only one of several metrics that must be considered when optimizing random forest parameters for commercial applications. We propose a novel metric that captures the stability of random forest predictions, which we argue is key for scenarios that require successive predictions. We motivate the need for multi-criteria optimization by showing that in practical applications, simply choosing the parameters that lead to the lowest error can introduce unnecessary costs and produce predictions that are not stable across independent runs. To optimize this multi-criteria trade-off, we present a new framework that efficiently finds a principled balance between these three considerations using Bayesian optimisation. The pitfalls of optimising forest parameters purely for error reduction are demonstrated using two publicly available real world datasets. We show that our framework leads to parameter settings that are markedly different from the values discovered by error reduction metrics alone.
TIMEDEL implements the time-delay method of determining resonance parameters from the characteristic Lorentzian form displayed by the largest eigenvalues of the time-delay matrix. TIMEDEL constructs the time-delay matrix from input K-matrices and analyses its eigenvalues. This new version implements multiresonance fitting and may be run serially or as a high performance parallel code with three levels of parallelism. TIMEDEL takes K-matrices from a scattering calculation, either read from a file or calculated on a dynamically adjusted grid, and calculates the time-delay matrix. This is then diagonalized, with the largest eigenvalue representing the longest time-delay experienced by the scattering particle. A resonance shows up as a characteristic Lorentzian form in the timedelay: the program searches the time-delay eigenvalues for maxima and traces resonances when they pass through different eigenvalues, separating overlapping resonances. It also performs the fitting of the calculated data to the Lorentzian form and outputs resonance positions and widths. Resonances are identified by peaks in the largest few eigenvalues of the time-delay matrix. Reasons for the new version:2 TIMEDEL includes a new procedure for fitting multiple overlapping resonances. It has also been parallelized to allow studies of complex systems (atoms and molecules) and generation of bulk data. Summary of revisions:TIMEDEL analyses the largest eigenvalues of the time-delay matrix and identifies those with resonance features which are then separated and fitted [6]. It has been modularized with calls to external libraries and user supplied routines abstracted for ease of modification. It has been parallelized, with a choice of a specific module allowing multi-level parallel structures or serial execution if preferred. It can run bulk simulations of 'similar but different' calculations (for example, varying fixed-nuclear geometries). Restrictions:When 'target' energies are calculated or supplied, the energy of the incident particle (electron) is currently defined with respect to the lowest supplied target energy (the ground state), although an expert user or developer would be able to modify this. Unusual features:TIMEDEL can be run from a user-supplied file for K-matrices or can be implemented to generate these as required. Additional comments:TIMEDEL has been implemented as part of the UKRMol suite of codes [7]. Running time:The actual time spent in TIMEDEL is short: however adaptive grid run times are dominated by the job-dependent time taken to generate the K-matrices (in user supplied routines). The parallelization framework over related calculations, energy sub-ranges and K-matrix generation compensates for this.
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