Calculation Of Electron Binding Energies Research Articles

Light one-electron molecular ions within the finite-basis-set method for the two-center Dirac equation

During the last decades outstanding results on the precision description of light diatomic molecular compounds have been achieved. The most advanced calculations of electron binding energies have been realized mainly in the framework of the nonrelativistic approach with a consistent account of relativistic and radiative QED corrections. Recently, it has been shown that methods based on the Dirac equation are also suitable for obtaining highly accurate results in simple light molecules. In this paper, we present a completely relativistic method and discuss its application to the description of diatomic systems. In particular, the electronic spectra of the light one-electron quasi-molecular compounds H-H+, He+-He2+ and He+-H+ are analyzed. For this purpose, the two-center Dirac equation is solved by a dual-kinetic balanced finite-basis-set method for axially symmetric systems, called A-DKB. This method allows for a complete relativistic consideration of the electron at fixed inter-nuclear distances. A comparison of the obtained results with the nonrelativistic and relativistic calculations presented in the literature is performed. Without pursuing the goal of high accuracy calculations, the advantages and disadvantages of the approach, as well as possible applications of the method, are discussed in detail.

New-Generation Electron-Propagator Methods for Molecular Electron-Binding Energies.

A new generation of electron-propagator methods for the calculation of electron binding energies has surpassed its antecedents with respect to accuracy, efficiency, and interpretability. No adjustable parameters are introduced in these fully ab initio procedures. Numerical tests versus several databases of valence, vertical electron binding energies of closed-shell molecules and atoms have been performed. Easily interpreted self-energy approximations with cubic arithmetic scaling produce mean absolute errors (MAEs) of 0.2 and 0.3 eV for electron detachments and attachments, respectively. The most accurate explicitly renormalized methods with fifth-power arithmetic scaling yield MAEs below 0.1 eV for detachments and attachments. Approximate renormalization leads to more efficient fifth-power alternatives for electron detachments that achieve similar accuracy with fewer bottleneck operations. Composite protocols generate excellent predictions versus highly accurate basis-extrapolated standards and experiments. The validity of the diagonal self-energy approximation and the accuracy of the approximate renormalizations are confirmed. The success of these perturbative methods based on canonical Hartree-Fock orbitals rests on a Hermitized, intermediately normalized superoperator metric. The results of all of the new-generation calculations may be analyzed in terms of final-state orbital relaxation and differential correlation effects.

Electron binding energies and the fundamental gap of a push-pull dye in a polar environment: p-nitroaniline in liquid water

The outer valence electron binding energies and the fundamental gap of p-nitroaniline (PNA) in water were determined by electron propagator theory. The adopted methodology relies on the calculation of electron binding energies by using configurations generated by Born-Oppenheimer molecular dynamics of PNA in water. The fundamental gap (Eg) of PNA in water was estimated from the first ionisation energy (IE) and the first vertical electron affinity VEA (Eg=IE-VEA). In liquid water Eg is predicted to be 6.5±0.5eV (OVGF), which is ∼3.3eV greater than the experimental optical gap (3.25eV).

Improving quasiparticle second order electron propagator calculations with the spin-component-scaled technique

A simple modification of the quasiparticle second order electron propagator (EP2) method based on the spin-component-scaled technique is proposed. In this new approach, the second order contributions to the self-energy of same and opposite spins are scaled by empirical parameters. Comparison with EP2 and higher order approaches for different sets of molecules reveals that the cost-free spin-component-scaled technique reduces average errors of EP2 up to 51%, thereby increasing its reliability and applicability for the calculation of electron binding energies in molecular systems.

Quasiparticle virtual orbitals in electron propagator calculations

The computational limits of accurate electron propagator methods for the calculation of electron binding energies of large molecules are usually determined by the rank of the virtual orbital space. Electron density difference matrices that correspond to these transition energies in the second-order quasiparticle approximation may be used to obtain a virtual orbital space of reduced rank that introduces only minor deviations with respect to the results produced with the full, original set of virtual orbitals. Numerical tests show the superior accuracy and efficiency of this approach compared to the usual practice of omission of virtual orbitals with the highest energies.

Ionization energies of tungsten ions: W 2+ through W 71+

A semi-empirical method is used to determine ionization energies of multiply charged tungsten ions, W 2+ through W 71+. The method is based on Hartree-Fock calculations of electron binding energies scaled according to experimental results. The relative uncertainties vary from 1.7% for W 2+ to 0.015% for W 71+. The resulting values are tabulated with results of experiments and precise theoretical calculations in a list of ionization energies for tungsten in all stages of ionization, W through W 73+.

Calculation of Electron Binding Energies and Affinities

Various methods for evaluating electron binding energies and affinities are discussed, and the (all-order) perturbative method is described in some detail. It is shown that for a single valence electron or valence hole the exact binding energy/affinity is given by the energy eigenvalue of the valence Brueckner or Dyson orbital.

Semidirect algorithms for third‐order electron propagator calculations

AbstractAn efficient procedure for third‐order electron propagator calculations of ionization energies and electron affinities is reported. Diagonal self‐energy expressions that are suitable for large molecules are empolyed. The outer‐valence Green's function method also is implemented. An integral transformation program for direct and semidirect algorithms is modified to store only nonzero integrals according to Abelian point group symmetry. Contributions to self‐energy matrix elements that depend on electron repulsion integrals with four virtual orbital indices are computed in a direct way. Intermediate batches of integrals are created by sort procedures while avoiding storage of transformed integrals in the main memory. This method permits calculation of electron binding energies for C with a 231 atomic orbital basis and for Zn(C5H5)2 with a 220 atomic orbital basis on an IBM RISC/6000 Model 550. During these calculations, the CPU is engaged approximately 90% of the time. © 1995 John Wiley & Sons, Inc.

On the calculation of electron binding energies

Theoretical determination of atomic and molecular electron binding energies (ionization potentials and electron affinities) is discussed and expressions derived which apply for the core as well as the valence region. Applications to Ne, H2O, LiH, and Li2 are used as indicators of the quality of the results.

The transition state, the electron propagator, and the equation of of motion method

The transition state idea is extended beyond the independent particle model and applied to the electron propagator theory and the so-called EOM method for calculation of electron binding energies. Application to the second order propagator equations for the neon atom yields excellent results for ionization energies of 1s, 2s, and 2p electrons.

Electron Spectroscopy - A Potentially Useful Tool for Environmental Studies

Abstract The technique of electron spectroscopy (ESCA) is reviewed. Those aspects are discussed which seem to be of greatest potential interest to workers in environmental studies. Basic theory of the photoelectron ejection process is considered along with the Auger effect. Factors affecting the calculation of electron binding energies are discussed. Instrumentation utilizing both magnetic and electrostatic monochromators is discussed in some detail. The nature of ESCA data is considered, along with an extensive tabulation of chemical shifts observed for 15 elements. Application of ESCA to surface studies is reviewed, using examples like effect of layers of material on electron intensities, investigations of zeolites and some elementary catalysis studies. A review of the quantitative aspects of ESCA considers the determination of arsenic in soils and the measurement of mixed oxide ratios.

Relativistic Calculations of Electron Binding Energies by a Modified Hartree-Fock-Slater Method

Relativistic atomic wave functions and electron binding energies have been calculated by a modified Hartree-Fock-Slater method. The local exchange approximation, originally introduced by Slater, is modified in such a way that the total energy of the system is minimized. Approximate expressions for the optimum exchange potential are suggested for all atoms and ions. The total atomic energies and electron binding energies obtained by this method agree extremely well with the corresponding Hartree-Fock results in the cases where such data are available. Various corrections to the theoretical binding energies are discussed, in particular the effect of rearrangement during the ionization process. It is found that this effect is of importance for inner shells in all elements and is responsible for the main discrepancy between experimental and previous theoretical results for light and medium-heavy elements. For heavy elements other effects are of importance, and various possible sources of the residual discrepancy between theory and experiments are discussed.