Double Ionization Energies Research Articles

Double-electron above-threshold ionization resonances as interference phenomena

We report calculations of double-ionization energy spectra and momentum distributions of laser-driven helium due to few-cycle pulses of wavelength 195 nm. The results are obtained from full-dimensional numerical integration of the two-electron time-dependent Schrödinger equation. A momentum-space analysis of doubly ionizing wavepackets shows that the concentric-ring structure of above-threshold double ionization, together with the associated structure of peaks in the total kinetic energy spectrum, may be attributed to wavepacket interference effects, where at least two doubly ionizing wavepackets from different recollision events populate the same spatial hemisphere.

Double ionization of cycloheptatriene and the reactions of the resulting C7Hn2+ dications (n = 6, 8) with xenon

The formation and fragmentation of the molecular dication C(7)H(8)(2+) from cycloheptatriene (CHT) and the bimolecular reactivities of C(7)H(8)(2+) and C(7)H(6)(2+) are studied using multipole-based tandem mass spectrometers with either electron ionization or photoionization using synchrotron radiation. From the photoionization studies, an apparent double-ionization energy of CHT of (22.67 ± 0.05) eV is derived, and the appearance energy of the most abundant fragment ion C(7)H(6)(2+), formed via H(2) elimination, is determined as (23.62 ± 0.07) eV. Analysis of both the experimental data as well as results of theoretical calculations strongly indicate, however, that an adiabatic transition to the dication state is not possible upon photoionization of neutral CHT and the experimental value is just considered as an upper bound. Instead, an analysis via two different Born-Haber cycles suggests (2)IE(CHT) = (21.6 ± 0.2) eV. Further, the bimolecular reactivities of the C(7)H(n)(2+) dications (n = 6, 8), generated via double ionization of CHT as a precursor, with xenon as well as nitrogen lead, inter alia, to the formation of the organo-xenon dication C(7)H(6)Xe(2+) and the corresponding nitrogen adduct C(7)H(6)N(2)(2+).

Core-valence double photoionization of the CS2 molecule

Double photoionization spectra of the CS(2) molecule have been recorded using the TOF-PEPECO technique in combination with synchrotron radiation at the photon energies hν=220, 230, 240, 243, and 362.7 eV. The spectra were recorded in the S 2p and C 1s inner-shell ionization regions and reflect dicationic states formed out of one inner-shell vacancy and one vacancy in the valence region. MCSCF calculations were performed to model the energies of the dicationic states. The spectra associated with a S 2p vacancy are well structured and have been interpreted in some detail by comparison to conventional S 2p and valence photoelectron spectra. The lowest inner-shell-valence dicationic state is observed at the vertical double ionization energy 188.45 eV and is associated with a (2p(3/2))(-1)(2π(g))(-1) double vacancy. The spectrum connected to the C 1s vacancy shows a distinct line at 310.8 eV, accompanied by additional broad features at higher double ionization energies. This line is associated with a (C 1s)(-1)(2π(g))(-1) double vacancy.

Cluster size dependence of double ionization energy spectra of spin-polarized aluminum and sodium clusters: All-electron spin-polarizedGW+T-matrix method

The double ionization energy (DIE) spectra are calculated for the spin-polarized aluminum and sodium clusters by means of the all-electron spin-polarized $GW+T$-matrix method based on the many-body perturbation theory. Our method using the one- and two-particle Green's functions enables us to determine the whole spectra at once in a single calculation. The smaller is the size of the cluster, the larger the difference between the minimal double ionization energy and the twice of the ionization potential. This is because the strong Coulomb repulsion between two holes becomes dominant in small confined geometry. Due to Pauli's exclusion principle, the parallel spin DIE is close to or smaller than the antiparallel spin DIE except for ${\text{Na}}_{4}$ that has well-separated highest and second highest occupied molecular-orbital levels calculated by the spin-dependent $GW$ calculation. In this paper, we compare the results calculated for aluminum and sodium clusters and discuss the spin-polarized effect and the cluster size dependence of the resulting spectra in detail.

Multiple ionization of atoms with xuv attosecond pulses: Two-photon double ionization of helium with 50 eV photons

We consider two-photon double ionization of helium by two xuv photons in the region around the sequential ionization threshold. We show that, on the attosecond timescale, the mechanism for double ionization is dominated by the absorption of one photon by each electron in the fundamental state He(1s2). We examine the dynamics of two-photon double ionization of helium for an averaged photon energy ω = 50 eV, with a pulse duration of two optical cycles. The double ionization rate, energy and angular distributions are calculated by solving the time-dependent Schrödinger equation. Results are discussed on the basis of a model.

Identification and theoretical investigation of the SiO2+ dication

The gas-phase diatomic dication SiO2+ has been observed by mass spectrometry and identified by its isotopic abundance. It was produced by energetic, high-current oxygen (16O−) ion beam sputtering of a silicon surface and survived a flight time of ∼10−5 s. In addition, a detailed theoretical study of SiO2+ has been performed. Our calculations show that SiO2+ is a metastable species with a large potential barrier towards dissociation (∼1.55 eV for the SiO2+ X ground state). We have derived a set of accurate spectroscopic constants and transition energies for SiO2+. The adiabatic double ionization energy of SiO is ∼31 eV.

A photoelectron and double photoionization study of the valence electronic structure of 1,4-bromofluorobenzene

Conventional photoelectron and time-of-flight photoelectron-photoelectron coincidence (TOF-PEPECO) spectra have been measured for the outer valence region of the 1,4-bromofluorobenzene molecule. The photoelectron spectra were recorded using HeI alpha radiation from a resonance source, and the TOF-PEPECO spectra were recorded using HeII alpha radiation from a pulsed resonance source. The former provide energies of the cationic states and the latter of the dicationic states. The spectra are adequately interpreted with the aid of accurate Green's function calculations, showing very significant correlation effects. The lowest double ionization energy is found at 23.45 eV associated with the (4b(1))(-2)X (1)A(1) dicationic state.

Synchrotron radiation VUV double photoionization of CHF 2Cl

VUV double photoionization of CHF 2Cl in an energy region 32–40 eV was investigated with photoionization mass spectroscopy by using synchrotron radiation. The double ionization energy of CHF 2Cl and appearance energies for its main fragment dications (CHCl 2+, CF 2 2+ and CHFCl 2+), were determined with photoionization efficiency spectroscopy for the first time. The single point energies of CHF 2Cl and its parent dication (CHF 2Cl 2+) were calculated using Gaussian 03 program and density functional theory (DFT and B3LYP functional). The vertical double ionization energy of CHF 2Cl was predicted by using B3LYP method and empirical equation. According to our research results, the experimental double ionization energy of CHF 2Cl is in good agreement with the theoretically calculated vertical double ionization energy. The mechanism of double photoionization of CHF 2Cl was discussed based on the comparison of our experimental results with those predicted theoretically.

A theoretical study of the BO 2+ dication

Potential energy curves for twelve low-lying electronic states of the BO 2+ dication have been calculated using internally contracted multireference MRCI, MRCI+Q and ACPF methods and the coupled-cluster RCCSD(T) approach. Spectroscopic constants and transition energies of BO 2+ have been determined and the double ionization energy of BO has been estimated. The spin-orbit induced predissociation from the lowest vibrational levels of the electronic ground state of BO 2+ has been predicted to be the most efficient decay route of the dication.

Density functional study of double ionization energies

In this paper, double ionization energies (DIEs) of gas-phase atoms and molecules are calculated by energy difference method with density functional theory. To determine the best functional for double ionization energies, we first study 24 main group atoms in the second, third, and fourth periods. An approximation is used in which the electron density is first obtained from a density functional computation with the exchange-correlation potential V xc known as statistical average of orbital potentials, after which the energy is computed from that density with 59 different exchange-correlation energy functionals E xc. For the 24 atoms, the two best E xc functional providing DIEs with average absolute deviation (AAD) of only 0.25 eV are the Perdew-Burke-Ernzerhof functional modified by Hammer et al. [Phys. Rev. B 59, 6413 (1999)] and one known as the Krieger-Chen-Iafrate-Savin functional modified by Krieger et al. (unpublished). Surprisingly, none of the 20 available hybrid functionals is among the top 15 functionals for the DIEs of the 24 atoms. A similar procedure is then applied to molecules, with opposite results: Only hybrid functionals are among the top 15 functionals for a selection of 29 molecules. The best E xc functional for the 29 molecules is found to be the Becke 1997 functional modified by Wilson et al. [J. Chem. Phys. 115, 9233 (2001)]. With that functional, the AAD from experiment for DIEs of 29 molecules is just under 0.5 eV. If the two suspected values for C2H2 and Fe(CO)5 are excluded, the AAD improves to 0.3(2) eV. Many other hybrid functionals perform almost as well.

Spectra of the dications of benzene, naphthalene and azulene

Spectra of the dications of benzene, naphthalene and azulene produced by double photoionisation of the parent compounds are presented. All the electron distributions show evidence of inner-valence Auger processes, which enhance population of low energy states of the dications. It is confirmed that the ground state of the benzene dication is a triplet, contrary to a recent theoretical prediction. The double ionisation energies of the three title molecules are determined as 24.65 ± 0.03, 21.28 ± 0.03 and 20.2 ± 0.2 eV, respectively.

Double photoionisation spectra of small molecules and a new empirical rule for double ionisation energies

Complete double photoelectron spectra are presented for 18 small molecules where the location of charges in the cations and dications is relatively clearly defined. The data demonstrate the importance of a coulombic repulsion contribution to the double ionisation energies. Examination of data for a wide range of molecules leads to a new empirical rule to calculate double ionisation energies from the molecules’ single ionisation energies and maximum dimensions. Where single and double ionisation energies are known the rule allows the deduction of plausible intercharge distances.

Short-Range Electron Correlations of CO<SUB>2</SUB> Molecule by First Principles <I>T</I>-Matrix Calculations

In this paper, we obtain the double ionization energy spectra and the two-electron distribution functions from the first principles evaluating the ladder diagrams up to the infinite order (T-matrix) and discuss the short-range electron correlations. The T-matrix, which describes the multiple scattering between electrons (or holes), can accurately represent the short-range repulsive Coulomb interaction. The double ionization energy spectra calculated for the CO2 molecule agree with the corresponding experiments very well. And the two-electron distribution function obtained from the T-matrix clearly shows ‘‘Coulomb hole’’ due to the avoidance of the antiparallel spin electrons confined in a small region. [doi:10.2320/matertrans.48.638]

Time-Dependent Schrödinger Equation Approach and Bethe-Salpeter Equation Approach

In this article, I will compare two different first-principles methods useful in the research of clusters and nanoscale materials. The first one is the time-dependent Schrodinger equation approach for chemical reactions or light harvesting functions in excited states, and the second one is the Bethe-Salpeter equation approach for photoabsorption spectra, exciton wavefunctions, double-ionization energy spectra, and two-electron distribution functions. I will newly derive some exact theorems related to these approaches. While the first approach is convenient and useful, the second approach, which satisfies Friedel sum rule, is more reliable and accurate.

An experimental and theoretical investigation of the valence double photoionisation of the ICl molecule

The double valence photoelectron spectrum of ICl has been measured at two photon energies, 303.78 Å and 379.3 Å, by the TOF-PEPECO technique. Relativistic molecular electronic structure calculations have been performed for electronic states connected to the three lowest groups of dissociation limits to support the interpretation, and vibrational constants have been calculated for the quasi-bound states. The two lowest double ionisation energies are found to be 27.45 ± 0.1 eV (vertical) and 27.69 ± 0.1 eV (vertical). They are associated with the X 3 Σ 0 , 1 - electronic states of ICl 2+, respectively, which are the only states predicted to be stable by the calculations. The two following states connected to the same configuration are in order a 1Δ 2 and b 1 Σ 0 + . The double ionisation processes building up the spectrum are found to be mainly direct, and energies and widths of the bands are well reproduced by the calculations.

First principles calculations of double ionization energy spectra and two-electron distribution function using T-matrix theory

Short-range electron correlation plays a very important role in small systems and significantly affects the double ionization energy (DIE) spectra and the two-electron distribution functions of a CO molecule, for example. In our calculations, the local density approximation (LDA) of the density functional theory is chosen as a starting point, the GW approximation (GWA) is performed in a next step, and finally the Bethe–Salpeter equation for the T-matrix, describing the particle–particle ladder diagrams up to the infinite order, is solved via the eigenvalue problem. The calculated DIE spectra, which are directly given by the eigenvalues, reflect the short-range electron correlation and are in good agreement with the experiment. We confirm that the Coulomb hole appears in the two-electron distribution function constructed from the eigenfunction.

An experimental and theoretical study of double photoionization of CF4 using time-of-flight photoelectron-photoelectron (photoion-photoion) coincidence spectroscopy

Single photon double ionization of CF4 has been studied by means of a time-of-flight photoelectron-photoelectron coincidence technique, which has very recently been extended towards ion detection, with energy analysis for the electrons and mass analysis for the ions. The complete single photon double ionization electron spectrum of CF4 up to a binding energy of approximately 51 eV is presented and discussed, also with the aid of accurate ab initio Green's function calculations. From ion detection in coincidence with the ejected electrons, we derive fragmentation pathway-selected double ionization electron spectra of CF4. From the same data we extract the yield of each doubly charged ion or ion pair as a function of the double ionization energy.

Two-electron distribution functions and short-range electron correlations of atoms and molecules by first principles T-matrix calculations

The accurate first principles description of the correlations between electrons has been a topic of interest in molecular physics. We have reported in our previous paper [J. Chem. Phys. 123, 144112 (2005)] that the T matrix, which is the ladder diagrams up to the infinite order, can accurately represent the short-range electron correlations while calculating the double ionization energy spectra of atoms and molecules. In this paper, we calculate the two-electron distribution functions of real systems (Ar, CO, CO(2), and C(2)H(2)) from the eigenvalue equation associated with the Bethe-Salpeter equation for the T matrix by beginning with the local density approximation of the density functional theory and the GW approximation. We found that when the interelectron distance is very small, the Coulomb hole appears between antiparallel spin electrons due to the short-range repulsive Coulomb interaction. The resulting two-electron distribution functions clearly show the Coulomb hole.

Double ionisation of ICN and BrCN studied by a new photoelectron–photoion coincidence technique

A double time-of-flight technique is described, whereby any number of electrons and ions produced by photoionisation can be detected in coincidence, with energy analysis for the electrons and mass analysis for the ions. Branching ratios, kinetic energy releases and mechanisms in doubly charged ion decays can be measured with selection of the initial double ionisation energy. The new technique, together with spectroscopy by the recently established time-of-flight photoelectron–photoelectron coincidence (TOF-PEPECO) method, is used to study the spectra and dissociation dynamics of ICN ++ and BrCN ++.

Energetics of fragmentations of indene dication from photoionization experiments

The formation and fragmentation of the indene dication C 9 H 8 2 + is studied using synchrotron radiation. The double-ionization energy of indene amounts to 21.8 ± 0.1 eV. The appearance energies of the fragments C 9 H 7 2 + and C 9 H 6 2 + are 25.8 ± 0.1 eV and 25.7 ± 0.2 eV, respectively. Although the appearance energies are almost the same, the dicationic fragment C 9 H 6 2 + is formed in a higher yield than C 9 H 7 2 + . It is suggested that the elimination of atomic hydrogen is associated with a considerable energy barrier, whereas the H 2 elimination proceeds via very small barrier or is barrier-less process with respect to the reaction endothermicity.