Single and double core-hole ionization energies in molecules

The recently demonstrated ability to measure double-hole core-ionization energies in first-row elements has led to a renewed interest in the use of such energies to investigate the effects of initial-state charge distribution and final-state charge rearrangement on the energies of chemical processes that involve addition of charge to a molecule. With theoretical calculations for the molecules CH(4-n)X(n), X = F, Cl, and for C(CH(3))(4) as a basis, the relationships between one-hole and two-hole ionization energies, on one hand, and initial-state and final-state effects, on the other, are reviewed. It is shown that higher-order corrections to the traditionally used relationships are quantitatively significant but do not lead to qualitatively different conclusions. The role of the Wagner plot as a way to display the relationships among the various quantities of interest is discussed, and a generalized Wagner plot for displaying two-site double-hole ionization energies is presented. Some possible applications of measurements of double-hole ionization energies to the investigation of molecular conformation and molecular fragmentation are discussed.     

Single and double K-shell ionization cross sections of silicon

A four-body classical trajectory Monte Carlo (CTMC) method is applied in the study of single and double ionization cross-sections of the silicon K-shell. The calculations are based on the independent particle model. As projectiles, we consider protons with energies between 0.25 and 4.5 MeV. Our CTMC results are compared with the existing theoretical and experimental data.     

Photoionization and ionic dissociation of the C3H3NS molecule induced by soft X‐ray near the C1s edge

Time of flight mass spectrometry, electron‐ion coincidence, and ion yield spectroscopy were employed to investigate for the first time the thiazole (C₃H₃NS) molecule in the gas phase excited by synchrotron radiation in the soft X‐ray domain. Total ion yield (TIY) and photoelectron‐photoion coincidence (PEPICO) spectra were recorded as a function of the photon energy in the vicinity of the carbon K edge (C1s). The C1s resonant transitions as well as the core ionization thresholds have been determined from the profile of TIY spectrum, and the features were discussed. The corresponding partial ion yields were determined from the PEPICO spectra for the cation species produced upon the molecular photodissociation. Additional ab initio calculations have also been performed from where relevant structural and electronic configuration parameters were obtained for this molecule.     

Photoelectron circular dichroism in core level ionization of randomly oriented pure enantiomers of the chiral molecule camphor

The inner-shell photoionization of unoriented camphor molecules by circularly polarized light has been investigated from threshold to a photoelectron kinetic energy of approximately 65 eV. Photoelectron spectra of the carbonyl C 1s orbital, recorded at the magic angle of 54.7 degrees with respect to the light propagation direction, show an asymmetry of up to 6% on change of either the photon helicity or molecular enantiomer. These observations reveal a circular dichroism in the angle resolved emission with an asymmetry between forward and backward scattering (i.e., 0 degrees and 180 degrees to the light beam) which can exceed 12%. Since the initial state is an atomiclike spherically symmetric orbital, this strongly suggests that the asymmetry is caused by final-state effects dependent on the chiral geometry of the molecule. These findings are confirmed by electron multiple scattering calculations of the photoionization dynamics in the electric-dipole approximation.     

Auger spectrum of a water molecule after single and double core ionization

The high intensity of free electron lasers opens up the possibility to perform single-shot molecule scattering experiments. However, even for small molecules, radiation damage induced by absorption of high intense x-ray radiation is not yet fully understood. One of the striking effects which occurs under intense x-ray illumination is the creation of double core ionized molecules in considerable quantity. To provide insight into this process, we have studied the dynamics of water molecules in single and double core ionized states by means of electronic transition rate calculations and ab initio molecular dynamics (MD) simulations. From the MD trajectories, photoionization and Auger transition rates were computed based on electronic continuum wavefunctions obtained by explicit integration of the coupled radial Schro?dinger equations. These rates served to solve the master equations for the populations of the relevant electronic states. To account for the nuclear dynamics during the core hole lifetime, the calculated electron emission spectra for different molecular geometries were incoherently accumulated according to the obtained time-dependent populations, thus neglecting possible interference effects between different decay pathways. We find that, in contrast to the single core ionized water molecule, the nuclear dynamics for the double core ionized water molecule during the core hole lifetime leaves a clear fingerprint in the resulting electron emission spectra. The lifetime of the double core ionized water was found to be significantly shorter than half of the single core hole lifetime.     

Theory of single and double ionization of helium through two-photon excitation of the1 S 0 e (1) doubly excited resonance

We present a theory and calculations of two-photon-resonant three-photon ionization of He via the lowest even parity doubly excited state¹ S ₀ ^e (1). We assess the importance of double ionization relative to single ionization into excited ionic states. Although double ionization is found to be quite small in the present context, our calculations reveal the importance of autoionizing doubly excited states as virtual intermediate states and suggest contexts in which double ionization may be relatively more efficient.     

Rotational effect in the ionization of a highly excited atom by collision with a polar molecule

If the collisional ionization is chiefly due to energy transfer from the polar-molecule rotation to an electron in a high Rydberg state of the atom, then theory predicts that the cross section averaged over a thermal distribution of rotational states should show step-like structure as a function of the energy of the Rydberg state. This structure has been experimentally detected, and it can be considered as direct evidence of the rotational effect in the collisional ionization.     

Diabatic representation for the excited states of the Na2 molecule: application to the associative ionization reaction between two excited sodium atoms

A two-electron model potential method is proposed to compute diabatic electronic excited states for Na₂. The configuration space is first divided into two subspaces corresponding to singly and doubly excited configurations respectively. Next this partition is modified to ensure a correct dissociation limit for the ground state. The matrix element of the electronic Hamiltonian between the two subspaces can be extrapolated along a Rydberg series up to the ionization continuum. The first order M.Q.D.T. treatment of Giusti (1980) is then used to estimate the cross-sections for the reaction Na(3p)+Na(3p)→Na ₂ ⁺ +e ^?, considering various symmetries of the intermediate Na₂ molecule. A marked selectivity in favour of the³Σ _u ⁺ symmetry is found and the estimated cross-section σ ～ 5 Ų for a collision energy of 0.05 eV is in satisfactory agreement with the experimental results.     

The C 1s and N 1s near edge x-ray absorption fine structure spectra of five azabenzenes in the gas phase

Near edge x-ray absorption fine structure spectra have been measured and interpreted by means of density functional theory for five different azabenzenes (pyridine, pyridazine, pyrimidine, pyrazine, and s-triazine) in the gas phase. The experimental and theoretical spectra at the N 1s and C 1s edges show a strong resonance assigned to the transition of the 1s electron in the respective N or C atoms to the lowest unoccupied molecular orbital with pi(*) symmetry. As opposed to the N 1s edge, at the C 1s edge this resonance is split due to the different environments of the core hole atom in the molecule. The shift in atomic core-level energy due to a specific chemical environment is explained with the higher electronegativity of the N atom compared to the C atom. The remaining resonances below the ionization potential (IP) are assigned to sigma or pi [corrected] orbitals with mixed valence/Rydberg [corrected] character. Upon N addition, a reduction of intensity is observed in the Rydberg region at both edges as compared to the intensity in the continuum. Above the IP one or more resonances are seen and ascribed here to transitions to sigma(*) orbitals. Calculating the experimental and theoretical Delta(pi) term values at both edges, we observe that they are almost the same within +/-1 eV as expected for isoelectronic bonded pairs. The term values of the pi(*) and sigma(*) resonances are discussed in terms of the total Z number of the atoms participating in the bond.     

饱和链状分子中C 1s电子电离能与基团拓扑电负性指数

由X-射线光电子谱测定的原子内层电子的电离能(也称结合能)能反映分子内部不同区域的原子特性,常用于估计分子内不同部位的化学活性、分子中的电子结构变化以及取代基效应[1]。还用于研究价电子性质[2-4]和化合物的气相酸碱性[5]。目前,对原子内层电子电离能的研究有实验测定和     

Ab initio-based double many-body expansion potential energy surface for the first excited triplet state of the ammonia molecule

A global single-sheeted double many-body expansion potential energy surface is reported for the first excited triplet state of NH(3). It employs an approximate cluster expansion of the molecular potential that utilizes previously reported functions of the same family for the triatomic fragments. Four-body energy terms have been calibrated from extensive accurate ab initio data so as to reproduce the main features of the title system. A new switching function formalism has been reported to approximate the true multisheeted nature of NH(3)((3)A(2) (')) potential energy surface, thus allowing the correct behavior at the NH(2)((2)A(")) + H((2)S) and NH(2)((4)A(")) + H((2)S) dissociation limits. The resulting fully six-dimensional potential energy function reproduces the correct symmetry under the permutation of identical atoms, and predicts the correct behavior at all dissociation channels while providing a realistic representation at all interatomic separations. The major attributes of the NH(3) double many-body expansion potential energy surface have also been characterized, and found to be in good agreement, both with the calculated ones from the raw ab initio energies and the theoretical results available in the literature.     

Electronically excited and ionized states of the chlorine molecule

Potentials curves for the ground and excited states of the chlorine molecules and its positive and negative ions have been calculated by means of the MRD-CI method. The standard AO basis employed consists of 74 functions including two atomic d and one set of s and p bond species, and the results at the corresponding full CI level are estimated for each state via a perturbation correction. Special emphasis is placed upon the treatment of Rydberg-valence mixing in this system, which phenomenon is found to be essential to the understanding of Cl₂ electronic absorption spectrum. All singlet states which correlate with the lowest dissociation limit plus many others which go to ionic Cl⁺+Cl^? or Rydberg Cl+Cl asymptotes are given explicit consideration. Among the triplet species of Cl₂ which dissociate into the ground state atoms only the ³Π_u state is not repulsive. The calculated D₀ value for the ground state is 2.455 eV compared to the experimental value of 2.475 eV, while the vertical ionization energy and electron affinity are found to be 11.48 and 2.38 eV respectively, also in very good agreement with the corresponding measured data of 11.50 and 2.51 ± 0.1 eV. In addition to Cl₂ laser line is confirmed to result from a ³Π_g → ³Π_u emission, whereby the calculated downward vertical transition energy of 4.86 eV fits in quite well with the known location of this line at 4.805 eV. The first two dipole-allowed transitions from the ground state of chlorine involve ¹Σ_u⁺ and ¹Π_u states which are calculated to be nearly isoenergetic, and these results also match very well with the location of the first absorption band in this spectrum. Finally quite similarly as in O₂ it is found that an avoided crossing between Rydberg and valences states produces a relatively steep potential well for an upper state (2 ¹Σ_u⁺), whose location concides with that of a second absorption band recently observed in synchrotron radiation studies.     

The ionization potential of the BeH molecule

The ionization potential of the BeH molecule is derived from a few Rydberg states observed in the absorption spectrum and from “ab initio” calculations of the energies of the ground states of the BeH and BeH⁺ molecules at their equilibrium distances. The values are in agreement and yield PI(BeH, X²Σ⁺) = 66 100 ± 500 cm^?1.     

Highly excited vibrational states of HCN around 30 000 cm-1

This article describes the analysis and interpretation of rovibrational spectra involving highly excited vibrational states in the molecule of HCN. The spectra were obtained by means of the vibrationally mediated photodissociation technique. Analysis of the spectra revealed four bands with Sigma-Sigma structures that, once fitted, provided the energies and rotational constants of four new, highly excited vibrational states in the region of the potential energy surface near and above 30 000 cm(-1). All the states could be identified with the help of a state-of-the-art variational calculation. Together with the states already observed in previous works, eight highly excited states have so far been identified in this region.     

Valence double ionization of O2 at photon energies below and above the molecular double ionization threshold

A recently developed time-of-flight photoelectron-photoelectron coincidence spectroscopy technique, which gives complete two-dimensional e(-)-e(-) spectra in single photon double ionization, is applied to molecular oxygen at photon energies below and above the adiabatic double ionization threshold of O(2). Analysis of the two-dimensional coincidence maps reveals specific indirect pathways for the double ionization process. Dissociative ionization paths with subsequent autoionization of atomic oxygen are found to be the dominant processes for all chosen photon energies. Spectra of the photoelectrons coincident with the autoionization electrons show that intermediate O(2)(+) states are involved which do not autoionize to molecular O(2)(2+). In particular, the ground state of O(2)(2+) is vibrationally resolved and shows a regular progression which can be well described by direct Franck-Condon transitions at an internuclear distance R(e)(X (1)Sigma(g)(+))=1.054 A. Quantum yields of double ionization for O(2), of a form discussed in this paper, are determined.     

Dissociation energy and ionization potential of the molecule CF

The gaseous equilibrium S + CF₂ = SF + CF was studied over the temperature range 1851 to 2232 K by mass spectrometry, and the derived enthalpy change was used to evaluate the heat of formation of CF ΔH₂₉₈ = 58.0 ± 2.4 kcal/mol (2.52 ± 0.10 eV), and the dissociation energy D₀⁰ (CF) = 130.8 ± 2.4 kcal/mol (5.67 ± 0.10 eV). The new thermochemical data indicate a slightly higher stability for CF than earlier determinations. Direct measurement by electron impact yielded a value of 9.17 ± 0.10 eV for the vertical ionization potential of CF, in agreement with an indirect result obtained from the photodissociative ionization of C₂F₄.     

A theoretical investigation of the singly excited two-electron atomic states 1s2s3S and 1s3s3S

The singly-excited two-electron states 1s2s ³S and ls3s ³S have been investigated by means of the variational perturbation theory procedure. The wave functions have been constructed as linear combinations of Hylleraas terms with hyperbolic factors in t, and the results obtained by carrying the computations through to 10th perturbation order and with 36(37)- 57(58)- and 85(86)-term basic sets, respectively, are reported. These results compare favourably with the corresponding best values from previous conventional variational calculations.     

Preliminary calculations on excited states of the oxygen molecule

It is well known that the energy interval separating ³ _u ^– and ³ _u ⁺ states of O₂, as given by the conventional ASMO method, is too large. In order to resolve this difficulty, removal of the equivalence restrictions usually employed in the orbital theory is proposed. Thus the orbital exponent of one antibonding _g MO is allowed to take a different value from the other _g's. Variational calculations show that the resulting outermost orbital is much more diffuse than the others. This model of a single diffuse orbital brings about a considerable energy lowering for the ³ _u ^– state and thus the agreement of the ³ _u ^– - ³ _u ⁺ interval with experiment is improved.

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Zusammenfassung Die konventionelle ASMO-Theorie liefert bekanntlich eine viel zu große Differenz der Terme ³ _u ^– und ³ _u ⁺ von O₂, weswegen der Vorschlag gemacht wird, die üblicherweise vorgenommene Äquivalenz-Einschränkung fallen zu lassen. Der Orbital-Exponent eines lockernden MO's kann von dem der übrigen _g's abweichen. Rechnungen zeigen, daß das äußerste MO viel diffuser als die anderen ist und daß die Energie des ³ _u ^– -Zustandes beträchtlich erniedrigt wird.

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Résumé La séparation entre les états ³ _u ^{– 3} _u ⁺ de O₂ donnée par la méthode ASMO conventionnelle est connue pour être trop grande. Afin de résoudre cette difficulté la levée des restrictions d'équivalence ordinairement utilisées est proposée. Ainsi l'exposant orbital d'une des orbitales moléculaires antiliantes _g peut prendre une valeur différente de celui de l'autre orbitale antiliante _g. Des calculs variationnels montrent que l'orbitale la plus haute ainsi obtenue est beaucoup plus diffuse que les autres. Ceci a pour effet de diminuer considérablement l'énergie de l'état ³ _u ^– , améliorant la séparation entre les états ³ _u ^– et ³ _u ⁺ .