A comprehensive photoabsorption, photoionization, and shake-up excitation study of the C 1s cross section of benzene

Molecular-Orbital Framework of Two-Electron Processes: Application to Auger and Intermolecular Coulomb Decay

States with core- or inner-shell vacancies, which are commonly created by absorption of high-energy photons, can decay by a two-electron process in which one electron fills the core hole and the second one is ejected. These processes accompany many X-ray spectroscopies. Depending on the nature of the initial core- or inner-shell-hole state and the decay valence-hole state, these processes are called Auger decay, intermolecular Coulomb decay, or electron-transfer-mediated decay. To connect many-body wave functions of the initial and final states with the molecular orbital picture of the decay, we introduce the concept of natural Auger orbitals (NAOs). NAOs are obtained by a two-step singular value decomposition of the two-body Dyson orbitals, reduced quantities that enter the expression of the decay rate in the Feshbach-Fano treatment. NAOs afford chemical insight and interpretation of the high-level ab initio calculations of Auger decay and related two-electron relaxation processes.

The Auger spectrum of benzene

We present an ab initio computational study of the Auger electron spectrum of benzene. Auger electron spectroscopy exploits the Auger-Meitner effect, and although it is established as an analytic technique, the theoretical modeling of molecular Auger spectra from first principles remains challenging. Here, we use coupled-cluster theory and equation-of-motion coupled-cluster theory combined with two approaches to describe the decaying nature of core-ionized states: (i) Feshbach-Fano resonance theory and (ii) the method of complex basis functions. The spectra computed with these two approaches are in excellent agreement with each other and also agree well with experimental Auger spectra of benzene. The Auger spectrum of benzene features two well-resolved peaks at Auger electron energies above 260 eV, which correspond to final states with two electrons removed from the 1e_1g and 3e_2g highest occupied molecular orbitals. At lower Auger electron energies, the spectrum is less well resolved, and the peaks comprise multiple final states of the benzene dication. In line with theoretical considerations, singlet decay channels contribute more to the total Auger intensity than the corresponding triplet decay channels.

First (e,e) coincidence measurements on solvated sodium benzoate in water using a magnetic bottle time-of-flight spectrometer

Sodium benzoate molecules solvated in water are studied using coincidence electron spectroscopy coupled with a liquid microjet device.

Molecular Auger Decay Rates from Complex-Variable Coupled-Cluster Theory

The emission of an Auger electron is the predominant relaxation mechanism of core-vacant states in molecules composed of light nuclei. In this non-radiative decay process, one valence electron fills the core vacancy while a second valence electron is emitted into the ionization continuum. Because of this coupling to the continuum, core-vacant states represent electronic resonances that can be tackled with standard quantum-chemical methods only if they are approximated as bound states, meaning that Auger decay is neglected. Here, we present an approach to compute Auger decay rates of core-vacant states from coupled-cluster and equation-of-motion coupled-cluster wave functions combined with complex scaling of the Hamiltonian or, alternatively, complex-scaled basis functions. Through energy decomposition analysis, we illustrate how complex-scaled methods are capable of describing the coupling to the ionization continuum without the need to model the wave function of the Auger electron explicitly. In addition, we introduce in this work several approaches for the determination of partial decay widths and Auger branching ratios from complex-scaled coupled-cluster wave functions. We demonstrate the capabilities of our new approach by computations on core-ionized states of neon, water, dinitrogen, and benzene. Coupled-cluster and equation-of-motion coupled-cluster theory in the singles and doubles approximation both deliver excellent results for total decay widths, whereas we find partial widths more straightforward to evaluate with the former method. We also observe that the requirements towards the basis set are less arduous for Auger decay than for other types of resonances so that extensions to larger molecules are readily possible.

NEXAFS and MS-AES spectroscopy of the C 1s and Cl 2p excitation and ionization of chlorobenzene: Production of dicationic species

We report on single- and double-charge photofragment formation by synchrotron radiation, following C 1s core excitation and ionization and Cl 2p inner excitation and ionization of chlorobenzene, C₆H₅Cl. From a comparison of experimental near-edge X-ray absorption fine structure spectra and theoretical ab initio calculations, the nature of various core and inner shell transitions of the molecule and pure atomic features were identified. To shed light on the normal Auger processes following excitation or ionization of the molecule at the Cl 2p or C 1s sites, we addressed the induced ionic species formation. With energy resolved electron spectra and ion time-of-flight spectra coincidence measurements, the ionic species were correlated with binding energy regions and initial states of vacancies. We explored the formation of the molecular dication C₆H₅Cl²⁺, the analogue benzene dication C₆H₄²⁺, and the singly charged species produced by single loss of a carbon atom, C₅H_nCl⁺. The appearance and intensities of the spectral features associated with these ionic species are shown to be strongly site selective and dependent on the energy ranges of the Auger electron emission. Unexpected intensities for the analogue double charged benzene C₆H₄²⁺ ion were observed with fast Auger electrons. The transitions leading to C₆H₅Cl²⁺ were identified from the binding energy representation of high resolution electron energy spectra. Most C₆H₅Cl²⁺ ions decay into two singly charged moieties, but intermediate channels are opened leading to other heavy dicationic species, C₆H₄²⁺ and C₆H₄Cl²⁺, the channel leading to the first of these being much more favored than the other.

Table-Top X-ray Spectroscopy of Benzene Radical Cation

Ultrafast table-top X-ray spectroscopy at the carbon K-edge is used to measure the X-ray spectral features of benzene radical cations (Bz⁺). The ground state of the cation is prepared selectively by two-photon ionization of neutral benzene, and the X-ray spectra are probed at early times after the ionization by transient absorption using X-rays produced by high harmonic generation (HHG). Bz⁺ is well-known to undergo Jahn-Teller distortion, leading to a lower symmetry and splitting of the π orbitals. Comparison of the X-ray absorption spectra of the neutral and the cation reveals a splitting of the two degenerate π* orbitals as well as an appearance of a new peak due to excitation to the partially occupied π-subshell. The π* orbital splitting of the cation, elucidated on the basis of high-level calculations in a companion theoretical paper [Vidal et al. J. Phys. Chem. A. http://dx.doi.org/10.1021/acs.jpca.0c08732], is discovered to be due to both the symmetry distortion and even more dominant spin coupling of the unpaired electron in the partially vacant π orbital (from ionization) with the unpaired electrons resulting from the transition from the 1s_C core orbital to the fully vacant π* orbitals.

Interplay of Open-Shell Spin-Coupling and Jahn-Teller Distortion in Benzene Radical Cation Probed by X-ray Spectroscopy

We report a theoretical investigation and elucidation of the X-ray absorption spectra of neutral benzene and of the benzene cation. The generation of the cation by multiphoton ultraviolet (UV) ionization and the measurement of the carbon K-edge spectra of both species using a table-top high-harmonic generation source are described in the companion experimental paper [Epshtein, M.; et al. J. Phys. Chem. A http://dx.doi.org/10.1021/acs.jpca.0c08736]. We show that the 1s_C → π transition serves as a sensitive signature of the transient cation formation, as it occurs outside of the spectral window of the parent neutral species. Moreover, the presence of the unpaired (spectator) electron in the π-subshell of the cation and the high symmetry of the system result in significant differences relative to neutral benzene in the spectral features associated with the 1s_C → π* transitions. High-level calculations using equation-of-motion coupled-cluster theory provide the interpretation of the experimental spectra and insight into the electronic structure of benzene and its cation. The prominent split structure of the 1s_C → π* band of the cation is attributed to the interplay between the coupling of the core → π* excitation with the unpaired electron in the π-subshell and the Jahn-Teller distortion. The calculations attribute most of the splitting (∼1-1.2 eV) to the spin coupling, which is visible already at the Franck-Condon structure, and we estimate the additional splitting due to structural relaxation to be around ∼0.1-0.2 eV. These results suggest that X-ray absorption with increased resolution might be able to disentangle electronic and structural aspects of the Jahn-Teller effect in the benzene cation.

Limitations of the equivalent core model for understanding core-level spectroscopies

The equivalent core model, or the Z + 1 approximation, has been used to interpret the binding energy, BE, shifts observed in X-ray photoelectron spectroscopy, XPS; in particular to relate these shifts to their origin in the electronic structure of the system. Indeed, a recent paper has claimed that the equivalent core model provides an intuitive chemical view of XPS BE shifts. In the present paper, we present a detailed comparison of the electronic structure provided from rigorous core-hole theory and from the equivalent core model to assess the validity and the utility of the use of the equivalent core model. This comparison shows that the equivalent core model provides a qualitative view of the different properties of initial and core-hole electronic structure. It is also shown that a very serious limitation of the equivalent core model is that it fails to distinguish between initial and final state contributions to the shifts of BEs which seriously reduces the utility of the information obtained with the equivalent core model. Indeed, there is a danger of making an incorrect assignment of the importance of relaxation because the equivalent core model appears to stress the role of final state effects. Given the importance of the distinction of initial and final state effects, we provide rigorous definitions of these two effects and we discuss an example where an incorrect interpretation was made based on the use of the equivalent core model.

Stability of radical-functionalized gold surfaces by self-assembly and on-surface chemistry

We have investigated the radical functionalization of gold surfaces with a derivative of the perchlorotriphenylmethyl (PTM) radical using two methods: by chemisorption from the radical solution and by on-surface chemical derivation from a precursor. We have investigated the obtained self-assembled monolayers by photon-energy dependent X-ray photoelectron spectroscopy. Our results show that the molecules were successfully anchored on the surfaces. We have used a robust method that can be applied to a variety of materials to assess the stability of the functionalized interface. The monolayers are characterized by air and X-ray beam stability unprecedented for films of organic radicals. Over very long X-ray beam exposure we observed a dynamic nature of the radical-Au complex. The results clearly indicate that (mono)layers of PTM radical derivatives have the necessary stability to withstand device applications.

A simple molecular orbital picture of RIXS distilled from many-body damped response theory

Ab initio calculations of resonant inelastic x-ray scattering (RIXS) often rely on damped response theory, which prevents the divergence of response solutions in the resonant regime. Within the damped response theory formalism, RIXS moments are expressed as the sum over all electronic states of the system [sum-over-states (SOS) expressions]. By invoking resonance arguments, this expression can be reduced to a few terms, an approximation commonly exploited for the interpretation of computed cross sections. We present an alternative approach: a rigorous formalism for deriving a simple molecular orbital picture of the RIXS process from many-body calculations using the damped response theory. In practical implementations, the SOS expressions of RIXS moments are recast in terms of matrix elements between the zero-order wave functions and first-order frequency-dependent response wave functions of the initial and final states such that the RIXS moments can be evaluated using complex response one-particle transition density matrices (1PTDMs). Visualization of these 1PTDMs connects the RIXS process with the changes in electronic density. We demonstrate that the real and imaginary components of the response 1PTDMs can be interpreted as contributions of the undamped off-resonance and damped near-resonance SOS terms, respectively. By analyzing these 1PTDMs in terms of natural transition orbitals, we derive a rigorous, black-box mapping of the RIXS process into a molecular orbital picture. We illustrate the utility of the new tool by analyzing RIXS transitions in the OH radical, benzene, para-nitroaniline, and 4-amino-4'-nitrostilbene. These examples highlight the significance of both the near-resonance and off-resonance channels.

Soft X-ray Absorption Spectroscopy of Liquids for Understanding Chemical Processes in Solution

Soft X-ray absorption spectroscopy (XAS) involving excitation processes of a core electron to unoccupied states is an effective method to study local structures around excited C, N, and O atoms in liquid samples. Since soft X-rays are strongly absorbed by air and liquid itself, we have developed transmission-type liquid flow cells, where the absorbance of liquid samples can be easily reduced and optimized by controlling the liquid thickness. By using the transmission-mode XAS techniques, we have investigated local structures of several liquid samples such as concentration dependence of aqueous pyridine solutions and unexpected temperature-dependent structural changes in liquid benzene from the precise energy shift measurements in XAS spectra with the help of molecular dynamics simulation and inner-shell calculations. These XAS techniques are also applied to in situ/operando observation of chemical processes in solutions such as catalytic and electrochemical reactions.

Theoretical assessment of vibrationally resolved C1s X-ray photoelectron spectra of simple cyclic molecules

Vibrationally-resolved K-edge XPS simulation by the full/equivalent core-hole method is enabled and assessment of the C1s spectra of cyclic molecules shows excellent/acceptable agreement with the experiment.

How to stay out of trouble in RIXS calculations within equation-of-motion coupled-cluster damped response theory? Safe hitchhiking in the excitation manifold by means of core–valence separation

We present a novel approach with robust convergence of the response equations for computing resonant inelastic X-ray scattering (RIXS) cross sections within the equation-of-motion coupled-cluster (EOM-CC) framework.

An experimental and theoretical study of the C 1s ionization satellites in CH3I

The C 1s ionization spectrum of CH₃I has been studied both experimentally and theoretically. Synchrotron radiation has been employed to record polarization dependent photoelectron spectra at a photon energy of 614 eV. These spectra encompass the main-line due to the C 1s single-hole state and the peaks associated with the shake-up satellites. Vertical ionization energies and relative photoelectron intensities have been computed using the fourth-order algebraic-diagrammatic construction approximation scheme for the one-particle Green's function and the 6-311++G^** basis set. The theoretical spectrum derived from these calculations agrees qualitatively with the experimental results, thereby allowing the principal spectral features to be assigned. According to our calculations, two ²A₁ shake-up states of the C 1s^-1 σ_CI → σ_CI ^* type with singlet and triplet intermediate coupling of the electron spins (S' = 0, 1) play an important role in the spectrum and contribute significantly to the overall intensity. Both of these states are expected to have dissociative diabatic potential energy surfaces with respect to the C-I separation. Whereas the upper of these states perturbs the manifold of Rydberg states, the lower state forms a band which is characterized by a strongly increased width. Our results indicate that the lowest shake-up peak with significant spectral intensity is due to the pair (S' = 0, 1) of ²E (C 1s^-1 I 5p → σ_CI ^*) states. We predict that these ²E states acquire photoelectron intensity due to spin-orbit interaction. Such interactions play an important role here due to the involvement of the I 5p orbitals.

Temperature-Dependent Structural Changes in Liquid Benzene

Benzene is the simplest aromatic molecule with intermolecular π-π interactions. Because ordered liquids are key structures used to study chemical and biological phenomena in the liquid state, ordered structures of benzene confined in nanopores have been extensively studied, whereas those in the liquid state are still unknown. In this study, we address fundamental questions regarding whether ordered structures of benzene are formed in the liquid state by using carbon K-edge X-ray absorption spectroscopy (XAS) as a sensitive local probe. By comparing unexpected temperature behaviors of the π* peak in XAS spectra with model calculations, we have investigated temperature-dependent changes of ordered structures in liquid benzene caused by the increase in abundance of the parallel sandwich orientation relative to parallel displaced structures for the higher temperature. These results are confirmed by infrared spectroscopy with additional support of vibrational mode calculations.

The study of the electronic structure of some N-heterocyclic carbenes (NHCs) by variable energy photoelectron spectroscopy

UV and X-ray photoelectron spectra of three N-heterocyclic carbenes under synchrotron radiation reveal details of their electronic structure and are used as a benchmark to test computational methods for treating core ionizations in systems with unusual electronic structures.

Double photoionization in ring molecules: search of the cooper pair formation

We provide a final state selective experimental study on the direct double photoionization of the valence states of benzene and pyrrole. The experiment is carried out using a magnetic-bottle electron time-of-flight coincidence setup at the incident photon energy region of 25-120 eV. We discuss on the recently discovered phenomenon of so-called Cooper pair formation [R. Wehlitz et al., Phys. Rev. Lett. 109, 193001 (2012)] and show that our experiment provides contradicting evidence on its existence in the proposed form. We confirm the finding of a new two-electron continuum resonance structure observed at about 30–70 eV above the double ionization threshold in benzene, provide further information from it, and suggest an alternative explanation.

Pyrimidine and halogenated pyrimidines near edge x-ray absorption fine structure spectra at C and N K-edges: experiment and theory

The inner shell excitation of pyrimidine and some halogenated pyrimidines near the C and N K-edges has been investigated experimentally by near edge x-ray absorption fine structure spectroscopy and theoretically by density functional theory calculations. The selected targets, 5-Br-pyrimidine, 2-Br-pyrimidine, 2-Cl-pyrimidine, and 5-Br-2-Cl-pyrimidine, allow the effects of the functionalization of the pyrimidine ring to be studied either as a function of different halogen atoms bound to the same molecular site or as a function of the same halogen atom bound to different molecular sites. The results show that the individual characteristics of the different spectra of the substituted pyrimidines can be rationalized in terms of variations in electronic and geometrical structures of the molecule depending on the localization and the electronegativity of the substituent.

Time-dependent density functional theory calculations of the spectroscopy of core electrons

Recent advances in X-ray sources have led to a renaissance in spectroscopic techniques in the X-ray region. These techniques that involve the excitation of core electrons can provide an atom specific probe of electronic structure and provide powerful analytical tools that are used in many fields of research. Theoretical calculations can often play an important role in the analysis and interpretation of experimental spectra. In this perspective, we review recent developments in quantum chemical calculations of X-ray absorption spectra, focusing on the use of time-dependent density functional theory to study core excitations. The practical application of these calculations is illustrated with examples drawn from surface science and bioinorganic chemistry, and the application of these methods to study X-ray emission spectroscopy is explored.

Electronic relaxation effects in condensed polyacenes: A high-resolution photoemission study

We present a high-resolution photoelectron spectroscopy investigation of condensed films of benzene, naphthalene, anthracene, tetracene, and pentacene. High spectroscopic resolution and a systematic variation of the molecular size allow a detailed analysis of the fine structures. The line shapes of the C 1s main lines are analyzed with respect to the different contributions of inhomogeneous broadening, vibronic coupling, and chemical shifts. The shake-up satellite spectra reveal trends, which give insight into the charge redistribution within the molecule upon photoexcitation. In particular, the shake-up between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) increases in intensity and moves closer toward the C 1s main line if the size of the aromatic system is increased. An explanation is given on the basis of the delocalization of the aromatic system and its capability in screening the photogenerated core hole. A comparison of the HOMO-LUMO shake-up position to the optical band gap gives additional insight into the reorganization of the electronic system upon photoexcitation.

Time-Resolved Synchrotron XPS Monitoring of Irradiation-Induced Nitrobenzene Reduction for Chemical Lithography

The irradiation-induced reduction of electrochemically grafted nitrobenzene films on Si(111) was monitored by high-resolution photoelectron spectroscopy. The experiments were performed using synchrotron soft X-ray irradiation at the BESSY II synchrotron facility. The evolution of different chemical species was monitored as a function of time. Careful fitting of the Si2p, C1s, N1s, and O1s core level spectra allowed us to follow this process in detail and to determine the constants of growth and decay of the specific components. The chemical changes were caused by the X-ray irradiation-induced secondary electron current through the aryl layer. A minor fraction (approximately 25%) of the initial nitro groups was split off and desorbed. The bulk of the NO2 groups was reduced to species in an amino-like chemical environment. A desorption of carbon fragments was not observed, and benzene ring specific shakeup satellites indicated that the aromatic ring structure remained intact. Irradiation-induced line-shape changes suggest a polymerization via -NH- bridges, which were formed after the irradiation-induced N-O bond splitting. A significant part of the released oxygen appeared to contribute to an oxidation of the silicon substrate at the Si(111)/benzene interface. The irradiation-induced aryl layer modification can be exploited for chemical lithography (i.e., a lateral structuring of functionalized silicon surfaces).

C 1s → π* excitation in variable size benzene clusters

The C 1s -->pi* transition in molecular benzene and benzene clusters is investigated by photoion yields at high energy resolution. The vibrationally resolved band shows the same shape in clusters as in the bare molecule, but it is redshifted by 50 meV in small clusters, i.e. near the threshold of cluster formation. This redshift increases to 70 meV with increasing cluster size. The results are assigned in comparison with ab initio calculations on model structures of dimers, trimers, and tetramers. These indicate that different carbon sites in the molecular moieties give rise to distinct spectral shifts, where carbon sites that are pointing to the pi-system of another molecule show a larger redshift than the other ones. Such structural properties are found in solid benzene, so that the gas-to-solid shift of C 1s -->pi* excited benzene is derived to be a redshift which is of the order of 100-180 meV.

Inner Shell Excitation Spectroscopy of Biphenyl and Substituted Biphenyls: Probing Ring−Ring Delocalization

Quantitative optical oscillator strength spectra for C 1s excitation and ionization of gas-phase biphenyl, decafluorobiphenyl, and 2,2'-bis(bromomethyl)-1,1'-biphenyl have been derived from electron energy loss spectroscopy recorded under electric dipole dominated conditions. The C 1s X-ray absorption spectrum of hexaphenylbenzene has been recorded in the solid state. The C 1s spectral features are interpreted with the aid of ab initio calculations for core excitation of benzene, biphenyl, hexafluorobenzene, and decafluorobiphenyl. A weak feature at 287.7 eV in biphenyl is identified as a C 1s --> pi(deloc) transition, characteristic of ring-ring delocalization. Its intensity and position are shown to be related to the average torsion angle and thus the extent of pi-pi-interaction between adjacent aromatic rings. The effects of perfluoro substitution on core excitation spectra are also characterized and discussed.

Functional and basis set dependence of K-edge shake-up spectra of molecules

A straightforward approach for computing the K-edge shake-up spectra of molecules based on equivalent core-hole linear response theory at both Hartree-Fock and density functional theory levels is proposed. Benchmark calculations have been performed to explore its sensitivity to different types of functionals and basis sets for the carbon 1s shake-up spectra of benzene and metal-free phthalocyanine (H2Pc). A very good agreement with previous theoretical and experimental works for the benzene molecule has been obtained for all the functionals and basis sets tested. Electron correlation is found to be essential for a good description of the H2Pc system, whose experimental C 1s shake-up spectrum is best reproduced by the hybrid density functional.