High resolution O 1s photoelectron shake-up satellite spectrum of H2O

Alternative Pathway to Double-Core-Hole States

Excited double-core-hole states of isolated water molecules resulting from the sequential absorption of two x-ray photons have been investigated. These states are formed through an alternative pathway, where the initial step of core ionization is accompanied by the shake-up of a valence electron, leading to the same final states as in the core-ionization followed by core-excitation pathway. The capability of the x-ray free-electron laser to deliver very intense, very short, and tunable light pulses is fully exploited to identify the two different pathways.

Isotope effects in dynamics of water isotopologues induced by core ionization at an x-ray free-electron laser

Dynamical response of water exposed to x-rays is of utmost importance in a wealth of science areas. We exposed isolated water isotopologues to short x-ray pulses from a free-electron laser and detected momenta of all produced ions in coincidence. By combining experimental results and theoretical modeling, we identify significant structural dynamics with characteristic isotope effects in H2O2+, D2O2+, and HDO2+, such as asymmetric bond elongation and bond-angle opening, leading to two-body or three-body fragmentation on a timescale of a few femtoseconds. A method to disentangle the sequences of events taking place upon the consecutive absorption of two x-ray photons is described. The obtained deep look into structural properties and dynamics of dissociating water isotopologues provides essential insights into the underlying mechanisms.

Benchmark of GW Methods for Core-Level Binding Energies

The GW approximation has recently gained increasing attention as a viable method for the computation of deep core-level binding energies as measured by X-ray photoelectron spectroscopy. We present a comprehensive benchmark study of different GW methodologies (starting point optimized, partial and full eigenvalue-self-consistent, Hedin shift, and renormalized singles) for molecular inner-shell excitations. We demonstrate that all methods yield a unique solution and apply them to the CORE65 benchmark set and ethyl trifluoroacetate. Three GW schemes clearly outperform the other methods for absolute core-level energies with a mean absolute error of 0.3 eV with respect to experiment. These are partial eigenvalue self-consistency, in which the eigenvalues are only updated in the Green's function, single-shot GW calculations based on an optimized hybrid functional starting point, and a Hedin shift in the Green's function. While all methods reproduce the experimental relative binding energies well, the eigenvalue self-consistent schemes and the Hedin shift yield with mean absolute errors <0.2 eV the best results.

Real-Time Equation-of-Motion CCSD Cumulant Green's Function

Many-body excitations in X-ray photoemission spectra have been difficult to simulate from first principles. We have recently developed a cumulant-based one-electron Green's function method using the real-time coupled-cluster-singles equation-of-motion approach (RT-EOM-CCS) that provides a general framework for treating these problems. Here we extend this approach to include double excitations in the ground-state energy and in the coupled cluster amplitudes, which have been implemented using subroutines generated by the Tensor Contraction Engine (TCE). As in the case of the singles approximation, RT-EOM-CCSD yields a nonperturbative cumulant form of the Green's function in terms of the time-dependent cluster amplitudes, adding nonlinear corrections to the traditional cumulant forms. The extended approach is applied to the core-hole spectral function for small molecular systems. We find that, when core-optimized basis sets are used, the doubles contributions reduce the mean absolute errors in the core binding energies of the 10e systems from 0.8 to 0.3 eV. They also significantly improve the quasiparticle-satellite gap by reducing its overestimation from about 3-5 to about 0-1 eV in CH₄, NH₃, and H₂O, and also improving the overall shape of the satellite features. Finally, we demonstrate the application of the new implementation to the larger, classical XPS ESCA series of molecules and show that the singles approximation can be paired with a modest basis set to study carbon speciation.

Specific chemical bond relaxation unraveled by analysis of shake-up satellites in the oxygen single site double core hole spectrum of CO2

We recently developed [A. Ferté, et al., J. Phys. Chem. Lett., 2020, 11, 4359] a method to compute single site double core hole (ssDCH or K^-2) spectra. We refer to that method as NOTA+CIPSI. In the present paper this method is applied to the O K^-2 spectrum of the CO₂ molecule, and we use this as an example to discuss in detail its convergence properties. Using this approach, theoretical spectra in excellent agreement with the experimental one are obtained. Thanks to a thorough interpretation of the shake-up states responsible for the main satellite peaks and through comparison with the O K^-2 spectrum of CO, we can highlight the clear signature of the two non-equivalent carbon oxygen bonds in the oxygen ssDCH CO₂ dication.

Equation-of-Motion Coupled-Cluster Cumulant Green's Function for Excited States and X-Ray Spectra

Green’s function methods provide a robust, general framework within many-body theory for treating electron correlation in both excited states and x-ray spectra. Conventional methods using the Dyson equation or the cumulant expansion are typically based on the GW self-energy approximation. In order to extend this approximation in molecular systems, a non-perturbative real-time coupled-cluster cumulant Green’s function approach has been introduced, where the cumulant is obtained as the solution to a system of coupled first order, non-linear differential equations. This approach naturally includes non-linear corrections to conventional cumulant Green’s function techniques where the cumulant is linear in the GW self-energy. The method yields the spectral function for the core Green’s function, which is directly related to the x-ray photoemission spectra (XPS) of molecular systems. The approach also yields very good results for binding energies and satellite excitations. The x-ray absorption spectrum (XAS) is then calculated using a convolution of the core spectral function and an effective, one-body XAS. Here this approach is extended to include the full coupled-cluster-singles (CCS) core Green’s function by including the complete form of the non-linear contributions to the cumulant as well as all single, double, and triple cluster excitations in the CC amplitude equations. This approach naturally builds in orthogonality and shake-up effects analogous to those in the Mahan-Noizeres-de Dominicis edge singularity corrections that enhance the XAS near the edge. The method is illustrated for the XPS and XAS of NH₃.

Real-Time Coupled-Cluster Approach for the Cumulant Green's Function

Green's function methods within many-body perturbation theory provide a general framework for treating electronic correlations in excited states and spectra. Here, we develop the cumulant form of the one-electron Green's function using a real-time coupled-cluster equation-of-motion approach, in an extension of our previous study (Rehr J.; et al. J. Chem. Phys. 2020, 152, 174113). The approach yields a nonperturbative expression for the cumulant in terms of the solution to a set of coupled first-order, nonlinear differential equations. The method thereby adds nonlinear corrections to traditional cumulant methods, which are linear in the self-energy. The approach is applied to the core-hole Green's function and is illustrated for a number of small molecular systems. For these systems, we find that the nonlinear contributions yield significant improvements, both for quasiparticle properties such as core-level binding energies and for inelastic losses that correspond to satellites observed in photoemission spectra.

Equation of motion coupled-cluster cumulant approach for intrinsic losses in x-ray spectra

We present a combined equation of motion coupled-cluster cumulant Green's function approach for calculating and understanding intrinsic inelastic losses in core level x-ray absorption spectra (XAS) and x-ray photoemission spectra. The method is based on a factorization of the transition amplitude in the time domain, which leads to a convolution of an effective one-body absorption spectrum and the core-hole spectral function. The spectral function characterizes intrinsic losses in terms of shake-up excitations and satellites using a cumulant representation of the core-hole Green's function that simplifies the interpretation. The one-body spectrum also includes orthogonality corrections that enhance the XAS at the edge.

Accurate Absolute and Relative Core-Level Binding Energies from GW

We present an accurate approach to compute X-ray photoelectron spectra based on the GW Green's function method that overcomes the shortcomings of common density functional theory approaches. GW has become a popular tool to compute valence excitations for a wide range of materials. However, core-level spectroscopy is thus far almost uncharted in GW. We show that single-shot perturbation calculations in the G0W0 approximation, which are routinely used for valence states, cannot be applied for core levels and suffer from an extreme, erroneous transfer of spectral weight to the satellite spectrum. The correct behavior can be restored by partial self-consistent GW schemes or by using hybrid functionals with almost 50% of exact exchange as a starting point for G0W0. We also include relativistic corrections and present a benchmark study for 65 molecular 1s excitations. Our absolute and relative GW core-level binding energies agree within 0.3 and 0.2 eV with experiment, respectively.

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.

Core Ionization Initiates Subfemtosecond Charge Migration in the Valence Shell of Molecules

After the ionization of a valence electron, the created hole can migrate ultrafast from one end of the molecule to another. Because of the advent of attosecond pulse techniques, the measuring and understanding of charge migration has become a central topic in attosecond science. Here, we pose the hitherto unconsidered question whether ionizing a core electron will also lead to charge migration. It is found that the created hole in the core stays put, but in response to this hole interesting electron dynamics takes place which can lead to intense charge migration in the valence shell. This migration is typically faster than that after the ionization of a valence electron and transpires on a shorter time scale than the natural decay of the core hole by the Auger process, making the subject very challenging to attosecond science.

Multi-reference approach to the calculation of photoelectron spectra including spin-orbit coupling

X-ray photoelectron spectra provide a wealth of information on the electronic structure. The extraction of molecular details requires adequate theoretical methods, which in case of transition metal complexes has to account for effects due to the multi-configurational and spin-mixed nature of the many-electron wave function. Here, the restricted active space self-consistent field method including spin-orbit coupling is used to cope with this challenge and to calculate valence- and core-level photoelectron spectra. The intensities are estimated within the frameworks of the Dyson orbital formalism and the sudden approximation. Thereby, we utilize an efficient computational algorithm that is based on a biorthonormal basis transformation. The approach is applied to the valence photoionization of the gas phase water molecule and to the core ionization spectrum of the [Fe(H2O)6](2+) complex. The results show good agreement with the experimental data obtained in this work, whereas the sudden approximation demonstrates distinct deviations from experiments.

Near-edge x-ray absorption fine structures revealed in core ionization photoelectron spectroscopy

Simultaneous core ionization and core excitation have been observed in the C(2)H(2n) (n=1, 2, 3) molecular series using synchrotron radiation and a magnetic bottle time-of-flight electron spectrometer. Rich satellite patterns corresponding to (K(-2)V) core excited states of the K(-1) molecular ions have been identified by detecting in coincidence the photoelectron with the two Auger electrons resulting from the double core hole relaxation. A theoretical model is proposed providing absolute photoionization cross sections and revealing clear signatures of direct (monopolar) and conjugate (dipolar near-edge x-ray absorption fine structure) shakeup lines of comparable magnitude.

Geometry Relaxations After Inner-Shell Excitations and Ionizations

The geometry relaxations due to the inner-shell excitations and ionizations have been studied by the SAC-CI method. The characteristic molecular geometry changes were predicted for the core-hole states of CH4, NH3, H2O and HF: the calculated CH bond length change agrees well with the result simulated by the observed spectrum. The C1s excitation spectrum of CH4 was also investigated for the Rydberg states of the principal quantum numbers n = 3, 4 and 5. The potential energy curves of the dipole-allowed excited states were calculated for the totally symmetric stretching mode. The vibrational structure and Franck-Condon factors for the C1s excitation spectrum were well reproduced, which shows that the equilibrium geometries of the excited states were accurately evaluated. The geometries of the inner-shell π* excited states of N2O and CO2 were also examined. The calculated geometries of these states qualitatively agreed with the experimental values of the corresponding equivalent-core molecules.

Anharmonicity and tunneling effects in revisited vibrational O(1s) photoelectron spectrum of water gas phase

The authors have revisited the description of the core-hole ionization dynamics of the oxygen atom in water by re-exploiting the high-resolution, vibrationally resolved, XPS photoelectron spectrum of gas phase at the O(1s) edge. The agreement between theory and experiments is mainly controlled by (i) the description of the tunneling behavior near the barrier top (linear H-O-H conformation) of wave functions with high vibrational quanta, and (ii) the relative displacement of the potential-energy minimum of the O(1s) final state with respect to the ground state one. Accurate change in bond angle between the neutral and core-ionized states is essential to account for the Franck-Condon factors. The O(1s) photoelectron spectrum of water is well reproduced by the molecular ab initio calculations based on density functional theory and Franck-Condon factors calculations in a double-well (2 x W) simulation of the bending motion.

Symmetry-adapted-cluster/symmetry-adapted-cluster configuration interaction methodology extended to giant molecular systems: ring molecular crystals

The symmetry adapted cluster (SAC)/symmetry adapted cluster configuration interaction (SAC-CI) methodology for the ground, excited, ionized, and electron-attached states of molecules was extended to giant molecular systems. The size extensivity of energy and the size intensivity of excitation energy are very important for doing quantitative chemical studies of giant molecular systems and are designed to be satisfied in the present giant SAC/SAC-CI method. The first extension was made to giant molecular crystals composed of the same molecular species. The reference wave function was defined by introducing monomer-localized canonical molecular orbitals (ml-CMO's), which were obtained from the Hartree-Fock orbitals of a tetramer or a larger oligomer within the electrostatic field of the other part of the crystal. In the SAC/SAC-CI calculations, all the necessary integrals were obtained after the integral transformation with the ml-CMO's of the neighboring dimer. Only singles and doubles excitations within each neighboring dimer were considered as linked operators, and perturbation selection was done to choose only important operators. Almost all the important unlinked terms generated from the selected linked operators were included: the unlinked terms are important for keeping size extensivity and size intensivity. Some test calculations were carried out for the ring crystals of up to 10 000-mer, confirming the size extensivity and size intensivity of the calculated results and the efficiency of the giant method in comparison with the standard method available in GAUSSIAN 03. Then, the method was applied to the ring crystals of ethylene and water 50-mers, and formaldehyde 50-, 100-, and 500-mers. The potential energy curves of the ground state and the polarization and electron-transfer-type excited states were calculated for the intermonomer distances of 2.8-100 A. Several interesting behaviors were reported, showing the potentiality of the present giant SAC/SAC-CI method for molecular engineering.

C1s and O1s photoelectron satellite spectra of CO with symmetry-dependent vibrational excitations

The photoelectron shake-up satellite spectra that accompany the C1s and O1s main lines of carbon monoxide have been studied by a combination of high-resolution x-ray photoelectron spectroscopy and accurate ab initio calculations. The symmetry-adapted cluster-expansion configuration-interaction general-R method satisfactorily reproduces the satellite spectra over a wide energy region, and the quantitative assignments are proposed for the 16 and 12 satellite bands for C1s and O1s spectra, respectively. Satellite peaks above the pi(-1)pi(*) transitions are mainly assigned to the Rydberg excitations accompanying the inner-shell ionization. Many shake-up states, which interact strongly with three-electron processes such as pi(-2)pi(*2) and n(-2)pi(*2), are calculated in the low-energy region, while the continuous Rydberg excitations are obtained with small intensities in the higher-energy region. The vibrational structures of low-lying shake-up states have been examined for both C1s and O1s ionizations. The vibrational structures appear in the low-lying C1s satellite states, and the symmetry-dependent angular distributions for the satellite emission have enabled the Sigma and Pi symmetries to be resolved. On the other hand, the potential curves of the low-lying O1s shake-up states are predicted to be weakly bound or repulsive.