Equivalent Core Approximation Research Articles

Analytical gradients for core-excited states in the algebraic diagrammatic construction (ADC) framework.

Expressions for analytical molecular gradients of core-excited states have been derived and implemented for the hierarchy of algebraic diagrammatic construction (ADC) methods up to extended second-order within the core-valence separation (CVS) approximation. We illustrate the use of CVS-ADC gradients by determining relaxed core-excited state potential energy surfaces and optimized geometries for water, formic acid, and benzene. For water, our results show that in the dissociative lowest core-excited state, a linear configuration is preferred. For formic acid, we find that the O K-edge lowest core-excited state is non-planar, a fact that is not captured by the equivalent core approximation where the core-excited atom with its hole is replaced by the "Z + 1" neighboring atom in the periodic table. For benzene, the core-excited state gradients are presented along the Jahn-Teller distorted geometry of the 1s → π* excited state. Our development may pave a new path to studying the dynamics of molecules in their core-excited states.

Differential many-body effects for initial and core ionic states: impact on XPS spectra

In this paper, the contribution of many-body effects to the X-ray photoelectron spectroscopy, XPS, of an NO molecule is studied using wavefunction theory where the specific consequences of different many-body terms are examined and contrasted. It is shown that there is a differential importance of the many-body effects for the different configurations involved in the XPS. These are the ground, initial state configuration and final, N(1s) and O(1s) core hole ionic configurations. The consequences of the many-body effects are examined for the binding energies, BEs, to the two final state multiplets, triplet, and singlet, for each of the core ions and for the relative intensities of the XPS transitions to these multiplets. The many-body effects examined are those described as static effects that arise for individual terms that are important. The objective is to understand the chemical and physical origins that determine the importance of the correlation effects for the XPS, rather than to obtain very accurate predictions of the BEs. An important theoretical construct that is tested and justified is the equivalent core approximation where the core-ionized atom is replaced by the next higher element in the periodic table. This construct allows us to establish a correlation for the relative importance of the many-body effects in terms of effective charges of the different atoms. This is a correlation that has not been considered before and that we expect may have general relevance. The potential of the effects that we have identified for the XPS of NO to be relevant for the XPS of more complex, condensed phase systems is considered.

An experimental and theoretical study of core-valence double ionisation of acetaldehyde (ethanal).

Core-valence double ionisation spectra of acetaldehyde (ethanal) are presented at photon energies above the carbon and oxygen 1s ionisation edges, measured by a versatile multi-electron coincidence spectroscopy technique. We use this molecule as a testbed for analyzing core-valence spectra by means of quantum chemical calculations of transition energies. These theoretical approaches range from two simple models, one based on orbital energies corrected by core valence interaction and one based on the equivalent core approximation, to a systematic series of quantum chemical electronic structure methods of increasing sophistication. The two simple models are found to provide a fast orbital interpretation of the spectra, in particular in the low energy parts, while the coverage of the full spectrum is best fulfilled by correlated models. CASPT2 is the most sophisticated model applied, but considering precision as well as computational costs, the single and double excitation configuration interaction model seems to provide the best option to analyze core-valence double hole spectra.

Interpreting core-level spectra of oxidizing phosphorene: Theory and experiment

We combine ab initio density functional theory calculations with the equivalent cores approximation to determine core-level binding-energy shifts at phosphorus sites caused by oxidation of phosphorene. We find that presence of oxygen increases the core-level binding energies of P atoms and expect binding-energy shifts of up to 6 eV in highly defective geometries. We have identified likely binding geometries of oxygen that help to interpret the observed core-level photoemission spectra in samples at different stages of oxidation and allow us to determine the fractions of specific local geometries.

Orientation of Si phthalocyanine investigated by X‐ray absorption spectroscopy and molecular orbital calculation

AbstractWe have investigated the orientation effect of silicon phthalocyanine dichloride evaporated on the highly oriented pyrolytic graphite (HOPG) surfaces using linearly polarized synchrotron radiation. Polarization angular dependences of Si 1s and Cl 1s near‐edge X‐ray absorption fine structure (NEXAFS) spectra were observed and compared with theoretical calculations based on equivalent core (Z + 1) approximation using the Hartree‐Fock molecular orbital method. The calculated properties are in agreement with the experimental spectra in symmetry, intensity and energy position. The intensities for the lowest energy peaks observed at both Si and Cl edges are enhanced when X‐ray electric field vector (E) is perpendicular to the surface. We assigned these peaks to out‐of‐plane transition into σz*(SiCl) final state orbital. We concluded that phthalocyanine plane is oriented parallel to the surface. Copyright © 2010 John Wiley & Sons, Ltd.

Distinct site- and state-selective dissociation of methyl-trifluoroacetate observed in core-electron excitation at the oxygen K-edge region

Distinct site- and state-selective dissociation following the O1s core-excitation has been found in the gaseous molecules of methyl trifluoroacetate (MTFA). The site- and state-selective dissociation was examined by measuring the branching ratios of dominant CH3+ and CHO+ fragments. The branching ratios from MTFA showed that site-selective dissociation takes place via the excitation from the different atomic sites to the same π*CO resonance state, (O1sCO-1π*CO) and (O1sOMe-1π*CO). A pronounced O1sOMe site-selectivity was identified by a significant increment of CHO+ formation at the (O1sOMe→π*CO) band. The site-selectivity was also justified by an equivalent core approximation using the density functional theory calculation. State-selective dissociation was identified among the (O1sOMe-1π*CO), (O1sOMe-1σ*O-Me) and (O1sOMe-1σ*C-OMe) transitions originated from the same OMe core. State-selective production of CH3+ could be found at the (O1sOMe→σ*O-Me) band, whereas state-selective formation of CHO+ was observed at the (O1sOMe→π*CO) and (O1sOMe→σ*C-OMe) bands.

Electronic excitation of gaseous acetic acid studied by K-shell electron energy loss spectroscopy and ab initio calculations

Ab initio Configuration Interaction calculations have been carried out in order to assign the bands observed in the carbon and oxygen K-shell spectra of gaseous acetic acid, measured using the inner-shell electron energy loss spectroscopy (ISEELS) method with better energy resolution than in previous studies. The good agreement between the theoretical and the measured spectra allows us to assign precisely most of the peaks, especially for the Rydberg states. Some of them have been shown to have strong valence character. The lowest energy band at the carbon edge is assigned to the transitions 1sC1→3pπ/σ*(C1–H) and 1sC1→π*(C2–O2). Simple Franck–Condon calculations, based on the linear coupling approximation, were performed in order to reproduce the vibrational structure observed for the first time in the oxygen and carbon core excited species as well as in the previously measured X-ray photoelectron spectroscopy spectra of the core ionised molecule. Finally, the calculated structural parameters of the core states of acetic acid match well those of the corresponding valence states of their Z+1 molecules, as predicted by the equivalent core approximation. However, significant differences between the geometry of the 1sC1→π*(C2–O2) state and the CH3NOOH ground state are obtained.

Probing interactions between core-electron transitions by ultrafast two-dimensional x-ray coherent correlation spectroscopy

Two-dimensional x-ray correlation spectra (2DXCS) obtained by varying two delay periods in a time-resolved coherent all-x-ray four-wave-mixing measurement are simulated for the N 1s and O 1s transitions of aminophenol. The necessary valence and core-excited states are calculated using singly and doubly substituted Kohn-Sham determinants within the equivalent-core approximation. Sum-over-states calculations of the 2DXCS signals of aminophenol isomers illustrate how novel information about electronic states can be extracted from the 2D spectra. Specific signatures of valence and core-excited states are identified in the diagonal and off-diagonal peaks arising from core transitions of the same and different types, respectively.

Vibrationally resolved nitrogen K-shell photoelectron spectra of the dinitrogen oxide molecule: Experiment and theory

Vibrationally resolved N c and N t K-shell photoelectron spectra of the dinitrogen oxide have been studied experimentally and theoretically. Vibrational frequencies for the N c and N t 1s ionized states obtained from the 2D potential surfaces computed by the CCSD(T) method within the equivalent core approximation reasonably agree with the experimental values. Experimental relative intensities of the vibrational structure are reasonably reproduced by the multi-channel Schwinger configuration interaction method (MCSCI) with the computed 2D potential surfaces. Improved relaxed geometries of these core–hole states are obtained from fitting the experimental spectra using the MCSCI calculations and regarding the bond lengths as fitting parameters.

Ab initio study of core excited cyclopropane

Ab initio configuration interaction calculations have been carried out in order to assign the bands observed in the carbon K-shell spectrum of gaseous cyclopropane, measured using the inner-shell electron energy loss spectroscopy (ISEELS) method. Simple Franck–Condon calculations, based on the linear coupling approximation, were performed in order to reproduce the observed vibrational structure. The good agreement between the theoretical and the measured spectra allows to assign precisely most of the peaks. The spectrum is dominated by an intense band, corresponding to the 1 s → σ ∗ ( CC ) ( 1 a 2 ′ ) transition, with large vibrational excitation. This is explained by the trimethylenic equilibrium geometry of this core state, very different from the D 3h ground state structure. On the other hand, the Rydberg core-excited states and the core ion are only slightly distorted. Finally, the calculated structural and energetic parameters of the NC 2H 6 valence states match well those of the corresponding core states of C 3H 6, illustrating the validity of the equivalent core approximation.

Evidence of Site-Specific Fragmentation on Thioacetic Acid, CH3C(O)SH, Irradiated with Synchrotron Radiation around the S 2p and O 1s Regions

Site-specific fragmentations following S 2p and O 1s photoexcitation of thioacetic acid, CH3C(O)SH, have been studied by means of synchrotron radiation. Total ion yield (TIY) spectra were measured and multicoincidence techniques, which include photoelectron-photoion coincidence (PEPICO) and photoelectron-photoion-photoion coincidence (PEPIPICO) time-of-flight mass spectrometry, were applied. The equivalent-core approximation was employed in order to estimate ionization transition values, and the observed peaks were tentatively assigned. A site-specific fragmentation is moderately observed by comparing the mass spectra collected at resonant energies around the inner and shallow inner shell S 2p and O 1s ionization edges. Beside H+ ion, the most abundant ions observed at the S 2p edge excitation were CH3CO+, SH+, S+, and CH3+. At the O 1s region the large CH3CO+ fragment was depressed, and small CHx+ (x = 0, 1, 2, 3), S+, and SH+ fragments were dominant. The dissociation dynamic for the main ion-pair production has been discussed. Two- and three-body dissociation channels have been observed in the PEPIPICO spectra, and the dissociation mechanisms were proposed.

Biexcitons in solid neon

We study the creation of biexcitons in neon films on a metal substrate by one-photon processes. We demonstrate that photon-stimulated desorption of ions is a perfect tool for the investigation of these excitation processes, which possess very low cross sections. We show that the principle of the equivalent-core approximation which is well known from inner shell experiments can also be applied to the neon biexciton case. Comparing the equivalent-core molecules Ne2** and Na2, we find that neon biexcitons can be described well in a Frenkel picture.

On the validity of the equivalent cores approximation for computing X-ray photoemission and photoabsorption spectral bands

We evaluate the performance of the equivalent cores (Z+1) approximation for computing core photoemission and photoabsorption spectral bands versus full self-consistent field optimizations. Franck–Condon factors are obtained using the linear coupling model with the multi-dimensional vibronic coupling constants computed from analytical calculations of the ground state frequencies and normal coordinates, and excited state energy gradients evaluated at the ground state equilibrium geometry. We use carbon monoxide, formaldehyde, chloromethanes and some mono-substituted benzenes for the purpose. Considering other inherent approximations in the calculations, we find that the equivalent core model works well for band shapes and comparatively better for excitations of strong modes and ionization of deeper core levels. The approximation also works somewhat better for photoemission than for discrete photoexcitation.

Photoelectron spectroscopy studies of growth, alloying, and segregation for transition-metal films on tungsten (211)

High resolution soft x-ray photoelectron spectroscopy using synchrotron radiation and Auger-electron spectroscopy are used to study late-transition-metal films (Pt, Pd, Ir, Rh, Au,) on W(211). It is found that the films grow in a layer mode at 300 K. As a function of the film thickness, different ${4f}_{7/2}$ photoemission peaks are observed, corresponding to a single monolayer, to an interface layer, to bulk atoms and to surface atoms. Single physical monolayers of these late-transition metals on tungsten are stable against thermal rearrangement. In contrast, when multilayer films of Pd, Pt, Ir, Rh are annealed above 700--1000 K, tungsten atoms diffuse into the overlayer to form an alloy film. Gold constitutes a different case; upon annealing it does not alloy with tungsten but the metal in excess of one monolayer forms clusters. The evolution of the bimetallic systems as a function of coverage and annealing temperature is interpreted by analysis of intensities and shapes of the ${4f}_{7/2}$ features. Born-Haber cycles and the equivalent core approximation are used to extract thermochemical data concerning energetics of adhesion, segregation, and alloying in these early-late transition-metal systems.

Molecular-field splitting and vibrational structure in the phosphorus 2p photoelectron spectrum of PF3

The experimental phosphorus 2p spectrum of PF3 shows vibrational structure corresponding to the symmetric phosphorus-fluorine stretching mode, with a fundamental frequency of 121.7 meV. In addition, the spectrum shows that the 2p3/2 peak is a doublet split by 146 meV. This molecular-field splitting arises because the anisotropic molecular environment lifts the threefold degeneracy of the 2p orbitals. The observed vibrational structure is compared with that predicted by theory, either treating the core hole explicitly or using the equivalent-cores approximation to simulate the effects of the core hole. Ab initio calculations of the molecular-field splitting that include core-valence electron correlation predict a value in good agreement with the experimental value.

Vibrational structure of theO 1sionization spectrum ofCO2

The dynamical localization of the $\mathrm{O} 1s$ core holes in the ${\mathrm{CO}}_{2}$ molecule is studied ab initio beyond the linear vibronic coupling model. The vibrational structure of the $\mathrm{O} 1s$ x-ray photoelectron spectrum (XPS) has been calculated employing accurate potential energy surfaces of the ground and ionized diabatic electronic states obtained at the self-consistent field and singles and doubles configuration-interaction (SDCI) methods. A very good agreement of the SDCI computed vibrational structure of the $\mathrm{O} 1s$ XPS with the respective experimental high-resolution spectrum has been obtained. The anharmonicity of the ionic state potential-energy surface induced mostly by the ground-state surface anharmonicity plays a crucial role in the proper description of the vibrational line intensities. The linear model is discussed in detail. The linear model based on the vibronic coupling constants obtained from the geometry change in the ionized state relative to the ground-state reference configuration has been shown to contain a hidden renormalization of the coupling constants. This improves the agreement of the calculated intensities of the vibrational lines in the spectrum with the experiment, compared to the case of the strict linear model. The limitations of this renormalized linear model are discussed. Electron relaxation and correlation considerably affect the vibrational line intensities. The popular equivalent core approximation is tested for ${\mathrm{CO}}_{2}$. The calculation of the $\mathrm{O} 1s$ XPS performed at the SDCI level with and without this approximation is shown to provide almost identical results on the vibrational intensities.

Vibrational fine structure in core level photoelectron lines of adsorbed molecules: System dependent effects

System dependent effects in resolving vibrational fine structure in the core-level lines of adsorbates are discussed. The example is carbon monoxide on transition metals. The importance of dynamic metallic screening is exemplified and the role of shake-up processes is discussed. The possible spin configurations and the magnetic state of the core-ionized adsorbate in the final state are investigated in terms of exchange splittings and the results extended within the equivalent core approximation to the ground state properties of adsorbed NO.

Equivalent-core calculation of core-level relaxation energies in photoelectron spectroscopy: A molecular-orbital approach

The equivalent-core approximation is implemented in a novel way so as to calculate core-level relaxation energies in photoelectron spectroscopy. The method is based on self-consistent field (SCF) Hartree–Fock molecular-orbital calculations via linear combinations of atomic orbitals, and involves evaluating the difference of sums of two-electron Coulomb and exchange integrals, for all electrons in an atom and in its equivalent-core ion. By thus avoiding SCF calculations with a core hole present (the true final state of photoemission), this procedure is shown to significantly save computing time in comparison with an exact SCF direct-hole calculation. Application of the method in single atoms and selected molecules shows about a 10% difference with respect to direct-hole calculation results. The approximation introduces about 1–6 eV errors compared to the experimental results of gas phase molecules. This method thus should be a generally useful procedure for estimating relaxation energies in core spectra.

Beyond the Chemical Shift: Vibrationally Resolved Core-Level Photoelectron Spectra of Adsorbed CO

Vibrational fine structure has been observed in the $\mathrm{C}1s$ and $\mathrm{O}1s$ photoelectron lines of CO adsorbed on Ni(100). This allows a detailed separation of vibrational and electronic contributions to the line profile. The main line is found to represent the fully screened final state. The width of the photoelectron lines is dominated by the intramolecular stretch mode, which strongly depends on the chemical state of the adsorbate. The identification of the adiabatic transition makes the determination of chemical shifts more precise. The equivalent core approximation is found to be highly accurate and electronic and geometric equilibrium properties of the core-ionized adsorbate are extracted.

Vibrational structure in the carbon 1s ionization of hydrocarbons: Calculation using electronic structure theory and the equivalent-cores approximation

A simple ab initio procedure is used to calculate the vibrational structure observed in the carbon 1s ionization of seven hydrocarbons (methane, deuteromethane, ethane, ethene, deuteroethene, ethyne, and deuteroethyne), with good agreement between experiment and theory. The method involves use of the equivalent-cores approximation, localized holes in molecules with equivalent carbons, and the harmonic oscillator approximation. The approach provides insight into the vibrational modes of the core-ionized molecules. It is potentially useful in extracting carbon 1s ionization energies from spectra from molecules having inequivalent carbons or in finding information on inner-hole lifetimes from inner-shell spectra.