Calculation Of Core-electron Binding Energies Research Articles

Combining the Δ-Self-Consistent-Field and GW Methods for Predicting Core Electron Binding Energies in Periodic Solids.

For the computational prediction of core electron binding energies in solids, two distinct kinds of modeling strategies have been pursued: the Δ-Self-Consistent-Field method based on density functional theory (DFT), and the GW method. In this study, we examine the formal relationship between these two approaches and establish a link between them. The link arises from the equivalence, in DFT, between the total energy difference result for the first ionization energy, and the eigenvalue of the highest occupied state, in the limit of infinite supercell size. This link allows us to introduce a new formalism, which highlights how in DFT─even if the total energy difference method is used to calculate core electron binding energies─the accuracy of the results still implicitly depends on the accuracy of the eigenvalue at the valence band maximum in insulators, or at the Fermi level in metals. We examine whether incorporating a quasiparticle correction for this eigenvalue from GW theory improves the accuracy of the calculated core electron binding energies, and find that the inclusion of vertex corrections is required for achieving quantitative agreement with experiment.

Efficient basis sets for core-excited states motivated by Slater's rules.

X-Ray photoemission spectroscopy is a commonly applied characterization technique that probes the local chemistry of atoms in molecules and materials via the photoexcitation of electrons from atomic core orbitals. These measurements can be interpreted by comparison with previous literature or through the calculation of core-electron binding energies (CEBEs) for model systems. However, physically and numerically accurate description of the core-excited electronic structures demands specializations beyond routine ground state setups. Inspired by Slater's rules, we focus on developing computationally efficient and physically motivated contractions to reproduce the core-excited atomic orbitals which led to improved numerical accuracy of calculated CEBEs. When applied to carbon 1s excitations in a wide range of molecules, these core-excited basis sets produce total energy differences (ΔSCF) using a hybrid exact-exchange density functional (B3LYP) that can reproduce core-excitation energies within experimental accuracy (∼0.1 eV). Due to missing relativistic effects, heavier elements (N, O) exhibit slightly larger systematic absolute errors, but still maintain a satisfactory 0.2 eV mean average error for relative CEBEs. We also connect the known variability in the core level binding energy with local atomic charge to demonstrate how the transferability of a given model should be measured against a diverse test set. We conclude by exploring one outlier, CO, and the outlook for extending this approach to other elements.

Density Functional Theory Calculations of Core-Electron Binding Energies at the K-Edge of Heavier Elements.

The capability to determine core-electron binding energies (CEBEs) is vital in the analysis of X-ray photoelectron spectroscopy, and the continued development of light sources has made inner shell spectroscopy of heavier elements increasingly accessible. Density functional theory is widely used to determine CEBEs of lighter elements (boron-fluorine). It is shown that good performance of exchange-correlation functionals for these elements does not necessarily translate to the calculation of CEBEs for the heavier elements from the next row of the periodic table, and in general, larger errors are observed. Two strategies are explored that improve the accuracy of the calculated CEBEs. The first is to apply element and functional dependent energy corrections, and the second is a reparametrization of a short-range corrected functional. This functional is able to reproduce experimental phosphorus and sulfur K-edge CEBEs with an average error of 0.15 eV demonstrating the importance of reducing the self-interaction error associated with the core electrons and represents progress toward a density functional theory calculation that performs equally well for ionization at the K-edge of all elements.

ΔDFT/MIX: A reliable and efficient method for calculating core electron binding energies of large molecules

A new method, ΔDFT/MIX, is calibrated for use in calculating core electron binding energies. Chemically relevant test sets were used to determine the most accurate functionals out of the 70 density functionals included in GAMESS. The best three functionals, B3LYP, TPSSm, and BLYP, were used to calculate 1s electron binding energies of nucleic acid base tautomers, and the results were compared to experimental values to demonstrate accuracy and sensitivity of the method. Previously suggested methods such as ACD(4) and ΔMP2/MIX are as accurate as our new method; the overall mean absolute deviation of ΔDFT/MIX is 0.19 eV with B3LYP. Comparing calculation time shows that using DFT instead of MP2 is much less computationally costly for larger molecules.

Basis sets for the calculation of core-electron binding energies

Core-electron binding energies (CEBEs) computed within a Δself-consistent field approach require large basis sets to achieve convergence with respect to the basis set limit. It is shown that supplementing a basis set with basis functions from the corresponding basis set for the element with the next highest nuclear charge (Z + 1) provides basis sets that give CEBEs close to the basis set limit. This simple procedure provides relatively small basis sets that are well suited for calculations where the description of a core-ionised state is important, such as time-dependent density functional theory calculations of X-ray emission spectroscopy.

Assessment of basis sets for density functional theory-based calculations of core-electron spectroscopies

The performance of Gaussian basis sets for density functional theory-based calculations of core-electron spectroscopies is assessed. The convergence of core-electron binding energies and core-excitation energies using a range of basis sets including split-valence, correlation-consistent, polarisation-consistent and individual gauge for localised orbitals basis sets is studied. For varDelta self-consistent field calculations of core-electron binding energies and core-excitation energies of first-row elements, relatively small basis sets can accurately reproduce the values of much larger basis sets, with the IGLO basis sets performing particularly well. Calculations for the K-edge of second-row elements are more challenging, and of the smaller basis sets, pcSseg-2 has the best performance. For the correlation-consistent basis sets, inclusion of core-valence correlation functions is important, with the cc-pCVTZ basis set giving accurate results. Time-dependent density functional theory-based calculations of core-excitation energies show less sensitivity to the basis set with relatively small basis sets, such as pcSseg-1 or pcSseg-2, reproducing the values for much larger basis sets accurately. In contrast, time-dependent density functional theory calculations of X-ray emission energies are highly dependent on the basis set, but the IGLO-II, IGLO-III and pcSseg-2 basis sets provide a good level of accuracy.

Benchmarking density functionals and Gaussian basis sets for calculation of core-electron binding energies in amino acids

A variety of density functionals and Gaussian basis sets has been studied for performance in calculations of core-electron binding energies of the carbon, nitrogen, and oxygen nuclei in the gaseous amino acids glycine, alanine, proline, threonine, and methionine. The main goal of this study is the identification of methods that will be sufficiently accurate and efficient to be used for analysis of experimental X-ray photoelectron spectra of amino acids, large polypeptides, and DNA nucleosides in various environments. The various methods studied are evaluated based on consideration of their performance for calculation of relative conformer energies, core-electron binding energies, and chemical shifts of the binding energies, using common popular density functionals with small basis sets.

Quantum mechanics capacitance molecular mechanics modeling of core-electron binding energies of methanol and methyl nitrite on Ag(111) surface.

We study a newly devised quantum mechanics capacitance molecular mechanics (QMCMM) method for the calculation of core-electron binding energies in the case of molecules adsorbed on metal surfaces. This yet untested methodology is applied to systems with monolayer of methanol/methyl nitrite on an Ag(111) surface at 100 K temperature. It was found out that the studied C, N, and O 1s core-hole energies converge very slowly as a function of the radius of the metallic cluster, which was ascribed to build up of positive charge on the edge of the Ag slab. Further analysis revealed that an extrapolation process can be used to obtain binding energies that deviated less than 0.5 eV against experiments, except in the case of methanol O 1s where the difference was as large as 1.8 eV. Additional QM-cluster calculations suggest that the latter error can be connected to the lack of charge transfer over the QM-CMM boundary. Thus, the results indicate that the QMCMM and QM-cluster methods can complement each other in a holistic picture of molecule-adsorbate core-ionization studies, where all types of intermolecular interactions are considered.

Possibility of NCS Group Anchor for Ru Dye Adsorption to Anatase TiO2(101) Surface: A Density Functional Theory Investigation

We examined the possibility of the presence of isothiocyanate (NCS) group anchor for Ru dye adsorption to anatase TiO2(101) surface in typical dye-sensitized solar cells (DSCs), motivated by the recent X-ray photoelectron spectroscopy (XPS) experimental observations of the NCS anchors. A variety of adsorption configurations were examined with model molecules of CH3NCS by density functional theory (DFT) calculations. To compare with the experimental XPS spectra, we also calculated core–electron binding energies using (TiO2)38 cluster model. We demonstrated that 0.6–0.7 eV of the observed chemical shift in the S 2p XPS spectra can be assigned to the S interactions with the surface Ti atom and O vacancy, while 8.8 eV shift in the S 1s level is connected to the S–Ti vacancy interaction. On the other hand, it is also confirmed that the adsorption energies of COOH group and acetonitrile solvent molecule are usually larger than that for the NCS group. Therefore, the Ru dye adsorption through the NCS anchor is less probable even on the surface in vacuum and further decreases in the solution environment. With these results, we conclude that the NCS group anchoring is possible in the vacuum environment as shown by the XPS studies, while it will be negligible on the working electrode of the solar cell.

Substituent effect in 1-X-decanes and 3-X-gonanes based on core-electron binding energies calculated with density-functional theory

The substituent effect in substituted n-decanes (1-X-decan), chain σ-systems of saturated hydrocarbon, and C3 substituted gonanes (3-X-gonane), fused ring σ-systems, where X=H, NO2, CHO, F, CH3, But (tertiary butyl), was investigated using calculated core electron binding energies. The energies were calculated using the density-functional theory (DFT) with the Perdew–Wang 1986 exchange and the Perdew–Wang 1991 correlation functionals. A triple-zeta polarized Slater type basis set was employed. The effect of the electron withdrawing substituents, NO2, F, and CHO, is felt all the way to the end of the 10-carbon chain in 1-X-decane. Similarly, the effect of the electron withdrawing substituents is felt to the D ring carbons in 3-X-gonane. A possible explanation of the long-range effect is given. It was shown that the substituent effect was very similar, but not identical, in 1-X-decane and 3-X-gonane in quality and quantity.

DFT calculation of core– and valence–shell electron excitation and ionization energies of 2,1,3-benzothiadiazole C6H4SN2, 1,3,2,4-benzodithiadiazine C6H4S2N2, and 1,3,5,2,4-benzotrithiadiazepine C6H4S3N2

The vertical core– and valence–shell electron excitation and ionization energies of the three title molecules, 1–3, were calculated by density functional theory (DFT) using adequate functional for each type of processes and atoms under study. The inner shells treated were C1s, N1s, S1s, S2s, S2p. Molecular geometry was optimized by DFT B3LYP/6-311+(d,p). The basis set of triple zeta plus polarization (TZP) Slater-type orbitals was employed for DFT calculations. The ΔSCF method was used to calculate ionization energies. The average absolute deviation (AAD) from experiment of 26 valence-electron ionization energies calculated by DFT for the three molecules 1–3 was 0.14eV; while that of 24 calculated core-electron binding energies (CEBEs) from experiment was 0.4eV. Selected core excitation energies were calculated by the multiplet approximation for the three molecules. The AAD of twelve calculated core excitation energies by the multiplet approximation that exclude S2s cases was 0.56eV. Time-dependent DFT (TDDFT) was employed to calculate the excitation energies and corresponding oscillator strengths of core- and valence-electrons of the molecules. Some selected occupied core orbitals were used to calculate the core-excitation energies with the TDDFT (Sterner–Frozoni–Simone scheme). The core excitation energies thus calculated were in an average error of ca. 28eV compared to observed values. They were shifted to the value calculated by the multiplet approximation. Convoluted spectra based upon the shifted energies and accompanying oscillator strengths reproduce low-energy region of observed spectra reasonably well, whereas they deviate from experiment in high-energy region. Reasonable agreement between theory and experiment was obtained for the valence electron excitations of the molecules.

Local Electronic Structure and Density of Edge and Facet Atoms at Rh Nanoclusters Self-Assembled on a Graphene Template

The chemical and physical properties of nanoclusters largely depend on their sizes and shapes. This is partly due to finite size effects influencing the local electronic structure of the nanocluster atoms which are located on the nanofacets and on their edges. Here we present a thorough study on graphene-supported Rh nanocluster assemblies and their geometry-dependent electronic structure obtained by combining high-energy resolution core level photoelectron spectroscopy, scanning tunneling microscopy, and density functional theory. We demonstrate the possibility to finely control the morphology and the degree of structural order of Rh clusters grown in register with the template surface of graphene/Ir(111). By comparing measured and calculated core electron binding energies, we identify edge, facet, and bulk atoms of the nanoclusters. We describe how small interatomic distance changes occur while varying the nanocluster size, substantially modifying the properties of surface atoms. The properties of under-coordinated Rh atoms are discussed in view of their importance in heterogeneous catalysis and magnetism.

Calibration and applications of the ΔMP2 method for calculating core electron binding energies

We calibrated a method for the evaluation of core electron binding energies, based on the energy differences between the cation and neutral molecule evaluated at the level of Møller-Plesset perturbation theory. The central feature of the method is the use of a mixed basis set: a large all-electron basis set is used for the atom whose core electron is removed, while the model core potential basis set is employed for all remaining atoms. Calibration was carried out for 55 molecules and 114 binding energies of 1s core electrons for the atoms C, N, O, and F. The average absolute deviation for all the core electron binding energies is 0.163 eV. The method was applied to the calculation of the core electron binding energies of five nucleic acid bases (uracil, adenine, cytosine, guanine, and thymine) and several of their low-energy tautomers.

Localized and delocalized 1s core-holes in DFT calculations

In DFT calculations of core-electron binding energies (CEBEs), one can use either localized or delocalized core-holes. In this Communication, we compare those two approaches applied to 20 molecules. The results indicate that the functional PW86-PW91, which gives excellent CEBEs for localized core holes, fails badly in treating delocalized core holes. The failure is probably quite general for all GGA functionals. The conclusion is obvious: one must use the localized core-holes when one uses ΔE(PW86-PW91) prediction for K-shell CEBEs.

Sulfur electronic environments in α-NiS and β-NiS: examination of the relationship between coordination number and core electron binding energies

X-ray photoelectron spectra have been obtained under the same experimental conditions for synthetic α-NiS and natural β-NiS in order to establish any difference in S electronic environment, and to test the proposition that S core electron binding energies increase measurably with coordination number when the same metal is in different sulfide structures or lattice sites. The Ni and S electronic environments in the two NiS structures have been further probed by near-edge X-ray absorption fine structure (NEXAFS) spectroscopy, and the NEXAFS spectra interpreted by reference to spectra simulated by ab initio calculations. The photoelectron and NEXAFS spectra for freshly prepared surfaces of α-NiS and β-NiS were found to be similar, with only subtle differences in electronic environment evident in the experimental and simulated NEXAFS spectra. The measured and calculated core electron binding energies did not support the previously postulated relationship between S coordination number and electron binding energies.

Accurate calculation of core-electron binding energies: multireference perturbation treatment.

Multireference perturbation theory (MRPT) with multiconfigurational self-consistent field (MCSCF) reference functions is applied to the calculations of core-electron binding energies (CEBEs) of atoms and molecules. Orbital relaxations in a core-ionized state and electron correlation are both taken into account in a conventional MCSCF-MRPT procedure. In the MCSCF calculation, the target core ionized state is directly optimized as an excited state and this treatment can completely prevent a variational collapse. Multireference Moller-Plesset perturbation theory and multiconfigurational self-consistent field reference quasidegenerated perturbation theory were used to treat electron correlation. The present method quite accurately reproduced the 1s CEBEs of CH4, NH3, H2O, and FH; the average deviation from the experimental data is 0.11 eV using Ahlrichs' VTZ basis set. The C 1s and O 1s CEBEs of formic acid and acetic acid were calculated and the results are consistent with the bonding characters of the atoms in these molecules. The present procedure can also be applied to CEBEs of higher angular momentum orbitals by including spin-orbit coupling. The calculated CEBEs of Ar 2p, HCl 2p, Kr 3d, and HBr 3d are in reasonable agreement with the available experimental values. In the calculation of the 3d CEBEs, a relativistic correction significantly improves the agreements. The effect of polarization functions is also discussed.

DFT calculation of core-electron binding energies

A total of 59 core-electron binding energies (CEBEs) were studied with the Amsterdam Density Functional Program (ADF) program and compared with the observed values. The results indicate that a polarized triple-zeta basis set of Slater-type orbitals is adequate for routine assessment of the performance of each method of computation. With such a basis set, seven density functionals were tested. In addition, the performance of 21 energy density functionals were computed from the density calculated with the statistical average of orbital potentials (SAOP). Among all the choices tested, the best density functional for core-electron binding energies of C to F turns out to be the combination of Perdew-Wang (1986) functional for exchange and the Perdew-Wang (1991) functional for correlation, confirming earlier studies based on contracted Gaussian-type orbitals. For this best functional, five Slater-type orbital basis sets were examined, ranging from polarized double-zeta quality to the largest set available in the ADF package. For the best functional with the best basis set, the average absolute deviation (AAD) of the calculated value from experiment is only 0.16 eV.

Ring hydrolysis in the electro-oxidation of pyrrolidone analogues

Upon oxidation in acetonitrile, pyrrolidone analogues, namely pyrrolidone, methyl-pyrrolidone, ethyl-pyrrolidone and N -vinyl pyrrolidone, afford thin organic films which can be analyzed by X-ray photoelectron spectroscopy. One common singular feature is noted in the XPS spectra: the advent of a very high energy C1s peak (288.9 eV), indicating the formation of a molecular structure with a carbon atom in an unusually electronegative environment. Considering the recently proposed reaction mechanisms for the oxidation of pyrrolidone analogues, a theoretical study is carried out: several molecular structures are proposed, on which very accurate calculations of core-electron binding energies are performed using the density functional theory. On comparison with the complete experimental spectrum, it is proposed that this peculiar high-energy peak stems from the opening of the pyrrolidone ring to yield carboxylic acid groups.

Accurate Density-Functional Calculation of Core-Electron Binding Energies of Some Substituted Benzenes

Abstract The core electron binding energies (CEBE's) of benzene, seven monosubstituted benzenes (Ph-X) and one disubstituted benzene (p-NH2-C6H4-NO2) were calculated using density-functional theory (DFT). The unrestricted generalized transition-state (uGTS) model was employed. The DeMon DFT program with a combined functional of Becke's exchange (B88) with Perdew's correlation (P86) was used. The average absolute deviation of the calculated CEBE's of the title compounds was 0.3 eV when the cc-pVDZ basis set was used. The ``CEBE shift'' of the ring carbon in Ph-X was calculated while taking the CEBE on the ring carbon in Ph-H as a reference. The thus-calculated CEBE shifts agree with experiment within the value of the average absolute deviation, 0.1 eV. The signs and quantitative numerical values of the CEBE shifts are very close to the corresponding Hammett σ constants.

Density functional calculation of core-electron binding energies of isomers of C3H6O2 and C3H5NO

The core-electron binding energies of six isomers of C3H6O2 and four isomers of C3H5NO were calculated by a DFT/uGTS/scaled-pVTZ approach. An average absolute deviation from experiment of 0.15 eV was found for 14 C, N, and O 1s energies. The results confirm the distinctive nature of the X-ray photoelectron spectra (XPS) of isomers and support the use of electron spectroscopy complemented by accurate theoretical predictions as a tool for chemical analysis. © 1999 John Wiley & Sons, Inc. Int J Quant Chem 76: 44–50, 2000