Final State Contributions Research Articles

Core level shifts in amorphous transition metal-tin alloys

X-ray and UV photoemission data are presented for core level binding energy shifts in amorphous TmSn (TMFe, Co, Ni, Pd) films prepared in situ at low temperature by means of a vapour quenching technique. The experimental results are compared to predictions based on the thermodynamical model of Martensson and Johansson using the Born-Haber cycle and the equivalent core approximation. The overall good agreement found between theory and experiment emphasizes the strong influence of the conduction electrons in the photoionization process. It is observed that relaxation effects and screening of the final core hole state can result in binding energy shifts of the same order of magnitude as those of the ground state due to alloying. As a consequence, photoemission core level binding energies in amorphous alloys generally cannot be interpreted within the ground state picture, but have to be corrected for final state contributions.

Two-photon double resonance spectroscopy of bacteriorhodopsin. Assignment of the electronic and dipolar properties of the low-lying 1A*−g-like and 1B*+u-like π, π* states

The electronic and dipolar properties of the all-trans retinyl polyene in light-adapted bacteriorhodopsin are examined by using two-photon double resonance spectroscopy to assign the Franck–Condon maxima, the absolute two-photon absorptivities and the change in dipole moments upon excitation of the low-lying ‘‘forbidden’’ 1A*−g -like and ‘‘allowed’’ 1B*+u -like π, π* excited singlet states. The second-order hyperpolarizability is also determined. The two-photon double resonance spectrum, collected with laser excitation from 820–1200 nm in 10 nm steps, displays two maxima, an intense band at ∼18 000 cm−1 assigned to the 1B*+u -like π, π* excited singlet state and a weaker shoulder at ∼21 000 cm−1 assigned to the 1A*−g -like π, π* excited singlet state. Thus, the 1A*−g -like state is 3500±500 cm−1 above the 1B*+u -like state, which is indicative of a protonated Schiff base chromophore. A log-normal fit of the two-photon spectrum indicates that the maximum two-photon absorptivity of the 1B*+u -like state is 290±50 GM whereas the maximum two-photon absorptivity of the 1A*−g -like state is less than half this value, 120±90 GM. The ‘‘1B*+u ’’ state exhibits an absorptivity that is dominated by initial and final state contributions to the two-photon tensor, and this observation allows an accurate assignment of the change in dipole moment upon excitation yielding Δμso=13.5±0.8 D. A similar analysis of the ‘‘1A*−g’’ state predicts that the change in dipole moment upon excitation into the latter state is slightly smaller (Δμso=9.1±4.8 D). We demonstrate that the second-order hyperpolarizability of a molecule can be determined directly from the two-photon absorptivity of the low-lying charge transfer state and other spectroscopic parameters, all but one of which can be determined directly from experiment. Our analysis of light adapted bacteriorhodopsin indicates that β=βxxx+(1/3)[βxyy +2βyyx+βxzz+2βzzx] =(2250±240)×10−30cm5/esu for a laser wavelength of 1.06μ assuming that the homogeneous linewidth is 250 cm−1. Preliminary analyses of the two-photon data indicate that the chromophore in bacteriorhodopsin is a protonated Schiff base chromophore in a very ionic, and possibly charged, binding site. The two-photon data are not consistent with charged species near the β-ionylidene ring, but are consistent with polar species near the β-ionylidene ring. Direct hydrogen bonding of a negative counterion with the imine proton is not supported by the two-photon data.

Relativistic cluster results for YBa2Cu3O7

The valence density of states, charge distribution, and core-level binding energies for a unit-cell cluster of YBaCuO are compared with solid state and experimental results. The cluster is shown to be a reasonable model, in particular for surface properties. Cu 3d spin-orbit effects and final state contributions in the photoemission process are investigated for the first time.

Final state core level binding energy shifts in binary alloys

The final state or relaxation contribution to core level binding energy shift is calculated for some noble metal/transition metal alloy systems, using the pseudopotential linear response method developed previously for pure metals. The core hole perturbation is described by an ab-initio pseudopotential. A basic parameter of the method is the homogeneous electron gas density for which, in the present case, a mean value between those corresponding to each pure metal is adopted. The final state contribution is generally found to be important and sometimes dominant. From the experimental core level shifts and the calculated final state shifts, some considerations about initial state contribution are given.

Final State Core Level Shifts in Supported and Free Metal Particles

AbstractThe final state contribution to core level electron binding energy shifts is analysed in the case of small free and supported particles. The results of a pseudopotential–electron gas linear response model that was developed in a preceding paper are compared with other jellium models (atom‐in‐jellium vacancy DFT, semi‐classical). As small particles are generally supported as clusters, the support contribution is also calculated, considering a possible charge transfer. Total relaxation contribution is then compared with the experimental results of Kohiki for the Pd/SiO2 system. Good agreement is obtained in the range 10 to 40 at. units.

Analysis of core-level shifts in some metallic Ni compounds

The core-level shifts of Ni${\mathrm{Si}}_{2}$, NiAl, Ni${\mathrm{Al}}_{3}$, and NiCu with respect to pure metallic Ni and atomic Ni, including both initial- and final-state contributions, are calculated by means of linear muffin-tin orbital energy-band calculations, and their origin is critically discussed in terms of charge-transfer and configuration changes.

Core-electron binding energies in atoms and monolayers adsorbed on metallic substrates

A Born-Haber cycle analysis of photoemission from atoms and monolayers adsorbed on metallic surfaces elucidates the effects of the substrate on the initial and final state contributions to measured core-electron binding energies. For rare gases both a dependence on the work function of the substrate and on the final state screening energy are identified. Depending on the relative magnitudes of the work function of the substrate and the ionization potential of the core-ionized atom, the screening charge may reside either in the substrate or on the adsorbate atom itself. Within the monolayer range, the coverage-dependence of the core-electron binding energy is shown to be largely a final-state effect. The Born-Haber cycle relating the Auger decay energy of an adsorbed core-ionized atom to that of a similar free atom is also presented. These formulations are tested using data for Xe adsorbed on Pd and Cs.

Final-state screening of core holes in metals.

Core-level photoemission is often employed to extract chemical information concerning the atomic site and this requires assumptions concerning the balance between initial-state chemical and final-state screening effects. With this in mind, we have calculated the binding energy of the 4f-italic level in gold metal using local-density total-energy calculations. We find a binding energy of 83.7 eV in good agreement with the experimental value of 83.9 eV. We are thus able to test several less complete computational schemes. For example, confining the response to a single site yields 84.3 eV, an error of 0.6 eV, while limiting the screening to the atom and its near neighbors produces an error of 0.07 eV. In additions, we have calculated the heat of solution of mercury in gold. This may be related via a Born-Haber cycle to the core-level binding energy assuming local screening and the equivalent core approximation. This yields a binding-energy error of 0.15 eV, which, while small, is of significance. Finally, we have explicitly decomposed the binding energy into initial- and final-state contributions and find a relaxation energy in gold of 17.7 eV compared to 13.1 eV for the isolated atom.

Impulse approximation in solid helium

The incoherent dynamic form factor S/sub i/(Q, ..omega..) is evaluated in solid helium for comparison with the impulse approximation (IA). The purpose is to determine the Q values for which the IA is valid for systems such a helium where the atoms interact via a potential having a steeply repulsive but not infinite hard core. For /sup 3/He, S/sub i/(Q, ..omega..) is evaluated from first principles, beginning with the pair potential. The density of states g(..omega..) is evaluated using the self-consistent phonon theory and S/sub i/(Q,..omega..) is expressed in terms of g(..omega..). For solid /sup 4/He resonable models of g(..omega..) using observed input parameters are used to evaluate S/sub i/(Q,..omega..). In both cases S/sub i/(Q, ..omega..) is found to approach the impulse approximation S/sub IA/(Q, ..omega..) closely for wave vector transfers Q> or approx. =20 A/sup -1/. The difference between S/sub i/ and S/sub IA/, which is due to final state interactions of the scattering atom with the remainder of the atoms in the solid, is also predominantly antisymmetric in (..omega..-..omega../sub R/), where ..omega../sub R/ is the recoil frequency. This suggests that the symmetrization procedure proposed by Sears to eliminate final state contributions should work well in solid helium.

Core binding energies for clusters deposited on different insulating substrates: esca spectra and theoretical electronic structure studies

The 4 f core-level X-ray photoemission of small Pt clusters deposited on Teflon and SiO 2 substrates has been investigated. The experimental results are discussed and related to other data reported in the literature. Parallel results are presented for ab initio selfconsistent field, SCF, calculations of the core ionization potentials, IPs, of small Li clusters. These model calculations provide qualitative information about the nature and magnitude of the initial and final state contributions to the IPs for small clusters. We find that the binding energy shifts and linewidth broadening depend primarily on the cluster size and on the cluster substrate interaction. They do not result from electrostatic effects of the unit positive charge remaining on the ionized cluster. Our calculations show that this Coulomb effect does not apply to very small clusters.

Site dependence of core-electron binding energies of adsorbates: I/Pt(111)

Core-electron binding energies of iodine adsorbed on Pt(111) surfaces have been measured as a function of coverage in both the ($\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$) and ($\sqrt{7}\ifmmode\times\else\texttimes\fi{}\sqrt{7}$) regimes. In the former, in which the iodines occupy the threefold hollows, the binding energy decreases only slightly up to the saturation coverage of ⅓ monolayer. In the latter regime two distinct binding energies are obtained, one close to the value in the ($\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$) regime, the other smaller by 0.95 eV. The smaller binding energy corresponds to atoms in the atop sites of the ($\sqrt{7}\ifmmode\times\else\texttimes\fi{}\sqrt{7}$) structure. The initial- and final-state contributions to this binding-energy shift are examined.

Bonding and photoemission of chemisorbed molecules: Molecular orbital cluster model theory

This paper will review the use of ab initio Hartree–Fock wave functions for small metal/ligand clusters as a basis for the interpretation of processes related to molecular chemisorption. The primary concern will be with absorbate derived photoemission spectra (PES). It will be shown that quite small clusters can, indeed, give considerable insight into the structure, shifts, and character of this spectra. Ab initio molecular orbital theory is a particularly valuable approach since it permits one to relate these features of the PES to the nature of the adsorbate bonding in a direct way. The satellite structure originating from screening of the absorbate hole by metal electrons will be analysed for both core and valence levels. The decomposition of adsorbate shifts into initial and final state contributions will be considered (in order to understand the relationship of these shifts to the binding).

Kinetics of peroxodisulphate oxidation of dicyanobis-(2,2′-bipyridyl)iron(II) and of the tetracyano-2,2′-bipyridylferrate(II) anion; initial state and transition state effects in reactions of tris-diimine and diimine-cyanide complexes of iron(II)

The rate law, rate constants, and activation parameters are reported for peroxodisulphate oxidation of the Fe(bipy) (CN)42− anion in aqueous solution. Rate constants are also reported for peroxodisulphate oxidation of Fe(bipy)(CN)42− and of Fe(bipy)2(CN)2 in various binary aqueous mixtures at 298.2 K. Solvent effects on reactivity in these oxidations and in dissociation of Fe(bipy)2(CN)2 and of Fe(phen)32+ are discussed in terms of initial state and transition state solvation effects and chemical potentials. Solvent effects on reactivity for Fe(bipy)32+ + 2CN− = Fe(bipy)2(CN)2 + bipy in aqueous methanol are analysed into initial state, transition state, and final state contributions.

Initial state and transition state solvent effects: Reactions in protic and dipolar aprotic media

Interpretation of the variation in reaction rates brought about by solvent changes has traditionally utilized relationships based on absolute rate theory. Thus the Laidler-Eyring equation satisfactorily correlates rate data for the Menschutkin reaction in a number of binary solvents. However solvent parameters such as the dielectric constant are limited as measures of solvent influence since correlation is attempted with a quantity (ΔG ≠ or ΔG o) which represents a difference of two states and these may be affected differentially by the solvent change. Direct information about the nature of solvent involvement requires dissection of the solvent effects into initial and transition state (final state) contributions. This dissection is possible using the thermodynamic transfer function appoach [1–5]. In this presentation we utilize the relationship δ Δ T tr = δΔG R tr + δΔG ≠ for the free energy of transfer of the transition state (δΔG T tr) on solvent change, from the experimentally determined free energies of transfer of the reactants (δΔG R tr) and the kinetic activation parameters (δΔG ≠, and correspondingly for the equilibrium process δΔG tr = δG P tr − δG R tr, to discuss solvent effects on various rate and equilibrium processes. The discussion emphasizes dipolar aprotic solvents such as dimethyl sulfoxide for which dramatic medium effects have been observed in a number of systems. Specific reactions considered include solvent effects on S N2 and S NAr processes; the competing σ-complex formation and proton abstraction in nitroaromatics-base interactions; and the hydroxide ion catalyzed isotopic exchange of D 2. Some future directions in this area are indicated, as for example synergistic and antagonistic effects as probes of changing transition states.

Pion-nucleon resonances and the angular distribution in pion electroproduction

Using the helicity formalism, we find the contributions from final states of definite spin and parity, together with the interference terms between different final-state contributions, to the angular distributions of pions electro-produced from protons. For a single resonant final state the azimuthal terms turn out to be particularly simple, and may well serve as a test for the spin of the resonance. We show that the angular distribution may be used to detect the possible presence of ap1/2 resonant state in the energy region of the second resonance.