A series of gold clusters spanning the size range from Au6 through Au147 (with diameters from 0.7 to 1.7 nm) in icosahedral, octahedral, and cuboctahedral structure has been theoretically investigated by means of a scalar relativistic all-electron density functional method. One of the main objectives of this work was to analyze the convergence of cluster properties toward the corresponding bulk metal values and to compare the results obtained for the local density approximation (LDA) to those for a generalized gradient approximation (GGA) to the exchange-correlation functional. The average gold–gold distance in the clusters increases with their nuclearity and correlates essentially linearly with the average coordination number in the clusters. An extrapolation to the bulk coordination of 12 yields a gold–gold distance of 289 pm in LDA, very close to the experimental bulk value of 288 pm, while the extrapolated GGA gold–gold distance is 297 pm. The cluster cohesive energy varies linearly with the inverse of the calculated cluster radius, indicating that the surface-to-volume ratio is the primary determinant of the convergence of this quantity toward bulk. The extrapolated LDA binding energy per atom, 4.7 eV, overestimates the experimental bulk value of 3.8 eV, while the GGA value, 3.2 eV, underestimates the experiment by almost the same amount. The calculated ionization potentials and electron affinities of the clusters may be related to the metallic droplet model, although deviations due to the electronic shell structure are noticeable. The GGA extrapolation to bulk values yields 4.8 and 4.9 eV for the ionization potential and the electron affinity, respectively, remarkably close to the experimental polycrystalline work function of bulk gold, 5.1 eV. Gold 4f core level binding energies were calculated for sites with bulk coordination and for different surface sites. The core level shifts for the surface sites are all positive and distinguish among the corner, edge, and face-centered sites; sites in the first subsurface layer show still small positive shifts.

We studied the cyclotrimerization of acetylene on size-selected Pd n clusters (1 e n e 30) supported on thin MgO(100) films by thermal desorption and Fourier transform infrared spectroscopy. Surprisingly, the production of benzene is already observed on a single palladium atom at low temperature (300 K). Using density functional theory (DFT) calculations we show that free inert Pd atoms are activated by charge transfer from defect sites of the MgO substrate upon deposition. For larger clusters (7 e n e 30) benzene is additionally produced at a temperature of 430 K and our results suggest the existence of a critical ensemble of seven palladium atoms for this high-temperature reaction mechanism.

We calculated electronic matrix elements for hole transfer between adjacent nucleobases in DNA. Calculations of the matrix elements for intrastrand and interstrand transfer were performed at the Hartree-Fock level employing the 6-31G* and 6-311G** basis sets. The matrix elements for intrastrand hole transfer, for which a wealth of experimental solution data is available, are almost independent of the basis set and exhibit an exponential interbase distance dependence, sensitivity to the donor-acceptor geometry, and dependence on 5′ f 3′ direction base sequence. The calculated intrastrand hole transfer matrix elements between adjacent thymines, v + (T,T) ) 0.16 eV, is in good agreement with the experimental estimate, v + (T,T) ) 0.18 eV, inferred from hole hopping in G + (T) m GGG (m ) 1-3). The features of the nucleobase bridge specificity for superexchange-induced hole hopping between guanines in G + XY...G (X,Y ) T or A) were elucidated, with the prediction of enhanced efficiency of thymine relative to adenine as mediator. Information on superexchangemediated intrastrand and direct interstrand hole hopping between guanine bases was also inferred. Our results for interstrand, adjacent G + G coupling predict the existence of zigzagging pathways for hole hopping, in line with experiment.

The purpose of this communication is two-fold. We introduce the fragment charge difference (FCD) method to estimate the electron transfer matrix element HDA between a donor D and an acceptor A, and we apply this method to several aspects of hole transfer electronic couplings in π-stacks of DNA, including systems with several donor–acceptor sites. Within the two-state model, our scheme can be simplified to recover a convenient estimate of the electron transfer matrix element HDA=(1−Δq2)1/2(E2−E1)/2 based on the vertical excitation energy E2–E1 and the charge difference Δq between donor and acceptor. For systems with strong charge separation, Δq≳0.95, one should resort to the FCD method. As favorable feature, we demonstrate the stability of the FCD approach for systems which require an approach beyond the two-state model. On the basis of ab initio calculations of various DNA related systems, we compared three approaches for estimating the electronic coupling: the minimum splitting method, the generalized Mulliken–Hush (GMH) scheme, and the FCD approach. We studied the sensitivity of FCD and GMH couplings to the donor–acceptor energy gap and found both schemes to be quite robust; they are applicable also in cases where donor and acceptor states are off resonance. In the application to π-stacks of DNA, we demonstrated for the Watson–Crick pair dimer [(GC),(GC)] how structural changes considerably affect the coupling strength of electron hole transfer. For models of three Watson–Crick pairs, we showed that the two-state model significantly overestimates the hole transfer coupling whereas simultaneous treatment of several states leads to satisfactory results.

Adsorption of CO on nanosize Pd particles was studied theoretically by density functional method and spectroscopically by means of infrared reflection absorption spectroscopy (IRAS) and sum frequency generation (SFG). A density functional approach was applied to three-dimensional crystallites of about 140 atoms. The model clusters were chosen as octahedral fragments of the face centered cubic (fcc) bulk, exhibiting (111) and (001) facets. Bare and adsorbate-decorated cluster models were calculated with O h symmetry constraints. Various types of adsorption sites were inspected:  3-fold hollow, bridge, and on-top positions at (111) facets; 4-fold hollow and on-top sites at (001) facets; bridge positions at cluster edges; on-top positions at cluster corners; and on single Pd atoms deposited at regular (111) facets. Adsorption properties of the relatively small regular cluster facets (111) and (001) are calculated similar to those of corresponding ideal (infinite) Pd surfaces. However, the strongest CO bonding was calculated for the bridge positions at cluster edges. The energy of adsorption on-top of low-coordinated Pd centers (kinks) is also larger than that for on-top sites of (111) and (001) facets. To correlate the theoretical results with spectroscopic data, vibrational spectra of CO adsorbed on supported Pd nanocrystallites of different size and structure (well-faceted and defect-rich) were measured using IRAS and SFG. For CO adsorption under ultrahigh vacuum conditions, a characteristic absorption in the frequency region 1950−1970 cm-1 was observed, which in agreement with the theoretical data was assigned to vibrations of bridge-bonded CO at particle edges and defects. SFG studies carried out at CO pressures up to 200 mbar showed that the edge-related species was still present under catalytic reaction conditions. By decomposition of methanol leading to the formation of carbon species, these sites can be selectively modified. As a result, CO occupies on-top positions at particle edges and defects. On the basis of the computational data, the experimentally observed differences in CO adsorption on alumina-supported Pd nanoparticles of different size and surface quality are interpreted. Differences between adsorption properties of Pd nanoparticles with a large fraction of (111) facets and adsorption properties of an ideal Pd(111) surface are also discussed.

Methanol steam re-forming, catalyzed by Pd/ZnO, is a potential hydrogen source for fuel cells, in particular in pollution-free vehicles. To contribute to the understanding of pertinent reaction mechanisms, density functional slab model studies on two competing decomposition pathways of adsorbed methoxide (CH(3)O) have been carried out, namely, dehydrogenation to formaldehyde and C-O bond breaking to methyl. For the (111) surfaces of Pd, Cu, and 1:1 Pd-Zn alloy, adsorption complexes of various reactants, intermediates, transition states, and products relevant for the decomposition processes were computationally characterized. On the surface of Pd-Zn alloy, H and all studied C-bound species were found to prefer sites with a majority of Pd atoms, whereas O-bound congeners tend to be located on sites with a majority of Zn atoms. Compared to Pd(111), the adsorption energy of O-bound species was calculated to be larger on PdZn(111), whereas C-bound moieties were less strongly adsorbed. C-H scission of CH(3)O on various substrates under study was demonstrated to proceed easier than C-O bond breaking. The energy barrier for the dehydrogenation of CH(3)O on PdZn(111) (113 kJ mol(-)(1)) and Cu(111) (112 kJ mol(-)(1)) is about 4 times as high as that on Pd(111), due to the fact that CH(3)O interacts more weakly with Pd than with PdZn and Cu surfaces. Calculated results showed that the decomposition of methoxide to formaldehyde is thermodynamically favored on Pd(111), but it is an endothermic process on PdZn(111) and Cu(111) surfaces.

A partially incoherent rate theory of long-range charge transfer in deoxyribose nucleic acid Electronic matrix elements for hole transfer between Watson-Crick pairs in desoxyribonucleic acid ͑DNA͒ of regular structure, calculated at the Hartree-Fock level, are compared with the corresponding intrastrand and interstrand matrix elements estimated for models comprised of just two nucleobases. The hole transfer matrix element of the GAG trimer duplex is calculated to be larger than that of the GTG duplex. ''Through-space'' interaction between two guanines in the trimer duplexes is comparable with the coupling through an intervening Watson-Crick pair. The gross features of bridge specificity and directional asymmetry of the electronic matrix elements for hole transfer between purine nucleobases in superstructures of dimer and trimer duplexes have been discussed on the basis of the quantum chemical calculations. These results have also been analyzed with a semiempirical superexchange model for the electronic coupling in DNA duplexes of donor ͑nuclobases͒-acceptor, which incorporates adjacent base-base electronic couplings and empirical energy gaps corrected for solvation effects; this perturbation-theory-based model interpretation allows a theoretical evaluation of experimental observables, i.e., the absolute values of donoracceptor electronic couplings, their distance dependence, and the reduction factors for the intrastrand hole hopping or trapping rates upon increasing the size of the nucleobases bridge. The quantum chemical results point towards some limitations of the perturbation-theory-based modeling.

Large octahedral and cuboctahedral palladium clusters, ranging from Pd55 to Pd146, have been investigated by means of all-electron relativistic density functional calculations. Adsorption of CO molecules on the (111) facets of these clusters was also studied. In particular, we focused on the interaction of CO (a single molecule per facet) with threefold hollow sites to inspect the variation of the calculated adsorption parameters with cluster size. We considered how observables calculated for that adsorption position on cluster facets relate to adsorption properties of the corresponding site at the single crystal surface Pd(111). We demonstrated for the first time that, with three-dimensional cluster models proposed here, one can reach cluster size convergence even for such a sensitive observable as the adsorption energy on a metal surface. We also addressed size effects on interatomic distances and the cohesive energy of bare Pd nanoclusters whose structure was fully optimized under the imposed Oh symmetry constraint. These quantities were found to correlate linearly with the average coordination number and the inverse of the cluster radius, respectively, allowing a rather accurate extrapolation to the corresponding values of Pd bulk. Finally, we considered the size convergence of adsorption properties of the optimized Pd clusters, as probed by CO adsorption. We also outlined implications of using these symmetric clusters for investigating adsorption and reactions on oxide-supported nanoparticles of model Pd catalysts.