The hydrogenated aluminium trimer: a theoretical examination of the formation and interconversion pathways

Five doublet isomers of the Al₃H₂ cluster lying within a narrow range of 5 kcal/mol, along with the isomerization transition states connecting them, have been located with the coupled-cluster CCSD(T) and DFT methods. The two most stable doublet structures, the C_2v planar including the two Hs bound terminally and C₁ non-planar showing one H in terminal site and the other in threefold site are found to be essentially degenerate. Although the reaction of Al₃ with H₂ to yield Al₃H₂ is found to be significantly exothermic, by 23.5 kcal/mol, this hydrogenation is impeded by a considerable kinetic barrier of 16 kcal/mol. Our result is consistent with the observed lack of reactivity of Al_n towards H₂(D₂) for n=3 under thermal conditions [3]. The quartet Al₃H₂ isomers are predicted to lie 16–21 kcal/mol higher in energy than the doublet analogues. Further dimerization of Al₃H₂ to form Al₆H₄ has also been examined. Electronic supplementary material Supplementary Online Material     

Improved endohedral fullerenelike structures of silicon clusters Si31–Si39 by density functional calculations

We extensively search for the endohedral silicon-fullerene structures of Si₃₁–Si₃₉ using the combination of a tight-binding potential with the density functional theory. The resulting structures of our best candidates characterize more compact features comparing to previous isomers [J. Am. Chem. Soc. 126, 13845 (2004); J. Chem. Phys. 124, 164311 (2006)]. Most of our best candidates belong to new families featuring different core/cage combinations or different original carbon fullerene cages with respect to those of previous isomers. Energy calculations reveal that our best candidates are more stable than the previous best ones at the PW91 level, except for n = 34 and 38. The predicted relative stabilities of these isomers remain even at finite temperatures. In addition, the densities of dangling-bond atoms in the surfaces of our Si₃₃ and Si₃₉ isomers are significantly lower than the previous best candidates, as well as lower than those of their neighbors. This finding together with the densities of the active sites in the surfaces of the previous best candidates of Si₃₄ and Si₃₈ is roughly consistent with the observed relative reactivities of the silicon clusters in the size range of n = 31-39.     

Optical absorption of isolated silver cluster-tryptophan: A joint experimental and theoretical study

We present a joint experimental and theoretical gas phase study of photoabsorption and photofragmentation of silver cluster-biomolecule complexes. We demonstrate on the example of [ Trp.Ag₃] ⁺ that binding of the metal cluster to a biomolecule leads to a significant enhancement of the photoabsorption in comparison with [Trp.H]⁺ and [Trp.Ag]⁺. This enhancement arises due to the coupling between the excitations in the metallic subunit with charge transfer excitations between silver cluster and tryptophan. Our experimental studies show that silver clusters up to eleven atoms can be bound to tryptophan and we present first results on the photofragmentation of the Trp.Ag₁₁ ⁺ complex cation, in which properties of cluster subunit remain preserved.     

Theoretical investigation of the ultrafast NeNePo spectroscopy of Au 4 and Ag 4 Clusters

Ultrafast ground state nuclear dynamics of Au₄ and Ag₄ is theoretically explored in the framework of negative ion - to neutral - to positive ion (NeNePo) pump-probe spectroscopy based on the ab initio Wigner distribution approach. This involves the preparation of a nonequilibrium neutral ensemble by pump induced photodetachment of a thermal anionic ground state distribution, gradient corrected DFT classical trajectory simulations “on the fly” on the neutral ground state, and detection of the relaxation process of the ensemble in the cationic ground state by a time-delayed probe pulse. In Au₄, the initially prepared linear structure is close to a local minimum of the neutral state giving rise to characteristic vibrations in the signals for probe wavelength near the initial Franck-Condon transition. A timescale of ∼1 ps for the structural relaxation towards the stable rhombic D_2h neutral isomer was determined by the increase of the signal for probe wavelength in vicinity of the vertical ionization energy of the rhombic structure. In contrast, the relaxation dynamics in Ag₄ is characterized by normal mode vibrations since both the initially prepared anionic ground state and the neutral ground state have rhombic minimum geometries. Thus, time-resolved oscillations of pump-probe signals are fingerprints of structural behaviour which can be used experimentally for the identification of particular isomers in the framework of NeNePo spectroscopy. Received 22 December 2000     

Structure of liquid Al and Al67Mg33 alloy: comparison between experiment and simulation

We report data on the structure of liquid Al and an Al₆₇Mg₃₃ alloy obtained from state-of-the-art X-ray diffraction experiments and ab initio molecular dynamics (AIMD) simulations. To facilitate a direct comparison between these data, we develop a method to elongate the AIMD pair correlation function in order to obtain reliable AIMD structure factors. The comparison reveals an appreciable level of discrepancy between experimental and AIMD liquid structures, with the latter being consistently more ordered than the former at the same temperature. The discrepancy noted in this study is estimated to have significant implications for simulation-based calculations of liquid transport properties and solid–liquid interface kinetic properties.     

Bifurcations of the normal modes of the Ne?Br2 complex

We study the classical dynamics of the rare gas-dihalogen Ne?Br₂ complex in its ground electronic state. By considering the dihalogen bond frozen at its equilibrium distance, the system has two degrees of freedom and its potential energy surface presents linear and T-shape isomers. We find the nonlinear normal modes of both isomers that determine the phase space structure of the system. By means of surfaces of section and applying the numerical continuation of families of periodic orbits, we detect and identify the different bifurcations suffered by the normal modes as a function of the system energy. Finally, using the Orthogonal Fast Lyapunov Indicator (OFLI), we study the evolution of the fraction of the phase space volume occupied by regular motions.     

Interaction of Ga<Subscript>3</Subscript> cluster with molecular hydrogen: combined DFT and CCSD(T) theoretical study

We have explored the lowest doublet and quartet potential energy surfaces (PES) for the reaction of gallium trimer with H₂. This reaction was studied experimentally by Margrave and co-workers in a noble gas matrix. The detailed reaction paths ending up with the low-energy Ga₃H₂ hydride isomers have been predicted based on the high level ab initio coupled-cluster calculations (CCSD(T)) with large basis set. We have found that the reaction occuring on the lowest doublet PES is described by the activation barrier for H₂ cleavage of about 15 kcal/mol, consistent with experiment. In the most stable Ga₃H₂ hydride structure, whose formation is exothermic by 15 kcal/mol, both H atoms assume three-fold bridged positions. The diterminal planar structure of Ga₃H₂, proposed experimentally from the observed IR spectra, is found to be only 1 kcal/mol less stable than the dibridged form.     

First-principles study of lattice dynamics of LiFePO4

Lattice dynamics of lithium iron orthophosphate (LiFePO₄) isostructural with olivine have been investigated using the first-principles calculations taking into account the on-site Coulomb interaction within the GGA + U scheme. Born effective charge tensors, phonon frequencies at the Brillouin zone center and phonon dispersion curves are calculated and analyzed. The Born effective charge tensors exhibit anisotropy, which gives a convincing evidence for the one-dimensional Li migration tunnel along the [010] direction in LiFePO₄, which has been proposed by other theoretical calculations and experimental observation. The calculated phonon frequencies at the Γ point of the Brillouin zone show good agreement with the available experimental observations.     

Comparative study on the structure and properties of small C<Subscript>n</Subscript> and NaC<Subscript>n</Subscript> clusters

The structures, binding energies, and electronic properties of C_n and NaC_n (n=2–12) clusters have been systematically investigated using density functional theory (DFT). A number of previously undiscovered isomers of NaC_n clusters are reported, including fan-like, linear and three-dimensional structures. Moreover, NaC_n clusters with even n are found to be more stable than those with odd n, in contrast with the case of C_n clusters.     

Structural properties and reactivity of bimetallic silver-gold clusters

Bimetallic silver-gold clusters are well suited to study changes in metallic versus ionic properties involving charge transfer as a function of the size and the composition. We present structures, ionization potentials (IP) and vertical detachment energies (VDE) for neutral and charged bimetallic Au_nAg_m ( 2(n + m)5) clusters obtained from density functional level of theory. In the stable structures of these clusters Au atoms assume positions which favor charge transfer from Ag atoms. In clusters with equal numbers of hetero atoms (n = m = 1- 4) heteronuclear bonding is preferred to homonuclear bonding, giving rise to large values of ionization potentials. For larger clusters (n=m=5, 10) stable structures do not favor neither hetero bonding nor segregation into the single components, although they exhibit more metallic than ionic features. This remains valid also for Au₈Ag₁₂ cluster characterized by strong charge transfer to gold subunit. The influence of doping of pure gold clusters with silver atoms on VDE and IP values is discussed in context of their reactivity towards O₂ and CO molecules. As a starting point we consider reactivity towards CO and O₂ molecules on the example of AgAu^- dimer. The results show that the catalytic cycle can be fullfilled.     

Ground state and excited state properties of ethylene isomers studied by a combined Feynman path integral-ab initio approach

Ground state and excited state properties of ethylene, C₂H₄, and several ethylene isomers have been studied by Feynman path integral Monte Carlo (PIMC) simulations. The PIMC treatment of the atomic nuclei has been combined with different electronic Hamiltonians in order to analyse the influence of the nuclear degrees of freedom on electronic quantities. Electronic expectation values at the minimum of the potential energy surface (PES) have been compared with PIMC based ensemble averaged values. Ensemble averaged quantities have been derived by Hamiltonians of the ab initio type and a tight-binding (TB) one-electron model. The combined influence of anharmonicities in the interatomic potential and the quantum fluctuations of the atomic nuclei lead to ensemble averaged bondlengths r _g which are significantly larger than the parameters r _e, at the minimum of the PES. The implications of this bond length elongation for the electronic properties of ethylene are discussed. The occupied canonical molecular orbitals (CMOs) of ethylene are destabilized under the influence of the nuclear degrees of freedom while virtual CMOs are stabilized. These shifts of one-electron energies suggest a comparison of electronic excitation energies at the minimum of the PES with PIMC based ensemble averages. The quantum fluctuations of the nuclei cause a strong redistribution in the intensities of electronic transitions. Transitions, which are dipole allowed in the planar D_2h geometry of ethylene, lose intensity under the influence of nuclear quantum effects, and vice versa for electronic excitations that are dipole forbidden under D_2h symmetry. This ‘vibrational borrowing’ is enhanced with decreasing atomic masses. The Feynman centroid density has been used to calculate the anharmonic vibrational wavenumbers of C₂H₄ and C₂D₄. The results of the present PIMC simulations have been employed to emphasize general problems of electronic structure calculations based on a single nuclear configuration (i.e. the configuration at the minimum of the PES).     

On the accuracy of classical, semiclassical and quantum methods in collision line broadening calculations: Comparative analysis for C2H2-Ar, He systems

Accuracies of classical, semiclassical and quantum methods are comprehensively examined in calculations of impact line widths of C₂H₂ molecules perturbed by Ar and He. The field of comparative study covers both infrared absorption and Raman scattering lines of acetylene having rotational quantum number J=0-30 at temperatures 173 and 296 K. Calculations have been made by fully classical method and by three basic least approximate semiclassical methods, namely, Neilsen-Gordon (NG) method, peaking approximation (PA) and Smith-Giraud-Cooper (SGC) method. Most accurate ab initio potential energy surfaces (PES) of Yang et al. (1996) [21] and Mozsynski et al. (1995) [22] have been applied to model C₂H₂-Ar and C₂H₂-He interactions. The comparison has been made also with available experimental data and with the results of rigorous fully quantum-mechanical calculations within close coupling and coupled states approaches in identical conditions. Semiclassical methods are proved to be not so much accurate as it is generally believed since all they gave in the cases considered seriously underestimated results. The fundamental issue of the adequacy of simplified trajectories in collision broadening calculations is finally reasonably solved. In cases of C₂H₂-Ar and C₂H₂-He systems the use of the “exact” isotropic trajectories (i.e. driven only by the isotropic part of PES) is the main reason of failing of NG, PA and SGC methods. Thus the neglecting of back-influence of the RT exchange on the classical path is a principal defect of semiclassical methods. Finally, the application of simplified trajectories is recognized as inadequate and risky in broadening calculations for molecules having relatively small rotational constants when accurate ab initio PES are applied.     

Electronic structure and reactivity of the CNO/NCO/CON isomers

Three-dimensional potential energy surfaces (PESs) have been calculated for the lowest electronic states of NCO, CNO and CON isomers, using internally contracted Multi Reference Configuration Interaction (MRCI) and Coupled-Clusters RCCSD(T) ab initio methods. For the low lying doublet and quartet excited states of the three isomers, the N–CO, O–CN, C–NO and C–ON collinear dissociation paths were mapped by the Complete Active Space SCF (CASSCF) approach and the energy variations with the bending coordinate have been explored. Several regions of conical intersections have been located and the spin–orbit interactions between states of different spin symmetry have been evaluated in the region of intersections of these states. The analysis of the PESs allows one to identify the main interactions governing the reactivity of the lowest electronic states. The NCO and CNO isomers have stable X²Π electronic ground states, for CON the X²Π ground state is separated from the dissociative [CO?+?N] asymptote by a barrier of 0.11 eV and crosses the dissociative ⁴Σ ^- state close to its minimum. At their equilibrium ground state geometries the spin–orbit interactions A _SO between the two electronic components of the X²Π states were calculated to be -95.6, -109.6 and -57.1 cm^?1 for NCO, CNO and CON, respectively. The predissociation of the vibrational levels of the A²Σ⁺ and B²Π states of NCO has been explained.     

Short-to-medium-range order in Mg65Cu25Y10 metallic glass

The atomic configurations of liquid and glassy Mg₆₅Cu₂₅Y₁₀ alloy have been simulated in the temperature range of 300 K to 2000 K via ab initio molecular dynamics. The variations of pair correlation function (PCF), structure factor (SF), coordination number (CN) and bond pairs with the temperature for this alloy are characterized. It has been shown that the atoms are near densely packed and icosahedral type of short-range order (SRO) is predominant in the glass state. Icosahedral medium range order (MRO) can be formed by vertex or intercross connection of icosahedral SROs. In this work, an icosahedral MRO which is composed of 55 atoms has been found. It has been also clarified that Mg and Cu occupy the centre or vertex, and Y atoms only occupy the vertex of the icosahedron in this glassy alloy. It is believed that these findings have implication for understanding the glass forming mechanism of magnesium based metallic glasses.     

Quasi-free Compton scattering and the polarizabilities of the neutron

Differential cross-sections for quasi-free Compton scattering from the proton and neutron bound in the deuteron have been measured using the Glasgow/Mainz photon tagging spectrometer at the Mainz MAMI accelerator together with the Mainz [48]cm ;SPMOslash; × [64]cm NaI(Tl) photon detector and the G?ttingen SENECA recoil detector. The data cover photon energies ranging from [200]MeV to [400]MeV at θ^LAB _γ = 136.2^°. Liquid deuterium and hydrogen targets allowed direct comparison of free and quasi-free scattering from the proton. The neutron detection efficiency of the SENECA detector was measured via the reaction p(γ,π⁺ n). The “free” proton Compton scattering cross-sections extracted from the bound proton data are in reasonable agreement with those for the free proton which gives confidence in the method to extract the differential cross-section for free scattering from quasi-free data. Differential cross-sections on the free neutron have been extracted and the difference of the electromagnetic polarizabilities of the neutron has been determined to be α_n - β_n = 9.8±3.6(stat)^+2.1 _-1.1(syst)±2.2(model) in units of [10^-4]fm ³. In combination with the polarizability sum α_n + β_n = 15.2±0.5 deduced from photoabsorption data, the neutron electric and magnetic polarizabilities, α_n = 12.5±1.8(stat)^+1.1 _-0.6(syst)±1.1(model) and β_n = 2.7±1.8(stat)^+0.6 _-1.1(syst)±1.1(model) are obtained. The backward spin polarizability of the neutron was determined to be γ⁽ⁿ⁾ _π = (58.6±4.0)×10^-4 fm ⁴. Received: 21 August 2002 / Accepted: 16 October 2002 / Published online: 11 February 2003 RID="a" ID="a"Part of the Doctoral Thesis. RID="b" ID="b"Present address: Physikalisch-Technische Bundesanstalt, Bundesallee 100, D-38116 Braunschweig. RID="a" ID="a"Part of the Doctoral Thesis. RID="b" ID="b"Present address: Physikalisch-Technische Bundesanstalt, Bundesallee 100, D-38116 Braunschweig. RID="c" ID="c"Part of the Habilitation Thesis. RID="d" ID="d"e-mail: schumacher@physik2.uni-goettingen.de Communicated by Th. Walcher     

Ag Raman modes of RBCO (R = Gd, Pr) by density functional theory approach

Ab initio total energy calculations have been performed for superconducting GdBa₂Cu₃O₇ and insulating PrBa₂Cu₃O₇ using the full-potential linear augmented plane-wave method in the local density approximation (LDA) and generalized gradient approximation (GGA). The comparison of the calculated unit cell volume and lattice parameters with the experimental data indicates the improvement of these parameters in the GGA relative to LDA. LDA and GGA give the equilibrium unit cell volume about 6% smaller and 1.25% larger than the experimental data, respectively for both systems. Thus frozen phonon calculations have been performed to determine the eigenvalues and eigenvectors of the k=0 A_g modes of the two systems in equilibrium structure have been obtained in GGA. The calculated frequencies in the GGA are in good agreement with the other LDA calculations for similar systems. Comparison of computational data with experimental data indicates that calculations determine the frequencies about ten percent below the experimental data. Even by improving LDA to GGA in these calculations, the calculated phonon frequencies have remained almost ten percent below the experimental data, even though the calculated unit cell volumes are nearly equal to the experimental data. So, applying GGA has not considerably decreased the difference between the computational and experimental data. The effect of Pr doping on the eigenvalues and eigenvectors have also been investigated.     

Ab initio molecular dynamics study on Ag (n = 4, 5, 6)

Ab initio Molecular Dynamics (MD) method, based on density functional theory (DFT) with planewaves and pseudopotentials, was used to study the stability and internal motion in silver cluster Ag_n, with n =4-6. Calculations on the neutral, cationic and anionic silver dimer Ag₂ show that the bond distance and vibrational frequency calculated by DFT are of good quality. Simulations of Ag₄, Ag₅, and Ag₆ in canonical ensemble reveal distinct characteristics and isomerization paths for each cluster. At a temperature of 800 K, an Ag₄ has no definite structure due to internal motion, while for Ag₅ and Ag₆the clusters maintain the planar structure, with atomic rearrangement observed for Ag₅ but not for Ag₆. At a temperature of 200 K, Ag₄ can exist in two planar structures whilst Ag₅ is found to be stable only in the planar form. In contrast Ag₆ is stable in both planar trigonal and 3D pentagonal structures. Micro-canonical MD simulation was performed for all three clusters to obtain the vibrational density of states (DOS). Received 5 May 1999 and Received in final form 20 August 1999     

Similar luminescent behavior in an established rhenacarborane complex, [3,3-(CO)2-3-NO-closo-3,1,2-ReC2B9H11] and a new complex anion, [3,3,3-(CO)3-8-I-closo-3,1,2-ReC2B9H10]

The compounds [3,3-(CO)₂-3-NO-closo-3,1,2-ReC₂B₉H₁₁] and [NEt₄][3,3,3-(CO)₃-8-I-closo-3,1,2-ReC₂B₉H₁₀] have been shown to be emissive in MeTHF at 77 K, with λ_max in the blue region of the visible spectrum. Emission from [3,3,3-(CO)₃-8-I-closo-3,1,2-ReC₂B₉H₁₀]^-, which has been structurally characterized, is phosphorescent with a single exponential decay lifetime, τ=1.65 ms. The complex [3,3-(CO)₂-3-NO-closo-3,1,2-ReC₂B₉H₁₁] also emits in the solid state at 298 K and has been shown by diffuse-reflectance UV-vis measurement to have a band gap of 2.66 eV.     

Theoretical study of the nuclear degrees of freedom in the isotropic and anisotropic hyperfine coupling constants of the C2H5 radical: a Feynman path integral–density functional approach

The isotropic and anisotropic hyperfine coupling (hfs) constants of the C₂H₅ radical have been theoretically studied under the conditions of thermal equilibrium, i.e. under the explicit consideration of the nuclear degrees of freedom. For this purpose the Feynman path integral quantum Monte Carlo (PIMC) formalism has been combined with an electronic Hamiltonian of the B3LYP–EPRIII type. The density functional operator has been used to derive both the distribution functions for the isotropic and anisotropic hfs constants of the ethyl radical as well as the thermal mean values. The electron paramagnetic resonance (EPR) timescale enables only the measurement of the thermal averages. The underlying distribution functions of these mean values, however, offer insight into the nature and strength of the nuclear degrees of freedom contributing to the observable thermal averages. The EPR parameters of C₂H₅ have been studied between 25 and 1000?K. This temperature (T?) window is large enough to consider nuclear fluctuations beyond zero-point effects. The deviations between the thermally averaged hfs constants and the values at the minimum of the potential energy surface (PES) are caused by (i) enlargements of the bond lengths in thermal equilibrium under the influence of anharmonicities in the internuclear potential, and (ii) by the intramolecular methylene rotation. The latter degree of freedom leads to a planar CH₂ unit in thermal equilibrium. At the minimum of the PES the methylene fragment exhibits a certain pyramidalization. The ensemble corrections as well as the T dependence of the isotropic hfs constants are larger than the ensemble shifts and T dependence of the anisotropic parameters. The non-validity of the crude Born–Oppenheimer approximation for the theoretical evaluation of physically meaningful isotropic hfs constants of the ethyl radical has been explained on the basis of specific nuclear degrees of freedom. Theoretical results of the ensemble averaged Monte Carlo type as well as single-nuclear configuration data are compared with experiment whenever available.     

Ab initio correlation approach to a ferric wheel-like molecular cluster

We present an ab initio study of electronic correlation effects in a molecular cluster derived from the hexanuclear ferric wheel [ LiFe₆(OCH₃)₁₂-(dbm)₆] PF₆. The electronic and magnetic properties of this cluster have been studied with all-electron Hartree-Fock, full-potential density functional calculations and multi-reference second-order perturbation theory. For different levels of correlation, a detailed study of the impact of the electronic correlation on the exchange parameter was feasible. As the main result, we found that the influence of the bridge oxygen atoms on the exchange parameter is less intense than the influence of the apical ligand groups, which is due to the geometry of the cluster. With respect to the cluster model approach, the experimental value of the exchange parameter was affirmed.