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Pericyclic reactions with energies E well above the potential energy barrier B (case E>B) proceed with quantum nuclear flux densities 〈j〉 which are essentially proportional to the nuclear densities ρ in the femtosecond time domain. This corresponds to the definition of classical (cl) mechanics, j_{cl}=υ_{cl} ρ_{cl}, with almost constant velocity v_{cl}. For the other case E<B, however, that is, in the domain of coherent tunneling, we discover the opposite trend, that is, 〈j〉 has maximum value close to the barrier where ρ is a minimum (in fact where ρ is close to zero). The general conclusion is that quantum mechanical nuclear flux densities may be at variance from traditional expectations based on classical trajectories. This prediction calls for experimental demonstration. The counterintuitive proofofprinciple is demonstrated for a simple, onedimensional model of the Cope rearrangement of semibullvalene.
The traditional wavepacket interferometry for nuclear densities is extended to nuclear flux densities. Accordingly, a molecule vibrating in an electronic excited state may be prepared such that at a given time, the nuclear densities correspond to a broad distribution of the molecular bond, from short to long distances, which is subdivided into a chain of lobes. We discover that neighbouring lobes, or groups of lobes, may flow towards alternating directions, implying alternating bond stretches and bond compressions. The corresponding nuclear flux densities may be controlled by appropriate parameters of the two laser pulses, which generate the underlying interferences. Similar patterns of the nuclear densities and flux densities may also be created by a single laser pulse, which may cause interferences of the overlapping tail and head of a wavepacket as they run towards or away from a turning point, respectively. The phenomena are demonstrated for the model system I_{2}(B).
A method for accurate calculations of the cohesive energy of molecular crystals is presented. The cohesive energy is evaluated as a sum of several components. The major contribution is captured by periodic Hartree–Fock (HF) coupled with the local Møller–Plesset perturbation theory of second order (LMP2) with a tripleζ basis set. PostMP2 corrections and corrections for the basis set incompleteness are calculated from inexpensive incremental calculations with finite clusters. This is an essential improvement with respect to the periodic LMP2 method and allows for results of benchmark quality for crystalline systems. The proposed technique is superior to the standard incremental scheme as concerns the cluster size and basis set convergence of the results. In contrast to the total energy or electron correlation energy, which are evaluated in standard incremental calculations, postMP2 and basis set corrections are rather insensitive to approximations and converge quickly both in terms of the order of the increments and the number of terms at a given order. Evaluation of the incremental corrections within the subkJ/mol precision requires computing very few of the most compact twocenter and threecenter nonembedded clusters, making the whole correction scheme computationally inexpensive. This method as well as alternative routes to compute the cohesive energy via the incremental scheme are tested on two molecular crystals: carbon dioxide (CO_{2}) and hydrogen cyanide (HCN).
The adsorption of multivalent thiols on gold (111) surface was investigated using density functional theory applying the Perdew–Burke–Ernzerhof functional. Through the comparison of differences in energetics, structure and charge density distribution of a set of monodentate and polydentate thiols, we have described in detail the factors affecting the adsorption energy and the role played by the multivalence, which causes a decreasing of adsorption energy because of both electronic and steric hindrance effects. Finally, the comparison between the adsorption of 1,2 and 1,3disulfides revealed how the chain length may affect the cleavage of the S[BOND]S bond when they adsorb on Au(111) surface.
Firstprinciples density functional theory (DFT) is used to study the solidstate modifications of carbon dioxide up to pressures of 60 GPa. All known molecular CO_{2} structures are investigated in this pressure range, as well as three nonmolecular modifications. To account for longrange van der Waals interactions, the dispersion corrected DFT method developed by Grimme and coworkers (DFTD3) is applied. We find that the DFTD3 method substantially improves the results compared to the uncorrected DFT methods for the molecular carbon dioxide crystals. Enthalpies at 0 K and cohesive energies support only one possibility of the available experimental solutions for the structure of phase IV: the R3c modification, proposed by Datchi and coworkers [Phys. Rev. Lett.103, 185701 (2009)]. Furthermore, comparing bulk moduli with experimental values, we cannot reproduce the quite large—rather typical for covalent crystal structures—experimental values for the molecular phases II and III.
The effect of nuclear motion on the synchronicity of the pincer motion type electronic rearrangement associated with bond making and bond breaking and vice versa is investigated for the degenerate Cope rearrangement of semibullvalene using a timeindependent quantum chemical approach. We find that distinct paths along the potential energy surface corresponding to synchronous nuclear rearrangement involve asynchronous electronic fluxes out of the old and into the new bond while synchronous electronic fluxes entail asynchronous nuclear rearrangement. In order to demonstrate the robustness of the results, various highlevel quantum chemical methods including full structure optimizations up to second order multireference perturbation theory using tripleζ basis sets (RS2/ccpVTZ), which are subsequently refined at the RS3/ccpVTZ and MRCI+Dav/ccpVTZ levels of theory, are used for solving the electronic Schrödinger equation. These benchmark results extend previous quantum chemical data for the degenerate Cope rearrangement of semibullvalene and are tested against lower level methods (e.g., density functional theory calculations using the B3LYP and B3PW91 functionals).
We propose a method to steer the outcome of reactive atomdiatom scattering, using rotational wavepackets excited by strong nonresonant laser pulses. Full closecoupled quantum mechanical scattering calculations of the D+H_{2} and F+H_{2} reactions are presented, where the H_{2} molecule exists as a coherent superposition of rotational states. The nuclear spin selective control over the molecular bond axis alignment afforded by the creation of rotational wavepackets is applied to reactive scattering systems, enabling a nuclear spin selective influence to be exerted over the reactive dynamics. The extension of the conventional eigenstatetoeigenstate scattering problem to the case in which the initial state is composed of a coherent superposition of rotational states is detailed, and a selection of example calculations are discussed, along with their mechanistic implications. The feasibility of the corresponding experiments is considered, and a suitable simple two pulse laser scheme is shown to strongly differentiate the reactivities of oH_{2} and pH_{2}.
When molecules move, their nuclei flow. The corresponding quantum observable, i.e., the nuclear flux density, was introduced by Schrödinger in 1926, but until now, it has not been measured. Here the first experimental results are deduced from highresolution pumpprobe measurements of the timedependent nuclear densities in a vibrating diatomic molecule or molecular ion. The nuclear densities are converted to flux densities by means of the continuity equation. The flux densities are much more sensitive to timedependent quantum effects than the densities. Applications to the sodium molecule and the deuterium molecular ion unravel four new effects; e.g., at the turns from bond stretch to compression, the flux of the nuclei exhibits multiple changes of directions, from small to large bond lengths, a phenomenon that we call the "quantum accordion."
Phys. Rev. A 87, 062512 (2013). DOI: 10.1103/PhysRevA.87.062512 A theoretical study of the electronic and nuclear flux densities of a vibrating H_{2}^{+} molecular ion is presented. The timedependent wave function is represented in the basis of vibronic eigenstates which are numerically obtained from the complete nonrelativistic Hamiltonian without the clampednuclei approximation. A onecenter expansion in terms of Bsplines and Legendre polynomials is employed to solve the corresponding eigenvalue equation. The electronic and nuclear flux densities are then calculated from the total wave function through their quantummechanical definition. Analysis of the flux densities close to the turning points shows that the nuclear wave packet takes longer time (1.4 fs) to change its direction compared to the electronic one (1 fs).
We present static electric dipole polarizabilities α_{d}(Z,N) from numerical nonrelativistic restricted HartreeFock (RHF) finitefield calculations for highspin openshell S states (L = 0) of atoms and isoelectronic ions with N ≤ 55 electrons. All these S states result from one or more halffilled shells. For eight isoelectronic sequences, those with N = 3, 7, 11, 15, 23, 29, 33 or 41 electrons where the electronic ground state of the neutral or nearly neutral members is conserved upon increase of the nuclear charge number Z, polarizability data are given for ions with charge number Q = Z − N up to Q = 90. In addition, these data are represented in terms of rational functions of Q (with absolute value of the relative error of the fit always below 4%). The rational functions are comparable to the classical nonrelativistic result α_{d}(Z,1) = 4.5 / Z^{4} = 4.5 / (Q + 1)^{4} for the polarizability of the ^{2}S ground state of a hydrogenlike system. Our results also contribute to constitute a reference database (i) for algebraic approaches relying on basis functions, and (ii) for the discussion of relativistic and correlation effects on polarizabilities along isoelectronic sequences.
Pericyclic reactions with energies E well above the potential energy barrier B (case E>B) proceed with quantum nuclear flux densities 〈j〉 which are essentially proportional to the nuclear densities ρ in the femtosecond time domain. This corresponds to the definition of classical (cl) mechanics, j_{cl}=υ_{cl}ρ_{cl}, with almost constant velocity v_{cl}. For the other case E<B, however, that is, in the domain of coherent tunneling, we discover the opposite trend, that is, 〈j〉 has maximum value close to the barrier where ρ is a minimum (in fact where ρ is close to zero). The general conclusion is that quantum mechanical nuclear flux densities may be at variance from traditional expectations based on classical trajectories. This prediction calls for experimental demonstration. The counterintuitive proofofprinciple is demonstrated for a simple, onedimensional model of the Cope rearrangement of semibullvalene.
The electronic structure of the intermetallic compound MgZn_{2}, a prototypical Laves phase, was investigated by firstprinciples calculations based on KohnSham densityfunctional theory. A variety of six exchangecorrelation energy density functionals, from local density approximation to hybrid functionals, was used to fully optimize the crystal structure. Cell parameters and mass density calculated with the density functional parameterization by Perdew, Burke, and Ernzerhof (PBE) were found closest to their corresponding experimental values. The revised version of the functional, PBEsol, recommended for solid state applications, gave inferior results. The electronic structure was analysed in terms of band structure, density of states and electron density.
scattering and UV–Vis spectroscopy'', J. Appl. Cryst. 46 (2013). DOI: 10.1107/S0021889813018190 Recently, a socalled `crownjewel' concept of preparation of Au/Pdbased colloidal nanoclusters has been reported [Zhang, Watanabe, Okumura, Haruta & Toshima (2011). Nat. Mater. 11, 49–52]. Here, a different way of preparing highly active Au/Pdbased nanoclusters is presented. The origin of the increased activity of Au/Pdbased colloidal bimetallic nanoclusters was unclear up to now. However, it is, in general, accepted that in the nanometre range (1–100 nm) the cluster size, shape and composition affect the structural characteristics (e.g. lattice symmetry, unit cell), electronic properties (e.g. band gap) and chemical properties (e.g. catalytic activity) of a material. Hence, a detailed study of the relationship between the nanostructure of nanoclusters and their catalytic activity is presented here. The results indicate that a high surfacetovolume ratio of the nanoclusters combined with the presence of `both' Au and Pd isolated regions at the surface are crucial to achieve a high catalytic activity. A detailed structure elucidation directly leads to a mechanistic proposal, which indeed explains the higher catalytic activity of Au/Pdbased catalysts compared with pure metallic Au or Pd. The mechanism is based on cascade catalysis induced by a single type of nanoparticle with an intermixed surface of Au and Pd.
Coherent tunnelling in molecular systems with cyclic and noncyclic symmetric double well potentials may proceed with similar nuclear densities, but with entirely different flux densities. For sufficiently high potential barriers, the nuclear densities may even become indistinguishable, whereas the patterns of the flux densities at a given time remain pincermotion type for the cyclic systems, but unidirectional for the noncyclic one. This effect is traced back to symmetry breaking of the cyclic to the noncyclic model. Accordingly, nuclear flux densities are much more sensitive to symmetry breaking than nuclear densities. For a proof of principle, the phenomenon is demonstrated by means of three onedimensional models. The cyclic model I represents torsion in oriented B_{2}Cl_{2}F_{2}, the noncyclic model II is constructed from I by symmetry breaking and the noncyclic model III represents tunnelling by inversion of oriented NH_{3}.
We present multireference calculations for the characterization of ring inversion and double bond shifting in cyclooctatetraene. The results show that it is necessary to treat the dynamical correlation very accurately to obtain correct values for the barrier heights. This can be done, for example, with multireference configuration interaction or with perturbation theory of third order. However, detailed analysis also shows that already a complete active space selfconsistent field treatment describes the processes surprisingly well. Thus, this method could be used as a computationally cheap method, for example, for dynamics simulations.
The electron distributions in position and in momentum space of the hcp metals magnesium and zinc are investigated experimentally and compared to results of quantumchemical calculations. Furthermore, a survey is given on recent analyses of the bonding properties of zinc and cadmium, using the method of increments. The experimental deformation densities were obtained by refining multipole models to Xray diffraction data sets measured at 100 K with either MoKα (Mg) or AgKα (Zn) radiation. The final R_{F} values (Valray/Jana2006) are 0.0028/0.0034 (Mg) and 0.0068/0.0068 (Zn). The differences to deformation densities obtained from periodic density functional calculations are discussed. The effect of dynamical electron correlation on the electron density was analyzed, using cluster models. Compton profiles were measured with 88.67 keV synchrotron radiation at beamline ID15B at the ESRF in Grenoble. Varied orientations of the samples allowed for probing the projected momentum distribution along the [100], [423] and [001] directions. Fourier transforms of the computed reciprocal form factor B(r) resulted in the corresponding theoretical Compton profiles. It is suggested that the anomalous hcp structure of zinc is favored by a kinetic balancing of the valence electrons, i.e. correlation mediated 4s3d interactions.
In recent years pyridine derivatives, namely 4(N,Ndimethylamino)pyridine and 4methoxypyridine, were found to be excellent agents for the stabilization of gold nanoparticles. In order to gain a better understanding of these systems we have simulated the interaction of gold nanoparticles with pyridine and pyridine derivatives with donor substituents in position 4 by quantumchemical calculations. The relatively large nanoparticles were modeled by the most stable and relevant surface, Au(111). To account for dispersion effects within the density functional theory approach a dispersion correction in the D3 scheme was applied. Due to the dispersion effects the preferred orientation on Au(111) changed from perpendicular for pyridine to parallel for pyridine derivatives. In addition, the adsorption at edges and corner sites of nanoparticles was considered through the use of gold adatoms on the surface. For the pyridine–gold interaction a change of the nature of binding was observed.
We have characterised the Lewis acidity of unsaturated surface cations of MgF_{2} crystals using periodic calculations at the B3LYP level. The relative importance of low index surfaces was determined by calculating surface energies, and these surfaces were then probed by CO adsorption. We found that a MgF_{2} microcrystal should expose mainly (110), (100) and (101) surfaces in which the undercoordinated cations are fivefold coordinated. The adsorption energies and CO stretching frequencies are discussed with respect to the coordination number of surface cations and the stability of the surfaces and are compared to IR spectra from the literature.
In this work the influence of manyelectron effects on the shape of characteristic Xray emission bands of the simple metals Mg and Al is examined by means of ab initio calculations and semiempirical models. These approaches are also used for the analysis of C Kemission and absorption spectra of graphene. Both the dynamical screening of the core vacancy and the Augereffect in the valence band (VB) have been taken into account. Dynamical screening of the core vacancy by valence electrons (the socalled MND effect) is considered ab initio in the framework of density functional theory. The Auger effect in the VB was taken into account within a semiempirical method, approximating the quadratic dependence of the VB hole level width on the difference between the level energy and the Fermi energy. All theoretical spectra are in very good agreement with available experimental data.
A molecule in the electronic ground state described in the Born–Oppenheimer approximation (BOA) by the wave function Ψ_{BO} = Φ_{0}χ_{0} (where Φ_{0} is the timeindependent electronic energy eigenfunction and χ_{0} is a timedependent nuclear wave packet) exhibits a nonzero nuclear flux density, whereas it always displays zero electronic flux density (EFD), because the electrons are in a stationary state. A hierarchical approach to the computation of the EFD within the context of the BOA, which utilizes only standard techniques of quantum chemistry (to obtain Φ_{0}) and quantum dynamics (to describe the evolution of χ_{0} on the groundstate potential energy surface), provides a resolution of this puzzling, nonintuitive result. The procedure is applied to H_{2}^{+} oriented parallel with the zaxis and vibrating in the ground state ^{2}Σ_{g}^{+}. First, Φ_{0} and χ_{0} are combined by the coupledchannels technique to give the normally dominant zcomponent of the EFD. Imposition of the constraints of electronic continuity, cylindrical symmetry of Φ_{0} and two boundary conditions on the EFD through a scaling procedure yields an improved zcomponent, which is then used to compute the complementary orthogonal ρcomponent. The resulting EFD agrees with its highly accurate counterpart furnished by a nonBOA treatment of the system.
Realization of graphene moiré superstructures on the surface of 4d and 5d transition metals offers templates with periodically modulated electron density, which is responsible for a number of fascinating effects, including the formation of quantum dots and the site selective adsorption of organic molecules or metal clusters on graphene. Here, applying the combination of scanning probe microscopy/spectroscopy and the density functional theory calculations, we gain a profound insight into the electronic and topographic contributions to the imaging contrast of the epitaxial graphene/Ir(111) system. We show directly that in STM imaging the electronic contribution is prevailing compared to the topographic one. In the force microscopy and spectroscopy experiments we observe a variation of the interaction strength between the tip and highsymmetry places within the graphene moiré supercell, which determine the adsorption sites for molecules or metal clusters on graphene/Ir(111). 
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This page was last modified on April 23, 2015, at 10:47 AM 