Volume 133, Issue 5, 07 August 2010

The authors report a detailed quantum mechanical study of the statetostate dynamics of the reaction on an accurate potential energy surface. The scattering dynamics was treated using a reactant coordinate based Chebyshev real wavepacket method with full Coriolis coupling. A total of 84 partial waves were calculated in order to achieve convergence up to the collision energy of 0.17 eV. The differential cross section is near forwardbackward symmetric, consistent with the complexforming mechanism. The product was found to have a monotonically decaying vibrational distribution and highly excited and inverted rotational distributions, also consistent with the formation of the intermediate. These quantum mechanical results were compared with those obtained in earlier quasiclassical trajectory and statistical studies and it is shown that the statistical theory gives a reasonably good description of the product state distributions despite its inability to predict the total reaction cross section.
 ARTICLES

 Theoretical Methods and Algorithms

A semiclassical correction for quantum mechanical energy levels
View Description Hide DescriptionWe propose a semiclassical method for correcting molecular energy levels obtained from a quantum mechanical variational calculation. A variational calculation gives the energy level (i.e., eigenvalue) as the expectation value of the molecular Hamiltonian , where is the trial wave function. The true (i.e., exact) eigenvalue can thus be expressed as this variational result plus a correction, i.e., , the correction being due to the lack of exactness of the trial wave function. A formally exact expression for is usually given (via Löwdin partitioning methodology) in terms of the Greens function of the Hamiltonian projected onto the orthogonal complement of . Formal treatment of this expression (using Brillouin–Wigner perturbation theory to infinite order) leads to an expression for that involves matrix elements of the Greens function for the unprojected, i.e., full molecular Hamiltonian, which can then be approximated semiclassically. (Specifically, the Greens function is expressed as the Fourier transform of the quantum mechanical time evolution operator, , which in turn is approximated by using an initial value representation of semiclassical theory.) Calculations for several test problems (a one dimensional quartic potential, and vibrational energy levels of and ) clearly support our proposition that the error in the total eigenvalue arises solely due to the semiclassical error in approximating , which is usually a small fraction of the total energy itself.

Unidirectional hopping transport of interacting particles on a finite chain
View Description Hide DescriptionParticle transport through an open, discrete onedimensional channel against a mechanical or chemical bias is analyzed within a master equation approach. The channel, externally driven by timedependent site energies, allows multiple occupation due to the coupling to reservoirs. Performance criteria and optimization of active transport in a twosite channel are discussed as a function of reservoir chemical potentials, the load potential, interparticle interaction strength, driving mode, and driving period. Our results, derived from exact rate equations, are used in addition to test a previously developed timedependent density functional theory, suggesting a wider applicability of that method in investigations of many particle systems far from equilibrium.

Theoretical studies of surface enhanced hyperRaman spectroscopy: The chemical enhancement mechanism
View Description Hide DescriptionHyperRaman spectra for pyridine and pyridine on the surface of a tetrahedral 20 silver atom cluster are calculated using static hyperpolarizability derivatives obtained from time dependent density functional theory. The stability of the results with respect to choice of exchangecorrelation functional and basis set is verified by comparison with experiment and with Raman spectra calculated for the same systems using the same methods. Calculated Raman spectra were found to match well with experiment and previous theoretical calculations. The calculated normal and surface enhanced hyperRaman spectra closely match experimental results. The chemical enhancement factors for hyperRaman are generally larger than for Raman ( versus ). Integrated hyperRaman chemical enhancement factors are presented for a set of substituted pyridines. A twostate model is developed to predict these chemical enhancement factors and this was found to work well for the majority of the molecules considered, providing a rationalization for the difference between hyperRaman and Raman enhancement factors.

Link atom bond length effect in ONIOM excited state calculations
View Description Hide DescriptionWe investigate how the choice of the link atom bond length affects an electronic transition energy calculation with the socalled our own layer integrated molecular orbital molecular mechanics (ONIOM) hybrid method. This follows our previous paper [M. Caricato et al., J. Chem. Phys.131, 134105 (2009)], where we showed that ONIOM is able to accurately approximate electronic transition energies computed at a high level of theory such as the equation of motion coupled cluster singles and doubles (EOMCCSD) method. In this study we show that the same guidelines used in ONIOM ground state calculations can also be followed in excited state calculations, and that the link atom bond length has little effect on the ONIOM energy when a sensible model system is chosen. We also suggest further guidelines for excited state calculations which can help in checking the effectiveness of the definition of the model system and controlling the noise in the calculation.

Steadystate current transfer and scattering theory
View Description Hide DescriptionThe correspondence between the steadystate theory of current transfer and scattering theory in a system of coupled tightbinding models of onedimensional wires is explored. For weak interwire coupling both calculations give nearly identical results, except at singular points associated with band edges. The effect of decoherence in each of these models is studied using a generalization of the Liouville–von Neuman equation suitable for steadystate situations. An example of a single impurity model is studied in detail, leading to a lattice model of scattering off target that affects both potential scattering and decoherence. For an impurity level lying inside the energy band, the transmission coefficient diminishes with increasing dephasing rate, while the opposite holds for impurity energy outside the band. The efficiency of current transfer in the coupled wire system decreases with increasing dephasing.

Optimal design strategies for electrostatic energy storage in quantum multiwell heterostructures
View Description Hide DescriptionWe study physical principles of optimal design of a nanoscale multiwell heterostructure functioning as an electrostaticenergy storage device. We performed numerical optimization of the multiwell trapping potential for electrons in the nanostructure with the goal to obtain the maximum possible static polarizability of the system. The response of the heterostructure is modeled microscopically using nonlocal linear response theory within the random phase approximation. Three main design strategies are identified which lead to the maximization of the stored energy. We found that the efficiency of each strategy crucially depends on the temperature and the broadening of electron levels. The stored energy for optimized heterostructures can exceed the nonoptimized ones by a factor of 450. These findings provide a theoretical basis for the development of new nanoscale capacitors with high energy density storage capabilities.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

About the collapse of the CH stretching band with ionization in polycyclic aromatic hydrocarbons: Configuration interaction and quantum Monte Carlo studies of the CH fragment
View Description Hide DescriptionThe puzzling difference between the IR spectra of polycyclic aromatic hydrocarbons(PAHs) and those of the corresponding positive ions is a well documented fact, although the basic reason for it is far from clear. In this report, the CH fragment, in its neutral and ionized forms is taken as a case study for investigating the collapse of the CH stretching vibration with ionization. A comprehensive study of the dipole moment function around the equilibrium geometries of the fragments using large scale configuration interaction and quantum Monte Carlo methods shows very different variations with the CH distance: a marked decrease for neutral and a perfect stability for ionized . These results are consistent with strong/weak intensities of the CH vibrations in the neutral/ionized PAHs, the key point being the presence, or not, of a hole in the shell. A topological analysis of the electronic densities shows that the collapse of the CH stretching with ionization is directly linked to the compensation between the internal charge transfer contribution and the distortion of the electronic density within the CH bond.

Statetostate quantum dynamics of the reaction
View Description Hide DescriptionThe authors report a detailed quantum mechanical study of the statetostate dynamics of the reaction on an accurate potential energy surface. The scattering dynamics was treated using a reactant coordinate based Chebyshev real wavepacket method with full Coriolis coupling. A total of 84 partial waves were calculated in order to achieve convergence up to the collision energy of 0.17 eV. The differential cross section is near forwardbackward symmetric, consistent with the complexforming mechanism. The product was found to have a monotonically decaying vibrational distribution and highly excited and inverted rotational distributions, also consistent with the formation of the intermediate. These quantum mechanical results were compared with those obtained in earlier quasiclassical trajectory and statistical studies and it is shown that the statistical theory gives a reasonably good description of the product state distributions despite its inability to predict the total reaction cross section.

Toward a realistic density functional theory potential energy surface for the cluster
View Description Hide DescriptionThe potential energy surface of is characterized using density functional theory. The hypersurface is evaluated at selected configurations employing different functionals, and compared with results obtained from ab initio CCSD(T) calculations. The lowest ten stationary points (minima and saddlepoints) on the surface are located, and the features of the short, intermediate, and longrange intermolecular interactions are also investigated. A detailed analysis of the surface’s topology, and comparisons with extensive CCSD(T) results, as well as a recent ab initio analytical surface, shows that density functional theory calculations using the B3(H) functional represent very well all aspects studied on the potential. These include the tiny energy difference between the minimum at configuration and the one corresponding to the transition state for the proton transfer between the two equivalent minima, and also the correct asymptotic behavior of the longrange interactions. The calculated binding energy and dissociationenthalpies compare very well with previous benchmark coupledcluster ab initio data, and with experimental data available. Based on these results the use of such approach to perform firstprinciples molecular dynamics simulations could provide reliable information regarding the dynamics of protonated hydrogen clusters.

band methyl halide dissociation via electronic curve crossing as studied by electron energy loss spectroscopy
View Description Hide DescriptionExcitation of the band lowlying electronic states in the methyl halides, , , , and , has been investigated for the transitions, using electron energy loss spectroscopy(EELS) in the range of 3.5–7.5 eV. For the methyl halides, , , and , three components of the complex (, , and ) were directly observed, with the exception of methyl fluoride, in the optically forbidden EELS experimental conditions of this investigation. The effect of electronicstate curve crossing emerged in the transition probabilities for the and states, with spinorbit splitting observed and quantified against results from recent ab initio studies.

production from reactions between water and small molybdenum suboxide cluster anions
View Description Hide DescriptionReactions between molybdenum suboxide cluster anions, , and water ( and ) have been studied using mass spectrometric analysis of products formed in a highpressure, fastflow reactor. Product distributions vary with the number of metal atoms in the cluster. Within the oxide series, product masses correspond to the addition of one water molecule, as well as a H/D exchange with . Within the oxide series, product evolution and distribution suggest sequential oxidation via reactions for , while for , is produced. does not appear to be reactive toward water. For the oxide series, sequential oxidation similarly is suggested for , while reactions result in formation. appears uniquely unreactive. and react to form and , respectively. Lower mass resolution in the mass range prevents unambiguous mass analysis, but intensity changes in the mass spectra do suggest that sequential oxidation with evolution occurs for , while addition products are formed in and reactions with water. The relative rate constants for sequential oxidation and addition for the series were determined. There is no evidence of a kinetic isotope effect when comparing reaction rates of with , suggesting that the and losses from the loweroxide/hydroxide intermediates are very fast relative to initial reaction complex formation with or . The rate constants determined here are two times higher than those determined in identical reactions between .

A perfectly matched layer applied to a reactive scattering problem
View Description Hide DescriptionThe perfectly matched layer (PML) technique is applied to a reactive scattering problem for accurate domain truncation. A twodimensional model for dissociative adsorbtion and associative desorption of from a flat surface is considered, using a finite difference spatial discretization and the Arnoldi method for timepropagation. We compare the performance of the PML to that of a monomial complex absorbing potential, a transmissionfree complex absorbing potential, and to exterior complex scaling. In particular, the reflection properties due to the numerical treatment are investigated. We conclude that the PML is accurate and efficient, especially if high accuracy is of significance. Moreover, we demonstrate that the errors from the PML can be controlled at a desired accuracy, enabling efficient numerical simulations.

Dynamics of highly excited barium atoms deposited on large argon clusters. I. General trends
View Description Hide Descriptionclusters were generated by associating the supersonic expansion and the pickup techniques. A femtosecond pump (266.3 nm)probe (792 or 399.2 nm) experiment was performed to document the dynamics of electronically excited barium within the very multidimensional environment of the argon cluster. Barium was excited in the vicinity of the state and probed by ionization. The velocity imaging technique was used to monitor the energy distribution of photoelectrons and photoions as a function of the delay time between the pump and the probe pulses. A complex dynamics was revealed, which can be interpreted as a sequence/superposition of elementary processes, one of which is the ejection of barium out of the cluster. The latter has an efficiency, which starts increasing 5 ps after the pump pulse, the largest ejection probability being at 10 ps. The ejection process lasts at a very long time, up to 60 ps. A competing process is the partial solvation of barium in low lying electronic states. Both processes are preceded by a complex electronic relaxation, which is not fully unraveled here, the present paper being the first one in a series.

Optimized basis sets for the calculation of indirect nuclear spinspin coupling constants involving the atoms B, Al, Si, P, and Cl
View Description Hide DescriptionThe augccpVTZJ series of basis sets for indirect nuclear spinspin coupling constants has been extended to the atoms B, Al, Si, P, and Cl. The basis sets were obtained according to the scheme previously described by Provasi et al. [J. Chem. Phys.115, 1324 (2001)]. First, the completely uncontracted correlation consistent augccpVTZ basis sets were extended with four tight and three tight functions. Second, the and basis functions were contracted with the molecular orbital coefficients of selfconsistentfield calculations performed with the uncontracted basis sets on the simplest hydrides of each atom. As a first illustration, we have calculated the onebond indirect spinspin coupling constants in , BF, AlH, AlF, , , , , , , HCl, and ClF at the level of density functional theory using the Becke three parameter Lee–Yang–Parr and the second order polarization propagator approximation with coupled cluster singles and doubles amplitudes.

Resonant twophoton ionization spectroscopy of jetcooled tantalum carbide, TaC
View Description Hide DescriptionThe optical spectrum of diatomic TaC has been investigated for the first time, with transitions recorded in the range from 17 850 to . Six bands were rotationally resolved and analyzed to obtain ground and excited state parameters, including band origins, upper and lower state rotational constants and bond lengths, Fermi contact parameter for the ground state, and lambda doubling parameters for the excited states. The ground state of TaC was found to be , originating from the electronic configuration, in which only the valence orbitals arising from the and orbitals are listed. All of the rotationally resolved and analyzed bands were found to originate from the ground state, giving , , and ( error limits) for . Comparison of the Fermi contact parameter to the atomic value shows that the orbital is approximately 75% in character. The other group 5 transition metalcarbides, VC and NbC, have long been known to have , ground states, with lowlying , excited states. The emergence of a different ground state in TaC, as compared to VC and NbC, is due to the relativistic stabilization of the orbital in Ta. This lowers the energy of the like orbital in TaC, causing the , state to fall below the , state.

Rovibronically selected and resolved twocolor laser photoionization and photoelectron study of nickel carbide cation
View Description Hide DescriptionWe have performed a twocolor laser photoionization and photoelectron study of nickelcarbide (NiC) and its cation . By preparing NiC in a single rovibronic level of an intermediate vibronic state via visible laser excitation prior to ultraviolet laser photoionization, we have measured the photoionization efficiency spectrum of NiC near its ionization threshold, covering the formation of . We have also obtained wellresolved rotational transitions for the and 1 vibrational bands of the ground state. The assignment of rotational transitions observed between the neutral NiC intermediate state and the ion ground state has allowed the direct determination of a highly precise value for the ionization energy of NiC, . This experiment also provides reliable values for the vibrational spacing , rotational constants ( and ), and equilibrium bond distance () for the ground state. The experimental results presented here are valuable for benchmarking the development of more reliable ab initio quantum computation procedures for energetic and spectroscopic calculations of transition metalcontaining molecules.
 Condensed Phase Dynamics, Structure, and Thermodynamics: Spectroscopy, Reactions, and Relaxation

Trading sensitivity for information: Carr–Purcell–Meiboom–Gill acquisition in solidstate NMR
View Description Hide DescriptionThe Carr–Purcell–Meiboom–Gill (CPMG) experiment has gained popularity in solidstate NMR as a method for enhancing sensitivity for anisotropically broadened spectra of both spin 1/2 and half integer quadrupolar nuclei. Most commonly, the train of CPMG echoes is Fourier transformed directly, which causes the NMR powder pattern to break up into a series of sidebands, sometimes called “spikelets.” Larger sensitivity enhancements are observed as the delay between the pulses is shortened. As the duration between the pulses is shortened, however, the echoes become truncated and information about the nuclear spin interactions is lost. We explored the relationship between enhanced sensitivity and loss of information as a function of the product , where is the span of the anisotropic lineshape and is the pulse spacing. For a lineshape dominated by the nuclear shielding anisotropy, we found that the minimum uncertainty in the tensor values is obtained using values in the range and for and , respectively. For an anisotropic secondorder quadrupolar central transition lineshape under magicangle spinning (MAS), the optimum range of was found. Additionally, we show how the Twodimensional One Pulse (TOP) like processing approach can be used to eliminate the cumbersome sideband pattern lineshape and recover a more familiar lineshape that is easily analyzed with conventional lineshape simulation algorithms.

On the paradoxical relation between the melting temperature and forbidden energy gap of nanoparticles
View Description Hide DescriptionWe comment on the paradox that seems to exist about a correlation between the sizedependent melting temperature and the forbidden energy gap of nanoparticles. By analyzing the reported expressions for the melting temperature and the band gap of nanoparticles, we conclude that there exists a relation between these two physical quantities. However, the variations of these two quantities with size for semiconductors are different from that of metals.

Twophoton resonances in femtosecond timeresolved fourwave mixing spectroscopy: carotene
View Description Hide DescriptionFemtosecondtimeresolved pumpdegenerate fourwave mixing (pumpDFWM) spectroscopy has been used to study the ultrafast dynamics of carotene involving several electronic and vibrational states. An initial pump pulse, resonant with the to transition, excites the molecular system and a DFWM process, resonant with the to transition, is used to probe the relaxation pathways. The transient shows a peculiar decay behavior, which is due to the contributions of resonantDFWM signal of the excited state, nonresonant DFWM signal of the ground state and vibrational hot state, and the twophotonresonantDFWM signal of the ground state. We have used a kinetic model including all the signal contributions to successfully fit the transient. The time constants extracted are in very good agreement with the known values for carotene. For comparison, a twopulse pumpprobe experiment was performed measuring the transient absorption at the wavelength of the DFWMexperiment.

Mesoscale spatial distribution of electron spins studied by timeresolved smallangle and ultrasmallangle neutron scattering with dynamic nuclear polarization: A case of 2,2,6,6tetramethylpiperidine 1oxyl (TEMPO) doped in highdensity polyethylene
View Description Hide DescriptionWe carried out timeresolved smallangle neutron scattering (SANS) and ultrasmallangle neutron scattering (USANS) studies of dynamically polarized highdensity polyethylene (HDPE) doped with 2,2,6,6tetramethylpiperidine 1oxyl (TEMPO) persistent free radicals. We observed a remarkable enhancement of the scattering intensity shortly after a switching of microwave frequency from positive (negative) to negative (positive) dynamic nuclear polarization (DNP). The enhancement was found to be due to spatially heterogeneous protonspin polarization generated as a result of heterogeneously distributed TEMPO in the HDPE sample. The spatial fluctuation of the polarization ranged up to the lengthscale of . This result strongly suggests that the TEMPO free radicals are localized more in nonfibrils but less in fibrils of HDPE. In this way, we propose that the timeresolved DNPSANS and DNPUSANS be general techniques to determine mesoscale spatial distribution of electron spins in dielectric materials.