Volume 134, Issue 14, 14 April 2011

The ordering kinetics of directed assembly of cylinderforming diblock copolymers is investigated by cell dynamics simulation of the timedependent Ginzburg–Landau theory. The directing field, mimicking chemically or topologically patternedsurfaces, is composed of a rectangular array of potential wells which are attractive to the minority blocks. The period of the templating fields is commensurate with the hexagonal lattice of the block copolymer domains. The ordering kinetics is described by the time evolution of the defect concentration, which reveals that the rectangular field of [1 m] for a given density multiplication has the best directing effect, and the reversed case of [m 1] has the worst. Compared with a hexagonal directing field, the rectangular field provides a better directing efficiency for a fixed high density multiplication. The difference of the directing effect can be understood by analyzing the ordering mechanisms in the two types of directing fields. The study reveals that the rectangular pattern is an alternative candidate to direct block copolymer assembly toward largescale ordered domains.
 COMMUNICATIONS


Communication: Suppression of sintering of sizeselected Pd clusters under realistic reaction conditions for catalysis
View Description Hide DescriptionThe stability of model catalysts based on sizeselected Pd clusters supported on graphitesurfaces has been explored under realistic conditions for catalyticoxidation of methane at mild temperatures. The experimental results show that aggregated films of nanoparticles are highly unstable, but clusters pinned to the surface in the submonolayer coverage regime are much more stable against sintering. The degree of sintering of the pinned clusters, which does occur, proceeds by the release of clusters from their pinning sites. The suppression of sintering depends on the cluster deposition energy with respect to the pinning threshold.

 ARTICLES

 Theoretical Methods and Algorithms

Dynamic kinetic energy potential for orbitalfree density functional theory
View Description Hide DescriptionA dynamic kinetic energy potential (DKEP) is developed for timedependent orbitalfree (TDOF) density functiontheory applications. This potential is constructed to affect only the dynamical (ω ≠ 0) response of an orbitalfree electronic system. It aims at making the orbitalfree simulation respond in the same way as that of a noninteracting homogenous electron gas (HEG), as required by a correct kinetic energy, therefore enabling extension of the success of orbitalfreedensity functional theory in the static case (e.g., for embedding and description of processes in bulk materials) to dynamic processes. The potential is constructed by expansions of terms, each of which necessitates only simple time evolution (concurrent with the TDOF evolution) and a spatial convolution at each timestep. With 14 such terms a good fit is obtained to the response of the HEG at a large range of frequencies, wavevectors, and densities. The method is demonstrated for simple jellium spheres, approximating Na_{9} ^{+} and Na_{65} ^{+} clusters. It is applicable both to small and large (even ultralarge) excitations and the results converge (i.e., do not blow up) as a function of time. An extension to iterative frequencyresolved extraction is briefly outlined, as well as possibly numerically simpler expansions. The approach could also be extended to fit, instead of the HEG susceptibility, either an experimental susceptibility or a theoretically derived one for a nonHEG system. The DKEP potential should be a powerful tool for embedding a dynamical system described by a more accurate method (such as timedependent density functional theory, TDDFT) in a large background described by TDOF with a DKEP potential. The type of expansions used and envisioned should be useful for other approaches, such as memory functionals in TDDFT. Finally, an appendix details the formal connection between TDOF and TDDFT.

Simultaneoustrajectory surface hopping: A parameterfree algorithm for implementing decoherence in nonadiabatic dynamics
View Description Hide DescriptionIn this paper, we introduce a trajectorybased nonadiabaticdynamics algorithm which aims to correct the wellknown overcoherence problem in Tully's popular fewestswitches surface hopping algorithm. Our simultaneoustrajectory surface hopping algorithm propagates a separate classical trajectory on each energetically accessible adiabatic surface. The divergence of these trajectories generates decoherence, which collapses the particle wavefunction onto a single adiabatic state. Decoherence is implemented without the need for any parameters, either empirical or adjustable. We apply our algorithm to several model problems and find a significant improvement over the traditional algorithm.

Computation of methodologyindependent singleion solvation properties from molecular simulations. III. Correction terms for the solvation free energies, enthalpies, entropies, heat capacities, volumes, compressibilities, and expansivities of solvated ions
View Description Hide DescriptionThe raw singleion solvation free energies computed from atomistic (explicitsolvent) simulations are extremely sensitive to the boundary conditions (finite or periodic system, system or box size) and treatment of electrostatic interactions (Coulombic, latticesum, or cutoffbased) used during these simulations. However, as shown by Kastenholz and Hünenberger [J. Chem. Phys.124, 224501 (2006)]10.1529/biophysj.106.083667, correction terms can be derived for the effects of: (A) an incorrect solvent polarization around the ion and an incomplete or/and inexact interaction of the ion with the polarized solvent due to the use of an approximate (not strictly Coulombic) electrostatic scheme; (B) the finitesize or artificial periodicity of the simulated system; (C) an improper summation scheme to evaluate the potential at the ion site, and the possible presence of a polarized air–liquid interface or of a constraint of vanishing average electrostatic potential in the simulated system; and (D) an inaccurate dielectric permittivity of the employed solvent model. Comparison with standard experimental data also requires the inclusion of appropriate cavityformation and standardstate correction terms. In the present study, this correction scheme is extended by: (i) providing simple approximate analytical expressions (empiricallyfitted) for the correction terms that were evaluated numerically in the above scheme (continuumelectrostatics calculations); (ii) providing correction terms for derivative thermodynamic singleion solvation properties (and corresponding partial molar variables in solution), namely, the enthalpy,entropy, isobaric heat capacity, volume, isothermal compressibility, and isobaric expansivity (including appropriate standardstate correction terms). The ability of the correction scheme to produce methodologyindependent singleion solvation free energies based on atomistic simulations is tested in the case of Na^{+} hydration, and the nature and magnitude of the correction terms for derivative thermodynamic properties is assessed numerically.

Computation of methodologyindependent singleion solvation properties from molecular simulations. IV. Optimized LennardJones interaction parameter sets for the alkali and halide ions in water
View Description Hide DescriptionThe raw singleion solvation free energies computed from atomistic (explicitsolvent) simulations are extremely sensitive to the boundary conditions and treatment of electrostatic interactions used during these simulations. However, as shown recently [M. A. Kastenholz and P. H. Hünenberger, J. Chem. Phys.124, 224501 (2006)10.1529/biophysj.106.083667; M. M. Reif and P. H. Hünenberger, J. Chem. Phys.134, 144103 (2010)], the application of appropriate correction terms permits to obtain methodologyindependent results. The corrected values are then exclusively characteristic of the underlying molecular model including in particular the ion–solvent van der Waals interaction parameters, determining the effective ion size and the magnitude of its dispersion interactions. In the present study, the comparison of calculated (corrected) hydration free energies with experimental data (along with the consideration of ionic polarizabilities) is used to calibrate new sets of ionsolvent van der Waals (LennardJones) interaction parameters for the alkali (Li^{+}, Na^{+}, K^{+}, Rb^{+}, Cs^{+}) and halide (F^{−}, Cl^{−}, Br^{−}, I^{−}) ions along with either the SPC or the SPC/E water models. The experimental dataset is defined by conventional singleion hydration free energies [Tissandier et al., J. Phys. Chem. A102, 7787 (1998)10.1021/jp982638r; Fawcett, J. Phys. Chem. B103, 11181] along with three plausible choices for the (experimentally elusive) value of the absolute (intrinsic) hydration free energy of the proton, namely, , −1075 or −1050 kJ mol^{−1}, resulting in three sets L, M, and H for the SPC water model and three sets L_{ E }, M_{ E }, and H_{ E } for the SPC/E water model (alternative sets can easily be interpolated to intermediate values). The residual sensitivity of the calculated (corrected) hydration free energies on the volumepressure boundary conditions and on the effective ionic radius entering into the calculation of the correction terms is also evaluated and found to be very limited. Ultimately, it is expected that comparison with other experimental ionic properties (e.g., derivative singleion solvation properties, as well as data concerning ionic crystals, melts, solutions at finite concentrations, or nonaqueous solutions) will permit to validate one specific set and thus, the associated value (atomistic consistency assumption). Preliminary results (firstpeak positions in the ionwater radial distribution functions, partial molar volumes of ionic salts in water, and structural properties of ionic crystals) support a value of close to −1100 kJ·mol^{−1}.

Canard explosion of limit cycles in templator models of selfreplication mechanisms
View Description Hide DescriptionTemplators are differential equation models for selfreplicating chemical systems. Beutel and PeacockLópez [J. Chem. Phys.126, 125104 (2007)]10.1063/1.2716396 have numerically analyzed a model for a crosscatalytic selfreplicating system and found two cases of canard explosion, that is, a substantial change of amplitude of a limit cycle over a very short parameter interval. We show how the model can be reduced to a twodimensional system and how canard theory for slow–fast equations can be applied to yield analytic information about the canard explosion. In particular, simple expressions for the parameter value where the canard explosion occurs are obtained. The connection to mixedmode oscillations also observed in the model is briefly discussed.

Magnetic circular dichroism in realtime timedependent density functional theory
View Description Hide DescriptionWe apply the adiabatic timedependent density functional theory to magnetic circular dichroism(MCD) spectra using the realspace, realtime computational method. The standard formulas for the MCD response and its and terms are derived from the observables in the timedependent wave function. We find realtime method is well suited for calculating the overall spectrum, particularly at higher excitation energies where individual excited states are numerous and overlapping. The MCDsum rules are derived and intepreted in the realtime formalism; we find that they are very useful for normalization purposes and assessing the accuracy of the theory. The method is applied to MCD spectrum of C_{60} using the adiabatic energy functional from the local density approximation. The theory correctly predicts the signs of the and terms for the lowest allowed excitations. However, the magnitudes of the terms only show qualitative agreement with experiment.

Mixed quantumclassical theory for the collisional energy transfer and the rovibrational energy flow: Application to ozone stabilization
View Description Hide DescriptionA mixed quantumclassical approach to the description of collisional energy transfer is proposed in which the vibrational motion of an energized molecule is treated quantum mechanically using wave packets, while the collisional motion of the molecule and quencher and the rotational motion of the molecule are treated using classical trajectories. This accounts rigorously for quantization of vibrational states, zeropoint energy, scattering resonances, and permutation symmetry of identical atoms, while advantage is taken of the classical scattering regime. Energy is exchanged between vibrational, rotational, and translational degrees of freedom while the total energy is conserved. Application of this method to stabilization of the van der Waals states in ozone is presented. Examples of mixed quantumclassical trajectories are discussed, including an interesting example of supercollision. When combined with an efficient grid mapping procedure and the reduced dimensionality approximation, the method becomes very affordable computationally.

Solution reaction space Hamiltonian based on an electrostatic potential representation of solvent dynamics
View Description Hide DescriptionQuantum chemical solvation models usually rely on the equilibrium solvation condition and is thus not immediately applicable to the study of nonequilibrium solvation dynamics, particularly those associated with chemical reactions. Here we address this problem by considering an effective Hamiltonian for solutionphase reactions based on an electrostatic potential (ESP) representation of solvent dynamics. In this approach a general ESP field of solvent is employed as collective solvent coordinate, and an effective Hamiltonian is constructed by treating both solute geometry and solvent ESP as dynamical variables. A harmonic bath is then attached onto the ESP variables in order to account for the stochastic nature of solvent dynamics. As an illustration we apply the above method to the proton transfer of a substituted phenol–amine complex in a polar solvent. The effective Hamiltonian is constructed by means of the reference interaction site model selfconsistent field method (i.e., a type of quantum chemical solvation model), and a mixed quantum/classical simulation is performed in the space of solute geometry and solvent ESP. The results suggest that important dynamical features of proton transfer in solution can be captured by the present approach, including spontaneous fluctuations of solvent ESP that drives the proton from reactant to product potential wells.

Polymer reversal rate calculated via locally scaled diffusion map
View Description Hide DescriptionA recent study on the dynamics of polymer reversal inside a nanopore by Huang and Makarov [J. Chem. Phys.128, 114903 (2008)]10.1063/1.2890006 demonstrated that the reaction rate cannot be reproduced by projecting the dynamics onto a single empirical reaction coordinate, a result suggesting the dynamics of this system cannot be correctly described by using a single collective coordinate. To further investigate this possibility we have applied our recently developed multiscale framework, locally scaled diffusion map (LSDMap), to obtain collective reaction coordinates for this system. Using a single diffusion coordinate, we obtain a reversal rate via Kramers expression that is in good agreement with the exact rate obtained from the simulations. Our mathematically rigorous approach accounts for the local heterogeneity of molecular configuration space in constructing a diffusion map, from which collective coordinates emerge. We believe this approach can be applied in general to characterize complex macromolecular dynamics by providing an accurate definition of the collective coordinates associated with processes at different time scales.

Higher order two and threebody dispersion coefficients for alkali isoelectronic sequences by a variationally stable procedure
View Description Hide DescriptionUsing the variationally stable method of Gao and Starace, and the simple ground statewave function of the valence electron previously suggested by Patil and Tang, the multipolar polarizabilities of Li, Na, K, Rb, Cs, Be^{+}, Mg^{+}, Ca^{+}, Sr^{+}, Ba^{+}, the twobody dispersion coefficients of homonuclear and heteronuclear interactions from C _{6} to C _{40}, as well as the threebody dispersion coefficients Z(L _{1}, L _{2}, L _{3}) (up to L _{ i } = 5), are investigated. Higher order van der Waals dispersion coefficients C _{ n } (n > 24) and Z(L _{1}, L _{2}, L _{3}) (L _{ i } > 3) are reported for the first time. Comparisons with previous calculations found in the literature show that this approach is capable of yielding precise and fast convergent values for higher order dispersion coefficients for alkalimetal atoms.

The Vliegenthart–Lekkerkerker relation: The case of the Miefluids
View Description Hide DescriptionThe Vliegenthart–Lekkerkerker relation for the second virial coefficient value at the critical temperature found in the work of Vliegenthart and Lekkerkerker [J. Chem. Phys.112, 5364 (2000)]10.1063/1.481106 is discussed in connection with the scale invariant meanfield approach proposed by Kulinskii and Bulavin [J. Chem. Phys.133, 134101 (2010)]10.1063/1.3457943. We study the case of the Mieclass potentials, which is widely used in simulations of the phase equilibrium of the fluids. It is shown that due to the homogeneity property of the Mieclass potentials it is possible to connect the loci of the fluids with these model potentials in different dimensions.

Decomposition of unitary matrices for finding quantum circuits: Application to molecular Hamiltonians
View Description Hide DescriptionConstructing appropriate unitary matrix operators for new quantum algorithms and finding the minimum cost gate sequences for the implementation of these unitary operators is of fundamental importance in the field of quantum information and quantum computation. Evolution of quantum circuits faces two major challenges: complex and huge search space and the high costs of simulating quantum circuits on classical computers. Here, we use the group leaders optimization algorithm to decompose a given unitary matrix into a properminimum cost quantum gate sequence. We test the method on the known decompositions of Toffoli gate, the amplification step of the Grover search algorithm, the quantum Fourier transform, and the sender part of the quantum teleportation. Using this procedure, we present the circuit designs for the simulation of the unitary propagators of the Hamiltonians for the hydrogen and the water molecules. The approach is general and can be applied to generate the sequence of quantum gates for larger molecular systems.

Gatecontrolled current and inelastic electron tunneling spectrum of benzene: A selfconsistent study
View Description Hide DescriptionWe use density functional theory based nonequilibrium Green's function to selfconsistently study the current through the 1,4benzenedithiol (BDT). The elastic and inelastic tunnelingproperties through this Au–BDT–Au molecular junction are simulated, respectively. For the elastictunneling case, it is found that the current through the tilted molecule can be modulated effectively by the external gate field, which is perpendicular to the phenyl ring. The gate voltage amplification comes from the modulation of the interaction between the electrodes and the molecules in the junctions. For the inelastic case, the electron tunneling scattered by the molecular vibrational modes is considered within the selfconsistent Born approximation scheme, and the inelastic electron tunneling spectrum is calculated.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

He–ThO(^{1}Σ^{+}) interactions at low temperatures: Elastic and inelastic collisions, transport properties, and complex formation in cold ^{4}He gas
View Description Hide DescriptionWe present an ab initio study of cold ^{4}He + ThO(^{1}Σ^{+}) collisions based on an accurate potential energy surface (PES) evaluated by the coupled cluster method with single, double, and noniterative triple excitations using an extended basis set augmented by bond functions. Variational calculations of rovibrational energy levels show that the ^{4}He–ThO van der Waals complex has a binding energy of 10.9 cm^{−1} in its ground J = 0 rotational state. The calculated energy levels are used to obtain the temperature dependence of the chemical equilibrium constant for the formation of the He–ThO complex. We find that complex formation is thermodynamically favored at temperatures below 1 K and predict the maximum abundance of free groundstate ThO(v = 0, j = 0) molecules between 2 and 3 K. The calculated cross sections for momentum transfer in elastic He + ThO collisions display a rich resonance structure below 5 cm^{−1} and decline monotonically above this collisionenergy. The cross sections for rotational relaxation accompanied by momentum transfer decline abruptly to zero at low collisionenergies (<0.1 cm^{−1}). We find that Stark relaxation in He + ThO collisions can be enhanced by applying an external dc electric field of less than 100 kV/cm. Finally, we present calculations of thermally averaged diffusion cross sections for ThO in He gas, and find these to be insensitive to small variations of the PES at temperatures above 1 K.

Excitation of electronic states in tetrahydrofuran by electron impact
View Description Hide DescriptionWe report on differential and integral cross section measurements for the electron impact excitation of the three lowest lying Rydberg bands of electronic states in tetrahydrofuran. The energy range of the present experiments was 15–50 eV with the angular range of the differential cross section measurements being 15°–90°. The important effects of the longrange target dipole moment and the target dipole polarizability, on the scattering dynamics of this system, are evident from the present results. To the best of our knowledge, there are no other theoretical or experimental data against which we can compare the cross section results from this study.

Laser adiabatic manipulation of the bond length of diatomic molecules with a single chirped pulse
View Description Hide DescriptionWe propose and test numerically a scheme for controlling the bond distance in a diatomic molecule that requires the use of a single chirped pulse. The laser prepares a superposition state of both nuclear and electronic degrees of freedom, where the main character of the electronic wave function is that of an excited dissociative state. The main limitation of the scheme is the need of ultra broadband pulses, where the bandwidth must be of the order of the dissociation energy to achieve large bond elongations. The scheme can be used to deform the bond during the laser excitation to an arbitrary large and constant value, or to allow slow timedependent bond elongations. Additionally, the scheme can be used to prepare highly excited vibrational wave packets in the ground potential after the pulse is switched off, at the expense of losing some population that dissociates. These wave packets are initially localized at the outer well of the potential, at energiescontrollable by the excitation process.

A vacuumultraviolet laser pulsed field ionizationphotoelectron study of sulfur monoxide (SO) and its cation (SO^{+})
View Description Hide DescriptionVacuum ultraviolet (VUV) laser pulsed field ionizationphotoelectron (PFIPE) spectroscopy has been applied to the study of the sulfur monoxide radical (SO) prepared by using a supersonically cooled radical beam source based on the 193 nm excimer laserphotodissociation of SO_{2}. The vibronic VUVPFIPE bands for the photoionization transitions SO^{+}(X ^{2}Π_{1/2}; v ^{+} = 0) ← SO(X ^{3}Σ^{−}; v = 0); and SO^{+}(^{2}Π_{3/2}; v ^{+} = 0) ← SO(X ^{3}Σ^{−}; v = 0) have been recorded. On the basis of the semiempirical simulation of rotational branch contours observed in these PFIPE bands, we have obtained highly precise ionization energies (IEs) of 83 034.2 ± 1.7 cm^{−1} (10.2949 ± 0.0002 eV) and 83 400.4 ± 1.7 cm^{−1} (10.3403 ± 0.0002 eV) for the formation of SO^{+}(X ^{2}Π_{1/2}; v ^{+} = 0) and SO^{+}(^{2}Π_{3/2}; v ^{+} = 0), respectively. The present VUVPFIPE measurement has enabled the direct determination of the spinorbit coupling constant (A _{0}) for SO^{+}(X ^{2}Π_{1/2,3/2}) to be 365.36 ± 0.12 cm^{−1}. We have also performed highlevel ab initio quantum chemical calculations at the coupledcluster level up to full quadruple excitations and complete basis set (CBS) extrapolation. The zeropoint vibrational energy correction, the corevalence electronic correction, the spinorbit coupling, and the highlevel correction are included in the calculation. The IE[SO^{+}(X ^{2}Π_{1/2,3/2})] and A _{0} predictions thus obtained are found to be in remarkable agreement with the experimental determinations.

A systematic study of neutral and charged 3dmetal trioxides and tetraoxides
View Description Hide DescriptionUsing density functional theory with generalized gradient approximation, we have performed a systematic study of the structure and properties of neutral and charged trioxides (MO_{3}) and tetraoxides (MO_{4}) of the 3dmetal atoms. The results of our calculations revealed a number of interesting features when moving along the 3dmetal series. (1) Geometrical configurations of the lowest total energy states of neutral and charged trioxides and tetraoxides are composed of oxo and/or peroxo groups, except for CuO_{3} ^{−} and ZnO_{3} ^{−} which possess a superoxo group, CuO_{4} ^{+} and ZnO_{4} ^{+} which possess two superoxo groups, and CuO_{3} ^{+}, ZnO_{3} ^{+}, and ZnO_{4} ^{−} which possess an ozonide group. While peroxo groups are found in the early and late transition metals, all oxygen atoms bind chemically to the metal atom in the middle of the series. (2) Attachment or detachment of an electron to/from an oxide often leads to a change in the geometry. In some cases, two dissociatively attached oxygen atoms combine and form a peroxo group or a peroxo group transforms into a superoxo group and vice versa. (3) The adiabatic electron affinity of as many as two trioxides (VO_{3} and CoO_{3}) and four tetraoxides (TiO_{4}, CrO_{4}, MnO_{4}, and FeO_{4}) are larger than the electron affinity of halogen atoms. All these oxides are hence superhalogens although only VO_{3} and MnO_{4} satisfy the general superhalogen formula.

Spectroscopic observation and structure of CS_{2} dimer
View Description Hide DescriptionInfrared spectra of the CS_{2} dimer are observed in the region of the CS_{2} ν_{3} fundamental band (∼1535 cm^{−1}) using a tunable diode laserspectrometer. The weakly bound complex is formed in a pulsed supersonic slitjet expansion of a dilute gas mixture of carbon disulfide in helium. Contrary to the planar slippedparallel geometry previously observed for (CO_{2})_{2}, (N_{2}O)_{2}, and (OCS)_{2}, the CS_{2} dimer exhibits a crossshaped structure with D _{2d } symmetry. Two bands were observed and analyzed: the fundamental (C–S asymmetric stretch) and a combination involving this mode plus an intermolecular vibration. In both cases, the rotational structure corresponds to a perpendicular (ΔK = ±1) band of a symmetric rotor molecule. The intermolecular center of mass separation (C–C distance) is determined to be 3.539(7) Å. Thanks to symmetry, this is the only parameter required to characterize the structure, if the monomer geometry is assumed to remain unchanged in the dimer. From the band centers of the fundamental and combination band an intermolecular frequency of 10.96 cm^{−1} is obtained, which we assign as the torsional bending mode. This constitutes the first high resolution spectroscopic investigation of CS_{2} dimer.