Volume 138, Issue 21, 07 June 2013
 ARTICLES

 Theoretical Methods and Algorithms

Power functional theory for Brownian dynamics
View Description Hide DescriptionClassical density functional theory (DFT) provides an exact variational framework for determining the equilibrium properties of inhomogeneous fluids. We report a generalization of DFT to treat the nonequilibrium dynamics of classical manybody systems subject to Brownian dynamics. Our approach is based upon a dynamical functional consisting of reversible free energy changes and irreversible power dissipation. Minimization of this “free power” functional with respect to the microscopic onebody current yields a closed equation of motion. In the equilibrium limit the theory recovers the standard variational principle of DFT. The adiabatic dynamical density functional theory is obtained when approximating the power dissipation functional by that of an ideal gas. Approximations to the excess (over ideal) power dissipation yield numerically tractable equations of motion beyond the adiabatic approximation, opening the door to the systematic study of systems far from equilibrium.

A constrained reduceddimensionality search algorithm to follow chemical reactions on potential energy surfaces
View Description Hide DescriptionA constrained reduceddimensionality algorithm can be used to efficiently locate transition states and products in reactions involving conformational changes. The search path (SP) is constructed stepwise from linear combinations of a small set of manually chosen internal coordinates, namely the predictors. The majority of the internal coordinates, the correctors, are optimized at every step of the SP to minimize the total energy of the system so that the path becomes a minimum energy path connecting products and transition states with the reactants. Problems arise when the set of predictors needs to include weak coordinates, for example, dihedral angles, as well as strong ones such as bond distances. Two principal constraining methods for the weak coordinates are proposed to mend this situation: static and dynamic constraints. Dynamic constraints are automatically activated and revoked depending on the state of the weak coordinates among the predictors, while static ones require preset control factors and act permanently. All these methods enable the successful application (4 reactions are presented involving cyclohexane, alanine dipeptide, trimethylsulfonium chloride, and azafulvene) of the reduced dimensionality method to reactions where the reaction path covers large conformational changes in addition to the formation/breaking of chemical bonds. Dynamic constraints are found to be the most efficient method as they require neither additional information about the geometry of the transition state nor fine tuning of control parameters.

Local hardness equalization and the principle of maximum hardness
View Description Hide DescriptionThe chemical potential, hardness, and hyperhardnesses equalization principles are used to show that the leading term associated with charge transfer in the total interaction energy among the fragments in which a molecule is divided is directly proportional to minus the hardness of the molecule in its ground state, as established by the principle of maximum hardness. The additional terms in the interaction energy, associated with the changes in the external potential of the fragments, provide explanation for deviations between the point of maximum hardness and the point of minimum energy. It is also found that the dual descriptor plays a very important role in hardness equalization.

Electron dynamics of interatomic Coulombic decay in quantum dots induced by a laser field
View Description Hide DescriptionIn this paper we investigated the dynamics of an electron in the presence of a timedependent laser field in a model potential for a twolevel singleelectron semiconductor quantum dot (QD) that is capable of undergoing interatomic Coulombic decay (ICD) together with an electron bound to a neighboring QD. We demonstrate that ICD can be initiated by coupling the twolevel QD to either a continuous or a pulsed moderate to strong laser and we obtain the total and partial decay widths of the resonance excited state in agreement with that from the solely decay of the resonance [A. Bande, K. Gokhberg, and L. S. Cederbaum, J. Chem. Phys.135, 144112 (Year: 2011)10.1063/1.3646205]. A detailed discussion of the effects of direct ionization by the laser in single or multiphoton process as well as Rabi oscillations is furthermore presented.

Constantforce approach to discontinuous potentials
View Description Hide DescriptionAiming to approach the thermodynamical properties of hardcore systems by standard molecular dynamics simulation, we propose setting a repulsive constantforce for overlapping particles. That is, the discontinuity of the pair potential is replaced by a linear function with a large negative slope. Hence, the corecore repulsion, usually modeled with a power function of distance, yields a large force as soon as the cores slightly overlap. This leads to a quasihardcore behavior. The idea is tested for a triangle potential of short range. The results obtained by replica exchange molecular dynamics for several repulsive forces are contrasted with the ones obtained for the discontinuous potential and by means of replica exchange Monte Carlo. We found remarkable agreements for the vaporliquid coexistence densities as well as for the surface tension.

Correlated fourcomponent EPR gtensors for doublet molecules
View Description Hide DescriptionThe first correlated ab initio fourcomponent calculations of electron paramagnetic resonance (EPR) gtensors for doublet radicals are reported. We have implemented a firstorder degenerate perturbation theory approach based on the fourcomponent DiracCoulomb Hamiltonian and fully relativistic configuration interaction wave functions in the DIRAC program package. We find that the correlation effects on the gtensors can be sufficiently well described with manageable basis sets of triplezeta quality and manageable configuration spaces. The new fully relativistic EPR module in DIRAC should be useful for benchmarking density functional theory approaches, however, with future optimization of the code we believe it will also be useful for applications.

The atomic orbitals of the topological atom
View Description Hide DescriptionThe effective atomic orbitals have been realized in the framework of Bader's atoms in molecules theory for a general wavefunction. This formalism can be used to retrieve from any type of calculation a proper set of orthonormalized numerical atomic orbitals, with occupation numbers that sum up to the respective Quantum Theory of Atoms in Molecules (QTAIM) atomic populations. Experience shows that only a limited number of effective atomic orbitals exhibit significant occupation numbers. These correspond to atomic hybrids that closely resemble the core and valence shells of the atom. The occupation numbers of the remaining effective orbitals are almost negligible, except for atoms with hypervalent character. In addition, the molecular orbitals of a calculation can be exactly expressed as a linear combination of this orthonormalized set of numerical atomic orbitals, and the Mulliken population analysis carried out on this basis set exactly reproduces the original QTAIM atomic populations of the atoms. Approximate expansion of the molecular orbitals over a much reduced set of orthogonal atomic basis functions can also be accomplished to a very good accuracy with a singular value decomposition procedure.

Evaluation of coarsegrained mapping schemes for polysaccharide chains in cellulose
View Description Hide DescriptionA fundamental understanding of the intermolecular forces that bind polysaccharide chains together in cellulose is crucial for designing efficient methods to overcome the recalcitrance of lignocellulosic biomass to hydrolysis. Because the characteristic time and length scales for the degradation of cellulose by enzymatic hydrolysis or chemical pretreatment span orders of magnitude, it is important to closely integrate the molecular models used at each scale so that, ultimately, one may switch seamlessly between quantum, atomistic, and coarsegrained descriptions of the system. As a step towards that goal, four multiscale coarsegrained models for polysaccharide chains in a celluloseIα microfiber are considered. Using the force matching method, effective coarsegrained forces are derived from allatom trajectories. Performance of the coarsegrained models is evaluated by comparing the intrachain radial distribution functions with those obtained using the allatom reference data. The allatom simulation reveals a double peak in the radial distribution function for sites within each glucose residue that arises from the distinct conformations sampled by the primary alcohol group in the glucose residues. The threesite and foursite coarsegrained models have sufficient degrees of freedom to predict this double peak while the onesite and twosite models do not. This is the first time that coarsegrained models have been shown to reproduce such subtle, yet important, molecular features in a polysaccharide chain. The relative orientations between glucose residues along the polysaccharide chain are evaluated and it is found that the foursite coarsegrained model is best at reproducing the glucoseglucose conformations observed in the allatom simulation. The success of the foursite coarsegrained model underscores the importance of decoupling the pyranose ring from the oxygen atom in the glycosidic bond when developing allatom to coarsegrained mapping schemes for polysaccharides.

Pathbreaking schemes for nonequilibrium free energy calculations
View Description Hide DescriptionWe propose a pathbreaking route to the enhancement of unidirectional nonequilibrium simulations for the calculation of free energy differences via Jarzynski's equality [C. Jarzynski, Phys. Rev. Lett.78, 2690 (Year: 1997)]10.1103/PhysRevLett.78.2690. One of the most important limitations of unidirectional nonequilibrium simulations is the amount of realizations necessary to reach suitable convergence of the work exponential average featuring the Jarzynski's relationship. In this respect, a significant improvement of the performances could be obtained by finding a way of stopping trajectories with negligible contribution to the work exponential average, before their normal end. This is achieved using pathbreaking schemes which are essentially based on periodic checks of the work dissipated during the pulling trajectories. Such schemes can be based either on breaking trajectories whose dissipated work exceeds a given threshold or on breaking trajectories with a probability increasing with the dissipated work. In both cases, the computer time needed to carry out a series of nonequilibrium trajectories is reduced up to a factor ranging from 2 to more than 10, at least for the processes under consideration in the present study. The efficiency depends on several aspects, such as the type of process, the number of checkpoints along the pathway and the pulling rate as well. The method is illustrated through radically different processes, i.e., the helixcoil transition of decaalanine and the pulling of the distance between two methane molecules in water solution.

Determining the bending modulus of a lipid membrane by simulating buckling
View Description Hide DescriptionThe force needed to buckle a thin elastic surface is proportional to its bending rigidity. This fact suggests using a buckling setup to measure the bending modulus of lipid membranes. Extending the work of Noguchi [Phys. Rev. E83, 061919 (Year: 2011)10.1103/PhysRevE.83.061919], we systematically derive highly accurate analytical expressions for the forces along and perpendicular to the buckle, and we elucidate some of their counterintuitive properties using the framework of a surface stress tensor. Furthermore, we estimate the corrections to buckling forces due to thermal fluctuations and find them significant only for stresses along the ridges. We then apply this buckling protocol to four different lipid membrane models, which widely differ in their level of resolution and the treatment of solvent, and show that in all cases buckling is a reliable and accurate means for measuring their rigidity. Finally, we show that monitoring both stresses and energies during a simulation offers additional insights into the thermodynamics of curvature elasticity and permits one to predict the bending rigidity for a range of temperatures around the actual simulation temperature.

Pathintegral simulations with fermionic and bosonic reservoirs: Transport and dissipation in molecular electronic junctions
View Description Hide DescriptionWe expand iterative numerically exact influence functional pathintegral tools and present a method capable of following the nonequilibrium time evolution of subsystems coupled to multiple bosonic and fermionic reservoirs simultaneously. Using this method, we study the realtime dynamics of charge transfer and vibrational mode excitation in an electron conducting molecular junction. We focus on nonequilibrium vibrational effects, particularly, the development of vibrational instability in a currentrectifying junction. Our simulations are performed by assuming large molecular vibrational anharmonicity (or low temperature). This allows us to truncate the molecular vibrational mode to include only a twostate system. Exact numerical results are compared to perturbative Markovian master equation calculations demonstrating an excellent agreement in the weak electronphonon coupling regime. Significant deviations take place only at strong coupling. Our simulations allow us to quantify the contribution of different transport mechanisms, coherent dynamics, and inelastic transport, in the overall charge current. This is done by studying two model variants: The first admits inelastic electron transmission only, while the second one allows for both coherent and incoherent pathways.
 Advanced Experimental Techniques

High resolution spatial map imaging of a gaseous target
View Description Hide DescriptionElectrostatic ion imaging with the velocity map imaging mode is a widely used method in atomic and molecular physics and physical chemistry. In contrast, the spatial map imaging (SMI) mode has received very little attention, despite the fact that it has been proposed earlier [A. T. J. B. Eppink and D. H. Parker, Rev. Sci. Instrum.68, 3477 (Year: 1997)]10.1063/1.1148310. Here, we present a detailed parametric characterization of SMI both by simulation and experiment. One, two and threedimensional imaging modes are described. The influence of different parameters on the imaging process is described by means of a Taylor expansion. To experimentally quantify elements of the Taylor expansion and to infer the spatial resolution of our spectrometer, photoionization of toluene with a focused laser beam has been carried out. A spatial resolution of better than 4 μm out of a focal volume of several mm in diameter has been achieved. Our results will be useful for applications of SMI to the characterization of laser beams, the overlap control of multiple particle or light beams, and the determination of absolute collision cross sections.

Optimization of nonlinear optical localization using electromagnetic surface fields (NOLES) imaging
View Description Hide DescriptionThe use of plasmon amplification of nonlinear optical wavemixing signals to generate optical images in which the position of the scattering point source can be determined with nanometer accuracy is described. Solid gold nanosphere dimers were used as a model system for the nonlinear medium, which converted the Ti:sapphire fundamental to its second harmonic frequency. Matching the fundamental wave energy to the localized surface plasmon resonance of the electromagnetically coupled nanospheres was critical for achieving the high localization accuracy. Our technique, named Nonlinear Optical Localization using Electromagnetic Surface fields (NOLES) imaging, routinely yielded nonlinear optical images with 1nm localization accuracy at rates ≥2 fps and can also be used as a photoswitching localization contrast method. This high level of accuracy in pinpointing the signal point source position exceeded that made possible using conventional diffractionlimited farfield methods by 160×. The NOLES technique, with its high temporal resolution and spatial accuracy that far surpass the performance typical of fluorescencebased imaging, will be relevant for imaging dynamic chemical, biological, and material environments.
 Atoms, Molecules, and Clusters

Measuring the internal energies of species emitted from hypervelocity nanoprojectile impacts on surfaces using recalibrated benzylpyridinium probe ions
View Description Hide DescriptionWe present herein a framework for measuring the internal energy distributions of vibrationally excited molecular ions emitted from hypervelocity nanoprojectile impacts on organic surfaces. The experimental portion of this framework is based on the measurement of lifetime distributions of “thermometer” benzylpyridinium ions dissociated within a time of flight mass spectrometer. The theoretical component comprises reevaluation of the fragmentation energetics of benzylpyridinium ions at the coupledcluster singles and doubles with perturbative triples level. Vibrational frequencies for the ground and transition states of select molecules are reported, allowing for a full description of vibrational excitations of these molecules via Rice–Ramsperger–Kassel–Marcus unimolecular fragmentation theory. Ultimately, this approach is used to evaluate the internal energy distributions from the measured lifetime distributions. The average internal energies of benzylpyridinium ions measured from 440 keV Au 400 +4 impacts are found to be relatively low (∼0.24 eV/atom) when compared with keV atomic bombardment of surfaces (1–2 eV/atom).

Sulfur 1s near edge xray absorption fine structure spectroscopy of thiophenic and aromatic thioether compounds
View Description Hide DescriptionThiophenic compounds are major constituents of fossil fuels and pose problems for fuel refinement. The quantification and speciation of these compounds is of great interest in different areas such as biology, fossil fuels studies, geology, and archaeology. Sulfur 1s NearEdge Xray Absorption Fine Structure (NEXAFS) spectroscopy has emerged as a qualitative and quantitative method for sulfur speciation. A firm understanding of the sulfur 1s NEXAFS spectra of organosulfur species is required for these analytical studies. To support this development, the sulfur 1s NEXAFS spectra of simple thiols and thioethers were previously examined, and are now extended to studies of thiophenic and aromatic thioether compounds, in the gas and condensed phases. Highresolution spectra have been further analyzed with the aid of Improved Virtual Orbital (IVO) and Δ(selfconsistent field) ab initio calculations. Experimental sulfur 1s NEXAFS spectra show fine features predicted by calculation, and the combination of experiment and calculation has been used to improve the assignment of spectroscopic features important for the speciation and quantification of sulfur compounds. Systematic differences between gas and condensed phases are also explored; these differences suggest a significant role for conformational effects in the NEXAFS spectra of condensed species.

A spherecutsplice crossover for the evolution of cluster structures
View Description Hide DescriptionA new crossover operator is proposed to evolve the structures of the atomic clusters. It uses a sphere rather than a plane to cut and splice the parent structures. The child cluster is constructed by the atoms of one parent which lie inside the sphere, and the atoms of the other parent which lie outside the sphere. It can reliably produce reasonable offspring and preserve the good schemata in parent structures, avoiding the drawbacks of the classical planecutsplice crossover in the global searching ability and the local optimization speed. Results of LennardJones clusters (30 ⩽ N ⩽ 500) show that at the same settings the genetic algorithm with the spherecutsplice crossover exhibits better performance than the one with the planecutsplice crossover. The average number of local minimizations needed to find the global minima and the average number of energy evaluation of each local minimization in the sphere scheme is 0.8075 and 0.8386 of that in the plane scheme, respectively. The mean speedup ratio for the entire testing clusters reaches 1.8207. Moreover, the sphere scheme is particularly suitable for large clusters and the mean speedup ratio reaches 2.3520 for the clusters with 110 ⩽ N ⩽ 500. The comparison with other successful methods in previous studies also demonstrates its good performance. Finally, a further analysis is presented on the statistical features of the cutting sphere and a modified strategy that reduces the probability of using tiny and large spheres exhibits better global search.

Oxidation and reduction of sizeselected subnanometer Pd clusters on Al_{2}O_{3} surface
View Description Hide DescriptionIn this paper, we investigate uniformly dispersed sizeselected Pd n clusters (n = 4, 10, and 17) on alumina supports. We study the changes of clustered Pd atoms under oxidizing and reducing (O2 and CO, respectively) conditions in situ using ambient pressure XPS. The behavior of Pd in the clusters is quite different from that of Pd foil under the same conditions. For all Pd clusters, we observe only one Pd peak. The binding energy of this Pd 3d peak is ∼11.4 eV higher than that of metallic Pd species and changes slightly in CO and O2 environments. On the Pd foil however many different Pd species coexist on the surface and change their oxidation states under different conditions. We find that the Pd atoms in direct contact with Al2O3 differ in oxidation state from the surface Pd atoms in a foil under reaction conditions. Compared to previous literature, we find that Pd 3d peak positions are greatly influenced by the different types of Al2O3 supports due to the combination of both initial and final state effects.

Cross sections for elastic scattering of electrons by CF_{3}Cl, CF_{2}Cl_{2}, and CFCl_{3}
View Description Hide DescriptionDifferential, integral, and momentum transfer cross sections have been determined for the elastic scattering of electrons from the molecules CF3Cl, CF2Cl2, and CFCl3.With the help of a crossed electron beam–molecular beam apparatus using the relative flow technique, the ratios of the elastic differential cross sections (DCSs) of CF3Cl, CF2Cl2, and CFCl3 to those of He were measured in the energy region from 1.5 to 100 eV and at scattering angles in the range 15° to 130°. From those ratios, the absolute DCSs were determined by utilizing the known DCS of He. For CF3Cl and CF2Cl2, at the common energies of measurement, we find generally good agreement with the results from the independent experiments of Mann and Linder [J. Phys. B25, 1621 (Year: 1992)10.1088/09534075/25/7/030; Mann and Linder J. Phys. B25, 1633 (Year: 1992)10.1088/09534075/25/7/031]. In addition, as a result of progressively substituting a Clatom, undulations in the angular distributions have been found to vary in a largely systematic manner in going from CF4 to CF3Cl to CF2Cl2 to CFCl3 and to CCl4. These observed features suggest that the elastic scattering process is, in an independently additive manner, dominated by the atomicCl atoms of the molecules. The present independent atom method calculation typically supports the experimental evidence, within the screened additivity rule formulation, for each species and for energies greater than about 10–20 eV. Integral elastic and momentum transfer cross sections were also derived from the measured DCSs, and are compared to the other available theoretical and experimental results. The elastic integral cross sections are also evaluated as a part of their contribution to the total cross section.

Dynamics study of the OH + NH_{3} hydrogen abstraction reaction using QCT calculations based on an analytical potential energy surface
View Description Hide DescriptionTo understand the reactivity and mechanism of the OH + NH3 → H2O + NH2 gasphase reaction, which evolves through wells in the entrance and exit channels, a detailed dynamics study was carried out using quasiclassical trajectory calculations. The calculations were performed on an analytical potential energy surface (PES) recently developed by our group, PES2012 [MongePalacios et al. J. Chem. Phys.138, 084305 (Year: 2013)]10.1063/1.4792719. Most of the available energy appeared as H2O product vibrational energy (54%), reproducing the only experimental evidence, while only the 21% of this energy appeared as NH2 coproduct vibrational energy. Both products appeared with cold and broad rotational distributions. The excitation function (constant collision energy in the range 1.0–14.0 kcal mol−1) increases smoothly with energy, contrasting with the only theoretical information (reduceddimensional quantum scattering calculations based on a simplified PES), which presented a peak at low collision energies, related to quantized states. Analysis of the individual reactive trajectories showed that different mechanisms operate depending on the collision energy. Thus, while at high energies (Ecoll ≥ 6 kcal mol−1) all trajectories are direct, at low energies about 20%–30% of trajectories are indirect, i.e., with the mediation of a trapping complex, mainly in the product well. Finally, the effect of the zeropoint energy constraint on the dynamics properties was analyzed.

Atomic orientation following predissociation of the C ^{3}Π_{ g } Rydberg state of molecular oxygen
View Description Hide Description(2 + 1) resonance enhanced multiphoton ionization in combination with timeofflight mass spectroscopy (TOFMS) has been used to detect both the O(3P) and O(1D) fragments produced as a result of predissociation of the C 3Π g (v = 0) and (v = 1) Rydberg states of O2, accessed via twophoton absorption from the ground X state. In particular, TOF profiles have been recorded at various fixed twophoton absorption wavelengths within the two bands, with circular polarized probe laser light used to probe the angular momentum orientation of these photofragments. All photofragments are found to display coherent orientation resulting from interference between two possible twophoton absorption pathways. The measured orientation is affected by rotational depolarization due to the long lifetime of the excited C state; once this effect is accounted for the orientation is found to be nearly constant over all dissociation wavelengths. The origin of the coherent orientation is attributed to twophoton absorption to different spinorbit components of the C state.