Volume 140, Issue 13, 07 April 2014
Index of content:

We investigate the origin and physical effects of “dynamic structural disorder” (DSD) in supported nanoscale catalysts. DSD refers to the intrinsic fluctuating, inhomogeneous structure of such nanoscale systems. In contrast to bulk materials, nanoscale systems exhibit substantial fluctuations in structure, charge, temperature, and other quantities, as well as large surface effects. The DSD is driven largely by the stochastic librational motion of the center of mass and fluxional bonding at the nanoparticle surface due to thermal coupling with the substrate. Our approach for calculating and understanding DSD is based on a combination of realtime density functional theory/molecular dynamics simulations, transient coupledoscillator models, and statistical mechanics. This approach treats thermal and dynamic effects over multiple timescales, and includes bondstretching and bending vibrations, and transient tethering to the substrate at longer ps timescales. Potential effects on the catalytic properties of these clusters are briefly explored. Model calculations of moleculecluster interactions and molecular dissociation reaction paths are presented in which the reactant molecules are adsorbed on the surface of dynamically sampled clusters. This model suggests that DSD can affect both the prefactors and distribution of energy barriers in reaction rates, and thus can significantly affect catalytic activity at the nanoscale.
 COMMUNICATIONS


Communication: Nucleation of quantized vortex rings in ^{4}He nanodroplets
View Description Hide DescriptionWhereas most of the phenomena associated with superfluidity have been observed in finitesize helium systems, the nucleation of quantized vortices has proven elusive. Here we show using timedependent density functional simulations that the solvation of a Ba^{+} ion created by photoionization of neutral Ba at the surface of a ^{4}He nanodroplet leads to the nucleation of a quantized ring vortex. The vortex is nucleated on a 10 ps timescale at the equator of a solidlike solvation structure that forms around the Ba^{+} ion. The process is expected to be quite general and very efficient under standard experimental conditions.

 ARTICLES


Theoretical Methods and Algorithms

Charge transfer in strongly correlated systems: An exact diagonalization approach to model Hamiltonians
View Description Hide DescriptionWe study charge transfer in bridged di and triruthenium complexes from a theoretical and computational point of view. Ab initio computations are interpreted from the perspective of a simple empirical Hamiltonian, a chemically specific MottHubbard model of the complexes' π electron systems. This Hamiltonian is coupled to classical harmonic oscillators mimicking a polarizable dielectric environment. The model can be solved without further approximations in a valence bond picture using the method of exact diagonalization and permits the computation of charge transfer reaction rates in the framework of Marcus' theory. In comparison to the exact solution, the HartreeFock mean field theory overestimates both the activation barrier and the magnitude of chargetransfer excitations significantly. For triruthenium complexes, we are able to directly access the interruthenium antiferromagnetic coupling strengths.

Efficiency analysis of diffusion on Tfractals in the sense of random walks
View Description Hide DescriptionEfficiently controlling the diffusion process is crucial in the study of diffusion problem in complex systems. In the sense of random walks with a single trap, mean trapping time (MTT) and mean diffusing time (MDT) are good measures of trapping efficiency and diffusion efficiency, respectively. They both vary with the location of the node. In this paper, we analyze the effects of node's location on trapping efficiency and diffusion efficiency of Tfractals measured by MTT and MDT. First, we provide methods to calculate the MTT for any target node and the MDT for any source node of Tfractals. The methods can also be used to calculate the mean firstpassage time between any pair of nodes. Then, using the MTT and the MDT as the measure of trapping efficiency and diffusion efficiency, respectively, we compare the trapping efficiency and diffusion efficiency among all nodes of Tfractal and find the best (or worst) trapping sites and the best (or worst) diffusing sites. Our results show that the hub node of Tfractal is the best trapping site, but it is also the worst diffusing site; and that the three boundary nodes are the worst trapping sites, but they are also the best diffusing sites. Comparing the maximum of MTT and MDT with their minimums, we find that the maximum of MTT is almost 6 times of the minimum of MTT and the maximum of MDT is almost equal to the minimum for MDT. Thus, the location of target node has large effect on the trapping efficiency, but the location of source node almost has no effect on diffusion efficiency. We also simulate random walks on Tfractals, whose results are consistent with the derived results.

Nuclear spin circular dichroism
View Description Hide DescriptionRecent years have witnessed a growing interest in magnetooptic spectroscopy techniques that use nuclear magnetization as the source of the magnetic field. Here we present a formulation of magnetic circular dichroism (CD) due to magnetically polarized nuclei, nuclear spininduced CD (NSCD), in molecules. The NSCD ellipticity and nuclear spininduced optical rotation (NSOR) angle correspond to the real and imaginary parts, respectively, of (complex) quadratic response functions involving the dynamic secondorder interaction of the electron system with the linearly polarized light beam, as well as the static magnetic hyperfine interaction. Using the complex polarization propagator framework, NSCD and NSOR signals are obtained at frequencies in the vicinity of optical excitations. HartreeFock and densityfunctional theory calculations on relatively small model systems, ethene, benzene, and 1,4benzoquinone, demonstrate the feasibility of the method for obtaining relatively strong nuclear spininduced ellipticity and optical rotation signals. Comparison of the proton and carbon13 signals of ethanol reveals that these resonant phenomena facilitate chemical resolution between nonequivalent nuclei in magnetooptic spectra.

A multiscale variational approach to the kinetics of viscous classical liquids: The coarsegrained mean field approximation
View Description Hide DescriptionA closed kinetic equation for the singleparticle density of a viscous simple liquid is derived using a variational method for the Liouville equation and a coarsegrained meanfield (CGMF) ansatz. The CGMF ansatz is based on the notion that during the characteristic time of deformation a given particle interacts with many others so that it experiences an average interaction. A trial function for the Nparticle probability density is constructed using a multiscale perturbation method and the CGMF ansatz is applied to it. The multiscale perturbation scheme is based on the ratio of the average nearestneighbor atom distance to the total size of the assembly. A constraint on the initial condition is discovered which guarantees that the kinetic equation is massconserving and closed in the singleparticle density. The kinetic equation has much of the character of the Vlasov equation except that true viscous, and not Landau, damping is accounted for. The theory captures condensation kinetics and takes much of the character of the GrossPitaevskii equation in the weakgradient shortrange force limit.

Exploring the vibrational fingerprint of the electronic excitation energy via molecular dynamics
View Description Hide DescriptionA Fourierbased method is presented to relate changes of the molecular structure during a molecular dynamics simulation with fluctuations in the electronic excitation energy. The method implies sampling of the ground state potential energy surface. Subsequently, the power spectrum of the velocities is compared with the power spectrum of the excitation energy computed using timedependent density functional theory. Peaks in both spectra are compared, and motions exhibiting a linear or quadratic behavior can be distinguished. The quadratically active motions are mainly responsible for the changes in the excitation energy and hence cause shifts between the dynamic and static values of the spectral property. Moreover, information about the potential energy surface of various excited states can be obtained. The procedure is illustrated with three case studies. The first electronic excitation is explored in detail and dominant vibrational motions responsible for changes in the excitation energy are identified for ethylene, biphenyl, and hexamethylbenzene. The proposed method is also extended to other lowenergy excitations. Finally, the vibrational fingerprint of the excitation energy of a more complex molecule, in particular the azo dye ethyl orange in a water environment, is analyzed.

Reduced quantum dynamics with arbitrary bath spectral densities: Hierarchical equations of motion based on several different bath decomposition schemes
View Description Hide DescriptionWe investigated applications of the hierarchical equation of motion (HEOM) method to perform high order perturbation calculations of reduced quantum dynamics for a harmonic bath with arbitrary spectral densities. Three different schemes are used to decompose the bath spectral density into analytical forms that are suitable to the HEOM treatment: (1) The multiple Lorentzian mode model that can be obtained by numerically fitting the model spectral density. (2) The combined Debye and oscillatory Debye modes model that can be constructed by fitting the corresponding classical bath correlation function. (3) A new method that uses undamped harmonic oscillator modes explicitly in the HEOM formalism. Methods to extract systembath correlations were investigated for the above bath decomposition schemes. We also show that HEOM in the undamped harmonic oscillator modes can give detailed information on the partial Wigner transform of the total density operator. Theoretical analysis and numerical simulations of the spinBoson dynamics and the absorption line shape of molecular dimers show that the HEOM formalism for high order perturbations can serve as an important tool in studying the quantum dissipative dynamics in the intermediate coupling regime.

A quantitative quantumchemical analysis tool for the distribution of mechanical force in molecules
View Description Hide DescriptionThe promising field of mechanochemistry suffers from a general lack of understanding of the distribution and propagation of force in a stretched molecule, which limits its applicability up to the present day. In this article, we introduce the JEDI (Judgement of Energy DIstribution) analysis, which is the first quantum chemical method that provides a quantitative understanding of the distribution of mechanical stress energy among all degrees of freedom in a molecule. The method is carried out on the basis of static or dynamic calculations under the influence of an external force and makes use of a Hessian matrix in redundant internal coordinates (bond lengths, bond angles, and dihedral angles), so that all relevant degrees of freedom of a molecule are included and mechanochemical processes can be interpreted in a chemically intuitive way. The JEDI method is characterized by its modest computational effort, with the calculation of the Hessian being the ratedetermining step, and delivers, except for the harmonic approximation, exact ab initio results. We apply the JEDI analysis to several example molecules in both static quantum chemical calculations and BornOppenheimer Molecular Dynamics simulations in which molecules are subject to an external force, thus studying not only the distribution and the propagation of strain in mechanically deformed systems, but also gaining valuable insights into the mechanochemically induced isomerization of trans3,4dimethylcyclobutene to trans,trans2,4hexadiene. The JEDI analysis can potentially be used in the discussion of sonochemical reactions, molecular motors, mechanophores, and photoswitches as well as in the development of molecular force probes.

Excited states with internally contracted multireference coupledcluster linear response theory
View Description Hide DescriptionIn this paper, the linear response (LR) theory for the variant of internally contracted multireference coupled cluster (icMRCC) theory described by Hanauer and Köhn [J. Chem. Phys.134, 204211 (2011)] has been formulated and implemented for the computation of the excitation energies relative to a ground state of pronounced multireference character. We find that straightforward application of the linearresponse formalism to the timeaveraged icMRCC Lagrangian leads to unphysical secondorder poles. However, the coupling matrix elements that cause this behavior are shown to be negligible whenever the internally contracted approximation as such is justified. Hence, for the numerical implementation of the method, we adopt a TammDancofftype approximation and neglect these couplings. This approximation is also consistent with an equationofmotion based derivation, which neglects these couplings right from the start. We have implemented the linearresponse approach in the icMRCC singlesanddoubles framework and applied our method to calculate excitation energies for a number of molecules ranging from CH2 to pbenzyne and conjugated polyenes (up to octatetraene). The computed excitation energies are found to be very accurate, even for the notoriously difficult case of doubly excited states. The icMRCCLR theory is also applicable to systems with openshell groundstate wavefunctions and is by construction not biased towards a particular reference determinant. We have also compared the linearresponse approach to the computation of energy differences by direct statespecific icMRCC calculations. We finally compare to MkMRCCLR theory for which spurious roots have been reported [T.C. Jagau and J. Gauss, J. Chem. Phys.137, 044116 (2012)], being due to the use of sufficiency conditions to solve the MkMRCC equations. No such problem is present in icMRCCLR theory.

Selfconsistent field theory based molecular dynamics with linear systemsize scaling
View Description Hide DescriptionWe present an improved fieldtheoretic approach to the grandcanonical potential suitable for linear scaling molecular dynamics simulations using forces from selfconsistent electronic structure calculations. It is based on an exact decomposition of the grand canonical potential for independent fermions and does neither rely on the ability to localize the orbitals nor that the Hamilton operator is wellconditioned. Hence, this scheme enables highly accurate allelectron linear scaling calculations even for metallic systems. The inherent energy drift of BornOppenheimer molecular dynamics simulations, arising from an incomplete convergence of the selfconsistent field cycle, is circumvented by means of a properly modified Langevin equation. The predictive power of the present approach is illustrated using the example of liquid methane under extreme conditions.

Brownian dynamics without Green's functions
View Description Hide DescriptionWe develop a Fluctuating Immersed Boundary (FIB) method for performing Brownian dynamics simulations of confined particle suspensions. Unlike traditional methods which employ analytical Green's functions for Stokes flow in the confined geometry, the FIB method uses a fluctuating finitevolume Stokes solver to generate the action of the response functions “on the fly.” Importantly, we demonstrate that both the deterministic terms necessary to capture the hydrodynamic interactions among the suspended particles, as well as the stochastic terms necessary to generate the hydrodynamically correlated Brownian motion, can be generated by solving the steady Stokes equations numerically only once per time step. This is accomplished by including a stochastic contribution to the stress tensor in the fluid equations consistent with fluctuating hydrodynamics. We develop novel temporal integrators that account for the multiplicative nature of the noise in the equations of Brownian dynamics and the strong dependence of the mobility on the configuration for confined systems. Notably, we propose a random finite difference approach to approximating the stochastic drift proportional to the divergence of the configurationdependent mobility matrix. Through comparisons with analytical and existing computational results, we numerically demonstrate the ability of the FIB method to accurately capture both the static (equilibrium) and dynamic properties of interacting particles in flow.

Computation of the free energy due to electron density fluctuation of a solute in solution: A QM/MM method with perturbation approach combined with a theory of solutions
View Description Hide DescriptionWe developed a perturbation approach to compute solvation free energy Δμ within the framework of QM (quantum mechanical)/MM (molecular mechanical) method combined with a theory of energy representation (QM/MMER). The energy shift η of the whole system due to the electronic polarization of the solute is evaluated using the secondorder perturbation theory (PT2), where the electric field formed by surrounding solvent molecules is treated as the perturbation to the electronic Hamiltonian of the isolated solute. The point of our approach is that the energy shift η, thus obtained, is to be adopted for a novel energy coordinate of the distribution functions which serve as fundamental variables in the free energy functional developed in our previous work. The most timeconsuming part in the QM/MMER simulation can be, thus, avoided without serious loss of accuracy. For our benchmark set of molecules, it is demonstrated that the PT2 approach coupled with QM/MMER gives hydration free energies in excellent agreements with those given by the conventional method utilizing the KohnSham SCF procedure except for a few molecules in the benchmark set. A variant of the approach is also proposed to deal with such difficulties associated with the problematic systems. The present approach is also advantageous to parallel implementations. We examined the parallel efficiency of our PT2 code on multicore processors and found that the speedup increases almost linearly with respect to the number of cores. Thus, it was demonstrated that QM/MMER coupled with PT2 deserves practical applications to systems of interest.

Roaming dynamics in ionmolecule reactions: Phase space reaction pathways and geometrical interpretation
View Description Hide DescriptionA model Hamiltonian for the reaction + H, parametrized to exhibit either early or late inner transition states, is employed to investigate the dynamical characteristics of the roaming mechanism. Tight/loose transition states and conventional/roaming reaction pathways are identified in terms of timeinvariant objects in phase space. These are dividing surfaces associated with normally hyperbolic invariant manifolds (NHIMs). For systems with two degrees of freedom NHIMS are unstable periodic orbits which, in conjunction with their stable and unstable manifolds, unambiguously define the (locally) nonrecrossing dividing surfaces assumed in statistical theories of reaction rates. By constructing periodic orbit continuation/bifurcation diagrams for two values of the potential function parameter corresponding to late and early transition states, respectively, and using the total energy as another parameter, we dynamically assign different regions of phase space to reactants and products as well as to conventional and roaming reaction pathways. The classical dynamics of the system are investigated by uniformly sampling trajectory initial conditions on the dividing surfaces. Trajectories are classified into four different categories: direct reactive and nonreactive trajectories, which lead to the formation of molecular and radical products respectively, and roaming reactive and nonreactive orbiting trajectories, which represent alternative pathways to form molecular and radical products. By analysing gap time distributions at several energies, we demonstrate that the phase space structure of the roaming region, which is strongly influenced by nonlinear resonances between the two degrees of freedom, results in nonexponential (nonstatistical) decay.

Conservative and dissipative force field for simulation of coarsegrained alkane molecules: A bottomup approach
View Description Hide DescriptionWe apply operational procedures available in the literature to the construction of coarsegrained conservative and friction forces for use in dissipative particle dynamics (DPD) simulations. The full procedure rely on a bottomup approach: large molecular dynamics trajectories of npentane and ndecane modeled with an anisotropic united atom model serve as input for the force field generation. As a consequence, the coarsegrained model is expected to reproduce at least semiquantitatively structural and dynamical properties of the underlying atomistic model. Two different coarsegraining levels are studied, corresponding to five and ten carbon atoms per DPD bead. The influence of the coarsegraining level on the generated force fields contributions, namely, the conservative and the friction part, is discussed. It is shown that the coarsegrained model of npentane correctly reproduces selfdiffusion and viscosity coefficients of real npentane, while the fully coarsegrained model for ndecane at ambient temperature overpredicts diffusion by a factor of 2. However, when the npentane coarsegrained model is used as a building block for larger molecule (e.g., ndecane as a two blobs model), a much better agreement with experimental data is obtained, suggesting that the force field constructed is transferable to large macromolecular systems.

Atoms, Molecules, and Clusters

Rotational quenching of H_{2}O by He: Mixed quantum/classical theory and comparison with quantum results
View Description Hide DescriptionThe mixed quantum/classical theory (MQCT) formulated in the spacefixed reference frame is used to compute quenching cross sections of several rotationally excited states of water molecule by impact of He atom in a broad range of collision energies, and is tested against the fullquantum calculations on the same potential energy surface. In current implementation of MQCT method, there are two major sources of errors: one affects results at energies below 10 cm^{−1}, while the other shows up at energies above 500 cm^{−1}. Namely, when the collision energy E is below the statetostate transition energy ΔE the MQCT method becomes less accurate due to its intrinsic classical approximation, although employment of the averagevelocity principle (scaling of collision energy in order to satisfy microscopic reversibility) helps dramatically. At higher energies, MQCT is expected to be accurate but in current implementation, in order to make calculations computationally affordable, we had to cut off the basis set size. This can be avoided by using a more efficient bodyfixed formulation of MQCT. Overall, the errors of MQCT method are within 20% of the fullquantum results almost everywhere through fourordersofmagnitude range of collision energies, except near resonances, where the errors are somewhat larger.

Spectroscopic characterization of the complex between water and the simplest Criegee intermediate CH_{2}OO
View Description Hide DescriptionThe hydrogenbonded complex between water and the simplest Criegee intermediate CH2OO was detected by Fouriertransform microwave spectroscopy under a jetcooled condition. Both atype and btype rotational transitions were observed for H2O–CH2OO and D2O–CH2OO. The determined rotational constants enable us to conclude that the complex has an almost planar ring structure with the terminal oxygen atom of CH2OO being a strong proton acceptor.

Crossing the dividing surface of transition state theory. I. Underlying symmetries and motion coordination in multidimensional systems
View Description Hide DescriptionThe objective of the present paper is to show the existence of motion coordination among a bundle of trajectories crossing a saddle point region in the forward direction. For zero total angular momentum, no matter how complicated the anharmonic part of the potential energy function, classical dynamics in the vicinity of a transition state is constrained by symmetry properties. Trajectories that all cross the plane R = R * at time t = 0 (where R * denotes the position of the saddle point) with the same positive translational momentum can be partitioned into two sets, denoted “gerade” and “ungerade,” which coordinate their motions. Both sets have very close average equations of motion. This coordination improves tremendously rapidly as the number of degrees of freedom increases. This property can be traced back to the existence of timedependent constants of the motion.

Crossing the dividing surface of transition state theory. II. Recrossing times for the atom–diatom interaction
View Description Hide DescriptionWe consider a triatomic system with zero total angular momentum and demonstrate that, no matter how complicated the anharmonic part of the potential energy function, classical dynamics in the vicinity of a saddle point is constrained by symmetry properties. At short times and at not too high energies, recrossing dynamics is largely determined by elementary local structural parameters and thus can be described in configuration space only. Conditions for recrossing are given in the form of inequalities involving structural parameters only. Explicit expressions for recrossing times, valid for microcanonical ensembles, are shown to obey interesting regularities. In a forward reaction, when the transition state is nonlinear and tight enough, onefourth of the trajectories are expected to recross the plane R = R * (where R * denotes the position of the saddle point) within a short time. Another fourth of them are expected to have previously recrossed at a short negative time, i.e., close to the saddle point. These trajectories do not contribute to the reaction rate. The reactive trajectories that obey the transition state model are to be found in the remaining half. However, no conclusion can be derived for them, except that if recrossings occur, then they must either take place in the distant future or already have taken place in the remote past, i.e., far away from the saddle point. Trajectories that all cross the plane R = R * at time t = 0, with the same positive translational momentum can be partitioned into two sets, distinguished by the parity of their initial conditions; both sets have the same average equation of motion up to and including terms cubic in time. Coordination is excellent in the vicinity of the saddle point but fades out at long (positive or negative) times, i.e., far away from the transition state.

Triplet state photochemistry and the threestate crossing of acetophenone within timedependent densityfunctional theory
View Description Hide DescriptionEven though timedependent densityfunctional theory (TDDFT) works generally well for describing excited states energies and properties in the FranckCondon region, it can dramatically fail in predicting photochemistry, notably when electronic state crossings occur. Here, we assess the ability of TDDFT to describe the photochemistry of an important class of triplet sensitizers, namely, aromatic ketones. We take acetophenone as a test molecule, for which accurate ab initio results exist in the literature. Triplet acetophenone is generated thanks to an exotic threestate crossing involving one singlet and two triplets states (i.e., a simultaneous intersystem crossing and triplet conical intersection), thus being a stringent test for approximate TDDFT. We show that most exchangecorrelation functionals can only give a semiqualitative picture of the overall photochemistry, in which the threestate crossing is rather represented as a triplet conical intersection separated from the intersystem crossing. The best result overall is given by the double hybrid functional mPW2PLYP, which is even able to reproduce quantitatively the threestate crossing region. We rationalize this results by noting that double hybrid functionals include a larger portion of double excitation character to the excited states.

Simulations of the dissociation of small helium clusters with ab initio molecular dynamics in electronically excited states
View Description Hide DescriptionThe dynamics resulting from electronic excitations of helium clusters were explored using ab initio molecular dynamics. The simulations were performed with configuration interaction singles and adiabatic classical dynamics coupled to a statefollowing algorithm. 100 different configurations of He7 were excited into the 2s and 2p manifold for a total of 2800 trajectories. While the most common outcome (90%) was complete fragmentation to 6 ground state atoms and 1 excited state atom, 3% of trajectories yielded bound, , and <0.5% yielded an excited helium trimer. The nature of the dynamics, kinetic energy release, and connections to experiments are discussed.
