Volume 139, Issue 23, 21 December 2013

Designing optimal structure favorable to diffusion and effectively controlling the trapping process are crucial in the study of trapping problem—random walks with a single trap. In this paper, we study the trapping problem occurring on unweighted and weighted networks, respectively. The networks under consideration display the striking scalefree, smallworld, and modular properties, as observed in diverse realworld systems. For binary networks, we concentrate on three cases of trapping problems with the trap located at a peripheral node, a neighbor of the root with the least connectivity, and a farthest node, respectively. For weighted networks with edge weights controlled by a parameter, we also study three trapping problems, in which the trap is placed separately at the root, a neighbor of the root with the least degree, and a farthest node. For all the trapping problems, we obtain the analytical formulas for the average trapping time (ATT) measuring the efficiency of the trapping process, as well as the leading scaling of ATT. We show that for all the trapping problems in the binary networks with a trap located at different nodes, the dominating scalings of ATT reach the possible minimum scalings, implying that the networks have optimal structure that is advantageous to efficient trapping. Furthermore, we show that for trapping in the weighted networks, the ATT is controlled by the weight parameter, through modifying which, the ATT can behave superlinearly, linearly, sublinearly, or logarithmically with the system size. This work could help improving the design of systems with efficient trapping process and offers new insight into control of trapping in complex systems.
 ARTICLES

 Theoretical Methods and Algorithms

Probing nonadiabatic conical intersections using absorption, spontaneous Raman, and femtosecond stimulated Raman spectroscopy
View Description Hide DescriptionWe present the timeframe calculated photoabsorption spectrum (ABS), spontaneous Raman excitation profile (REP), femtosecond stimulated Raman spectroscopy (FSRS) spectrum, and femtosecond stimulated Raman excitation profile (FSREP) results of a twomode and threemode, threeelectronicstates model Hamiltonians containing conical intersections (CIs) along its two upper diabatic electronic states, e 1 (dark) and e 2 (bright), with and without coupling (nonadiabatic dynamics) along an asymmetric mode. For every electronic state in each model, there is one coupling mode and the rest of the modes are symmetric tuning modes. The CI appears in the Hamiltonian as offdiagonal entries to the potential term that couple the two upper states, in the form of a linear function of the coupling mode. We show that: (a) the ABS, REP, and FSREP for Stokes and antiStokes lines contain similar information about the e 1 and e 2 vibrational bands, (b) the FSRS spectra feature narrow stationary peaks and broader moving peaks contributed by the different resonant components of the thirdorder polarization terms from perturbation theory, and (c) a relatively strong and narrow stationary band of the allowed first overtone of the asymmetric coupling mode is observed in the Stokes FSREP in the e 1 energy region with coupling to e 2.

Golden rule kinetics of transfer reactions in condensed phase: The microscopic model of electron transfer reactions in disordered solid matrices
View Description Hide DescriptionThe algorithm for a theoretical calculation of transfer reaction rates for light quantum particles (i.e., the electron and Hatom transfers) in nonpolar solid matrices is formulated and justified. The mechanism postulated involves a local mode (an either intra or intermolecular one) serving as a mediator which accomplishes the energy exchange between the reacting highfrequency quantum mode and the phonon modes belonging to the environment. This approach uses as a background the Fermi golden rule beyond the usually applied spinboson approximation. The dynamical treatment rests on the onedimensional version of the standard quantum relaxation equation for the reduced density matrix, which describes the frequency fluctuation spectrum for the local mode under consideration. The temperature dependence of a reaction rate is controlled by the dimensionless parameter ξ0 = ℏω0/k B T where ω0 is the frequency of the local mode and T is the temperature. The realization of the computational scheme is different for the high/intermediate (ξ0 < 1 − 3) and for low (ξ0 ≫ 1) temperature ranges. For the first (quasiclassical) kinetic regime, the Redfield approximation to the solution of the relaxation equation proved to be sufficient and efficient in practical applications. The study of the essentially quantummechanical lowtemperature kinetic regime in its asymptotic limit requires the implementation of the exact relaxation equation. The coherent mechanism providing a nonvanishing reaction rate has been revealed when T → 0. An accurate computational methodology for the crossover kinetic regime needs a further elaboration. The original model of the hopping mechanism for electronic conduction in photosensitive organic materials is considered, based on the above techniques. The electron transfer (ET) in active centers of such systems proceeds via local intra and intermolecular modes. The active modes, as a rule, operate beyond the kinetic regimes, which are usually postulated in the existing theories of the ET. Our alternative dynamic ET model for local modes immersed in the continuum harmonic medium is formulated for both classical and quantum regimes, and accounts explicitly for the mode/medium interaction. The kinetics of the energy exchange between the local ET subsystem and the surrounding environment essentially determine the total ET rate. The efficient computer code for rate computations is elaborated on. The computations are available for a wide range of system parameters, such as the temperature, external field, local mode frequency, and characteristics of mode/medium interaction. The relation of the present approach to the Marcus ET theory and to the quantumstatistical reaction rate theory [V. G. Levich and R. R. Dogonadze, Dokl. Akad. Nauk SSSR, Ser. Fiz. Khim.124, 213 (1959); J. Ulstrup, Charge Transfer in Condensed Media (Springer, Berlin, 1979); M. Bixon and J. Jortner, Adv. Chem. Phys.106, 35 (1999)] underlying it is discussed and illustrated by the results of computations for practically important target systems.

Geometric phase effects in lowenergy dynamics near conical intersections: A study of the multidimensional linear vibronic coupling model
View Description Hide DescriptionIn molecular systems containing conical intersections (CIs), a nontrivial geometric phase (GP) appears in the nuclear and electronic wave functions in the adiabatic representation. We study GP effects in nuclear dynamics of an Ndimensional linear vibronic coupling (LVC) model. The main impact of GP on lowenergy nuclear dynamics is reduction of population transfer between the local minima of the LVC lower energy surface. For the LVC model, we proposed an isometric coordinate transformation that confines nonadiabatic effects within a twodimensional subsystem interacting with an N − 2 dimensional environment. Since environmental modes do not couple electronic states, all GP effects originate from nuclear dynamics within the subsystem. We explored when the GP affects nuclear dynamics of the isolated subsystem, and how the subsystemenvironment interaction can interfere with GP effects. Comparing quantum dynamics with and without GP allowed us to devise simple rules to determine significance of the GP for nuclear dynamics in this model.

Adapting SAFTγ perturbation theory to sitebased molecular dynamics simulation. I. Homogeneous fluids
View Description Hide DescriptionIn this work, we aim to develop a version of the Statistical Associating Fluid Theory (SAFT)γ equation of state (EOS) that is compatible with unitedatom force fields, rather than experimental data. We rely on the accuracy of the force fields to provide the relation to experimental data. Although, our objective is a transferable theory of interfacial properties for soft and fused heteronuclear chains, we first clarify the details of the SAFTγ approach in terms of sitebased simulations for homogeneous fluids. We show that a direct comparison of Helmholtz free energy to molecular simulation, in the framework of a third order WeeksChandlerAndersen perturbation theory, leads to an EOS that takes force field parameters as input and reproduces simulation results for VaporLiquid Equilibria (VLE) calculations. For example, saturated liquid density and vapor pressure of nalkanes ranging from methane to dodecane deviate from those of the Transferable Potential for Phase Equilibria (TraPPE) force field by about 0.8% and 4%, respectively. Similar agreement between simulation and theory is obtained for critical properties and second virial coefficient. The EOS also reproduces simulation data of mixtures with about 5% deviation in bubble point pressure. Extension to inhomogeneous systems and unitedatom site types beyond those used in description of nalkanes will be addressed in succeeding papers.

Direct numerical simulations of rigid body dispersions. I. Mobility/friction tensors of assemblies of spheres
View Description Hide DescriptionAn improved formulation of the “Smoothed Profile” method is introduced to perform direct numerical simulations of arbitrary rigid body dispersions in a Newtonian host solvent. Previous implementations of the method were restricted to spherical particles, severely limiting the types of systems that could be studied. The validity of the method is carefully examined by computing the friction/mobility tensors for a wide variety of geometries and comparing them to reference values obtained from accurate solutions to the StokesEquation.

Random walks in unweighted and weighted modular scalefree networks with a perfect trap
View Description Hide DescriptionDesigning optimal structure favorable to diffusion and effectively controlling the trapping process are crucial in the study of trapping problem—random walks with a single trap. In this paper, we study the trapping problem occurring on unweighted and weighted networks, respectively. The networks under consideration display the striking scalefree, smallworld, and modular properties, as observed in diverse realworld systems. For binary networks, we concentrate on three cases of trapping problems with the trap located at a peripheral node, a neighbor of the root with the least connectivity, and a farthest node, respectively. For weighted networks with edge weights controlled by a parameter, we also study three trapping problems, in which the trap is placed separately at the root, a neighbor of the root with the least degree, and a farthest node. For all the trapping problems, we obtain the analytical formulas for the average trapping time (ATT) measuring the efficiency of the trapping process, as well as the leading scaling of ATT. We show that for all the trapping problems in the binary networks with a trap located at different nodes, the dominating scalings of ATT reach the possible minimum scalings, implying that the networks have optimal structure that is advantageous to efficient trapping. Furthermore, we show that for trapping in the weighted networks, the ATT is controlled by the weight parameter, through modifying which, the ATT can behave superlinearly, linearly, sublinearly, or logarithmically with the system size. This work could help improving the design of systems with efficient trapping process and offers new insight into control of trapping in complex systems.

A comprehensive analysis of moleculeintrinsic quasiatomic, bonding, and correlating orbitals. I. HartreeFock wave functions
View Description Hide DescriptionThrough a basissetindependent web of localizing orbitaltransformations, the electronic wave function of a molecule is expressed in terms of a set of orbitals that reveal the atomic structure and the bonding pattern of a molecule. The analysis is based on resolving the valence orbital space in terms of an internal space, which has minimal basis set dimensions, and an external space. In the internal space, oriented quasiatomic orbitals and splitlocalized molecular orbitals are determined by new, fast localization methods. The density matrix between the oriented quasiatomic orbitals as well as the locations of the splitlocalized orbitals exhibit atomic populations and interatomic bonding patterns. A correlationadapted quasiatomic basis is determined in the external orbital space. The general formulations are specified in detail for HartreeFock wave functions. Applications to specific molecules exemplify the general scheme.

Computing UV/vis spectra from the adiabatic and vertical FranckCondon schemes with the use of Cartesian and internal coordinates
View Description Hide DescriptionWe address the effects of using Cartesian or internal coordinates in the adiabatic FranckCondon (AFC) and vertical FranckCondon (VFC) approaches to electronic spectra. The adopted VFC approach is a simplified variant of the original approach [A. Hazra, H. H. Chang, and M. Nooijen, J. Chem. Phys.151, 2125 (2004)], as we omit any contribution from normal modes with imaginary frequency. For our test molecules ranging from ethylene to flavin compounds, VFC offers several advantages over AFC, especially by preserving the properties of the FC region and by avoiding complications arising from the crossing of excitedstate potential surfaces or from the failure of the harmonic approximation. The spectral quality for our target molecules is insensitive to the chosen approach. We also explore the effects of Duschinsky rotation and relate the need for internal coordinates to the absence of symmetry elements. When using Duschinsky rotation and treating larger systems without planar symmetry, internal coordinates are found to outperform Cartesian coordinates in the AFC spectral calculations.

The intrapair electron correlation in natural orbital functional theory
View Description Hide DescriptionA previously proposed [M. Piris, X. Lopez, F. Ruipérez, J. M. Matxain, and J. M. Ugalde, J. Chem. Phys.134, 164102 (2011)] formulation of the twoparticle cumulant, based on an orbitalpairing scheme, is extended here for including more than two natural orbitals. This new approximation is used to reconstruct the twoparticle reduced density matrix (2RDM) constrained to the D, Q, and G positivity necessary conditions of the Nrepresentable 2RDM. In this way, we have derived an extended version of the Piris natural orbital functional 5 (PNOF5e). An antisymmetrized product of strongly orthogonal geminals with the expansion coefficients explicitly expressed by the occupation numbers is also used to generate the PNOF5e. The theory is applied to the homolytic dissociation of selected diatomic molecules: H2, LiH, and Li2. The Bader's theory of atoms in molecules is used to analyze the electron density and the presence of nonnuclear maxima in the case of a set of light atomic clusters: Li2, , , and . The improvement of PNOF5e over PNOF5 was observed by visualizing the electron densities.

Automated fit of highdimensional potential energy surfaces using cluster analysis and interpolation over descriptors of chemical environment
View Description Hide DescriptionWe present a method for fitting highdimensional potential energy surfaces that is almost fully automated, can be applied to systems with various chemical compositions, and involves no particular choice of function form. We tested it on four systems: Ag20, Sn6 Pb 6, Si10, and Li8. The cost for energy evaluation is smaller than the cost of a density functional theory (DFT) energy evaluation by a factor of 1500 for Li8, and 60 000 for Ag20. We achieved intermediate accuracy (errors of 0.4 to 0.8 eV on atomization energies, or, 1% to 3% on cohesive energies) with rather small datasets (between 240 and 1400 configurations). We demonstrate that this accuracy is sufficient to correctly screen the configurations with lowest DFT energy, making this function potentially very useful in a hybrid global optimization strategy. We show that, as expected, the accuracy of the function improves with an increase in the size of the fitting dataset.

Exciton localizationdelocalization transition in an extended dendrimer
View Description Hide DescriptionExcitonmediated quantum state transfer between the periphery and the core of an extended dendrimer is investigated numerically. By mapping the dynamics onto that of a linear chain, it is shown that a localizationdelocalization transition arises for a critical value of the generation number G c ≈ 5. This transition originates in the quantum interferences experienced by the excitonic wave due to the multiple scatterings that arise each time the wave tunnels from one generation to another. These results suggest that only smallsize dendrimers could be used for designing an efficient quantum communication protocol.

Symmetrical windowing for quantum states in quasiclassical trajectory simulations: Application to electronically nonadiabatic processes
View Description Hide DescriptionA recently described symmetrical windowing methodology [S. J. Cotton and W. H. Miller, J. Phys. Chem. A117, 7190 (2013)] for quasiclassical trajectory simulations is applied here to the MeyerMiller [H.D. Meyer and W. H. Miller, J. Chem. Phys.70, 3214 (1979)] model for the electronic degrees of freedom in electronically nonadiabatic dynamics. Results generated using this classical approach are observed to be in very good agreement with accurate quantum mechanical results for a variety of test applications, including problems where coherence effects are significant such as the challenging asymmetric spinboson system.

Linearized Jastrowstyle fluctuations on spinprojected HartreeFock
View Description Hide DescriptionThe accurate and efficient description of strong electronic correlations remains an important objective in electronic structure theory. Projected HartreeFock theory, where symmetries of the Hamiltonian are deliberately broken and projectively restored, all with a meanfield computational scaling, shows considerable promise in this regard. However, the method is neither size extensive nor size consistent; in other words, the correlation energy per particle beyond brokensymmetry mean field vanishes in the thermodynamic limit, and the dissociation limit of a molecule is not the sum of the fragment energies. These two problems are closely related. Recently, Neuscamman [Phys. Rev. Lett.109, 203001 (2012)] has proposed a method to cure the lack of size consistency in the context of the antisymmetrized geminal power wave function (equivalent to numberprojected HartreeFockBogoliubov) by using a Jastrowtype correlator in Hilbert space. Here, we apply the basic idea in the context of projected HartreeFock theory, linearizing the correlator for computational simplicity but extending it to include spin fluctuations. Results are presented for the Hubbard Hamiltonian and for some simple molecular systems.

Finite domain simulations with adaptive boundaries: Accurate potentials and nonequilibrium movesets
View Description Hide DescriptionWe extend the theory of hybrid explicit/implicit solvent models to include an explicit domain that grows and shrinks in response to a solute's evolving configuration. The goal of this model is to provide an appropriate but not excessive amount of solvent detail, and the inclusion of an adjustable boundary provides a significant computational advantage for solutes that explore a range of configurations. In addition to the theoretical development, a successful implementation of this method requires (1) an efficient moveset that propagates the boundary as a new coordinate of the system, and (2) an accurate continuum solvent model with parameters that are transferable to an explicit domain of any size. We address these challenges and develop boundary updates using Monte Carlo moves biased by nonequilibrium paths. We obtain the desired level of accuracy using a “decoupling interface” that we have previously shown to remove boundary artifacts common to hybrid solvent models. Using an uncharged, coarsegrained solvent model, we then study the efficiency of nonequilibrium paths that a simulation takes by quantifying the dissipation. In the spirit of optimization, we study this quantity over a range of simulation parameters.

A transferable coarsegrained model for diphenylalanine: How to represent an environment driven conformational transition
View Description Hide DescriptionOne of the major challenges in the development of coarse grained (CG) simulation models that aim at biomolecular structure formation processes is the correct representation of an environmentdriven conformational change, for example, a folding/unfolding event upon interaction with an interface or upon aggregation. In the present study, we investigate this transferability challenge for a CG model using the example of diphenylalanine. This dipeptide displays a transition from a translike to a cislike conformation upon aggregation as well as upon transfer from bulk water to the cyclohexane/water interface. Here, we show that one can construct a single CG model that can reproduce both the bulk and interface conformational behavior and the segregation between hydrophobic/hydrophilic medium. While the general strategy to obtain nonbonded interactions in the present CG model is to reproduce solvation free energies of small molecules representing the CG beads in the respective solvents, the success of the model strongly depends on nontrivial decisions one has to make to capture the delicate balance between the bonded and nonbonded interactions. In particular, we found that the peptide's conformational behavior is qualitatively affected by the cyclohexane/water interaction potential, an interaction that does not directly involve the peptide at all but merely influences the properties of the hydrophobic/hydrophilic interface. Furthermore, we show that a small modification to improve the structural/conformational properties of the CG model could dramatically alter the thermodynamic properties.
 Atoms, Molecules, and Clusters

Infrared laser spectroscopy of the heliumsolvated allyl and allyl peroxy radicals
View Description Hide DescriptionInfrared spectra in the C–H stretch region are reported for the allyl (CH2CHCH2) and allyl peroxy (CH2=CH–CH2OO·) radicals solvated in superfluid helium nanodroplets. Nine bands in the spectrum of the allyl radical have resolved rotational substructure. We have assigned three of these to the ν1 (a 1), ν3 (a 1), and ν13 (b 2) C–H stretch bands and four others to the ν14/(ν15+2ν11) (b 2) and ν2/(ν4+2ν11) (a 1) Fermi dyads, and an unassigned resonant polyad is observed in the vicinity of the ν1 band. Experimental coupling constants associated with Fermi dyads are consistent with quartic force constants obtained from density functional theory computations. The peroxy radical was formed within the He droplet via the reaction between allyl and O2 following the sequential pickup of the reactants. Five stable conformers are predicted for the allyl peroxy radical, and a computed twodimensional potential surface for rotation about the CC–OO and CC–CO bonds reveals multiple isomerization barriers greater than ≈300 cm^{−1}. Nevertheless, the C–H stretch infrared spectrum is consistent with the presence of a single conformer following the allyl + O2 reaction within helium droplets.

Spinrotation and NMR shielding constants in HCl
View Description Hide DescriptionThe spinrotation and nuclear magnetic shielding constants are analysed for both nuclei in the HCl molecule. Nonrelativistic ab initio calculations at the CCSD(T) level of approximation show that it is essential to include relativistic effects to obtain spinrotation constants consistent with accurate experimental data. Our best estimates for the spinrotation constants of ^{1}H^{35}Cl are C Cl = −53.914 kHz and C H = 42.672 kHz (for the lowest rovibrational level). For the chlorine shielding constant, the ab initio value computed including the relativistic corrections, σ(Cl) = 976.202 ppm, provides a new absolute shielding scale; for hydrogen we find σ(H) = 31.403 ppm (both at 300 K). Combining the theoretical results with our new gasphase NMR experimental data allows us to improve the accuracy of the magnetic dipole moments of both chlorine isotopes. For the hydrogen shielding constant, including relativistic effects yields better agreement between experimental and computed values.

Structure, stability, and dissociation of small ionic silicon oxide clusters [SiO_{n} ^{+}(n = 3, 4)]: Insight from density functional and topological exploration
View Description Hide DescriptionThe structures, energies, isomerization, and decomposition pathways of small ionic silicon oxide clusters, SiOn ^{+} (n = 3, 4), on doublet and quartet energy surfaces are investigated by density functional theory. New structural isomers of these ionic clusters have been obtained with this systematic study. The energy ordering of the isomeric cluster ions on doublet spin surface is found to follow the same general trend as that of the neutral ones, while it differs on the quartet surface. Our computational results reveal the energetically most preferred decomposition pathways of the ionic clusters on both spin surfaces. To comprehend the reaction mechanism, bonding evolution theory has also been employed using atoms in molecules formalism. The possible reasons behind the structural deformation of some isomers on quartet surface have also been addressed. Our results are expected to provide important insight into the decomposition mechanism and relative stability of the SiOn ^{+} clusters on both the energy surfaces.

On the role of the simplest Snitrosothiol, HSNO, in atmospheric and biological processes
View Description Hide DescriptionUsing stateoftheart theoretical methods, we investigate the lowest electronic states of singlet and triplet spin multiplicities of HSNO. These computations are done using configuration interaction ab initio methods and the augccpV5Z basis set. Onedimensional cuts of the sixdimensional potential energy surfaces of these electronic states along the HS, SN stretches and HSN, SNO bending and torsion coordinates are calculated. Several avoided crossings and conical intersections are found. We computed also radiative lifetimes and spinorbit couplings of these electronic states. Our work shows that the dynamics on these excited states is very complex, and suggest that multistep mechanisms will populate the ground state via radiationless processes or lead to predissociation or intramolecular isomerization. For instance, these potentials are used to propose mechanisms for the IR, Vis, and UV lightinduced cistrans interconversions of HSNO and reactivity towards HS + NO and H + SNO products. Our findings are in good agreement with previous experimental studies on the photochemistry of HSNO. The atmospheric implication of HSNO is also discussed.

Quantum effects and anharmonicity in the H_{2}Li^{+}benzene complex: A model for hydrogen storage materials
View Description Hide DescriptionQuantum and anharmonic effects are investigated in H2Li^{+}benzene, a model for hydrogen adsorption in metalorganic frameworks and carbonbased materials. Three and 8dimensional quantum diffusion Monte Carlo (QDMC) and rigidbody diffusion Monte Carlo (RBDMC) simulations are performed on potential energy surfaces interpolated from electronic structure calculations at the M052X/631+G(d,p) and M052X/6311+G(2df,p) levels of theory using a threedimensional spline or a modified Shepard interpolation. These calculations investigate the intermolecular interactions in this system, with three and 8dimensional 0 K H2 binding enthalpy estimates, ΔHbind (0 K), being 16.5 kJ mol^{−1} and 12.4 kJ mol^{−1}, respectively: 0.1 and 0.6 kJ mol^{−1} higher than harmonic values. Zeropoint energy effects are 35% of the value of ΔHbind (0 K) at M052X/6311+G(2df,p) and cannot be neglected; uncorrected electronic binding energies overestimate ΔHbind (0 K) by at least 6 kJ mol^{−1}. Harmonic intermolecular binding enthalpies can be corrected by treating the H2 “helicopter” and “ferris wheel” rotations as free and hindered rotations, respectively. These simple corrections yield results within 2% of the 8dimensional anharmonic calculations. Nuclear ground state probability density histograms obtained from the QDMC and RBDMC simulations indicate the H2 molecule is delocalized above the Li^{+}benzene system at 0 K.