Volume 144, Issue 24, 28 June 2016

The extent to which solventmediated effective interactions between nanoparticles can be predicted based on structure and associated thermodynamic estimators for bulk solvents and for solvation of single and pairs of nanoparticles is studied here. As a test of the approach, we analyse the strategy for creating temperatureindependent solvent environments using a series of homologous chain fluids as solvents, as suggested by an experimental paper [M. I. Bodnarchuk et al., J. Am. Chem. Soc. 132, 11967 (2010)]. Our conclusions are based on molecular dynamics simulations of Au 140(SC10H21)62 nanoparticles in nalkane solvents, specifically hexane, octane, decane and dodecane, using the TraPPEUA potential to model the alkanes and alkylthiols. The 140atom gold core of the nanocrystal is held rigid in a truncated octahedral geometry and the goldthiolate interaction is modeled using a Morse potential. The experimental observation was that the structural and rheological properties of nalkane solvents are constant over a temperature range determined by equivalent solvent vapour pressures. We show that this is a consequence of the fact that long chain alkane liquids behave to a good approximation as simple liquids formed by packing of monomeric methyl/methylene units. Over the corresponding temperature range (233–361 K), the solvation environment is approximately constant at the single and pair nanoparticle levels under good solvent conditions. However, quantitative variations of the order of 10%–20% do exist in various quantities, such as molar volume of solute at infinite dilution, entropy of solvation, and onset distance for soft repulsions. In the opposite limit of a poor solvent, represented by vacuum in this study, the effective interactions between nanoparticles are no longer temperatureindependent with attractive interactions increasing by up to 50% on decreasing the temperature from 361 K to 290 K, accompanied by an increase in emergent anisotropy due to correlation of mass dipoles on the two nanoparticles. One expects therefore that during selfassembly using solvent evaporation, temperature can be used as a structuredirecting factor as long as good solvent conditions are maintained. It also suggests that disordered configurations may emerge as solvent quality decreases due to increasing role of shortrange attractions and ligand fluctuationdriven anisotropy. The possibilities of using structural estimators of various thermodynamic quantities to analyse the interplay of ligand fluctuations and solvent quality in selfassembly as well as to design solvation environments are discussed.
 COMMUNICATIONS


Communication: Proton NMR dipolarcorrelation effect as a method for investigating segmental diffusion in polymer melts
View Description Hide DescriptionA simple and fast method for the investigation of segmental diffusion in high molar mass polymer melts is presented. The method is based on a special function, called proton dipolarcorrelation buildup function, which is constructed from Hahn Echo signals measured at times t and t/2. The initial rise of this function contains additive contributions from both inter and intramolecular magnetic dipoledipole interactions. The intermolecular contribution depends on the relative mean squared displacements (MSDs) of polymer segments from different macromolecules, while the intramolecular part reflects segmental reorientations. Separation of both contributions via isotope dilution provides access to segmental displacements in polymer melts at millisecond range, which is hardly accessible by other methods. The feasibility of the method is illustrated by investigating protonated and deuterated polybutadiene melts with molecular mass 196 000 g/mol at different temperatures. The observed exponent of the power law of the segmental MSD is close to 0.32 ± 0.03 at times when the root MSD is in between 45 Å and 75 Å, and the intermolecular proton dipoledipole contribution to the total proton Hahn Echo NMR signal is larger than 50% and increases with time.

Communication: Visualization and spectroscopy of defects induced by dehydrogenation in individual silicon nanocrystals
View Description Hide DescriptionWe present results of a scanning tunneling spectroscopy (STS) study of the impact of dehydrogenation on the electronic structures of hydrogenpassivated silicon nanocrystals (SiNCs) supported on the Au(111) surface. Gradual dehydrogenation is achieved by injecting highenergy electrons into individual SiNCs, which results, initially, in reduction of the electronic bandgap, and eventually produces midgap electronic states. We use theoretical calculations to show that the STS spectra of midgap states are consistent with the presence of silicon dangling bonds, which are found in different charge states. Our calculations also suggest that the observed initial reduction of the electronic bandgap is attributable to the SiNC surface reconstruction induced by conversion of surface dihydrides to monohydrides due to hydrogen desorption. Our results thus provide the first visualization of the SiNC electronic structure evolution induced by dehydrogenation and provide direct evidence for the existence of diverse dangling bond states on the SiNC surfaces.
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 ARTICLES

 Theoretical Methods and Algorithms

Dissipative particle dynamics of diffusionNMR requires high Schmidtnumbers
View Description Hide DescriptionWe present an efficient mesoscale model to simulate the diffusion measurement with nuclear magnetic resonance (NMR). On the level of mesoscopic thermal motion of fluid particles, we couple the Bloch equations with dissipative particle dynamics (DPD). Thereby we establish a physically consistent scaling relation between the diffusion constant measured for DPDparticles and the diffusion constant of a real fluid. The latter is based on a splitting into a centreofmass contribution represented by DPD, and an internal contribution which is not resolved in the DPDlevel of description. As a consequence, simulating the centreofmass contribution with DPD requires high Schmidt numbers. After a verification for fundamental pulse sequences, we apply the NMRDPD method to NMR diffusion measurements of anisotropic fluids, and of fluids restricted by walls of microfluidic channels. For the latter, the free diffusion and the localisation regime are considered.

Tensor representation techniques for full configuration interaction: A Fock space approach using the canonical product format
View Description Hide DescriptionIn this proofofprinciple study, we apply tensor decomposition techniques to the Full Configuration Interaction (FCI) wavefunction in order to approximate the wavefunction parameters efficiently and to reduce the overall computational effort. For this purpose, the wavefunction ansatz is formulated in an occupation number vector representation that ensures antisymmetry. If the canonical product format tensor decomposition is then applied, the Hamiltonian and the wavefunction can be cast into a multilinear product form. As a consequence, the number of wavefunction parameters does not scale to the power of the number of particles (or orbitals) but depends on the rank of the approximation and linearly on the number of particles. The degree of approximation can be controlled by a single threshold for the rank reduction procedure required in the algorithm. We demonstrate that using this approximation, the FCI Hamiltonian matrix can be stored with N^{5} scaling. The error of the approximation that is introduced is below Millihartree for a threshold of ϵ = 10^{−4} and no convergence problems are observed solving the FCI equations iteratively in the new format. While promising conceptually, all effort of the algorithm is shifted to the required rank reduction procedure after the contraction of the Hamiltonian with the coefficient tensor. At the current state, this crucial step is the bottleneck of our approach and even for an optimistic estimate, the algorithm scales beyond N^{10} and future work has to be directed towards reductionfree algorithms.

On the existence of the optimal order for wavefunction extrapolation in BornOppenheimer molecular dynamics
View Description Hide DescriptionWavefunction extrapolation greatly reduces the number of selfconsistent field (SCF) iterations and thus the overall computational cost of BornOppenheimer molecular dynamics (BOMD) that is based on the Kohn–Sham density functional theory. Going against the intuition that the higher order of extrapolation possesses a better accuracy, we demonstrate, from both theoretical and numerical perspectives, that the extrapolation accuracy firstly increases and then decreases with respect to the order, and an optimal extrapolation order in terms of minimal number of SCF iterations always exists. We also prove that the optimal order tends to be larger when using larger MD time steps or more strict SCF convergence criteria. By example BOMD simulations of a solid copper system, we show that the optimal extrapolation order covers a broad range when varying the MD time step or the SCF convergence criterion. Therefore, we suggest the necessity for BOMD simulation packages to open the user interface and to provide more choices on the extrapolation order. Another factor that may influence the extrapolation accuracy is the alignment scheme that eliminates the discontinuity in the wavefunctions with respect to the atomic or cell variables. We prove the equivalence between the two existing schemes, thus the implementation of either of them does not lead to essential difference in the extrapolation accuracy.

The electron localization as the information content of the conditional pair density
View Description Hide DescriptionIn the present work, the information gained by an electron for “knowing” about the position of another electron with the same spin is calculated using the KullbackLeibler divergence (DKL) between the samespin conditional pair probability density and the marginal probability. DKL is proposed as an electron localization measurement, based on the observation that regions of the space with high information gain can be associated with strong correlated localized electrons. Taking into consideration the scaling of DKL with the number of σspin electrons of a system (N ^{σ}), the quantity χ = (N ^{σ} − 1) DKLfcut is introduced as a general descriptor that allows the quantification of the electron localization in the space. fcut is defined such that it goes smoothly to zero for negligible densities. χ is computed for a selection of atomic and molecular systems in order to test its capability to determine the region in space where electrons are localized. As a general conclusion, χ is able to explain the electron structure of molecules on the basis of chemical grounds with a high degree of success and to produce a clear differentiation of the localization of electrons that can be traced to the fluctuation in the average number of electrons in these regions.

NonCondon equilibrium Fermi’s golden rule electronic transition rate constants via the linearized semiclassical method
View Description Hide DescriptionIn this paper, we test the accuracy of the linearized semiclassical (LSC) expression for the equilibrium Fermi’s golden rule rate constant for electronic transitions in the presence of nonCondon effects. We do so by performing a comparison with the exact quantummechanical result for a model where the donor and acceptor potential energy surfaces are parabolic and identical except for shifts in the equilibrium energy and geometry, and the coupling between them is linear in the nuclear coordinates. Since nonCondon effects may or may not give rise to conical intersections, both possibilities are examined by considering: (1) A modified GargOnuchicAmbegaokar model for charge transfer in the condensed phase, where the donoracceptor coupling is linear in the primary mode coordinate, and for which nonCondon effects do not give rise to a conical intersection; (2) the linear vibronic coupling model for electronic transitions in gas phase molecules, where nonCondon effects give rise to conical intersections. We also present a comprehensive comparison between the linearized semiclassical expression and a progression of more approximate expressions. The comparison is performed over a wide range of frictions and temperatures for model (1) and over a wide range of temperatures for model (2). The linearized semiclassical method is found to reproduce the exact quantummechanical result remarkably well for both models over the entire range of parameters under consideration. In contrast, more approximate expressions are observed to deviate considerably from the exact result in some regions of parameter space.

Simulation of optical response functions in molecular junctions
View Description Hide DescriptionWe discuss theoretical approaches to nonlinear optical spectroscopy of molecular junctions. Optical response functions are derived in a form convenient for the implementation of Green function techniques, and their expressions in terms of pseudoparticle nonequilibrium Green functions are proposed. The formulation allows to account for both intramolecular interactions and hybridization of molecular states with those of contacts. Within a generic model and utilizing twodimensional optical spectroscopy as an example, the methodology is compared with exact simulations and is shown to work where the traditional Liouville space approach fails.

Exits in order: How crowding affects particle lifetimes
View Description Hide DescriptionDiffusive processes are often represented using stochastic random walk frameworks. The amount of time taken for an individual in a random walk to intersect with an absorbing boundary is a fundamental property that is often referred to as the particle lifetime, or the first passage time. The mean lifetime of particles in a random walk model of diffusion is related to the amount of time required for the diffusive process to reach a steady state. Mathematical analysis describing the mean lifetime of particles in a standard model of diffusion without crowding is well known. However, the lifetime of agents in a random walk with crowding has received much less attention. Since many applications of diffusion in biology and biophysics include crowding effects, here we study a discrete model of diffusion that incorporates crowding. Using simulations, we show that crowding has a dramatic effect on agent lifetimes, and we derive an approximate expression for the mean agent lifetime that includes crowding effects. Our expression matches simulation results very well, and highlights the importance of crowding effects that are sometimes overlooked.

Quantum dynamics of incoherently driven Vtype systems: Analytic solutions beyond the secular approximation
View Description Hide DescriptionClosedform analytic solutions to nonsecular BlochRedfield master equations for quantum dynamics of a Vtype system driven by weak coupling to a thermal bath, relevant to light harvesting processes, are obtained and discussed. We focus on noiseinduced Fano coherences among the excited states induced by incoherent driving of the Vsystem initially in the ground state. For suddenly turnedon incoherent driving, the time evolution of the coherences is determined by the damping parameter , where γi are the radiative decay rates of the excited levels i = 1, 2, and depends on the excitedstate level splitting Δ > 0 and the angle between the transition dipole moments in the energy basis. The coherences oscillate as a function of time in the underdamped limit (ζ ≫ 1), approach a longlived quasisteady state in the overdamped limit (ζ ≪ 1), and display an intermediate behavior at critical damping (ζ = 1). The sudden incoherent turnon is shown to generate a mixture of excited eigenstates e 1〉 and e 2〉 and their inphase coherent superposition , which is remarkably longlived in the overdamped limit (where r 1 and r 2 are the incoherent pumping rates). Formation of this coherent superposition enhances the decay rate from the excited states to the ground state. In the strongly asymmetric Vsystem where the coupling strengths between the ground state and the excited states differ significantly, additional asymptotic quasistationary coherences are identified, which arise due to slow equilibration of one of the excited states. Finally, we demonstrate that noiseinduced Fano coherences are maximized with respect to populations when r 1 = r 2 and the transition dipole moments are fully aligned.

Accelerating ringpolymer molecular dynamics with parallelreplica dynamics
View Description Hide DescriptionNuclear quantum effects are important for systems containing light elements, and the effects are more prominent in the low temperature regime where the dynamics also becomes sluggish. We show that parallel replica (ParRep) dynamics, an accelerated molecular dynamics approach for infrequentevent systems, can be effectively combined with ringpolymer molecular dynamics, a semiclassical trajectory approach that gives a good approximation to zeropoint and tunneling effects in activated escape processes. The resulting RPParRep method is a powerful tool for reaching long time scales in complex infrequentevent systems where quantum dynamics are important. Two illustrative examples, symmetric Eckart barrier crossing and interstitial helium diffusion in Fe and Fe–Cr alloy, are presented to demonstrate the accuracy and longtime scale capability of this approach.

Hubbard physics in the PAW GW approximation
View Description Hide DescriptionIt is demonstrated that the signatures of the Hubbard Model in the strongly interacting regime can be simulated by modifying the screening in the limit of zero wavevector in ProjectorAugmented Wave GW calculations for systems without significant nesting. This modification, when applied to the Mott insulator CuO, results in the opening of the Mott gap by the splitting of states at the Fermi level into upper and lower Hubbard bands, and exhibits a giant transfer of spectral weight upon electron doping. The method is also employed to clearly illustrate that the M1 and M2 forms of vanadium dioxide are fundamentally different types of insulator. Standard GW calculations are sufficient to open a gap in M1 VO2, which arise from the Peierls pairing filling the valence band, creating homopolar bonds. The valence band wavefunctions are stabilized with respect to the conduction band, reducing polarizability and pushing the conduction band eigenvalues to higher energy. The M2 structure, however, opens a gap from strong onsite interactions; it is a Mott insulator.

A minimalistic approach to static and dynamic electron correlations: Amending generalized valence bond method with extended random phase approximation correlation correction
View Description Hide DescriptionA perfectpairing generalized valence bond (GVB) approximation is known to be one of the simplest approximations, which allows one to capture the essence of static correlation in molecular systems. In spite of its attractive feature of being relatively computationally efficient, this approximation misses a large portion of dynamic correlation and does not offer sufficient accuracy to be generally useful for studying electronic structure of molecules. We propose to correct the GVB model and alleviate some of its deficiencies by amending it with the correlation energy correction derived from the recently formulated extended random phase approximation (ERPA). On the examples of systems of diverse electronic structures, we show that the resulting ERPAGVB method greatly improves upon the GVB model. ERPAGVB recovers most of the electron correlation and it yields energy barrier heights of excellent accuracy. Thanks to a balanced treatment of static and dynamic correlation, ERPAGVB stays reliable when one moves from systems dominated by dynamic electron correlation to those for which the static correlation comes into play.

Interpolation of propertyvalues between electron numbers is inconsistent with ensemble averaging
View Description Hide DescriptionIn this work we explore the physical foundations of models that study the variation of the ground state energy with respect to the number of electrons (E vs. N models), in terms of general grandcanonical (GC) ensemble formulations. In particular, we focus on E vs. N models that interpolate the energy between states with integer number of electrons. We show that if the interpolation of the energy corresponds to a GC ensemble, it is not differentiable. Conversely, if the interpolation is smooth, then it cannot be formulated as any GC ensemble. This proves that interpolation of electronic properties between integer electron numbers is inconsistent with any form of ensemble averaging. This emphasizes the role of derivative discontinuities and the critical role of a subsystem’s surroundings in determining its properties.

Quantum Monte Carlo with variable spins
View Description Hide DescriptionWe investigate the inclusion of variable spins in electronic structure quantum Monte Carlo, with a focus on diffusion Monte Carlo with Hamiltonians that include spinorbit interactions. Following our previous introduction of fixedphase spinorbit diffusion Monte Carlo, we thoroughly discuss the details of the method and elaborate upon its technicalities. We present a proof for an upperbound property for complex nonlocal operators, which allows for the implementation of Tmoves to ensure the variational property. We discuss the time step biases associated with our particular choice of spin representation. Applications of the method are also presented for atomic and molecular systems. We calculate the binding energies and geometry of the PbH and Sn2 molecules, as well as the electron affinities of the 6p row elements in close agreement with experiments.

On the widths of Stokes lines in Raman scattering from molecules adsorbed at metal surfaces and in molecular conduction junctions
View Description Hide DescriptionWithin a generic model we analyze the Stokes linewidth in surface enhanced Raman scattering (SERS) from molecules embedded as bridges in molecular junctions. We identify four main contributions to the offresonant Stokes signal and show that under zero voltage bias (a situation pertaining also to standard SERS experiments) and at low bias junctions only one of these contributions is pronounced. The linewidth of this component is determined by the molecular vibrational relaxation rate, which is dominated by interactions with the essentially bosonic thermal environment when the relevant molecular electronic energy is far from the metal(s) Fermi energy(ies). It increases when the molecular electronic level is close to the metal Fermi level so that an additional vibrational relaxation channel due to electronhole (eh) exciton in the molecule opens. Other contributions to the Raman signal, of considerably broader linewidths, can become important at larger junction bias.

Assessing the utility of phasespacelocalized basis functions: Exploiting direct product structure and a new basis function selection procedure
View Description Hide DescriptionIn this paper we show that it is possible to use an iterative eigensolver in conjunction with Halverson and Poirier’s symmetrized Gaussian (SG) basis [T. Halverson and B. Poirier, J. Chem. Phys. 137, 224101 (2012)] to compute accurate vibrational energy levels of molecules with as many as five atoms. This is done, without storing and manipulating large matrices, by solving a regular eigenvalue problem that makes it possible to exploit directproduct structure. These ideas are combined with a new procedure for selecting which basis functions to use. The SG basis we work with is orders of magnitude smaller than the basis made by using a classical energy criterion. We find significant convergence errors in previous calculations with SG bases. For sumofproduct Hamiltonians, SG bases large enough to compute accurate levels are orders of magnitude larger than even simple pruned bases composed of products of harmonic oscillator functions.

Rate constants of chemical reactions from semiclassical transition state theory in full and one dimension
View Description Hide DescriptionSemiclassical Transition State Theory (SCTST), a method for calculating rate constants of chemical reactions, offers gains in computational efficiency relative to more accurate quantum scattering methods. In fulldimensional (FD) SCTST, reaction probabilities are calculated from third and fourth potential derivatives along all vibrational degrees of freedom. However, the computational cost of FD SCTST scales unfavorably with system size, which prohibits its application to larger systems. In this study, the accuracy and efficiency of 1D SCTST, in which only third and fourth derivatives along the reaction mode are used, are investigated in comparison to those of FD SCTST. Potential derivatives are obtained from numerical ab initio Hessian matrix calculations at the MP2/ccpVTZ level of theory, and Richardson extrapolation is applied to improve the accuracy of these derivatives. Reaction barriers are calculated at the CCSD(T)/ccpVTZ level. Results from FD SCTST agree with results from previous theoretical and experimental studies when Richardson extrapolation is applied. Results from our implementation of 1D SCTST, which uses only 4 singlepoint MP2/ccpVTZ energy calculations in addition to those for conventional TST, agree with FD results to within a factor of 5 at 250 K. This degree of agreement and the efficiency of the 1D method suggest its potential as a means of approximating rate constants for systems too large for existing quantum scattering methods.

Singletpaired coupled cluster theory for open shells
View Description Hide DescriptionRestricted singlereference coupled cluster theory truncated to single and double excitations accurately describes weakly correlated systems, but often breaks down in the presence of static or strong correlation. Good coupled cluster energies in the presence of degeneracies can be obtained by using a symmetrybroken reference, such as unrestricted HartreeFock, but at the cost of good quantum numbers. A large body of work has shown that modifying the coupled cluster ansatz allows for the treatment of strong correlation within a singlereference, symmetryadapted framework. The recently introduced singletpaired coupled cluster doubles (CCD0) method is one such model, which recovers correct behavior for strong correlation without requiring symmetry breaking in the reference. Here, we extend singletpaired coupled cluster for application to open shells via restricted openshell singletpaired coupled cluster singles and doubles (ROCCSD0). The ROCCSD0 approach retains the benefits of standard coupled cluster theory and recovers correct behavior for strongly correlated, openshell systems using a spinpreserving ROHF reference.
 Advanced Experimental Techniques

Double resonant absorption measurement of acetylene symmetric vibrational states probed with cavity ring down spectroscopy
View Description Hide DescriptionA novel midinfrared/nearinfrared double resonant absorption setup for studying infraredinactive vibrational states is presented. A strong vibrational transition in the midinfrared region is excited using an idler beam from a singly resonant continuouswave optical parametric oscillator, to populate an intermediate vibrational state. High output power of the optical parametric oscillator and the strength of the midinfrared transition result in efficient population transfer to the intermediate state, which allows measuring secondary transitions from this state with a high signaltonoise ratio. A secondary, nearinfrared transition from the intermediate state is probed using cavity ringdown spectroscopy, which provides high sensitivity in this wavelength region. Due to the narrow linewidths of the excitation sources, the rovibrational lines of the secondary transition are measured with subDoppler resolution. The setup is used to access a previously unreported symmetric vibrational state of acetylene, in the normal mode notation. Singlephoton transitions to this state from the vibrational ground state are forbidden. Ten lines of the newly measured state are observed and fitted with the linear leastsquares method to extract the band parameters. The vibrational term value was measured to be at 9775.0018(45) cm^{−1}, the rotational parameter B was 1.162 222(37) cm^{−1}, and the quartic centrifugal distortion parameter D was 3.998(62) × 10^{−6} cm^{−1}, where the numbers in the parenthesis are onestandard errors in the least significant digits.