Volume 141, Issue 8, 28 August 2014

Despite its importance in atmospheric science, much remains unknown about the microscopic mechanism of heterogeneous ice nucleation. In this work, we perform hybrid Monte Carlo simulations of the heterogeneous nucleation of ice on a range of generic surfaces, both flat and structured, in order to probe the underlying factors affecting the nucleation process. The structured surfaces we study comprise one basal plane bilayer of ice with varying lattice parameters and interaction strengths. We show that what determines the propensity for nucleation is not just the surface attraction, but also the orientational ordering imposed on liquid water near a surface. In particular, varying the ratio of the surface's attraction and orientational ordering can change the mechanism by which nucleation occurs: ice can nucleate on the structured surface even when the orientational ordering imposed by the surface is weak, as the water molecules that interact strongly with the surface are themselves a good template for further growth. We also show that lattice matching is important for heterogeneous nucleation on the structured surface we study. We rationalise these bruteforce simulation results by explicitly calculating the interfacial free energies of ice and liquid water in contact with the nucleating surface and their variation with surface interaction parameters.
 COMMUNICATIONS


Communication: Ab initio study of O_{4}H^{+}: A tracer molecule in the interstellar medium?
View Description Hide DescriptionThe structure and energetics of the protonated molecular oxygen dimer calculated via ab initio methods is reported. We find structures that share analogies with the eigen and zundel forms for the protonated water dimer although the symmetrical sharing of the proton is more prevalent. Analysis of different fragmentation channels show charge transfer processes which indicate the presence of conical intersections for various states including the ground state. An accurate estimate for the proton affinity of O4 leads to a significantly larger value (5.6 eV) than for O2 (4.4 eV), implying that the reaction + O4 → O4H^{+} + H2 is exothermic by 28 Kcal/mol as opposed to the case of O2 which is nearly thermoneutral. This opens up the possibility of using O4H^{+} as a tracer molecule for oxygen in the interstellar medium.

Communication: Rigorous quantum dynamics of O + O_{2} exchange reactions on an ab initio potential energy surface substantiate the negative temperature dependence of rate coefficients
View Description Hide DescriptionThe kinetics and dynamics of several O + O2 isotope exchange reactions have been investigated on a recently determined accurate global O3 potential energy surface using a timedependent wave packet method. The agreement between calculated and measured rate coefficients is significantly improved over previous work. More importantly, the experimentally observed negative temperature dependence of the rate coefficients is for the first time rigorously reproduced theoretically. This negative temperature dependence can be attributed to the absence in the new potential energy surface of a submerged “reef” structure, which was present in all previous potential energy surfaces. In addition, contributions of rotational excited states of the diatomic reactant further accentuate the negative temperature dependence.

Communication: Slab thickness dependence of the surface tension: Toward a criterion of liquid sheets stability
View Description Hide DescriptionMicroscopic Monte Carlo simulations of liquid sheets of copper and tin have been performed in order to study the dependence of the surface tension on the thickness of the sheet. It results that the surface tension is constant with the thickness as long as the sheet remains in one piece. When the sheet is getting thinner, holes start to appear, and the calculated surface tension rapidly decreases with thickness until the sheet becomes totally unstable and forms a cylinder. We assume here that this decrease is not due to a confinement effect as proposed by Werth et al. [Physica A392, 2359 (2013)] on LennardJones systems, but to the appearance of holes that reduces the energy cost of the surface modification. We also show in this work that a link can be established between the stability of the sheet and the local fluctuations of the surface position, which directly depends on the value of the surface tension. Finally, we complete this study by investigating systems interacting through different forms of LennardJones potentials to check if similar conclusions can be drawn.

Communication: Charge, diffusion, and mobility of proteins through nanopores
View Description Hide DescriptionImplementation of Einstein's law connecting charge, diffusion coefficient, and mobility to interpret experimental data on proteins from single molecule electrophoresis through nanopores faces serious difficulties. The protein charge and diffusion coefficient, inferred with the Einstein law, can be orders of magnitude smaller than their bare values depending on the electrolyte concentration, pore diameter, chemical nature of the pore wall, and the externally applied voltage. The main contributors to the discrepancies are the coupled dynamics of the protein and its counterion cloud, confinement effects inside the pore, and the proteinporesurface interaction. We have addressed these ingredients by harking on classical theories of electrophoresis of macroions and hydrodynamics inside pores, and deriving new results for poreprotein interactions. Putting together various components, we present approximate analytical formulas for the effective charge, diffusion coefficient, and mobility of a protein in the context of single molecule electrophoresis experiments. For the omnipresent poreprotein interactions, nonlinear dependence of the velocity of protein on voltage sets in readily and analytical formulas for this effect are presented. The derived formulas enable the determination of the bare charge and size of a protein from the experimentally measured apparent values.
 Top

 ARTICLES

 Theoretical Methods and Algorithms

Concentration effects on the rates of irreversible diffusioninfluenced reactions
View Description Hide DescriptionWe formulate a new theory of the effects of likeparticle interactions on the irreversible diffusioninfluenced bimolecular reactions of the type A + B → P + B by considering the evolution equation of the triplet ABB number density field explicitly. The solution to the evolution equation is aided by a recently proposed method for solving the Fredholm integral equation of the second kind. We evaluate the theory by comparing its predictions with the results of extensive computer simulations. The present theory provides a reasonable explanation of the simulation results.

Computing thermal Wigner densities with the phase integration method
View Description Hide DescriptionWe discuss how the Phase Integration Method (PIM), recently developed to compute symmetrized time correlation functions[M. Monteferrante, S. Bonella, and G. Ciccotti, Mol. Phys.109, 3015 (2011)], can be adapted to sampling/generating the thermal Wigner density, a key ingredient, for example, in many approximate schemes for simulating quantum time dependent properties. PIM combines a path integral representation of the density with a cumulant expansion to represent the Wigner function in a form calculable via existing Monte Carlo algorithms for sampling noisy probability densities. The method is able to capture highly nonclassical effects such as correlation among the momenta and coordinates parts of the density, or correlations among the momenta themselves. By using alternatives to cumulants, it can also indicate the presence of negative parts of the Wigner density. Both properties are demonstrated by comparing PIM results to those of reference quantum calculations on a set of model problems.

Validity conditions for moment closure approximations in stochastic chemical kinetics
View Description Hide DescriptionApproximations based on momentclosure (MA) are commonly used to obtain estimates of the mean molecule numbers and of the variance of fluctuations in the number of molecules of chemical systems. The advantage of this approach is that it can be far less computationally expensive than exact stochastic simulations of the chemical master equation. Here, we numerically study the conditions under which the MA equations yield results reflecting the true stochastic dynamics of the system. We show that for bistable and oscillatory chemical systems with deterministic initial conditions, the solution of the MA equations can be interpreted as a valid approximation to the true moments of the chemical master equation, only when the steadystate mean molecule numbers obtained from the chemical master equation fall within a certain finite range. The same validity criterion for monostable systems implies that the steadystate mean molecule numbers obtained from the chemical master equation must be above a certain threshold. For mean molecule numbers outside of this range of validity, the MA equations lead to either qualitatively wrong oscillatory dynamics or to unphysical predictions such as negative variances in the molecule numbers or multiple steadystate moments of the stationary distribution as the initial conditions are varied. Our results clarify the range of validity of the MA approach and show that pitfalls in the interpretation of the results can only be overcome through the systematic comparison of the solutions of the MA equations of a certain order with those of higher orders.

Symmetrical windowing for quantum states in quasiclassical trajectory simulations: Application to electron transfer
View Description Hide DescriptionIt has recently been shown [S. J. Cotton and W. H. Miller, J. Chem. Phys. 139, 234112 (2013)] that a symmetrical windowing quasiclassical (SQC) approach [S. J. Cotton and W. H. Miller, J. Phys. Chem. A 117, 7190 (2013)] applied to the MeyerMiller model [H.D. Meyer and W. H. Miller, J. Chem. Phys. 70, 3214 (1979)] for the electronic degrees of freedom in electronically nonadiabatic dynamics is capable of quantitatively reproducing quantum mechanical results for a variety of test applications, including cases where “quantum” coherence effects are significant. Here we apply this same SQC methodology, within a fluxside correlation function framework, to calculate thermal rate constants corresponding to several proposed models of electron transfer processes [P. Huo, T. F. Miller III, and D. F. Coker, J. Chem. Phys. 139, 151103 (2013); A. R. Menzeleev, N. Ananth, and T. F. Miller III, J. Chem. Phys. 135, 074106 (2011)]. Good quantitative agreement with Marcus Theory is obtained over several orders of magnitude variation in nonadiabatic coupling. Moreover, the “inverted regime” in thermal rate constants (with increasing bias) known from Marcus Theory is also reproduced with good accuracy by this very simple classical approach. The SQC treatment is also applied to a recent model of photoinduced proton coupled electron transfer [C. Venkataraman, A. V. Soudackov, and S. HammesSchiffer, J. Chem. Phys. 131, 154502 (2009)] and population decay of the photoexcited donor state is found to be in reasonable agreement with results calculated via reduced density matrix theory.

Stochastic manybody perturbation theory for anharmonic molecular vibrations
View Description Hide DescriptionA new quantum Monte Carlo (QMC) method for anharmonic vibrational zeropoint energies and transition frequencies is developed, which combines the diagrammatic vibrational manybody perturbation theory based on the Dyson equation with Monte Carlo integration. The infinite sums of the diagrammatic and thus sizeconsistent first and secondorder anharmonic corrections to the energy and selfenergy are expressed as sums of a few m or 2mdimensional integrals of wave functions and a potential energy surface (PES) (m is the vibrational degrees of freedom). Each of these integrals is computed as the integrand (including the value of the PES) divided by the value of a judiciously chosen weight function evaluated on demand at geometries distributed randomly but according to the weight function via the Metropolis algorithm. In this way, the method completely avoids cumbersome evaluation and storage of highorder force constants necessary in the original formulation of the vibrational perturbation theory; it furthermore allows even higherorder force constants essentially up to an infinite order to be taken into account in a scalable, memoryefficient algorithm. The diagrammatic contributions to the frequencydependent selfenergies that are stochastically evaluated at discrete frequencies can be reliably interpolated, allowing the selfconsistent solutions to the Dyson equation to be obtained. This method, therefore, can compute directly and stochastically the transition frequencies of fundamentals and overtones as well as their relative intensities as pole strengths, without fixednode errors that plague some QMC. It is shown that, for an identical PES, the new method reproduces the correct deterministic values of the energies and frequencies within a few cm^{−1} and pole strengths within a few thousandths. With the values of a PES evaluated on the fly at random geometries, the new method captures a noticeably greater proportion of anharmonic effects.

FranckCondon factors perturbed by damped harmonic oscillators: Solvent enhanced X ^{1}A_{g} ↔ A^{1}B_{1u} absorption and fluorescence spectra of perylene
View Description Hide DescriptionDamped harmonic oscillators are utilized to calculate FranckCondon factors within displaced harmonic oscillator approximation. This is practically done by scaling unperturbed Hessian matrix that represents local modes of force constants for molecule in gaseous phase, and then by diagonalizing perturbed Hessian matrix it results in direct modification of Huang–Rhys factors which represent normal modes of solute molecule perturbed by solvent environment. Scaling parameters are empirically introduced for simulating absorption and fluorescence spectra of an isolated solute molecule in solution. The present method is especially useful for simulating vibronic spectra of polycyclic aromatic hydrocarbon molecules in which hydrogen atom vibrations in solution can be scaled equally, namely the same scaling factor being applied to all hydrogen atoms in polycyclic aromatic hydrocarbons. The present method is demonstrated in simulating solvent enhanced X ^{1}Ag ↔ A^{1}B1u absorption and fluorescence spectra of perylene (mediumsized polycyclic aromatic hydrocarbon) in benzene solution. It is found that one of six active normal modes v 10 is actually responsible to the solvent enhancement of spectra observed in experiment. Simulations from all functionals (TD) B3LYP, (TD) B3LYP35, (TD) B3LYP50, and (TD) B3LYP100 draw the same conclusion. Hence, the present method is able to adequately reproduce experimental absorption and fluorescence spectra in both gas and solution phases.

Average local ionization energy generalized to correlated wavefunctions
View Description Hide DescriptionThe average local ionization energy function introduced by Politzer and coworkers [Can. J. Chem.68, 1440 (1990)] as a descriptor of chemical reactivity has a limited utility because it is defined only for onedeterminantal selfconsistentfield methods such as the Hartree–Fock theory and the Kohn–Sham densityfunctional scheme. We reinterpret the negative of the average local ionization energy as the average total energy of an electron at a given point and, by rewriting this quantity in terms of reduced density matrices, arrive at its natural generalization to correlated wavefunctions. The generalized average local electron energy turns out to be the diagonal part of the coordinate representation of the generalized Fock operator divided by the electron density; it reduces to the original definition in terms of canonical orbitals and their eigenvalues for onedeterminantal wavefunctions. The discussion is illustrated with calculations on selected atoms and molecules at various levels of theory.

Validity of virial theorem in allelectron mixed basis density functional, Hartree–Fock, and GW calculations
View Description Hide DescriptionIn this paper, we calculate kinetic and potential energy contributions to the electronic groundstate total energy of several isolated atoms (He, Be, Ne, Mg, Ar, and Ca) by using the local density approximation (LDA) in density functional theory, the Hartree–Fock approximation (HFA), and the selfconsistent GW approximation (GWA). To this end, we have implemented selfconsistent HFA and GWA routines in our allelectron mixed basis code, TOMBO. We confirm that virial theorem is fairly well satisfied in all of these approximations, although the resulting eigenvalue of the highest occupied molecular orbital level, i.e., the negative of the ionization potential, is in excellent agreement only in the case of the GWA. We find that the wave function of the lowest unoccupied molecular orbital level of noble gas atoms is a resonating virtual bound state, and that of the GWA spreads wider than that of the LDA and thinner than that of the HFA.

Reference hypernetted chain theory for ferrofluid bilayer: Distribution functions compared with Monte Carlo
View Description Hide DescriptionProperties of ferrofluid bilayer (modeled as a system of two planar layers separated by a distance h and each layer carrying a soft sphere dipolar liquid) are calculated in the framework of inhomogeneous OrnsteinZernike equations with reference hypernetted chain closure (RHNC). The bridge functions are taken from a soft sphere (1/r ^{12}) reference system in the pressureconsistent closure approximation. In order to make the RHNC problem tractable, the angular dependence of the correlation functions is expanded into special orthogonal polynomials according to Lado. The resulting equations are solved using the NewtonGRMES algorithm as implemented in the publicdomain solver NITSOL. Orientational densities and pair distribution functions of dipoles are compared with Monte Carlo simulation results. A numerical algorithm for the FourierHankel transform of any positive integer order on a uniform grid is presented.
 Atoms, Molecules, and Clusters

Relativistic coupled cluster study of diatomic compounds of Hg, Cn, and Fl
View Description Hide DescriptionThe structure and energetics of eight diatomic heavyatom molecules are presented. These include the species MAu, M2, and MHg, with M standing for the Hg, Cn (element 112), and Fl (element 114) atoms. The infiniteorder relativistic 2component Hamiltonian, known to closely reproduce 4component results at lower computational cost, is used as framework. Highaccuracy treatment of correlation is achieved by using the coupled cluster scheme with single, double, and perturbative triple excitations in large converged basis sets. The calculated interatomic separation and bond energy of Hg 2, the only compound with known experimental data, are in good agreement with measurements. The binding of Fl to Au is stronger than that of Cn, predicting stronger adsorption on gold surfaces. The bond in the M2 species is strongest for Fl2, being of chemical nature; weaker bonds appear in Cn2 and Hg 2, which are bound by van der Waals interactions, with the former bound more strongly due to the smaller van der Waals radius. The same set of calculations was also performed using the relativistic density functional theory approach, in order to test the performance of the latter for these weakly bound systems with respect to the more accurate coupled cluster calculations. It was found that for the MAu species the B3LYP functional provides better agreement with the coupled cluster results than the B88/P86 functional. However, for the M2 and the MHg molecules, B3LYP tends to underestimate the binding energies.

Alloying and oxidation of in situ produced coreshell Al@Yb nanoalloy particles—An “onthefly” study
View Description Hide DescriptionCoreshellstructured nanoalloy particles with an Aldominated interior covered by few Yb monolayers have been fabricated using a vaporaggregation method involving magnetron sputtering. The radially segregated structure of the YbAl nanoparticles has been disclosed by “onthefly” photoelectron spectroscopy monitoring of the nanoparticle beam in Yb 4f and Al 2p electron binding energy regions. Both, the binding energy values and the electron microscopy images taken on the deposited nanoparticles, allow estimating their dimensions to be in the 5–10 nm range. The photoelectron spectroscopy results suggest that in these nanoparticles no trivalent Yb – the typical case for the macroscopic YbAl alloy – is present. The oxidation of preformed YbAl nanoparticles was successfully attempted, leading to the appearance of divalent Yb surface oxide – in contrast to the bulk macroscopic Yb which is trivalent in the oxide. Our results suggest that at intermediate oxygen exposures “sandwichlike” nanoparticles of YbO/Yb/Al were synthesized. At higher O2 exposures, the oxygen seems to penetrate all the way to the YbAl interface. The results of the present study have to be considered when photonic applications of Ybdoped garnet nanoparticles are planned.

Chargetransfer excitations in lowgap systems under the influence of solvation and conformational disorder: Exploring rangeseparation tuning
View Description Hide DescriptionCharge transfer excitations play a prominent role in the fields of molecular electronics and light harvesting. At the same time they have developed a reputation for being hard to predict with timedependent density functional theory, which is the otherwise predominant method for calculating molecular structure and excitations. Recently, it has been demonstrated that rangeseparated hybrid functionals, in particular with an “optimally tuned” range separation parameter, describe chargetransfer excitations reliably for different molecules. Many of these studies focused on molecules in vacuum. Here we investigate the influence of solvation on the electronic excitations of thiophene oligomers, i.e., paradigm low gap systems. We take into account bulk solvation using a continuum solvation model and geometrical distortions from molecular dynamics. From our study, three main findings emerge. First, geometrical distortions increase absorption energies by about 0.5 eV for the longer thiophene oligomers. Second, combining optimal tuning of the range separation parameter with a continuum solvation method is not straightforward and has to be approached with great care. Third, optimally tuned rangeseparated hybrids without a shortrange exchange component tend to inherit undesirable characteristics of semilocal functionals: with increasing system size the range separation parameter takes a smaller value, leading to a functional of effectively more semilocal nature and thus not accurately capturing, e.g., the saturation of the optical gap with increasing system size.

High resolution electronic spectroscopy of the A ^{2}Σ^{−} − X ^{2}Π_{1/2} transition of PtN
View Description Hide DescriptionThe (2,0) vibrational band of the A ^{2}Σ^{−} − X ^{2}Π1/2 transition of platinum nitride, PtN, was recorded at Dopplerlimited resolution using intracavity laser absorption spectroscopy (ILS) and at subDoppler resolution using molecular beam laser induced fluorescence (LIF) spectroscopy. Isotopologue structure for ^{194}PtN, ^{195}PtN, and ^{196}PtN, magnetic hyperfine splitting due to ^{195}Pt (I = ½), and nuclear quadrupole splitting due to ^{14}N (I = 1) were observed in the spectrum. Molecular constants for the ground and excited states are derived. The hyperfine interactions are used to illuminate the nature of the A ^{2}Σ^{−} excited electronic state.

Nonadiabatic photofragmentation dynamics of BrCN^{−}
View Description Hide DescriptionThe photofragmentation dynamics of BrCN^{−} in the 270–355 nm and the 430–600 nm wavelength regions is explored both experimentally and theoretically. In the case of excitation between 430 nm and 600 nm, it is found that the molecular ion accesses two dissociation channels with a measured 60:40 branching ratio that is nearly constant over this range of photon energies. The dominant product channel corresponds to Br^{−} + CN, while the second channel correlates to spinorbit excited Br^{*} with CN^{−}. A larger wavelength dependence of the branching ratio is observed at shorter wavelengths, where the fraction of Br^{−} based products ranges from 80% to 95% at 355 nm and 270 nm, respectively. These branching ratios are reproduced and the mechanisms are explored by quantum dynamics calculations based on ground and excited state potential energy surfaces for BrCN^{−}, evaluated at the SOMRCISD level of theory. It is found that the electronic states that correlate to the two observed product channels are coupled through the spinorbit terms in the electronic Hamiltonian. The strength of this coupling displays a strong dependence on the BrCN angle. Specifically, after promotion to the excited state that is energetically accessible with 430–600 nm photons, it is found that when the wave packet accesses BrCN separations of between 4 Å and 6 Å, predominantly the Br^{−} + CN products are formed when the BrCN angle is smaller than 120°. For larger values of the BrCN angle, the Br^{*} + CN^{−} channel dominates. At the shorter wavelength excitation, the dynamics is complicated by a pair of states that correlate to electronically excited CN^{*} + Br^{−} products that borrow oscillator strength from the bright state, leading to an increase in the amount of Br^{−} relative to CN^{−}. The implications of these findings are discussed and compared to the experimentally measured product branching ratios for the photodissociation of BrCN^{−}.

Pressureinduced oligomerization of benzene at room temperature as a precursory reaction of amorphization
View Description Hide DescriptionOligomerization of benzene at high pressures up to 16 GPa was investigated at room temperature using an opposedanvil type pressure apparatus. The recovered samples were analyzed using GCMS to identify and quantify the products after the highpressure experiments. Some structural isomers of benzene dimer as well as biphenyl, naphthalene, and terphenyl isomers were detected at pressures higher than 13 GPa. The molar yield of the polycyclic aromatic hydrocarbons increased concomitantly with increasing pressure, although benzene still remained. The oligomerization is likely to occur when the neighbor distance of the benzene molecules exceeds the threshold of the reaction distance. The oligomerization is regarded as a precursory phenomenon of the amorphization that occurs at higher pressure.

Accurate double manybody expansion potential energy surface for the 2^{1} A′ state of
View Description Hide DescriptionAn accurate double manybody expansion potential energy surface is reported for the 2^{1} A′ state of . The new double manybody expansion (DMBE) form has been fitted to a wealth of ab initio points that have been calculated at the multireference configuration interaction level using the fullvalencecompleteactivespace wave function as reference and the ccpVQZ basis set, and subsequently corrected semiempirically via double manybody expansionscaled external correlation method to extrapolate the calculated energies to the limit of a complete basis set and, most importantly, the limit of an infinite configuration interaction expansion. The topographical features of the novel potential energy surface are then examined in detail and compared with corresponding attributes of other potential functions available in the literature. Exploratory trajectories have also been run on this DMBE form with the quasiclassical trajectory method, with the thermal rate constant so determined at room temperature significantly enhancing agreement with experimental data.