Volume 137, Issue 19, 21 November 2012

Molecular simulations as well as single molecule experiments have been widely analyzed in terms of order parameters, the latter representing candidate probes for the relevant degrees of freedom. Notwithstanding this approach is very intuitive, mounting evidence showed that such descriptions are inaccurate, leading to ambiguous definitions of states and wrong kinetics. To overcome these limitations a framework making use of order parameter fluctuations in conjunction with complex network analysis is investigated. Derived from recent advances in the analysis of single molecule time traces, this approach takes into account the fluctuations around each time point to distinguish between states that have similar values of the order parameter but different dynamics. Snapshots with similar fluctuations are used as nodes of a transition network, the clusterization of which into states provides accurate Markovstatemodels of the system under study. Application of the methodology to theoretical models with a noisy order parameter as well as the dynamics of a disordered peptide illustrates the possibility to build accurate descriptions of molecular processes on the sole basis of order parameter time series without using any supplementary information.
 COMMUNICATIONS


Communication: Formation of slow electrons in the Auger decay of coreionized water molecules
View Description Hide DescriptionDouble Auger decay of O1s ^{−1} and its satellite states in H_{2}O has been studied with a multielectron coincidence method, and a process leading to autoionizing O^{*} fragments has been revealed. The breaking of the two O–H bonds producing the autoionizing O^{*} fragments occurs for highly excited H_{2}O^{2+} populated by the initial Auger decay. The O^{*} fragments are more favorably produced in the decay from the satellite states, resulting from the larger population of highly excited H_{2}O^{2+} states inheriting the valence excitation in the initial state.

Communication: Excited states, dynamic correlation functions and spectral properties from full configuration interaction quantum Monte Carlo
View Description Hide DescriptionIn this communication, we propose a method for obtaining isolated excited states within the full configuration interaction quantum Monte Carlo framework. This method allows for stable sampling with respect to collapse to lower energy states and requires no uncontrolled approximations. In contrast with most previous methods to extract excited state information from quantum Monte Carlo methods, this results from a modification to the underlying propagator, and does not require explicit orthogonalization, analytic continuation, transient estimators, or restriction of the Hilbert space via a trial wavefunction. Furthermore, we show that the propagator can directly yield frequencydomain correlation functions and spectral functions such as the density of states which are difficult to obtain within a traditional quantum Monte Carlo framework. We demonstrate this approach with pilot applications to the neon atom and beryllium dimer.
 Top

 ARTICLES

 Theoretical Methods and Algorithms

Accounting for the kinetics in order parameter analysis: Lessons from theoretical models and a disordered peptide
View Description Hide DescriptionMolecular simulations as well as single molecule experiments have been widely analyzed in terms of order parameters, the latter representing candidate probes for the relevant degrees of freedom. Notwithstanding this approach is very intuitive, mounting evidence showed that such descriptions are inaccurate, leading to ambiguous definitions of states and wrong kinetics. To overcome these limitations a framework making use of order parameter fluctuations in conjunction with complex network analysis is investigated. Derived from recent advances in the analysis of single molecule time traces, this approach takes into account the fluctuations around each time point to distinguish between states that have similar values of the order parameter but different dynamics. Snapshots with similar fluctuations are used as nodes of a transition network, the clusterization of which into states provides accurate Markovstatemodels of the system under study. Application of the methodology to theoretical models with a noisy order parameter as well as the dynamics of a disordered peptide illustrates the possibility to build accurate descriptions of molecular processes on the sole basis of order parameter time series without using any supplementary information.

Testing recent chargeonspring type polarizable water models. I. Melting temperature and ice properties
View Description Hide DescriptionWe determined the freezing point of eight molecular models of water. All models use the chargeonspring (COS) method to express polarization. The studied models were the COS/G2, COS/G3 [H. Yu and W. F. van Gunsteren, J. Chem. Phys.121, 9549 (2004)10.1063/1.1805516], the COS/B2 [H. Yu, T. Hansson, and W. F. van Gunsteren, J. Chem. Phys.118, 221 (2003)10.1063/1.1523915], the SWM4DP [G. Lamoureux, A. D. MacKerell, Jr., and B. Roux, J. Chem. Phys.119, 5185 (2003)10.1063/1.1598191], the SWM4NDP [G. Lamoureux, E. Harder, I. V. Vorobyov, B. Roux, and A. D. MacKerell, Jr., Chem. Phys. Lett.418, 245 (2006)10.1016/j.cplett.2005.10.135], and three versions of our model, the BKd1, BKd2, and BKd3. The BKd1 is the original Gaussian model [P. T. Kiss, M. Darvas, A. Baranyai, and P. Jedlovszky, J. Chem. Phys.136, 114706 (2012)10.1063/1.3692602] with constant polarization and with a simple exponential repulsion. The BKd2 applies fielddependent polarizability[A. Baranyai and P. T. Kiss, J. Chem. Phys.135, 234110 (2011)10.1063/1.3670962], while the BKd3 model has variable size to approximate the temperaturedensity (Tρ) curve of water [P. T. Kiss and A. Baranyai, J. Chem. Phys.137, 084506 (2012)10.1063/1.4746419]. We used the thermodynamic integration (TI) and the GibbsHelmholtz equation to determine the equality of the free energy for liquid water and hexagonal ice (Ih) at 1 bar. We used the TIP4P and the SPC/E models as reference systems of the TI. The studied models severely underestimate the experimental melting point of ice Ih. The calculated freezing points of the models are the following: COS/G2, 215 K; COS/G3, 149 K; SWM4DP, 186 K; BKd1, 207 K; BKd2, 213 K; BKd3, 233 K. The freezing temperature of the SWM4NDP system is certainly below 120 K. It might even be that the water phase is more stable than the ice Ih at 1 bar in the full temperature range. The COS/B2 model melts below 100 K. The best result was obtained for the BKd3 model which indicates that correct description of the (Tρ) curve improves the estimation of the freezing point. We also determined and compared the densities of highpressurepolymorphs of ice for these models.

Testing the recent chargeonspring type polarizable water models. II. Vaporliquid equilibrium
View Description Hide DescriptionWe studied the vaporliquid coexistence region of seven molecular models of water. All models use the chargeonspring (COS) method to express polarization. The studied models were the COS/G2, COS/G3 [H. Yu and W. F. van Gunsteren, J. Chem. Phys.121, 9549 (2004)10.1063/1.1805516], the SWM4DP [G. Lamoureux, A. D. MacKerell, Jr., and B. Roux, J. Chem. Phys.119, 5185 (2003)10.1063/1.1598191], the SWM4NDP [G. Lamoureux, E. Harder, I. V. Vorobyov, B. Roux, and A. D. MacKerell, Jr., Chem. Phys. Lett.418, 245 (2006)10.1016/j.cplett.2005.10.135], and three versions of our model, the BKd1, BKd2, and BKd3. The BKd1 is the original Gaussian model [P. T. Kiss, M. Darvas, A. Baranyai, and P. Jedlovszky, J. Chem. Phys.136, 114706 (2012)10.1063/1.3692602] with constant polarization and with a simple exponential repulsion. The BKd2 applies fielddependent polarizability[A. Baranyai and P. T. Kiss, J. Chem. Phys.135, 234110 (2011)10.1063/1.3670962], while the BKd3 model has variable size to approximate the temperaturedensity (Tρ) curve of water [P. T. Kiss and A. Baranyai, J. Chem. Phys.137, 194102 (2012)10.1063/1.4767063]. We calculated the second virial coefficient, the heat of vaporization,equilibrium vapor pressure, the vaporliquid coexistence curve, and the surface tension in terms of the temperature. We determined and compared the critical temperatures, densities, and pressures of the models. We concluded that the high temperature slope of the (Tρ) curve accurately predicts the critical temperature. We found that Gaussian charge distributions have clear advantages over the point charges describing the critical region. It is impossible to describe the vaporliquid coexistence properties consistently with nonpolarizable models, even if their critical temperature is correct.

On the suppression and significance of ghost transmission in electron transport modeling of single molecule junctions
View Description Hide DescriptionThe difficulty in achieving experimental control over a metalmoleculemetal junction formation hinders the understanding of the relationship between the contact geometry and electron transmittance. Computational studies on the other hand have the potential to resolve structural effects on the transport in molecular junctions. In a recent computational effort substantial transport was indicated even in the case where all the junction atoms were removed, while their corresponding atomic basis functions were included in the basis set (i.e., ghost atoms). In this report we explain the origin of the artifact termed as “ghost transmission.” We provide a systematic analysis of the factors that enhance or suppress the artifact. We find that symmetric electronic densities at the two metalmolecule interfaces can lead to an amplification of the artificial transmission. In addition, interaction between an unpaired electron of the left electrode with one in the right electrode results with a substantial increase in “ghost transmission.” Finally we find that a selfconsistent single particle Green's function formalism that solves the junction electronic structure selfconsistently with respect to the electrodes selfenergies, reduces the artifact substantially.

Spindependent gradient correction for more accurate atomization energies of molecules
View Description Hide DescriptionWe discuss, simplify, and improve the spindependent correction of Constantin et al. [Phys. Rev. B84, 233103 (2011)10.1103/PhysRevB.84.233103] for atomization energies, and develop a density parameter of the form v∝∇n/n ^{10/9}, found from the statistical ensemble of oneelectron densities. The here constructed exchangecorrelation generalized gradient approximations (GGAs), named zvPBEsol and zvPBEint, show a broad applicability, and a good accuracy for many applications, because these corrected functionals significantly improve the atomization and binding energies of molecular systems, without worsening the behavior of the original functionals (PBEsol and PBEint) for other properties. This spindependent correction is also applied to metaGGA dynamical correlation functionals combined with exactexchange; in this case a significant (about 30%) improvement in atomization energies of small molecules is found.

Explicit systembath correlation calculated using the hierarchical equations of motion method
View Description Hide DescriptionThe hierarchical equations of motion (HEOM) method has recently been widely applied to many problems of quantum dynamics in condensed phase. It is now well known that the auxiliary density operators (ADOs) in the HEOM formalism contain systembath correlations that are important in calculating various dynamical properties, yet quantitative relations to explicitly calculate such correlations from the ADOs are still scarce. This paper extends a previous study [Q. Shi et al., J. Chem. Phys.130, 164518 (2009)10.1063/1.3125003] in investigating the physical meaning of ADOs to general spectral densities and lower temperature cases. Using the pathintegral technique, we derive exact relations between the expectation values of the collective bath coordinate and the ADOs, which could be very useful in investigating the correlated systembath dynamics directly with the HEOM formalism. Numerical examples concerning the evolution of the expectation values of the collective bath coordinate are also presented.

Estimating timecorrelation functions by sampling and unbiasing dynamically activated events
View Description Hide DescriptionTransition path sampling is a rareevent method that estimates statetostate timecorrelation functions in manybody systems from samples of short trajectories. In this framework, it is proposed to bias the importance function using the lowest Jacobianeigenvalue moduli along the dynamical trajectory. A lowest eigenvalue modulus is related to the lowest eigenvalue of the Hessian matrix and is evaluated here using the Lanczos algorithm as in activationrelaxation techniques. This results in favoring the sampling of activated trajectories and enhancing the occurrence of the rare reactive trajectories of interest, those corresponding to transitions between locally stable states. Estimating the timecorrelation functions involves unbiasing the sample of simulated trajectories which is done using the multistate Bennett acceptance ratio (MBAR) method. To assess the performance of our procedure, we compute the timecorrelation function associated with the migration of a vacancy in αiron. The derivative of the estimated timecorrelation function yields a migration rate in agreement with the one given by transition state theory. Besides, we show that the information relative to rejected trajectories can be recycled within MBAR, resulting in a substantial speedup. Unlike original transition pathsampling, our approach does not require computing the reversible work to confine the trajectory endpoints to a reactive state.

Optimal diabatic states based on solvation parameters
View Description Hide DescriptionA new method for obtaining diabatic electronic states of a molecular system in a condensed environment is proposed and evaluated. This technique, which we denote as EdmistonRuedenberg (ER)ɛ diabatization, forms diabatic states as a linear combination of adiabatic states by minimizing an approximation to the total coupling between states in a medium with temperature T and with a characteristic Pekar factor C. ERɛ diabatization represents an improvement upon previous localized diabatization methods for two reasons: first, it is sensitive to the energy separation between adiabatic states, thus accounting for fluctuations in energy and effectively preventing overmixing. Second, it responds to the strength of systemsolvent interactions via parameters for the dielectric constant and temperature of the medium, which is physically reasonable. Here, we apply the ERɛ technique to both intramolecular and intermolecular excitation energy transfer systems. We find that ERɛ diabatic states satisfy three important properties: (1) they have small derivative couplings everywhere; (2) they have small diabatic couplings at avoided crossings, and (3) they have negligible diabatic couplings everywhere else. As such, ERɛ states are good candidates for socalled “optimal diabatic states.”

A mathematical proof of the zeroth “law” of thermodynamics and the nonlinear Fourier “law” for heat flow
View Description Hide DescriptionWhat is now known as the zeroth “law” of thermodynamics was first stated by Maxwell in 1872: at equilibrium, “Bodies whose temperatures are equal to that of the same body have themselves equal temperatures.” In the present paper, we give an explicit mathematical proof of the zeroth “law” for classical, deterministic, Tmixing systems. We show that if a body is initially not isothermal it will in the course of time (subject to some simple conditions) relax to isothermal equilibrium where all parts of the system will have the same temperature in accord with the zeroth “law.” As part of the derivation we give for the first time, an exact expression for the far from equilibrium thermal conductivity. We also give a general proof that the infinitetime integral, of transient and equilibrium autocorrelation functions of fluxes of nonconserved quantities vanish. This constitutes a proof of what was called the “heat death of the Universe” as was widely discussed in the latter half of the 19th century.

Foraging on the potential energy surface: A swarm intelligencebased optimizer for molecular geometry
View Description Hide DescriptionWe present a stochastic, swarm intelligencebased optimization algorithm for the prediction of global minima on potential energy surfaces of molecular clusterstructures. Our optimization approach is a modification of the artificial bee colony (ABC) algorithm which is inspired by the foraging behavior of honey bees. We apply our modified ABC algorithm to the problem of global geometryoptimization of molecular clusterstructures and show its performance for clusters with 2–57 particles and different interatomic interaction potentials.

Calculations of potential energy surfaces using Monte Carlo configuration interaction
View Description Hide DescriptionWe apply the method of Monte Carloconfiguration interaction (MCCI) to calculate groundstatepotential energy curves for a range of small molecules and compare the results with full configuration interaction. We show that the MCCI potential energy curve can be calculated to relatively good accuracy, as quantified using the nonparallelity error, using only a very small fraction of the full configuration interaction space. In most cases the potential curve is of better accuracy than its constituent singlepoint energies. We finally test the MCCI program on systems with basis sets beyond full configuration interaction: a lattice of 50 hydrogen atoms and ethylene. The results for ethylene agree fairly well with other computational work while for the lattice of 50 hydrogens we find that the fraction of the full configuration interaction space we were able to consider appears to be too small as, although some qualitative features are reproduced, the potential curve is less accurate.

Electronic energy transfer: Localized operator partitioning of electronic energy in composite quantum systems
View Description Hide DescriptionA Hamiltonian based approach using spatially localized projection operators is introduced to give precise meaning to the chemically intuitive idea of the electronic energy on a quantum subsystem. This definition facilitates the study of electronic energy transfer in arbitrarily coupled quantum systems. In particular, the decomposition scheme can be applied to molecular components that are strongly interacting (with significant orbital overlap) as well as to isolated fragments. The result defines a consistent electronic energy at all internuclear distances, including the case of separated fragments, and reduces to the wellknown Förster and Dexter results in their respective limits. Numerical calculations of coherent energy and charge transfer dynamics in simple model systems are presented and the effect of collisionally induced decoherence is examined.
 Atoms, Molecules, and Clusters

Excess protons in mesoscopic wateracetone nanoclusters
View Description Hide DescriptionWe carried out molecular dynamics simulation experiments to examine equilibrium and dynamical characteristics of the solvation of excess protons in mesoscopic, [m:n] binary polar clusters comprising m = 50 water molecules and n = 6, 25, and 100 acetone molecules. Contrasting from what is found in conventional macroscopic phases, the characteristics of the proton solvation are dictated, to a large extent, by the nature of the concentration fluctuations prevailing within the clusters. At low acetone contents, the overall cluster morphology corresponds to a segregated aqueous nucleus coated by an external aprotic phase. Under these circumstances, the proton remains localized at the surface of the water core, in a region locally deprived from acetone molecules. At higher acetone concentrations, we found clear evidence of the onset of the mixing process. The cluster structures present aqueous domains with irregular shape, fully embedded within the acetone phase. Still, the proton remains coordinated to the aqueous phase, with its closest solvation shell composed exclusively by three water molecules. As the relative concentration of acetone increases, the time scales characterizing proton transfer events between neighboring water molecules show considerable retardations, stretching into the nanosecond time domain already for n ∼ 25. In waterrich aggregates, and similarly to what is found in the bulk, proton transfers are controlled by acetone/water exchange processes taking place at the second solvation shell of the proton. As a distinctive feature of the transfer mechanism, translocation pathways also include diffusive motions of the proton from the surface down into inner regions of the underlying water domain.

Kinetics of chemical ordering in a AgPt nanoalloy particle via firstprinciples simulations
View Description Hide DescriptionThe energetics and kinetic energy barriers of vacancy/atom exchange in a 37atom truncated octahedron AgPt binary cluster in the Agrich range of compositions are investigated via a firstprinciples atomistic approach. The energy of the local minima obtained considering various distributions of a single vacancy and a few Pt atoms within the cluster and the energy barriers connecting them are evaluated using accurate densityfunctional calculations. The effects of the simultaneous presence of a vacancy and Pt atoms are found to be simply additive when their distances are larger than firstneighbors, whereas when they can be stabilizing at low Pt content due to the release of strain by the Pt/vacancy interaction or destabilizing close to a perfect Pt(core)/Ag(shell) arrangement. It is found that alloying with Pt appreciably increases the barriers for homotops transformations, thus rationalizing the issues encountered at the experimental level in producing AgPt equilibrated nanoparticles and bulk phase diagram.

Theoretical prediction on the structures and stability of the noblegas containing anions FNgCC^{−} (Ng=He, Ar, Kr, and Xe)
View Description Hide DescriptionWe have made highlevel theoretical study on a new type of noblegas (Ng) containing anions FNgCC^{−}. The calculated short Ng−CC bond lengths of 1.13, 1.77, 1.89, and 2.04 Å for Ng=He, Ar, Kr, and Xe, respectively, and the electron density distributions indicated strong covalent interactions between the Ng and CC induced by the polarizing fluoride ion. Except for FHeCC^{−}, the structures of all other FNgCC^{−} were predicted to be linear. The intrinsic stability of the FNgCC^{−} was studied by calculating the energies of the threebody dissociation reaction: FNgCC^{−} → F^{−} + Ng + CC and by calculating the energy barriers of the twobody dissociation reaction: FNgCC^{−} → Ng + FCC^{−}. The results showed that FNgCC^{−} (Ng=Ar, Kr, Xe) could be kinetically stable in the gas phase with the threebody dissociation energies of 17, 37, and 64 kcal/mol and two bodydissociation barriers of 22, 31, and 42 kcal/mol, respectively, at the coupledcluster single double (triple)/augccpVQZ level of theory. The structures and the stability were also confirmed using the multireference CASPT2 calculation. Future experimental identification of the FNgCC^{−} anions is expected under cryogenic conditions.

Vapor–liquid nucleation in two dimensions: On the intriguing sign switch of the errors of the classical nucleation theory
View Description Hide DescriptionA nucleation study of a twodimensional (2D) LennardJones (LJ) system is done using the aggregationvolumebias Monte Carlo with umbrella sampling method. The results obtained from this simulation study was compared to those predicted by the classical nucleation theory (CNT). It was found that the nucleationfree energy obtained for this 2D LJ system was underestimated by CNT; however, this result is significantly different from that found for the 3D LJ system where CNT overestimates the free energy. These results are generally in agreement with previous studies on these systems. While both errors can be traced to the incorrect description of the smallest clusters by the theory, structural analysis reveals striking differences between 2D and 3D clusters, leading to a possible source for this observed sign switch. In particular, the radius of gyration data indicates that for the 3D LJ system, clusters formed at the beginning are fractal and the cluster growth is accompanied by an increase of the dimensionality, whereas clusters in 2D show little sign of this dimensionality transition.

Quantum dynamical study of the electronic nonadiabaticity in the D + DBr → Br(Br^{*}) + D_{2} reaction on new diabatic potential energy surfaces
View Description Hide DescriptionA set of diabatic potential energy surfaces, that describe the D + DBr → Br(P_{1/2},_{3/2}) + D_{2}reaction, is constructed based on MRCI/augccpV5Z calculations at 29 526 grid points. Timedependent wave packet calculations are performed for groundstate DBr initially with collision energies up to 2.0 eV to investigate possible electronic nonadiabaticity in this reaction.Reaction probabilities and integral cross sections are calculated. The results show negligible nonadiabatic effects for the title reaction in the energy range considered here, confirming experimental work of Zare and coworkers. In addition, the calculated thermal rate constants are in good agreement with experimental ones.

Core and valence excitations in resonant Xray spectroscopy using restricted excitation window timedependent density functional theory
View Description Hide DescriptionWe report simulations of Xray absorption near edge structure(XANES), resonant inelastic Xray scattering (RIXS) and 1D stimulated Xray Raman spectroscopy (SXRS) signals of cysteine at the oxygen, nitrogen, and sulfur K and edges. Comparison of the simulated XANES signals with experiment shows that the restricted window timedependent density functional theory is more accurate and computationally less expensive than the static exchange method. Simulated RIXS and 1D SXRS signals give some insights into the correlation of different excitations in the molecule.