Volume 131, Issue 13, 07 October 2009

We report on the phase behavior of an aqueous binary charged sphere suspension under exhaustively deionized conditions as a function of number fraction of small particles and total number density. The mixture of size ratio displays a complex phase diagram. Formation of bcc crystals with no compositional order dominates. We observe a region of drastically decreased crystal stability at with the minimum located at at densities above . A peaked region of enhanced stability is observed at . Further light scattering experiments were conducted to characterize the crystallization time scales, the density profiles, and the composition of formed phases. For crystal formation is partially assisted by gravity, i.e., gravitational separation of the two species precedes crystal formation for samples in the coexistence range. In the composition range corresponding to the decreased crystal stability only lower bounds of the freezing and melting line are obtained, but the general shape of the phase diagram is retained. At and two different crystalline phases coexist in the bulk, while at additional Bragg peaks appear in the static light scattering experiments. This strongly suggests that we observe an eutectic in the region of decreased stability, while the enhanced stability at seems to correlate with compound formation.
 COMMUNICATIONS


Molecular structure determination from xray scattering patterns of laseraligned symmetrictop molecules
View Description Hide DescriptionWe investigate the molecular structure information contained in the xray diffraction patterns of an ensemble of rigid molecules aligned by an intense laser pulse at finite rotational temperature. The diffraction patterns are calculated at an xray photon energy of 20 keV to probe molecular structure at angstromscale resolution. We find that a structural reconstruction algorithm based on iterative phase retrieval fails to extract a reliable structure. However, the high atomic number of Br compared with C or F allows each diffraction pattern to be treated as a hologram. Using this approach, the azimuthal projection of the molecular electron density about the alignment axis may be retrieved.
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 ARTICLES

 Theoretical Methods and Algorithms

Unified expression for the rate constant of the bridged electron transfer derived by renormalization
View Description Hide DescriptionElectron transfer(ET) from a donor to an acceptor through an energetically close intermediary state on a midway molecule is a process found often in natural and artificial solarenergy capturing systems such as photosynthesis. This process has often been thought of in terms of opposing “superexchange” and “sequential or hopping” mechanisms, and the recent theory of Sumi and Kakitani (SK) [J. Phys. Chem. B105, 9603 (2001)] has shown an interpolation between these mechanisms. In their theory, however, dynamics governing the most interesting intermediary region between them has artificially been introduced by phenomenologies. The dynamics is played by decoherence among electronic states, their decay, and thermalization of phonons in the medium. The present work clarifies the dynamics on a microscopic basis by means of renormalization in electronic coupling among the states, and gives a complete unified expression of the rate constant of the ET. It merges to that given by the SK theory in the semiclassical approximation for phononsinteracting with an electron transferred.

Generalized Langevin models of molecular dynamics simulations with applications to ion channels
View Description Hide DescriptionWe present a new methodology, which combines molecular dynamics and stochastic dynamics, for modeling the permeation of ions across biological ion channels. Using molecular dynamics, a free energy profile is determined for the ion(s) in the channel, and the distribution of random and frictional forces is measured over discrete segments of the ion channel. The parameters thus determined are used in stochastic dynamics simulations based on the nonlinear generalized Langevin equation. We first provide the theoretical basis of this procedure, which we refer to as “distributional molecular dynamics,” and detail the methods for estimating the parameters from molecular dynamics to be used in stochastic dynamics. We test the technique by applying it to study the dynamics of ion permeation across the gramicidin pore. Given the known difficulty in modeling the conduction of ions in gramicidin using classical molecular dynamics, there is a degree of uncertainty regarding the validity of the MDderived potential of mean force (PMF) for gramicidin. Using our techniques and systematically changing the PMF, we are able to reverse engineer a modified PMF which gives a currentvoltage curve closely matching experimental results.

Modified adiabatic approximation: Charge asymmetry in and HD
View Description Hide DescriptionThe modified adiabatic approximation is discussed, in which the interaction of electrons with nuclei is partitioned between the electronic and nuclear Hamiltonian, in order to simulate the finite nuclear mass effect. The proposed formalism is universal and can be used in calculations for molecules of any size. The effect of electron localization on the deuteron in vibrationally excited states of and the permanent dipole moment of HD, typically both explained in terms of nonadiabatic couplings between and states, are well reproduced with this method.

Exploration of effective potential landscapes using coarse reverse integration
View Description Hide DescriptionWe describe a reverse integration approach for the exploration of lowdimensional effective potential landscapes. Coarse reverse integration initialized on a ring of coarse states enables efficient navigation on the landscape terrain: Escape from local effective potential wells, detection of saddle points, and identification of significant transition paths between wells. We consider several distinct ring evolution modes: Backward stepping in time, solution arc length, and effective potential. The performance of these approaches is illustrated for a deterministic problem where the energy landscape is known explicitly. Reverse ring integration is then applied to noisy problems where the ring integration routine serves as an outer wrapper around a forwardintime inner simulator. Two versions of such inner simulators are considered: A Gillespietype stochastic simulator and a molecular dynamics simulator. In these “equationfree” computational illustrations, estimation techniques are applied to the results of short bursts of inner simulation to obtain the unavailable (in closedform) quantities (local drift and diffusion coefficient estimates) required for reverse ring integration; this naturally leads to approximations of the effective landscape.

Using the ONIOM hybrid method to apply equation of motion CCSD to larger systems: Benchmarking and comparison with timedependent density functional theory, configuration interaction singles, and timedependent Hartree–Fock
View Description Hide DescriptionEquation of motion coupledcluster singles and doubles (EOMCCSD) is one of the most accurate computational methods for the description of oneelectron vertical transitions. However, its scaling, where is the number of basis functions, often makes the study of molecules larger than 10–15 heavy atoms prohibitive. In this work we investigate how accurately less expensive methods can approximate the EOMCCSD results. We focus on our own layer integrated molecular orbital molecular mechanics (ONIOM) hybrid scheme, where the system is partitioned into regions which are treated with different levels of theory. For our set of benchmark calculations, the comparison of conventional configuration interaction singles (CIS), timedependent Hartree–Fock (TDHF), and timedependent density functional theory (TDDFT) methods and ONIOM (with different low level methods) showed that the best accuracycomputational time combination is obtained with ONIOM(EOM:TDDFT), which has a rms of the error with respect to the conventional EOMCCSD of 0.06 eV, compared with 0.47 eV of the conventional TDDFT.

Comprehensive investigation about the second order term of thermodynamic perturbation expansion
View Description Hide DescriptionMonte Carlo simulations are carried out for the second order term in the thermodynamicperturbation expansion around a hard sphere reference fluid. The sample potentials considered cover a wide spectrum: From two frequently employed, namely hard sphere plus square well potential and hard core attractive Yukawa potential, to two kinds of repulsive potentials, namely hard sphere plus square shoulder potential and hard sphere plus triangle shoulder potential; the investigated potential range also extends from extremely short range to rather long range. The obtained simulation data are used to evaluate performance of two theoretical approaches, i.e., a traditional macroscopic compressibility approximation (MCA) and a recent coupling parameter expansion. Extensive comparison shows that the coupling parameter expansion provides a reliable method for accurately calculating the second order term of the high temperature series expansion, while the widely accepted MCA fails quantitatively or even qualitatively for most of the situations investigated.

Inversion of radial distribution functions to pair forces by solving the Yvon–Born–Green equation iteratively
View Description Hide DescriptionWe develop a new method to invert the target profiles of radial distribution functions (RDFs) to the pair forces between particles. The target profiles of RDFs can be obtained from allatom molecular dynamics (MD) simulations or experiments and the inverted pair forces can be used in molecular simulations at a coarsegrained (CG) scale. Our method is based on a variational principle that determines the mean forces between CG sites after integrating out the unwanted degrees of freedom. The solution of this variational principle has been shown to correspond to the Yvon–Born–Green (YBG) equation [Noid et al., J. Phys. Chem. B111, 4116 (2007)]. To invert RDFs, we solve the YBG equation iteratively by running a CG MD simulation at each step of iteration. A novelty of the iterativeYBG method is that during iteration, CG forces are updated according to the YBG equation without imposing any approximation as is required by other methods. As a result, only three to ten iterations are required to achieve convergence for all cases tested in this work. Furthermore, we show that not only are the target RDFs reproduced by the iterative solution; the profiles of the threebody correlation function in the YBG equation computed from allatom and CG simulations also have a better agreement. The iterativeYBG method is applied to compute the CG forces of four molecular liquids to illustrate its efficiency and robustness: water, ethane, ethanol, and a water/methanol mixture. Using the resulting CG forces, all of the target RDFs observed in allatom MD simulations are reproduced. We also show that the iterativeYBG method can be applied with a virial constraint to expand the representability of a CG force field. The iterativeYBG method thus provides a general and robust framework for computing CG forces from RDFs and could be systematically generalized to go beyond pairwise forces and to include higherbody interactions in a CG force field by applying the aforementioned variational principle to derive the corresponding YBG equation for iterative solution.

Quantum mechanical scoring for protein docking
View Description Hide DescriptionWe develop a docking protocol based on quantum mechanical/molecular mechanical calculations in which quantum mechanical energy is used as scoring. We test the protocol with three groups of examples with various binding site characteristics. The new docking method performs as well as or better than conventional docking methods in all three groups. In particular, for proteins with primarily hydrophobicbinding sites,structural motifs with possible interactions are often found and it is shown that these can be better modeled with quantum mechanical scoring docking than force field based methods. It seems that the new method performs in such cases to a great accuracy.

Toward improved density functionals for the correlation energy
View Description Hide DescriptionEleven density functionals, including some of the most widely used ones, are tested on their ability to predict nonrelativistic, electron correlation energies for the 17 atoms from He to Ar, the 17 cations from to , and 11 state atoms from Ca to Rn. They all lead to relatively poor predictions for the heavier atoms. Reparametrization of these functionals improves their performance for light atoms but does not alleviate their problems with the heavier, closedshell atoms. Several novel, fewparameter, density functionals for the correlation energy are developed heuristically. Four new functionals lead to qualitatively improved predictions for the heavier atoms without unreasonably compromising accuracy for the lighter atoms. Further progress would be facilitated by reliable estimates of electron correlation energies for more atoms, particularly heavy ones.

Optimal estimators and asymptotic variances for nonequilibrium pathensemble averages
View Description Hide DescriptionExisting optimal estimators of nonequilibrium pathensemble averages are shown to fall within the framework of extended bridge sampling. Using this framework, we derive a general minimalvariance estimator that can combine nonequilibrium trajectory data sampled from multiple pathensembles to estimate arbitrary functions of nonequilibrium expectations. The framework is also applied to obtain asymptotic variance estimates, which are a useful measure of statistical uncertainty. In particular, we develop asymptotic variance estimates pertaining to Jarzynski’s equality for free energies and the Hummer–Szabo expressions for the potential of mean force, calculated from uni or bidirectional path samples. These estimators are demonstrated on a model singlemolecule pulling experiment. In these simulations, the asymptotic variance expression is found to accurately characterize the confidence intervals around estimators when the bias is small. Hence, the confidence intervals are inaccurately described for unidirectional estimates with large bias, but for this model it largely reflects the true error in a bidirectional estimator derived by Minh and Adib.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Dissociative charge exchange dynamics of and
View Description Hide DescriptionTranslational spectroscopy coupled with coincidence detection techniques has been used to study the dissociation dynamics of ground state products resulting from charge exchange between keV beams of and cesium. Analysis of the product kinetic energy release suggests that dissociation of and proceeds from initial populations in the , , and Rydberg electronic states of the neutral molecule. Although all three excited electronic states must eventually couple to the ground state of , the resulting dissociation dynamics exhibit a significant dependence on the initial electronic state. Potential mechanisms are discussed in light of the observed product kinetic energy release distributions.

A theoretical study of water equilibria: The cluster distribution versus temperature and pressure for , , and ice
View Description Hide DescriptionThe size distribution of waterclusters at equilibrium is studied using quantumchemical calculations in combination with statistical thermodynamics. The necessary energetic data is obtained by quantumchemical B3LYP computations and through extrapolations from the B3LYP results for the larger clusters.Clusters with up to 60 molecules are included in the equilibrium computations. Populations of different cluster sizes are calculated using both an ideal gas model with noninteracting clusters and a model where a correction for the interactionenergy is included analogous to the van der Waals law. In standard vapor the majority of the water molecules are monomers. For the ideal gas model at 1 atm large clusters [56mer (0–120 K) and 28mer (100–260 K)] dominate at low temperatures and separate to smaller clusters [21–22mer (170–280 K) and 4–6mer (270–320 K) and to monomers (300–350 K)] when the temperature is increased. At lower pressure the transition from clusters to monomers lies at lower temperatures and fewer cluster sizes are formed. The computed size distribution exhibits enhanced peaks for the clusters consisting of 21 and 28 water molecules; these sizes are for protonated waterclusters often referred to as magic numbers. If clustercluster interactions are included in the model the transition from clusters to monomers is sharper (i.e., occurs over a smaller temperature interval) than when the idealgas model is used. Clusters with 20–22 molecules dominate in the liquid region. When a large icelike cluster is included it will dominate for temperatures up to 325 K for the noninteracting clusters model. Thermodynamic properties (, ) were calculated with in general good agreement with experimental values for the solid and gas phase. A formula for the number of Hbond topologies in a given cluster structure is derived. For the 20mer it is shown that the number of topologies contributes to making the population of dodecahedronshaped cluster larger than that of a lowerenergy fused prismcluster at high temperatures.

The photoelectron spectrum of the ethoxide anion: Conical intersections, the spinorbit interaction, and sequence bands
View Description Hide DescriptionThe negative ion photoelectron spectrum of the ethoxide anion (ethoxide) and that of its fully deuterated analog, ethoxide, are calculated using the multimode vibronic coupling approach. A two state quasidiabatic Hamiltonian is constructed which includes all terms through second order in the full 18 dimensional internal coordinate space. is centered at the ab initio determined minimum energy crossing (MEX) point on the symmetryallowed accidental seam of conical intersection and determined from ab initio energy gradients and derivative couplings. It reproduces the local topography of the MEX, in addition to accurately representing the geometries, energetics, and harmonic frequencies of equilibrium and saddle point structures located on the ground electronic statepotential energy surface in the vicinity of the MEX. Spinorbit effects are included. The results for ethoxy are compared to photoelectron and slow electron velocitymap imaging (SEVI) spectra. By comparing the measured and predicted photoelectron spectrum, the accuracy of the electronic structure treatment is inferred. The existence of sequence bands in the SEVI spectrum is established.

Theoretical investigation of the potential energy surface of the van der Waals complex
View Description Hide DescriptionThe interactionpotential energy surface of the van der Waals complex has been calculated for a broad range of intermolecular separations and configurations in the approximation of rigid interacting molecules at the CCSD(T) and MP2 levels of theory using the correlation consistent augccpVTZ basis set. The BSSE correction was taken into account for all the calculations. The most stable configurations of the complex were found. Binding energies were calculated in the CBS limit with accounting for the molecular deformations. The harmonic and anharmonic fundamental vibrational frequencies and rotational constants for the ground and first excited vibrational states were calculated for the most stable configurations at the MP2 level of theory with BSSE correction. Fitting parameters were found for the most stable configuration for the LennardJones and Esposti–Werner potentials.

Homogeneous nucleation with magic numbers: Aluminum
View Description Hide DescriptionHomogeneous nucleation of clusters that exhibit magic numbers is studied numerically, using as an example aluminum at 2000 K, based on recent calculations of free energies [Li et al., J. Phys. Chem. C111, 16227 (2007)] and condensationrate constants [Li and Truhlar, J. Phys. Chem. C112, 11109 (2008)] that provide a database for up to . The nucleation behavior for saturation ratios greater than about 4.5 is found to be dominated by a peak in the free energy change associated with the reaction at , making it the critical size over a wide range of saturation ratios. Calculated steadystate nucleation rates are many orders of magnitude lower than predicted by classical nucleation theory (CNT). The onset of nucleation is predicted to occur at a saturation ratio of about 13.3, compared to about 5.1 in CNT, while for saturation ratios greater than about 25 the abundance of magicnumbered clusters becomes high enough to invalidate the assumption that cluster growth occurs solely by monomer addition. Transient nucleation is also predicted to be substantially different than predicted by CNT, with a much longer time required to reach steady state: about at a saturation ratio of 20, compared to about from CNT. Magic numbers are seen to play an important role in transient nucleation, as the nucleation currents for clusters of adjacent sizes become equal to each other in temporally successive groups, where the largest cluster in each group is the magicnumbered one.

Multidimensional steric effects for the (B, C) formations in the oriented reaction
View Description Hide DescriptionSteric effects for the (B) and (C) formations in the oriented reaction have been observed as a function of the mutual configuration between molecular orientation and atomic alignment in the collision frame. The mutual configuration exercises the significant influences on the stereoanisotropy for both the reactivity and the branching to the (B) and (C) channels.

Photochemistry of the water dimer: Timedependent quantum wavepacket description of the dynamics at the conical intersection
View Description Hide DescriptionThe photoinduced electrondriven protontransfer dynamics of the waterdimer system has been investigated by timedependent quantum wavepacket calculations. The main nuclear degrees of freedom driving the system from the Frank–Condon region to the conical intersection are the distance between the oxygen atoms and the displacement of the hydrogen atom from the oxygenoxygen bond center. Two important coupling modes have been investigated: Rotation of the Hdonating water dangling proton and asymmetric stretching of the Haccepting water dangling protons’ bonds. Potential energy surfaces of the ground and lowest excited electronic states have been constructed on the basis of ab initio calculations. The timedependent quantum wavepacket propagation has been employed within the (2 + 1)dimensional systems for the description of the nonadiabatic dynamics of water dimer. The effects of the initial vibrational state of the system on the electronic population transfer and dissociation dynamics are presented. To approximate the photochemical behavior of water dimer in bulk water, we add a boundary condition into the (2 + 1)dimensional systems to simulate the existence of water bulk. The results provide insight into the mechanisms of excited state deactivation of the waterdimer system in gas phase and in bulk water through the electrondriven protontransfer process.

Femtosecond pumpprobe photoionizationphotofragmentation spectroscopy: Photoionizationinduced twisting and coherent vibrational motion of azobenzene cation
View Description Hide DescriptionWe report studies of ultrafast dynamics of azobenzene cation using femtosecond photoionizationphotofragmentation spectroscopy. In our experiments, a femtosecond pump pulse first produces an ensemble of azobenzene cations via photoionization of the neutrals. A delayed probe pulse then brings the evolving ionic system to excited states that ultimately undergo ion fragmentation. The dynamics is followed by monitoring either the parention depletion or fragmention formation as a function of the pumpprobe delay time. The observed transients for azobenzene cation are characterized by a constant ion depletion modulated by a rapidly damped oscillatory signal with a period of about 1 ps. Theoretical calculations suggest that the oscillation arises from a vibration motion along the twisting inversion coordinate involving displacements in CNNC and phenylring torsions. The oscillation is damped rapidly with a time constant of about 1.2 ps, suggesting that energy dissipation from the active mode to bath modes takes place in this time scale.

Penning ionization and ion fragmentation of formamide by , , and in molecular beams
View Description Hide DescriptionMass spectra from Penning ionization by metastable atom bombardment (MAB) in the title system at kinetic energies near 1 kcal/mol are reported. The experiments employ a supersonic excited noble gas beam crossing an effusive beam of formamide vapor. Product ions are extracted perpendicular to the plane of the beams, analyzed by a quadrupole mass filter, and counted by a scintillationtype ion counter. Relative to 70 eV electron impact, the and spectra show more extensive breakage of C–N and C–H bonds despite the smaller available energy, while the spectrum shows only the molecular ion ( 45), H atom elimination (44), and the decarbonylation products (17). Fragmentation in the latter system has been analyzed using a combination of ab initio calculations and Rice–Ramsperger–Kassel–Marcus theory with tunneling correction; good agreement with the experimental 45/44/17 intensity ratio is obtained. 15% of 17 and 50% of 44 is attributed to tunneling. The ab initio decarbonylation reaction path yields a hydrogen bonded transition state, which transfers a proton while proceeding downhill to the observed products, while both the path and the energetics support the earlier conclusion that the lowest lying electronically excited state of the ion ( or ) crosses the ground state early along the reaction path, thereby dominating the dynamics of decarbonylation.