Volume 130, Issue 20, 28 May 2009

In this work, lattice Monte Carlo was used to study the effects of crowding on the selfassembly of surfactants. Simulation results show that crowding strongly shifts the critical micelle concentration (CMC) of surfactants from the bulk value. Two effects originated from crowding are found to govern the CMC shift: one is the depletion effect by crowding agents and the other is the available volume for micelle formation. The depletion effects inevitably result in the enrichment of surfactants in crowdingfree regions and cause the decrease in CMC. On the other hand, the appearance of crowding agents decreases the available volume for micelle formation, which reduces the conformational entropy and impedes the micelle formation. Three factors, including the radius of crowding agents, the arrangement of crowding agents, and the volume fraction of crowding agents, are considered in this work to study the crowding effects. The trends of CMC shifts are interpreted from the competition between the depletion effects and the available volume for micelle formation.
 ARTICLES

 Theoretical Methods and Algorithms

Ab initio potential energy curve of . IV. Transition from the covalent to the van der Waals region: Competition between multipolar and correlation forces
View Description Hide DescriptionThe potential energy curve of the fluorine molecule in the ground electronic state is determined and analyzed in the longrange region. The analysis is based on expressing the potential as the sum of the potential energy curve of the uncorrelated, but properly dissociating wave function and the correlation energy contribution. It is shown that, in the longrange region, the former becomes identical with the interaction between the quadrupoles of the fluorine atoms and the latter becomes the London dispersioninteraction. The former is repulsive because of the coaxial quadrupole alignments in the ground state and proportional to . The latter is attractive and proportional to . There moreover exists an additional repulsive force due to the loss of spinorbit coupling upon the bond formation. As a result of these antagonistic interactions, the potential energy curve has a barrier at about 4 Å, with a value about . The descent of the potential toward the minimum, when the atoms approach each other from infinity, begins therefore only at internuclear distances less than about twice the equilibrium distance and is then very steep.

Densitydependent analysis of nonequilibrium paths improves free energy estimates
View Description Hide DescriptionWhen a system is driven out of equilibrium by a timedependent protocol that modifies the Hamiltonian, it follows a nonequilibrium path. Samples of these paths can be used in nonequilibrium work theorems to estimate equilibrium quantities such as free energy differences. Here, we consider analyzing paths generated with one protocol using another one. It is posited that analysis protocols which minimize the lag, the difference between the nonequilibrium and the instantaneous equilibrium densities, will reduce the dissipation of reprocessed trajectories and lead to better free energy estimates. Indeed, when minimal lag analysis protocols based on exactly soluble propagators or relative entropies are applied to several test cases, substantial gains in the accuracy and precision of estimated free energy differences are observed.

Tailored Gauss quadratures, a promising route for an efficient evaluation of multicenter integrals over functions
View Description Hide DescriptionIn the framework of the Fourier integral transform, complicated multicenter integrals, e.g., threecenter nuclear attraction and exchange integrals, over functions involve a multiple integral (double or triple), the innermost of which is a Hankel transform of an exponentially decreasing term. Because of the oscillatory nature of the Hankel transform and the order in which it occurs in the definition of multicenter integrals, i.e., innermost, an efficient evaluation of such a quantity requires highly performant algorithms. In this context, extrapolation techniques emerged, during the past decade, as a possible solution to the problem of evaluating the oscillating semiinfinite integral. With a view to improving the efficiency of future algorithms, this contribution introduces a new technique for the evaluation of the oscillating integral by means of a tailored Gaussian quadrature. Using the case of threecenter nuclear attraction integrals as a working example, it is shown that the new approach allows the semiinfinite integral to be evaluated accurately if not exactly. Further, when the roots and weights of the quadrature are available, a complexity analysis of our algorithm shows encouraging results compared to nonlinear extrapolation techniques.

Capture of particles undergoing discrete random walks
View Description Hide DescriptionIt is shown that particles undergoing discretetime jumps in three dimensions, starting at a distance from the center of an adsorbing sphere of radius , are captured with probability for , where is related to the Fourier transform of the scaled jump distribution and is the distribution’s rootmean square jump length. For particles starting on the surface of the sphere, the asymptotic survival probability is nonzero (in contrast to the case of Brownian diffusion) and has a universal behavior depending only upon . These results have applications to computer simulations of reaction and aggregation.

A fast and efficient algorithm for Slater determinant updates in quantum Monte Carlo simulations
View Description Hide DescriptionWe present an efficient lowrank updating algorithm for updating the trial wave functions used in quantum Monte Carlo (QMC) simulations. The algorithm is based on lowrank updating of the Slater determinants. In particular, the computational complexity of the algorithm is during the step compared to traditional algorithms that require computations, where is the system size. For single determinant trial wave functions the new algorithm is faster than the traditional Sherman–Morrison algorithm for up to updates. For multideterminant configurationinteractiontype trial wave functions of determinants, the new algorithm is significantly more efficient, saving both work and storage. The algorithm enables more accurate and significantly more efficient QMC calculations using configurationinteractiontype wave functions.

A homogeneous nonequilibrium molecular dynamics method for calculating thermal conductivity with a threebody potential
View Description Hide DescriptionIn this work, Evans’ homogeneous nonequilibrium molecular dynamics method for estimating thermal conductivity is extended to systems employing threebody potentials. This extension is put on a firm theoretical basis and applied to a silicon lattice modeled by the Stillinger–Weber potential. Two new methods are suggested for estimating the thermal conductivity based on a range of values of the fictitious force. Also, kinetic theory is used to estimate the linear range of the fictitious force necessary to bias the heat flow, thereby potentially reducing the number of simulations needed to estimate thermal conductivity.

New model core potentials for gold
View Description Hide DescriptionFour model core potentials (MCPs) for gold were developed using results from the thirdorder Douglas–Kroll–Hess relativistic allelectron calculations. The MCPs were developed with four different valence spaces, ranging from the , , and orbitals to , , , , and orbitals. The new MCPs were applied in the calculations of atomic properties and potential energy curves of AuH and . Results indicate that the orbital may be excluded but the orbital must be included in the valence space because of the importance of electron correlation. The model core potential that has the valence space comprising the , , , and orbitals is considered to be the most accurate and efficient of these new potentials.

The irreducible bundle: Further structure in the kinetic energy distribution
View Description Hide DescriptionModern molecular sciences are often concerned with the properties and dynamics of chemical bonds. With the ability to experimentally measure charge density, there is a pressing need to find the relationships between charge density and the properties of chemical bonds. Here we show molecules can be partitioned into unique bond volumes characterized by well defined properties. Moreover, this partitioning recovers unrecognized structure in the kinetic energy distribution.

High order Chin actions in path integral Monte Carlo
View Description Hide DescriptionHigh order actions proposed by Chin have been used for the first time in path integral Monte Carlo simulations. Contrary to the Takahashi–Imada action, which is accurate to the fourth order only for the trace, the Chin action is fully fourth order, with the additional advantage that the leading fourthorder error coefficients are finely tunable. By optimizing two free parameters entering in the new action, we show that the time step error dependence achieved is best fitted with a sixth order law. The computational effort per bead is increased but the total number of beads is greatly reduced and the efficiency improvement with respect to the primitive approximation is approximately a factor of 10. The Chin action is tested in a onedimensional harmonic oscillator, a drop, and bulk liquid. In all cases a sixthorder law is obtained with values of the number of beads that compare well with the pair action approximation in the stringent test of superfluid.

Nonlinear response of vibrational excitons: Simulating the twodimensional infrared spectrum of liquid water
View Description Hide DescriptionA simulation formalism for the nonlinear response of vibrational excitons is presented and applied to the OH stretching vibrations of neat liquid . The method employs numerical integration of the Schrödinger equation and allows explicit treatment of fluctuating transition frequencies, vibrational couplings, dipole moments, and the anharmonicities of all these quantities, as well as nonadiabatic effects. The split operator technique greatly increases computational feasibility and performance. The electrostatic map for the OH stretching vibrations in liquid water employed in our previous study [A. Paarmann et al., J. Chem. Phys.128, 191103 (2008)] is presented. The twodimensional spectra are in close agreement with experiment. The fast 100 fs dynamics are primarily attributed to intramolecular mixing between states in the twodimensional OH stretching potential. Small intermolecular couplings are sufficient to reproduce the experimental energy transfer time scales. Interference effects between Liouville pathways in excitonic systems and their impact on the analysis of the nonlinear response are discussed.

Calculating rate constants and committor probabilities for transition networks by graph transformation
View Description Hide DescriptionA graph transformation procedure is described that enables waiting times, rate constants, and committor probabilities to be calculated within a single scheme for finitestate discretetime Markov processes. The scheme is applicable to any transition network where the states, equilibrium occupation probabilities, and transition probabilities are specified. For networks involving many states or slow overall kinetics, the deterministic graph transformation approach is faster and more accurate than direct diagonalization of the transition matrix, kinetic Monte Carlo, or iterative procedures.

Choleskydecomposed densities in Laplacebased secondorder Møller–Plesset perturbation theory
View Description Hide DescriptionBased on our linearscaling atomic orbital secondorder Møller–Plesset perturbation theory (AOMP2) method [J. Chem. Phys.130, 064107 (2009)], we explore the use of Choleskydecomposed pseudodensity (CDD) matrices within the Laplace formulation. Numerically significant contributions are preselected using our multipolebased integral estimates as upper bounds to twoelectron integrals so that the decay behavior of transformed Coulombtype products is exploited. In addition, we combine our new CDDMP2 method with the resolution of the identity (RI) approach. Even though the use of RI results in a method that shows a quadratic scaling behavior in the dominant steps, gains of up to one or two orders of magnitude vs. our original AOMP2 method are observed in particular for larger basis sets.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Ionospheric chemistry: Theoretical treatment of and of
View Description Hide DescriptionIn light of accurate ab initio calculations, we discuss the charge transfer, vibrational and electronic deexcitations between and through the formation and decomposition of and . For that purpose, we generated the potentials of the electronic ground and excited states of the colliding and molecular species involved in these reactions. We used configuration interaction methods and a large basis set. We predict multistep pathways, which involve both the long range and the molecular regions of the potential energy surfaces of the electronic states of the stable isomers of and those of the weakly bound charge transfer complex . The couplings between these electronic states such as vibronic, Renner–Teller, Jahn–Teller, and spin orbit are believed to play crucial roles during these important ionospheric ionmolecule reactions.

Collisional quenching of NO between 125 and 294 K
View Description Hide DescriptionWe report measurements of the temperaturedependent cross sections for the quenching of fluorescence from the state of NO for temperatures between 125 and 294 K. Thermally averaged cross sections were measured for quenching by , , , and CO in a cryogenically cooled gas flow cell. Picosecond laserinduced fluorescence was time resolved, and the thermally averaged quenching cross sections were determined from the dependence of the fluorescence decay rate on the quenchergas pressure. These measurements extend to lower temperature the range of previously published results for NO and and constitute the first reported measurements of the and CO cross sections for temperatures below 294 K. Between 125 and 294 K, a negative temperature dependence is observed for quenching by NO, , and CO, implicating collisioncomplex formation in all three cases. Over the same temperature range, a constant, nonzero cross section is measured for quenching by . Updated empirical models for the temperature dependence of the cross sections between 125 and 4500 K are recommended based on weighted leastsquares fits to the current lowtemperature results and previously published measurements at higher temperature. The results of over 250 measurements presented here indicate that the collisionless lifetime of NO is approximately 192 ns.

Phase coexistence in melting aluminum clusters
View Description Hide DescriptionThe internal energy distributions for meltingaluminum cluster cations with 100, 101, 126, and 127 atoms have been investigated using multicollision induced dissociation. The experimental results can be best fit with a statistical thermodynamic model that incorporates only fully solidlike and fully liquidlike clusters so that the internal energy distributions become bimodal during melting. This result is consistent with computer simulations of small clusters, where rapid fluctuations between entirely solidlike and entirely liquidlike states occur during the phase change. To establish a bimodal internal energy distribution, the time between the melting and freezing transitions must be longer than the time required for equilibration of the energy distribution (which is estimated to be around under our conditions). For and , the results indicate that this criterion is largely met. However, for and , it appears that the bimodal energy distributions are partly filled in, suggesting that either the time between the melting and freezing transitions is comparable to the equilibration time or that the system starts to switch to macroscopic behavior where the phase change occurs with the two phases in contact.

Dependence of elastic depolarization cross sections on the potential: and
View Description Hide DescriptionElastictensor and depolarization cross sections are computed for the collision of two exemplary diatomic molecules with electronic ground states—OH and NO—with argon. The interaction of a diatomic molecule in a state with a spherical collision partner must be described by two potential energy surfaces (PESs), corresponding to the two asymptotically degenerate electronic states, of and symmetry. Quantum scattering calculations are most naturally based on the average and halfdifference of these two PESs. When is neglected, the depolarization cross sections are found to be significantly reduced in magnitude, while the cross sections are relatively unaffected. In addition, treating the molecules as closedshell species with a corresponding rotational level structure and using to model the PES, we predict depolarization cross sections which differ significantly from those based on full inclusion of the electronic degeneracy and fine structure of these molecules. This indicates that any singlePESbased simulation of the collisional depolarization of these two molecules would be subject to significant error.

Rotational excitation and deexcitation of by para
View Description Hide DescriptionFor the van der Waals molecular system, we generated a new ab initiopotential energy surface (PES). We mapped this PES at the multireference internally contracted configurationinteraction method including the Davidson correction together with a large diffuse basis set. Then, we incorporated our PES into quantum scattering calculations at the close coupling and infinite order sudden approximation methods to cover collision energies ranging from 0.1 up to . After Boltzmann thermal averaging, rate coefficients for temperatures of up to 1000 K are deduced. Discrepancies between our new rates and those computed previously are noticed. This should induce deviations in astrophysical modeling.

Investigation of the van der Waals complex in the overtone range using cw cavity ringdown spectroscopy
View Description Hide DescriptionA slit nozzle supersonic expansion containing acetylene [492 SCCM (SCCM denotes cubic centimeter per minute at STP)] and carbon dioxide (740 SCCM) seeded into Ar (837 SCCM) is investigated using cwcavity ringdown spectroscopy, in the range. The van der Waals complex is observed around the acetylenic band. The rotational temperature is estimated to be close to 60 K from the comparison between observed and simulated spectra. The analysis of the main, perturbed type band centered near , is performed. It is attributed to a dimer with the known planar, geometry. The present overtone data, involving ground state levels with higher states ( and ) than previously reported, are combined to data [D. G. Prichard, R. N. Nandi, J. S. Muenter, and B. J. Howard, J. Chem. Phys.89, 1245 (1988); Z. S. Huang and R. E. Miller, Chem. Phys.132, 185 (1989)] to determine improved ground state parameters. The major perturbations affecting the upper state are accounted for through type Coriolis resonances involving one dark state, whose symmetry must therefore be . Upper state constants are obtained for the bright and dark states. The dependence upon vibrational excitation is demonstrated to arise from excitation in the acetylene unit, only, for the former, but cannot be unravelled for the latter.

A density functional theory study of the correlation between analyte basicity, ZnPc adsorption strength, and sensor response
View Description Hide DescriptionDensity functional theory(DFT) simulations were used to determine the binding strength of 12 electrondonating analytes to the zinc metal center of a zinc phthalocyanine molecule (ZnPc monomer). The analyte binding strengths were compared to the analytes’ enthalpies of complex formation with boron trifluoride , which is a direct measure of their electron donating ability or Lewis basicity. With the exception of the most basic analyte investigated, the ZnPc binding energies were found to correlate linearly with analyte basicities. Based on natural population analysis calculations, analyte complexation to the Zn metal of the ZnPc monomer resulted in limited charge transfer from the analyte to the ZnPc molecule, which increased with analyteZnPc binding energy. The experimental analyte sensitivities from chemiresistor ZnPc sensor data were proportional to an exponential of the binding energies from DFT calculations consistent with sensitivity being proportional to analyte coverage and binding strength. The good correlation observed suggests DFT is a reliable method for the prediction of chemiresistor metallophthalocyanine binding strengths and response sensitivities.

Spectroscopic detection of isolated carbonic acid
View Description Hide DescriptionCarbonic acid (cistrans ) in the gas phase has been successfully produced in a supersonic jet using a pulsed discharge nozzle, and pure rotational transitions of this molecule have been observed by Fouriertransform microwave spectroscopy. Although the observed cistrans conformer is not the global minimum structure, it is an important conformer as a starting point of its dissociation to and . Three deuterated isotopologues of the cistrans conformer (cistrans , cistrans , and cistrans ) have also been observed, yielding the structure of cistrans . The present result is accurate enough to be used in radio astronomical observations.