Volume 139, Issue 2, 14 July 2013

Despite their fundamental and practical interest, the physical properties of hard ellipses remain largely unknown. In this paper, we present an eventdriven molecular dynamics study for hard ellipses and assess the effects of aspect ratio and area fraction on their physical properties. For state points in the plane of aspect ratio (1 ⩽ k ⩽ 9) and area fraction (0.01 ⩽ ϕ ⩽ 0.8), we identify three different phases, including isotropic, plastic, and nematic states. We analyze in detail the thermodynamic, structural, and selfdiffusive properties in the formed various phases of hard ellipses. The equation of state (EOS) is shown for a wide range of aspect ratios and is compared with the scaled particle theory (SPT) for the isotropic states. We find that SPT provides a good description of the EOS for the isotropic phase of hard ellipses. At large fixed ϕ, the reduced pressure p increases with k in both the isotropic and the plastic phases and, interestingly, its dependence on k is rather weak in the nematic phase. We rationalize the thermodynamics of hard ellipses in terms of particle motions. The static structures of hard ellipses are then investigated both positionally and orientationally in the different phases. The plastic crystal is shown to form for aspect ratios up to k = 1.4, while appearance of the stable nematic phase starts approximately at k = 3. We quantitatively determine the locations of the isotropicplastic (IP) transition and the isotropicnematic (IN) transition by analyzing the bondorientation correlations and the angular correlations, respectively. As expected, the IP transition point is found to increase with k, while a larger k leads to a smaller area fraction where the IN transition takes place. Moreover, our simulations strongly support that the twodimensional nematic phase in hard ellipses has only quasilongrange orientational order. The selfdiffusion of hard ellipses is further explored and connections are revealed between the structure and the selfdiffusion. We discuss the relevance of our results to the glass transition in hard ellipses. Finally, the results of the isodiffusivity lines are evaluated for hard ellipses and we discuss the effect of spatial dimension on the diffusive dynamics of hard ellipsoidal particles.
 COMMUNICATIONS


Communication: Selection rules for tunneling splitting of vibrationally excited levels
View Description Hide DescriptionFive symmetrybased selection rules are formulated that relate the tunneling splitting of a vibrationally excited level to that of the ground level in molecules with a symmetric doubleminimum potential. The rules, which explain why excited levels frequently have smaller splittings than zeropoint levels, are used to interpret the observed and calculated splittings in malonaldehyde.

Communication: The distinguishable cluster approximation
View Description Hide DescriptionWe present a method that accurately describes strongly correlated states and captures dynamical correlation. It is derived as a modification of coupledcluster theory with single and double excitations (CCSD) through consideration of particle distinguishability between dissociated fragments, whilst retaining the key desirable properties of particlehole symmetry, size extensivity, invariance to rotations within the occupied and virtual spaces, and exactness for twoelectron subsystems. The resulting method, called the distinguishable cluster approximation, smoothly dissociates difficult cases such as the nitrogen molecule, with the modest N 6 computational cost of CCSD. Even for molecules near their equilibrium geometries, the new model outperforms CCSD. It also accurately describes the massively correlated states encountered when dissociating hydrogen lattices, a proxy for the metalinsulator transition, and the fully dissociated system is treated exactly.

Communication: Spectral representation of the Lamb shift for atomic and molecular calculations
View Description Hide DescriptionA spectral representation of the selfenergy based on hydrogenic atomic data is examined for its usefulness to evaluate the selfenergy of manyelectron atoms, and thus its potential for molecular calculations. Use of the limited hydrogenic data with a diagonal projection overestimates the valence selfenergy by an order of magnitude. The same diagonal projection for the vacuum polarization produces a similar overestimate, but a full projection produces values that are within a factor of 2 of the exact value, as does a densityfitting procedure.

Communication: Twodeterminant mixing with a strongcorrelation density functional
View Description Hide DescriptionIn recent papers [A. D. Becke, J. Chem. Phys.138, 074109 (Year: 2013)10.1063/1.4790598;A. D. Becke, J. Chem. Phys.138, 161101 (Year: 2013)10.1063/1.4802982], a density functional for strong correlations in quantum chemistry was introduced. The functional is designed to capture molecular dissociation limits using symmetryrestricted orbitals. Here we demonstrate that the functional describes, with good accuracy, twodeterminant multireference states. The examples of this work involve 50/50 mixing of symmetryequivalent Slater determinants at avoided crossings. We employ exactlycomputed exchange and fractional spinorbital occupancies. The connection with dissociated systems and singledeterminant reference states is explained.

Communication: Spinfree quantum computational simulations and symmetry adapted states
View Description Hide DescriptionThe ideas of digital simulation of quantum systems using a quantum computer parallel the original ideas of numerical simulation using a classical computer. In order for quantum computational simulations to advance to a competitive point, many techniques from classical simulations must be imported into the quantum domain. In this article, we consider the applications of symmetry in the context of quantum simulation. Building upon well established machinery, we propose a form of first quantized simulation that only requires the spatial part of the wave function, thereby allowing spinfree quantum computational simulations. We go further and discuss the preparation of Nbody states with specified symmetries based on projection techniques. We consider two simple examples, molecular hydrogen and cyclopropenyl cation, to illustrate the ideas. The methods here are the first to explicitly deal with preparing Nbody symmetryadapted states and open the door for future investigations into group theory, chemistry, and quantum simulation.

Communication: Vibrational spectroscopy of Au_{4} from high resolution photoelectron imaging
View Description Hide DescriptionHigh resolution photoelectron spectroscopy of Au 4 − is reported using a new photoelectron imaging apparatus. A broad vibrational progression is resolved for the detachment transition from the ground electronic state of the Yshaped Au 4 − to that of the Yshaped Au 4 neutral (C2v, 1A1) in the ν2 vibrational mode with a harmonic frequency of 171(7) cm−1 and an anharmonicity of ∼0.5 cm−1. In addition, two low frequency modes with weak FranckCondon factors are observed: the v 3 mode with a frequency of 97(7) cm−1 and the v 6 mode with a frequency of 17(7) cm−1. An accurate electron affinity of 2.7098(6) eV is obtained for the Yshaped Au 4 neutral cluster. The current study shows that very low frequency vibrational modes can be resolved for sizeselected clusters using high resolution photoelectron imaging, providing valuable additional experimental information for cluster structure determination.

Communication: Fouriertransform infrared probing of remarkable quantities of gas trapped in cold homogeneously nucleated nanodroplets
View Description Hide DescriptionStudies of catalyzed allvapor gashydrate formation on a subsecond timescale have been extended with a special focus on liquiddroplet compositions at the instant of hydrate crystallization. This focus has been enabled by inclusion of methanol in the allvapor mixture. This slows droplet to gashydrate conversion near 200 K to a time scale suited for standard FTIR sampling. Such droplet data are sought as a guide to ongoing efforts to reduce the amount of guest catalyst required for instant formation of the gas hydrates. For the same reason, allvapor sampling has also been extended to the generation of longlived liquid droplets with reduced or no water content. Observations of singlesolvent droplets show that surprising quantities of gas molecules are trapped during rapid droplet growth. For example, CO2 is trapped at levels near 50 mol. % in droplets of acetone, tetrahydrofuran, or trimethylene oxide formed under CO2 pressures of several Torr in a coldchamber at 170 K. Less but significant amounts of gas are trapped at higher temperatures, or in methanol or watermethanol droplets. The droplet metastability appears to commonly lead to formation of bubbles larger than the original nanodroplets. Besides serving as a guide for the allvapor gashydrate studies, the semiquantitative evidence of extensive trapping of gases is expected to have a role in future studies of atmospheric aerosols.

Communication: Activespace decomposition for molecular dimers
View Description Hide DescriptionWe have developed an activespace decomposition strategy for molecular dimers that allows for the efficient computation of the dimer's completeactivespace wavefunction while only constructing the monomers’ activespace wavefunctions. Dimer states are formed from linear combinations of direct products of localized orthogonal monomer states and Hamiltonian matrix elements are computed directly without explicitly constructing the product space. This decomposition is potentially exact in the limit where a full set of monomer states is included. The adiabatic states are then found by diagonalizing the dimer Hamiltonian matrix. We demonstrate the convergence of our method to a completeactivespace calculation of the full dimer with two test cases: the benzene and naphthalene dimers.
 Top

 ARTICLES

 Theoretical Methods and Algorithms

The application of the thermodynamic perturbation theory to study the hydrophobic hydration
View Description Hide DescriptionThe thermodynamic perturbation theory was tested against newly obtained Monte Carlo computer simulations to describe the major features of the hydrophobic effect in a simple 3DMercedesBenz water model: the temperature and hydrophobe size dependence on entropy, enthalpy, and free energy of transfer of a simple hydrophobic solute into water. An excellent agreement was obtained between the theoretical and simulation results. Further, the thermodynamic perturbation theory qualitatively correctly (with respect to the experimental data) describes the solvation thermodynamics under conditions where the simulation results are difficult to obtain with good enough accuracy, e.g., at high pressures.

Double asymptotic expansion of threecenter electronic repulsion integrals
View Description Hide DescriptionA double asymptotic expansion for the evaluation of threecenter electron repulsion integrals (ERIs) in the longrange limit is presented. For the definition of this limit, a natural division of space based on the atomic coordinates and basis function exponents in utilized. The resulting analytical expression for the calculation of threecenter ERIs in the longrange limit are implemented in the density functional theory program deMon2k. Validation and benchmark calculations of nalkanes, hydrogen saturated graphene sheets and hydrogen saturated diamond blocks are discussed. It is shown that for a sufficient large number of longrange ERIs, the linear scaling regime is reached.

Accurate basis set truncation for wavefunction embedding
View Description Hide DescriptionDensity functional theory (DFT) provides a formally exact framework for performing embedded subsystem electronic structure calculations, including DFTinDFT and wavefunction theoryinDFT descriptions. In the interest of efficiency, it is desirable to truncate the atomic orbital basis set in which the subsystem calculation is performed, thus avoiding highorder scaling with respect to the size of the MO virtual space. In this study, we extend a recently introduced projectionbased embedding method [F. R. Manby, M. Stella, J. D. Goodpaster, and T. F. Miller III, J. Chem. Theory Comput.8, 2564 (Year: 2012)]10.1021/ct300544e to allow for the systematic and accurate truncation of the embedded subsystem basis set. The approach is applied to both covalently and noncovalently bound test cases, including water clusters and polypeptide chains, and it is demonstrated that errors associated with basis set truncation are controllable to well within chemical accuracy. Furthermore, we show that this approach allows for switching between accurate projectionbased embedding and DFT embedding with approximate kinetic energy (KE) functionals; in this sense, the approach provides a means of systematically improving upon the use of approximate KE functionals in DFT embedding.

On asymptotic behavior of density functional theory
View Description Hide DescriptionThe performance of several previously proposed as well as of some novel approaches for correcting the asymptotic behavior of electron densities in density functional theory (DFT) is evaluated. The comparisons are made for molecular properties that are known to be sensitive to the asymptotic behavior of densities such as polarizabilities, energies of excitations to Rydberg states, and interaction energies (computed using symmetryadapted perturbation theory). We find that whereas DFTbased methods without asymptotic corrections predict the investigated properties with errors often as large as a dozen or so percent relative to the best known values, the best performing asymptotically corrected hybrid functionals reduce these errors to below 2%. In many cases, the errors are just a fraction of one percent and in a few cases DFT reproduces benchmark values to all figures. These errors are also very close to those produced by the coupledcluster methods at the highest levels of electron excitations applicable in practice. Such performance is unprecedented for any applications of DFT and is due to high sensitivity of the investigated properties to tails of the electron densities. Rangeseparated hybrid (RSH) functionals are also examined and found to perform comparably to the asymptotically corrected hybrid functionals for excitation energies and only somewhat worse for polarizabilities. However, very surprisingly, RSH functionals fail completely in interaction energy calculations. We explain the latter problem by showing that, despite some expectations in the literature reflected by the alternative name, longrange corrected, used for the RSH functionals, these methods give densities that are not better in the asymptotic region than those produced by asymptotically uncorrected standard DFT methods. We further show that this failure can be corrected by cutting, displacing, and splicing the exchangecorrelation potentials of RSH methods such that these potentials approach the correct value at infinity.

Modeling optoelectronic properties of a dye molecule in proximity of a semiconductor nanoparticle
View Description Hide DescriptionA general methodology is presented to model the optoelectronic properties of a dye molecule in the presence of a semiconductor nanoparticle (NP), a model system for the architecture of dyesensitized solar cells. The method is applied to the L0 organic dye solvated with acetonitrile in the neighborhood of a TiO2 NP. The total reaction potential due to the polarization of the solvent and the metal oxide is calculated by extending the polarizable continuum model integral equation formalism. The ground state energy is computed by using density functional theory (DFT) while the vertical electronic excitations are obtained by timedependent DFT in a statespecific corrected linear response scheme. We calculate the excited state oxidation potential (ESOP) for the protonated and deprotonated forms of the L0 dye at different distances and configurations with respect to the NP surface. The stronger renormalizations of the ESOP values due to the presence of the TiO2 nanostructure are found for the protonated dye, reaching a maximum of about −0.15 eV. The role of protonation effect is discussed in terms of the atomic Löwdin charges of the oxidized and reduced species. On the other hand, we observed a weak effect on the L0 optical excitation gap due to the polarization response of the NP.

Controlling the efficiency of trapping in treelike fractals
View Description Hide DescriptionEfficiently controlling the trapping process, especially the trapping efficiency, is central in the study of trap problem in complex systems, since it is a fundamental mechanism for diverse other dynamic processes. Thus, it is of theoretical and practical significance to study the control technique for trapping problem. In this paper, we study the trapping problem in a family of proposed directed fractals with a deep trap at a central node. The directed fractals are a generalization of previous undirected fractals by introducing the directed edge weights dominated by a parameter. We characterize all the eigenvalues and their degeneracies for an associated matrix governing the trapping process. The eigenvalues are provided through an exact recursive relation deduced from the selfsimilar structure of the fractals. We also obtain the expressions for the smallest eigenvalue and the mean firstpassage time (MFPT) as a measure of trapping efficiency, which is the expected time for the walker to first visit the trap. The MFPT is evaluated according to the proved fact that it is approximately equal to reciprocal of the smallest eigenvalue. We show that the MFPT is controlled by the weight parameter by modifying which the MFPT can scale superlinealy, linearly, or sublinearly with the system size. Thus, this work paves a way to delicately controlling the trapping process in the fractals.

Using the uncertainty principle to design simple interactions for targeted selfassembly
View Description Hide DescriptionWe present a method that systematically simplifies isotropic interactions designed for targeted selfassembly. The uncertainty principle is used to show that an optimal simplification is achieved by a combination of heat kernel smoothing and Gaussian screening of the interaction potential in real and reciprocal space. We use this method to analytically design isotropic interactions for selfassembly of complex lattices and of materials with functional properties. The derived interactions are simple enough to narrow the gap between theory and experimental implementation of theory based designed selfassembling materials.

Predicting phase behavior in multicomponent mixtures
View Description Hide DescriptionMixtures with a large number of components can undergo phase transitions of a hybrid character, with both condensation and demixing contributions. We describe a robust Monte Carlo simulation method for calculating phase coexistence in multicomponent mixtures. We use this approach to study the phase behavior of lattice models of multicomponent mixtures with strongly varying pair interactions. Such a system can be thought of as a simplified model of the cytosol, with both specific and nonspecific interactions. We show that mapping a multicomponent mixture onto an approximately equivalent onecomponent system yields both upper and lower bounds on the maximum solute volume fraction of a stable, homogeneous phase. By following the minimum excessfreeenergy path from the dilute phase freeenergy minimum, we predict the difference in composition between the condensed and dilute phases at the boundary of the homogeneous phase. We find that this “direction” of phase separation rarely aligns with the dominant direction of density fluctuations in the dilute phase. We also show that demixing transitions tend to lower the maximum solute volume fraction at which the homogeneous phase is stable. By considering statistical ensembles of mixtures with random interactions, we show that the demixing contribution to phase separation is selfaveraging and dependent only on the mean and variance of the distribution of interactions.

Quantum dephasing of a twostate system by a nonequilibrium harmonic oscillator
View Description Hide DescriptionIn this paper, we investigate coherent quantum dynamics in a nonequilibrium environment. We focus on a twostate quantum system strongly coupled to a single classical environmental oscillator, and explore the effect of nonstationary statistical properties of the oscillator on the quantum evolution. A simple nonequilibrium model, consisting of an oscillator with a welldefined initial phase which undergoes subsequent diffusion, is introduced and studied. Approximate but accurate analytic expressions for the evolution of the offdiagonal density matrix element of the quantum system are derived in the secondorder cumulant approximation. The effect of the initial phase choice on the subsequent quantum evolution is quantified. It is observed that the initial phase can have a significant effect on the preservation of coherence on short time scales, suggesting this variable as a control parameter for optimizing coherence in manybody quantum systems.

Orbital optimized doublehybrid density functionals
View Description Hide DescriptionThis paper advocates development of a new class of doublehybrid (DH) density functionals where the energy is fully orbital optimized (OO) in presence of all correlation, rather than using a final noniterative second order perturbative correction. The resulting OODH functionals resolve a number of artifacts associated with conventional DH functionals, such as first derivative discontinuities. To illustrate the possibilities, two nonempirical OODH functionals are obtained from existing DH functionals based on PBE: OOPBE0DH and OOPBE02. Both functionals share the same functional form, with parameters determined on the basis of different physical considerations. The new functionals are tested on a variety of bonded, nonbonded and symmetrybreaking problems.

Phasefield approach to implicit solvation of biomolecules with Coulombfield approximation
View Description Hide DescriptionA phasefield variational implicitsolvent approach is developed for the solvation of charged molecules. The starting point of such an approach is the representation of a solutesolvent interface by a phase field that takes one value in the solute region and another in the solvent region, with a smooth transition from one to the other on a small transition layer. The minimization of an effective freeenergy functional of all possible phase fields determines the equilibrium conformations and free energies of an underlying molecular system. All the surface energy, the solutesolvent van der Waals interaction, and the electrostatic interaction are coupled together selfconsistently through a phase field. The surface energy results from the minimization of a doublewell potential and the gradient of a field. The electrostatic interaction is described by the Coulombfield approximation. Accurate and efficient methods are designed and implemented to numerically relax an underlying charged molecular system. Applications to single ions, a twoplate system, and a twodomain protein reveal that the new theory and methods can capture capillary evaporation in hydrophobic confinement and corresponding multiple equilibrium states as found in molecular dynamics simulations. Comparisons of the phasefield and the original sharpinterface variational approaches are discussed.
 Advanced Experimental Techniques

Infrared absorption imaging of 2D supersonic jet expansions: Free expansion, cluster formation, and shock wave patterns
View Description Hide DescriptionN2O/He gas mixtures are expanded through a 10 × 0.5 mm2 slit nozzle and imaged by direct absorption vibrational spectroscopy, employing a HgCdTe focal plane array detector after interferometric modulation. N2O cluster formation in the free supersonic expansion is visualized. The expansion structure behind the frontal shock is investigated as a function of background pressure. At high pressures, a sequence of stationary density peaks along a narrow directed flow channel is characterized. The potential of the technique for the elucidation of aggregation mechanisms is emphasized.