Volume 135, Issue 15, 21 October 2011

Dense polyhedron packings are useful models of a variety of condensed matter and biological systems and have intrigued scientists and mathematicians for centuries. Here, we analytically construct the densest known packing of truncated tetrahedra with a remarkably high packing fraction ϕ = 207/208 = 0.995192…, which is amazingly close to unity and strongly implies its optimality. This construction is based on a generalized organizing principle for polyhedra lacking central symmetry that we introduce here. The “holes” in the putative optimal packing are perfect tetrahedra, which leads to a new tessellation of space by truncated tetrahedra and tetrahedra. Its packing characteristics and equilibrium meltingproperties as the system undergoes decompression are discussed.
 COMMUNICATIONS


Communication: A packing of truncated tetrahedra that nearly fills all of space and its melting properties
View Description Hide DescriptionDense polyhedron packings are useful models of a variety of condensed matter and biological systems and have intrigued scientists and mathematicians for centuries. Here, we analytically construct the densest known packing of truncated tetrahedra with a remarkably high packing fraction ϕ = 207/208 = 0.995192…, which is amazingly close to unity and strongly implies its optimality. This construction is based on a generalized organizing principle for polyhedra lacking central symmetry that we introduce here. The “holes” in the putative optimal packing are perfect tetrahedra, which leads to a new tessellation of space by truncated tetrahedra and tetrahedra. Its packing characteristics and equilibrium meltingproperties as the system undergoes decompression are discussed.

Communication: Quasiclassical trajectory calculations of correlated productstate distributions for the dissociation of (H_{2}O)_{2} and (D_{2}O)_{2}
View Description Hide DescriptionStimulated by recent experiments [B. E. RocherCasterline, L. C. Ch'ng, A. K. Mollner, and H. Reisler, J. Chem. Phys.134, 211101 (2011)], we report quasiclassical trajectory calculations of the dissociation dynamics of the water dimer, (H_{2}O)_{2} (and also (D_{2}O)_{2}) using a fulldimensional ab initiopotential energy surface. The dissociation is initiated by exciting the Hbonded OH(OD)stretch, as done experimentally for (H_{2}O)_{2}. Normal mode analysis of the fragment pairs is done and the correlated vibrational populations are obtained by (a) standard histogram binning (HB), (b) harmonic normalmode energybased Gaussian binning (GB), and (c) a modified version of (b) using accurate vibrational energies obtained in the Cartesian space. We show that HB allows opening quantum mechanically closed states, whereas GB, especially via (c), gives physically correct results. Dissociation of both (H_{2}O)_{2} and (D_{2}O)_{2} mainly produces either fragment in the bending excited (010) state. The H_{2}O(J) and D_{2}O(J) rotational distributions are similar, peaking at J = 3–5. The computations do not show significant difference between the rovibrational distributions of the donor and acceptor fragments. Diffusion Monte Carlo computations are performed for (D_{2}O)_{2} providing an accurate zeropoint energy of 7247 cm^{−1}, and thus, a benchmark D _{0} of 1244 ± 5 cm^{−1}.

Communication: Orbital instabilities and triplet states from timedependent density functional theory and longrange corrected functionals
View Description Hide DescriptionLongrange corrected hybrids represent an increasingly popular class of functionals for density functional theory(DFT) that have proven to be very successful for a wide range of chemical applications. In this Communication, we examine the performance of these functionals for timedependent (TD)DFT descriptions of triplet excited states. Our results reveal that the triplet energies are particularly sensitive to the rangeseparation parameter; this sensitivity can be traced back to triplet instabilities in the ground state coming from the large effective amounts of HartreeFock exchange included in these functionals. As such, the use of standard longrange corrected functionals for the description of triplet states at the TDDFT level is not recommended.
 Top

 ARTICLES

 Theoretical Methods and Algorithms

Electric field polarization in conventional density functional theory: From quasilinear to twodimensional and threedimensional extended systems
View Description Hide DescriptionThe large overshoot in (hyper)polarizabilities of quasilinear (1D) chains calculated by applying density functional theory with conventional functionals is investigated for several 2D and 3D extended systems. These systems include arrays of molecular hydrogen chains, as well as 2D coronenetype structures and LiF in 1D, 2D, and 3D. Contrary to a recently proposed model it is found that the overshoot persists in all of these cases. A simple explanation is provided by an analysis of the fieldinduced charges for molecular hydrogen, which shows an excessive buildup at the chain ends regardless of where the chain is located within the 2D and 3D array.

Entanglement of polar symmetric top molecules as candidate qubits
View Description Hide DescriptionProposals for quantum computing using rotational states of polar molecules as qubits have previously considered only diatomic molecules. For these the Stark effect is secondorder, so a sizable external electric field is required to produce the requisite dipole moments in the laboratory frame. Here we consider use of polar symmetric top molecules. These offer advantages resulting from a firstorder Stark effect, which renders the effective dipole moments nearly independent of the field strength. That permits use of much lower external field strengths for addressing sites. Moreover, for a particular choice of qubits, the electric dipole interactions become isomorphous with NMR systems for which many techniques enhancing logic gate operations have been developed. Also inviting is the wider chemical scope, since many symmetric top organic molecules provide options for auxiliary storage qubits in spin and hyperfine structure or in internal rotation states.

Precise simulation of the freezing transition of supercritical LennardJones
View Description Hide DescriptionThe fluidsolid transition of the LennardJones model is analyzed along a supercritical isotherm. The analysis is implemented via a simulation method which is based on a modification of the constrained cell model of Hoover and Ree. In the context of hardsphere freezing, Hoover and Ree simulated the solid phase using a constrained cell model in which each particle is confined within its own WignerSeitz cell. Hoover and Ree also proposed a modified cell model by considering the effect of an external field of variable strength. Highfield values favor configurations with a single particle per WignerSeitz cell and thus stabilize the solid phase. In previous work, a simulation method for freezing transitions, based on constantpressure simulations of the modified cell model, was developed and tested on a system of hard spheres. In the present work, this method is used to determine the freezing transition of a LennardJones model system on a supercritical isotherm at a reduced temperature of 2. As in the case of hard spheres, constantpressure simulations of the fully occupied constrained cell model of a system of LennardJones particles indicate a point of mechanical instability at a density which is approximately 70% of the density at close packing. Furthermore, constantpressure simulations of the modified cell model indicate that as the strength of the field is reduced, the transition from the solid to the fluid is continuous below the mechanical instability point and discontinuous above. The fluidsolid transition of the LennardJones system is obtained by analyzing the fieldinduced fluidsolid transition of the modified cell model in the highpressure, zerofield limit. The simulations are implemented under constant pressure using tempering and histogram reweighting techniques. The coexistence pressure and densities are determined through finitesize scaling techniques for firstorder phase transitions which are based on analyzing the sizedependent behavior of susceptibilities and dimensionless moment ratios of the order parameter.

Allelectron timedependent density functional theory with finite elements: Timepropagation approach
View Description Hide DescriptionWe present an allelectron method for timedependent density functional theory which employs hierarchical nonuniform finiteelement bases and the timepropagation approach. The method is capable of treating linear and nonlinear response of valence and core electrons to an external field. We also introduce () a preconditioner for the propagation equation, () a stable way to implement absorbing boundary conditions, and () a new kind of absorbing boundary condition inspired by perfectly matched layers.

Calculating dispersion interactions using maximally localized Wannier functions
View Description Hide DescriptionWe investigate a recently developed approach [P. L. Silvestrelli, Phys. Rev. Lett.100, 053002 (2008)10.1103/PhysRevLett.100.053002; J. Phys. Chem. A113, 5224 (2009)] that uses maximally localized Wannier functions to evaluate the van der Waals contribution to the total energy of a system calculated with densityfunctional theory. We test it on a set of atomic and molecular dimers of increasing complexity (argon, methane, ethene, benzene, phthalocyanine, and copper phthalocyanine) and demonstrate that the method, as originally proposed, has a number of shortcomings that hamper its predictive power. In order to overcome these problems, we have developed and implemented a number of improvements to the method and show that these modifications give rise to calculated binding energies and equilibrium geometries that are in closer agreement to results of quantumchemical coupledcluster calculations.

A fast variational Gaussian wavepacket method: Sizeinduced structural transitions in large neon clusters
View Description Hide DescriptionThe variational Gaussian wavepacket (VGW) approximation provides an alternative to path integral Monte Carlo for the computation of thermodynamic properties of manybody systems at thermal equilibrium. It provides a direct access to the thermal density matrix and is particularly efficient for Monte Carlo approaches, as for an Nbody system it operates in a noninflated 3Ndimensional configuration space. Here, we greatly accelerate the VGW method by retaining only the relevant shortrange correlations in the (otherwise full) 3N × 3N Gaussian width matrix without sacrificing the accuracy of the fully coupled VGW method. This results in the reduction of the original scaling to . The fastVGW method is then applied to quantum LennardJones clusters with sizes up to N = 6500 atoms. Following Doye and Calvo [JCP116, 8307 (2002)10.1063/1.1469616] we study the competition between the icosahedral and decahedral structural motifs in Ne_{ N } clusters as a function of N.

Vibrational contributions to cubic response functions from vibrational configuration interaction response theory
View Description Hide DescriptionIn continuation of our recent paper on vibrational quadratic response functions for vibrational configuration interactionwave functions, we present in this paper a derivation and implementation of the pure vibrational cubic response function for vibrational configuration interactionwave functions. In addition, we present combined electronic and vibrational cubic response functions derived from sumoverstates expressions in the BornOppenheimer framework and a discussion of complicating issues. The implementation enables analytic calculation of the pure vibrational cubic response function via response theory, which constitutes a part of the vibronic cubic response function.

Rapid, accurate calculation of the swave scattering length
View Description Hide DescriptionTransformation of the conventional radial Schrödinger equation defined on the interval r ∈ [0, ∞) into an equivalent form defined on the finite domain y(r) ∈ [a, b] allows the swave scattering length a _{ s } to be exactly expressed in terms of a logarithmic derivative of the transformed wave function ϕ(y) at the outer boundary point y = b, which corresponds to r = ∞. In particular, for an arbitrary interaction potential that dies off as fast as 1/r ^{ n } for n ⩾ 4, the modified wave function ϕ(y) obtained by using the twoparameter mapping function has no singularities, and For a well bound potential with equilibrium distance r _{ e }, the optimal mapping parameters are and . An outward integration procedure based on Johnson's logderivative algorithm [J. Comp. Phys.13, 445 (1973)] combined with a Richardson extrapolation procedure is shown to readily yield high precision a _{ s }values both for model LennardJones (2n, n) potentials and for realistic published potentials for the Xe–e^{−}, ), and ^{3, 4} systems. Use of this same transformed Schrödinger equation was previously shown [V. V. Meshkov et al., Phys. Rev. A78, 052510 (2008)] to ensure the efficient calculation of all bound levels supported by a potential, including those lying extremely close to dissociation.

Controlling the transmission line shape of molecular tstubs and potential thermoelectric applications
View Description Hide DescriptionAsymmetric line shapes can occur in the transmission function describing electron transport in the vicinity of a minimum caused by quantum interference effects. Such asymmetry can be used to increase the thermoelectric efficiency of molecular junctions. So far, however, asymmetric line shapes have been only empirically found for just a few rather complex organic molecules where the origins of the line shapes relation to molecular structure were not resolved. In the present, work we introduce a method to analyze the structure dependence of the asymmetry of interference dips from simple two site tightbinding models, where one site corresponds to a molecular π orbital of the wire and the other to an atomic p _{ z } orbital of a side group, which allows us to characterize analytically the peak shape in terms of just two parameters. We assess our scheme with firstprinciples electron transport calculations for a variety of tstub molecules and also address their suitability for thermoelectric applications.

Reaction coordinates for the crystal nucleation of colloidal suspensions extracted from the reweighted path ensemble
View Description Hide DescriptionWe study the mechanisms of the homogeneous crystal nucleation from the supercooled liquid to the crystal phase in the Gaussian core model for colloidal suspensions with the aim to find optimal reaction coordinates. We introduce a set of novel collective variables based on the local structure of particles. By applying likelihood maximization of the committor function for the reweighted path ensemble constructed by replica exchange transition interface sampling, we select the optimal reaction coordinates from the set of collective variables. We find that the size of the cloud of prestructured particles surrounding the crystalline nucleus enhances the description of the transition. Further, we show that the rearrangement of the inner core of the nucleus according to Ostwald's step rule is a separate process, independent of the growth of the nucleus.

Evaluation of coupling terms between intra and intermolecular vibrations in coarsegrained normalmode analysis: Does a stronger acid make a stiffer hydrogen bond?
View Description Hide DescriptionUsing theory of harmonic normalmode vibration analysis, we developed a procedure for evaluating the anisotropic stiffness of intermolecular forces. Our scheme for coarsegraining of molecular motions is modified so as to account for intramolecular vibrations in addition to relative translational/rotational displacement. We applied this new analytical scheme to four carboxylic acid dimers, for which coupling between intra and intermolecular vibrations is crucial for determining the apparent stiffness of the intermolecular double hydrogen bond. The apparent stiffness constant was analyzed on the basis of a conjunct spring model, which defines contributions from true intermolecular stiffness and molecular internal stiffness. Consequently, the true intermolecular stiffness was in the range of 43–48 N m^{−1} for all carboxylic acids studied, regardless of the molecules’ acidity. We concluded that the difference in the apparent stiffness can be attributed to differences in the internal stiffness of the respective molecules.

Electronic excitation dynamics in multichromophoric systems described via a polaronrepresentation master equation
View Description Hide DescriptionWe derive a manysite version of the nonMarkovian timeconvolutionless polaron master equation[Jang et al., J. Chem Phys.129, 101104 (2008)]10.1063/1.2977974 to describe electronic excitation dynamics in multichromophoric systems. By treating electronic and vibrational degrees of freedom in a combined frame (polaron frame), this theory is capable of interpolating between weak and strong excitonphonon coupling and is able to account for initial nonequilibrium bath states and spatially correlated environments. Besides outlining a general expression for the expected value of any electronic system observable in the original frame, we also discuss implications of the Markovian and Secular approximations highlighting that they need not hold in the untransformed frame despite being strictly satisfied in the polaron frame. The key features of the theory are illustrated using as an example a foursite subsystem of the FennaMathewsOlson lightharvesting complex. For a spectral density including a localised mode, we show that oscillations of site populations may only be observed when nonequilibrium bath effects are taken into account. Furthermore, we illustrate how this formalism allows us to identify the electronic and vibrational components of the oscillatory dynamics.

Intermediate state representation approach to physical properties of dicationic states
View Description Hide DescriptionThe secondorder algebraic construction (ADC(2)) approach to the twoparticle (pp) propagator, devised to compute double ionization energies and associated spectroscopic amplitudes, is reformulated and extended using the concept of intermediate state representations (ISR). The ISR formulation allows one to go beyond the general limitations inherent to the propagator approach, as here (N−2)electron wave functions and properties become directly accessible. The (N−2)electron ISR(2) equations for a general oneparticle operator have been derived and implemented in a recent version of the double ionization ADC(2) program. As a first test of the method, the dipole moments of a series of 2h states of LiH, HF, and H_{2}O were computed and compared to the results of a full configuration interaction (FCI) treatment. The dipole moments obtained at the ADC(2)/ISR(2) computational level are in good agreement with the FCI results.

Timeaveraging approximation in the interaction picture: Absorption line shapes for coupled chromophores with application to liquid water
View Description Hide DescriptionThe timeaveraging approximation (TAA), originally developed to calculate vibrational line shapes for coupled chromophores using mixed quantum/classical methods, is reformulated. In the original version of the theory, time averaging was performed for the full oneexciton Hamiltonian, while herein the time averaging is performed on the coupling (offdiagonal) Hamiltonian in the interaction picture. As a result, the influence of the dynamic fluctuations of the transition energies is more accurately described. We compare numerical results of the two versions of the TAA with numerically exact results for the vibrational absorptionline shape of the OH stretching modes in neat water. It is shown that the TAA in the interaction picture yields theoretical line shapes that are in better agreement with exact results.

Physical interpretation of mean local accumulation time of morphogen gradient formation
View Description Hide DescriptionThe paper deals with a reactiondiffusion problem that arises in developmental biology when describing the formation of the concentration profiles of signaling molecules, called morphogens, which control gene expression and, hence, cell differentiation. The mean local accumulation time, which is the mean time required to reach the steady state at a fixed point of a patterned tissue, is an important characteristic of the formation process. We show that this time is a sum of two times, the conditional mean firstpassage time from the source to the observation point and the mean local accumulation time in the situation when the source is localized at the observation point.
 Advanced Experimental Techniques

Sizes of large He droplets
View Description Hide DescriptionHelium droplets spanning a wide size range, N _{He} = 10^{3}–10^{10}, were formed in a continuousnozzle beam expansion at different nozzle temperatures and a constant stagnation pressure of 20 bars. The average sizes of the droplets have been obtained by attenuation of the dropletbeam through collisions with argon and helium gases at room temperature. The results obtained are in good agreement with previous measurements in the size range N _{He} = 10^{5}–10^{7}. Moreover, the measurements give the average sizes in the previously uncharacterized range of very large droplets of 10^{7}–10^{10} atoms. The droplet sizes and beam flux increase rapidly at nozzle temperatures below 6 K, which is ascribed to the formation of droplets within the nozzle interior. The mass spectra of the dropletbeam upon electron impact ionization have also been obtained. The spectra show a large increase in the intensity of the He_{4} ^{+} signal upon increase of the droplet size, an effect which can be used as a secondary size standard in the droplet size range N _{He} = 10^{4}–10^{9} atoms.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Simulations of light induced processes in water based on ab initio path integrals molecular dynamics. I. Photoabsorption
View Description Hide DescriptionWe have performed largescale simulations of UVabsorption spectra of water clusters (monomer to octamer) using a combination of ab initio pathintegral molecular dynamics with reflection principle. The aim of the present work is fourfold: (1) To explore the transition from isolated molecules to bulk water from the perspective of UV photoabsorption. (2) To investigate quantum nuclear and thermal effects on the shape of the water UV spectra. (3) To make an assessment of the density functional theory functionals to be used for water excited states. (4) To check the applicability of the QM/MM schemes for a description of the UVabsorption. Within the path integral molecular dynamics (PIMD)/reflection principle approach both the thermal and quantum vibrational effects including anharmonicities are accounted for. We demonstrate that shape of the spectra is primarily controlled by the nuclear quantum effects. The excited states and transition characteristics of the water clusters were calculated with the timedependent density functional theory and equationofmotion coupled clusters singles and doubles methods. Based on our benchmark calculations considering the whole UVspectrum we argue that the BHandHLYP method performs best among the 6 functionals tested (B3LYP, BHandHLYP, BNL, CAMB3LYP, LCωPBE, and M06HF). We observe a gradual blueshift of the maximum of the first absorption peak with the increasing cluster size. The UVabsorptionspectrum for the finite size clusters (i.e., the peak centers, peak widths, and photoabsorption cross section) essentially converges into the corresponding bulk water spectrum. The effect of distant molecules accounted for within the polarizable continuum model is shown to be almost negligible. Using the natural transition orbitals we demonstrate that the first absorption band is formed by localized excitations while the second band includes delocalized excited states. Consequently, the QM/MM electrostatic embedding scheme can only be used for the modeling of the low energy part of the spectrum.