Volume 145, Issue 11, 21 September 2016

This perspective will overview an emerging paradigm for selforganized soft materials, geometrically frustrated assemblies, where interactions between selfassembling elements (e.g., particles, macromolecules, proteins) favor local packing motifs that are incompatible with uniform global order in the assembly. This classification applies to a broad range of material assemblies including selftwisting protein filament bundles, amyloid fibers, chiral smectics and membranes, particlecoated droplets, curved protein shells, and phaseseparated lipid vesicles. In assemblies, geometric frustration leads to a host of anomalous structural and thermodynamic properties, including heterogeneous and internally stressed equilibrium structures, selflimiting assembly, and topological defects in the equilibrium assembly structures. The purpose of this perspective is to (1) highlight the unifying principles and consequences of geometric frustration in soft matter assemblies; (2) classify the known distinct modes of frustration and review corresponding experimental examples; and (3) describe outstanding questions not yet addressed about the unique properties and behaviors of this broad class of systems.
 PERSPECTIVES


Perspective: Geometrically frustrated assemblies
View Description Hide DescriptionThis perspective will overview an emerging paradigm for selforganized soft materials, geometrically frustrated assemblies, where interactions between selfassembling elements (e.g., particles, macromolecules, proteins) favor local packing motifs that are incompatible with uniform global order in the assembly. This classification applies to a broad range of material assemblies including selftwisting protein filament bundles, amyloid fibers, chiral smectics and membranes, particlecoated droplets, curved protein shells, and phaseseparated lipid vesicles. In assemblies, geometric frustration leads to a host of anomalous structural and thermodynamic properties, including heterogeneous and internally stressed equilibrium structures, selflimiting assembly, and topological defects in the equilibrium assembly structures. The purpose of this perspective is to (1) highlight the unifying principles and consequences of geometric frustration in soft matter assemblies; (2) classify the known distinct modes of frustration and review corresponding experimental examples; and (3) describe outstanding questions not yet addressed about the unique properties and behaviors of this broad class of systems.
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 COMMUNICATIONS


Communication: Inverse design for selfassembly via onthefly optimization
View Description Hide DescriptionInverse methods of statistical mechanics have facilitated the discovery of pair potentials that stabilize a wide variety of targeted lattices at zero temperature. However, such methods are complicated by the need to compare, within the optimization framework, the energy of the desired lattice to all possibly relevant competing structures, which are not generally known in advance. Furthermore, groundstate stability does not guarantee that the target will readily assemble from the fluid upon cooling from higher temperature. Here, we introduce a molecular dynamics simulationbased, optimization design strategy that iteratively and systematically refines the pair interaction according to the fluid and crystalline structural ensembles encountered during the assembly process. We successfully apply this probabilistic, machinelearning approach to the design of repulsive, isotropic pair potentials that assemble into honeycomb, kagome, square, rectangular, truncated square, and truncated hexagonal lattices.

Communication: Projected Hartree Fock theory as a polynomial similarity transformation theory of single excitations
View Description Hide DescriptionSpinprojected HartreeFock is written as a particlehole excitation ansatz over a symmetryadapted reference determinant. Remarkably, this expansion has an analytic expression that we were able to decipher. While the form of the polynomial expansion is universal, the excitation amplitudes need to be optimized. This is equivalent to the optimization of orbitals in the conventional projected HartreeFock framework of nonorthogonal determinants. Using the inverse of the particlehole expansion, we similarity transform the Hamiltonian in a coupledcluster style theory. The left eigenvector of the nonHermitian Hamiltonian is constructed in a similar particlehole expansion fashion, and we show that to numerically reproduce variational projected HartreeFock results, one needs as many pair excitations in the bra as the number of strongly correlated entangled pairs in the system. This singleexcitation polynomial similarity transformation theory is an alternative to our recently presented double excitation theory, but supports projected HartreeFock and coupled cluster simultaneously rather than interpolating between them.
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 ARTICLES

 Theoretical Methods and Algorithms

Analytic energy derivatives for the calculation of the firstorder molecular properties using the domainbased local pairnatural orbital coupledcluster theory
View Description Hide DescriptionThe domainbased local pairnatural orbital coupledcluster (DLPNOCC) theory has recently emerged as an efficient and powerful quantumchemical method for the calculation of energies of molecules comprised of several hundred atoms. It has been demonstrated that the DLPNOCC approach attains the accuracy of a standard canonical coupledcluster calculation to about 99.9% of the basis set correlation energy while realizing linear scaling of the computational cost with respect to system size. This is achieved by combining (a) localized occupied orbitals, (b) large virtual orbital correlation domains spanned by the projected atomic orbitals (PAOs), and (c) compaction of the virtual space through a truncated pair natural orbital (PNO) basis. In this paper, we report on the implementation of an analytic scheme for the calculation of the first derivatives of the DLPNOCC energy for basis set independent perturbations within the singles and doubles approximation (DLPNOCCSD) for closedshell molecules. Perturbationindependent oneparticle density matrices have been implemented in order to account for the response of the CC wave function to the external perturbation. Orbitalrelaxation effects due to external perturbation are not taken into account in the current implementation. We investigate in detail the dependence of the computed firstorder electrical properties (e.g., dipole moment) on the three major truncation parameters used in a DLPNOCC calculation, namely, the natural orbital occupation number cutoff used for the construction of the PNOs, the weak electronpair cutoff, and the domain size cutoff. No additional truncation parameter has been introduced for property calculation. We present benchmark calculations on dipole moments for a set of 10 molecules consisting of 2040 atoms. We demonstrate that 98%99% accuracy relative to the canonical CCSD results can be consistently achieved in these calculations. However, this comes with the price of tightening the threshold for the natural orbital occupation number cutoff by an order of magnitude compared to the DLPNOCCSD energy calculations.

From generalized Langevin equations to Brownian dynamics and embedded Brownian dynamics
View Description Hide DescriptionWe present the reduction of generalized Langevin equations to a coordinateonly stochastic model, which in its exact form involves a forcing term with memory and a general Gaussian noise. It will be shown that a similar fluctuationdissipation theorem still holds at this level. We study the approximation by the typical Brownian dynamics as a first approximation. Our numerical test indicates how the intrinsic frequency of the kernel function influences the accuracy of this approximation. In the case when such an approximate is inadequate, further approximations can be derived by embedding the nonlocal model into an extended dynamics without memory. By imposing noises in the auxiliary variables, we show how the second fluctuationdissipation theorem is still exactly satisfied.

FMO3LCMO study of electron transfer coupling matrix element and pathway: Application to hole transfer between two tryptophans through cis and transpolyprolinelinker systems
View Description Hide DescriptionThe linearcombination of fragment molecular orbitals with threebody correction (FMO3LCMO) is examined for electron transfer (ET) coupling matrix elements and ET pathway analysis, with application to hole transfer between two tryptophans bridged by cis and transpolyproline linker conformations. A projection to the minimalvalencepluscore FMO space was found to give sufficient accuracy with significant reduction of computational cost while avoiding the problem of linear dependence of FMOs stemming from involvement of bond detached atoms.

Extraction of stateresolved information from systems with a fractional number of electrons within the framework of timedependent density functional theory
View Description Hide DescriptionThe determination of the stateresolved physical information within the framework of timedependent density functional theory has remained a widely open question. We demonstrated the ability to extract the stateresolved probability from the knowledge of only the timedependent density, which has been used as the basic variable within the timedependent density functional theory, with the help of stateresolved singleelectron capture experiments for collisions of protons on helium in the energy range of 2100 keV/amu. The present theoretical results for capture into states of H(1s), H(2s), and H(2p) are in good agreement with the most sophisticated experimental results of H^{+} + He(1s ^{2}) system, validating our approach and numerical implementation.

A nonscaleinvariant form for coarsegrained diffusionreaction equations
View Description Hide DescriptionThe process of mixing and reaction is a challenging problem to understand mathematically. Although there have been successes in describing the effective properties of mixing and reaction under a number of regimes, process descriptions for early times have been challenging for cases where the structure of the initial conditions is highly segregated. In this paper, we use the method of volume averaging to develop a rigorous theory for diffusive mixing with reactions from initial to asymptotic times under highly segregated initial conditions in a bounded domain. One key feature that arises in this development is that the functional form of the averaged differential mass balance equations is not, in general, scale invariant. Upon upscaling, an additional source term arises that helps to account for the initial configuration of the reacting chemical species. In this development, we derive the macroscopic parameters (a macroscale source term and an effectiveness factor modifying the reaction rate) defined in the macroscale diffusionreaction equation and provide example applications for several initial configurations.

Efficient method for calculations of rovibrational states in triatomic molecules near dissociation threshold: Application to ozone
View Description Hide DescriptionA method for calculations of rotationalvibrational states of triatomic molecules up to dissociation threshold (and scattering resonances above it) is devised, that combines hyperspherical coordinates, sequential diagonalizationtruncation procedure, optimized grid DVR, and complex absorbing potential. Efficiency and accuracy of the method and new code are tested by computing the spectrum of ozone up to dissociation threshold, using two different potential energy surfaces. In both cases good agreement with results of previous studies is obtained for the lower energy states localized in the deep (∼10 000 cm^{−1}) covalent well. Upper part of the bound state spectrum, within 600 cm^{−1} below dissociation threshold, is also computed and is analyzed in detail. It is found that long progressions of symmetricstretching and bending states (up to 8 and 11 quanta, respectively) survive up to dissociation threshold and even above it, whereas excitations of the asymmetricstretching overtones couple to the local vibration modes, making assignments difficult. Within 140 cm^{−1} below dissociation threshold, largeamplitude vibrational states of a floppy complex O⋯O2 are formed over the shallow van der Waals plateau. These are assigned using two local modes: the rockingmotion and the dissociativemotion progressions, up to 6 quanta in each, both with frequency ∼20 cm^{−1}. Many of these plateau states are mixed with states of the covalent well. Interestingly, excitation of the rockingmotion helps keeping these states localized within the plateau region, by raising the effective barrier.
 Advanced Experimental Techniques

Strain imaging of a LiCoO2 cathode in a Liion battery
View Description Hide DescriptionLiion batteries have been recognized as promising devices for a sustainable society. Layered LiCoO2 and graphite are commonly used as electrode materials for Liion batteries. When charging and discharging, Liions are extracted or inserted into the interlayers, which causes changes in volume. Scanning probe microscopy (SPM) can allow high resolution imaging of these volume changes, which enables us to investigate Liion migration without destruction. We observed volume changes in the LiCoO2 cathode using SPM and successfully imaged the distribution of the volume changes corresponding to the LiCoO2 particles. Volume changes in the interspace were significantly larger than those in the particles. The large volume changes are caused by electrolyte flux induced by changes in concentration of Li ions. The volume changes were greatly reduced when the electrolyte dried out. The dryout and infiltration of electrolyte between the LiCoO2 particles and the current collector spread out with the procedure of degradation of the batteries. The boundaries between the dryout and infiltration regions acted as barriers of electrolyte flux.

Processing of CP MAS kinetics: Towards NMR crystallography for complex solids
View Description Hide DescriptionVariable temperature and high data point density measurements of ^{1}H–^{31}P crosspolarization kinetics in the powdered ammonium dihydrogen phosphate (ADP) have been carried out in the range of −40 °C to +90 °C upon 7 and 10 kHz MAS. The advanced route of processing CP MAS kinetic data has been developed. It is based on reducing the incoherent far range order spin couplings and extracting the CP oscillatory term with the sequent mathematical treatment. The proper replica has been found, which allowed to reduce the FourierBessel (Hankel) transform calculating the angularly averaged and purely distancedepending spin distribution profile to the routine Fourier transform. The shortest ^{31}P–^{1}H distances determined by CP MAS kinetics get between the values obtained by neutron and Xray diffraction, whereas those for more remote protons are slightly larger. The changes in P⋯H distances are hardly noticeable, though a certain trend to increase upon the heating can be deduced. The clearly pronounced effect was the increase of the spindiffusion rate constant upon heating. It allows to state that the communication between interacting spins is the process extremely easy to activate.

Broadband multiresonant strong field coherence breaking as a tool for single isomer microwave spectroscopy
View Description Hide DescriptionUsing standard hardware available in chirpedpulse Fourier transform microwave (CPFTMW) spectroscopy, an experimental method is introduced to selectively extract from the microwave spectrum of an otherwise complicated multicomponent mixture a set of transitions due to a single component, thereby speeding spectral assignment. The method operates the broadband chirpedpulse used to excite the sample in the strongfield limit through a combination of high power and control of the sweep rate. A procedure is introduced that leads to selection of three transition frequencies that can be incorporated as a set of resonant sequential singlefrequency microwave pulses that follow broadband chirpedpulse excitation, resulting in a reduction in the coherent signal from a set of transitions ascribable to the component of interest. The difference in the CPFTMW spectrum with and without this set of multiresonant singlefrequency pulses produces a set of transitions that can confidently be assigned to a single component of the mixture, aiding the analysis of its spectrum. The scheme is applied to (i) selectively extract the spectrum of one of five singly ^{13}Csubsituted isotopologues of benzonitrile in natural abundance, (ii) obtain the microwave spectra of the two structural isomers (E) and (Z)phenylvinylnitrile, and (iii) obtain conformerspecific microwave spectra of methylbutyrate.
 Atoms, Molecules, and Clusters

Ab initio potential energy surfaces describing the interaction of CH(X^{2}Π) with H2
View Description Hide DescriptionWe have determined fourdimensional ab initio quasidiabatic potential energy surfaces describing the interaction of CH(X ^{2}Π) with H2, under the assumption of fixed CH and H2 internuclear separations. These calculations employed the multireference configuration interaction method [MRCISD+Q(Davidson)]. The computed points were fit to an analytical form suitable for timeindependent quantum scattering calculations of rotationally inelastic cross sections and rate constants.

Nitrogen isotopic fractionations in the low temperature (80 K) vacuum ultraviolet photodissociation of N2
View Description Hide DescriptionN2 is a diatomic molecule with complex electronic structure. Interstate crossings are prominent in the high energy domain, introducing significant perturbations to the system. Nitrogen mainly photodissociates in the vacuum ultraviolet (VUV) region of the electromagnetic spectrum through both direct and indirect predissociation. Due to the complexity introduced by these perturbations, the nitrogen isotopic fractionation in N2 photodissociation is extremely hard to calculate, and an experimental approach is required. Here we present new data of Nisotopic fractionation in N2 photodissociation at low temperature (80 K), which shows a distinctly different ^{15}N enrichment profile compared to that at relatively higher temperatures (200 and 300 K). The new data, important to understanding the Nisotopic compositions measured in meteorites and other planetary bodies, are discussed in light of the knowledge of N2 photochemistry and calculated photoabsorption cross sections in the VUV.

Structure, hydrolysis, and diffusion of aqueous vanadium ions from CarParrinello molecular dynamics
View Description Hide DescriptionA molecular level understanding of the properties of electroactive vanadium species in aqueous solution is crucial for enhancing the performance of vanadium redox flow batteries. Here, we employ CarParrinello molecular dynamics simulations based on density functional theory to investigate the hydration structures, first hydrolysis reaction, and diffusion of aqueous V^{2+}, V^{3+}, VO^{2+}, and VO ions at 300 K. The results indicate that the first hydration shell of both V^{2+} and V^{3+} contains six water molecules, while VO^{2+} is coordinated to five and VO to three water ligands. The first acidity constants (pK a) estimated using metadynamics simulations are 2.47, 3.06, and 5.38 for aqueous V^{3+}, VO, and VO^{2+}, respectively, while V^{2+} is predicted to be a fairly weak acid in aqueous solution with a pK a value of 6.22. We also show that the presence of chloride ions in the first coordination sphere of the aqueous VO ion has a significant impact on water hydrolysis leading to a much higher pK a value of 4.8. This should result in a lower propensity of aqueous VO for oxide precipitation reaction in agreement with experimental observations for chloridebased electrolyte solutions. The computed diffusion coefficients of vanadium species in water at room temperature are found to increase as V and thus correlate with the simulated hydrolysis constants, namely, the higher the pK a value, the greater the diffusion coefficient.

Laserinduced reconstruction of Ag clusters in helium droplets
View Description Hide DescriptionSilver clusters were assembled in helium droplets of different sizes ranging from 10^{5} to 10^{10} atoms. The absorption of the clusters was studied upon laser irradiation at 355 nm and 532 nm, which is close to the plasmon resonance maximum in spherical Ag clusters and in the range of the absorption of the complex, branched Ag clusters, respectively. The absorption of the pulsed (7 ns) radiation at 532 nm shows some pronounced saturation effects, absent upon the continuous irradiation. This phenomenon has been discussed in terms of the melting of the complex Ag clusters at high laser fluence, resulting in a loss of the 532 nm absorption. Estimates of the heat transfer also indicate that a bubble may be formed around the hot cluster at high fluences, which may result in ejection of the cluster from the droplet, or disintegration of the droplet entirely.

Largescale calculations of gas phase thermochemistry: Enthalpy of formation, standard entropy, and heat capacity
View Description Hide DescriptionLarge scale quantum calculations for molar enthalpy of formation (Δf H ^{0}), standard entropy (S ^{0}), and heat capacity (CV) are presented. A large data set may help to evaluate quantum thermochemistry tools in order to uncover possible hidden shortcomings and also to find experimental data that might need to be reinvestigated, indeed we list and annotate approximately 200 problematic thermochemistry measurements. Quantum methods systematically underestimate S ^{0} for flexible molecules in the gas phase if only a single (minimum energy) conformation is taken into account. This problem can be tackled in principle by performing thermochemistry calculations for all stable conformations [Zheng et al., Phys. Chem. Chem. Phys. 13, 10885–10907 (2011)], but this is not practical for large molecules. We observe that the deviation of composite quantum thermochemistry recipes from experimental S ^{0} corresponds roughly to the Boltzmann equation (S = RlnΩ), where R is the gas constant and Ω the number of possible conformations. This allows an empirical correction of the calculated entropy for molecules with multiple conformations. With the correction we find an RMSD from experiment of ≈13 J/mol K for 1273 compounds. This paper also provides predictions of Δf H ^{0}, S ^{0}, and CV for well over 700 compounds for which no experimental data could be found in the literature. Finally, in order to facilitate the analysis of thermodynamics properties by others we have implemented a new tool obthermo in the OpenBabel program suite [O’Boyle et al., J. Cheminf. 3, 33 (2011)] including a table of reference atomization energy values for popular thermochemistry methods.

Excited state dynamics of acrylonitrile: Substituent effects at conical intersections interrogated via timeresolved photoelectron spectroscopy and ab initio simulation
View Description Hide DescriptionWe report a joint experimental and theoretical study on the photoinitiated ultrafast dynamics of acrylonitrile (AN) and two methylated analogs: crotonitrile (CrN) and methacrylonitrile (MeAN). Timeresolved photoelectron spectroscopy (TRPES) and ab initio simulation are employed to discern the conical intersection mediated vibronic dynamics leading to relaxation to the ground electronic state. Each molecule is pumped with a femtosecond pulse at 200 nm and the ensuing wavepackets are probed by means of one and two photon ionization at 267 nm. The predominant vibrational motions involved in the deexcitation process, determined by ab initio trajectory simulations, are an initial twisting about the C=C axis followed by pyramidalization at a carbon atom. The decay of the timeresolved photoelectron signal for each molecule is characterized by exponential decay lifetimes for the passage back to the ground state of 60 ± 10, 86 ± 11, and 97 ± 9 fs for AN, CrN, and MeAN, respectively. As these results show, the excited state dynamics are sensitive to the choice of methylation site and the explanation for the observed trend may be found in the trajectory simulations. Specifically, since the pyramidalization motion leading to the conical intersection with the ground state is accompanied by the development of a partial negative charge at the central atom of the pyramidal group, the electron donation of the cyano group ensures that this occurs exclusively at the medial carbon atom. In this way, the donated electron density from the cyano group “directs” the wavepacket to a particular region of the intersection seam. The excellent agreement between the experimental and simulated TRPES spectra, the latter determined by employing trajectory simulations, demonstrates that this mechanistic picture is consistent with the spectroscopic results.

Microwave spectra of the SiH4H2O complex: A new sort of intermolecular interaction
View Description Hide DescriptionMicrowave spectral patterns observed for the silanewater complex were found much different from those of the methanewater complex. The SiH4H2O complex is likely to have a tightly bound structure. The effective rotational and centrifugal distortion constants: B = 3621.1193 (45) MHz and DJ = 49.84 (30) kHz led to the distance between the Si and O atoms in the complex to be 3.3 Å, much shorter than the C and O separation in the CH4H2O of 3.7 Å, and to the silanewater stretching force constant and stretching frequency to be 2.88 N/m and 65 cm^{−1}, respectively, which are to be compared with 1.52 N/m and 55 cm^{−1} of the CH4H2O. The characteristic features of the spectra observed for the main species ^{28}SiH4H2O are common to those of isotopic species: ^{29}SiH4H2O, ^{30}SiH4H2O, ^{28}SiH4H2 ^{18}O, ^{28}SiH4D2O, ^{29}SiH4D2O, ^{30}SiH4D2O, ^{28}SiH4HDO, ^{29}SiH4HDO, ^{30}SiH4HDO, ^{28}SiD4H2O, ^{28}SiD4D2O, and ^{28}SiD4HDO. The observed spectra also indicate that the silane executes a threefold internal rotation about one of its four Si–H bonds, while the C 2 symmetry axis of the water is bent away from the internalrotation axis. An internal axis method analysis yielded an estimate of the internalrotation potential barrier V 3 to be 140 ± 50 cm^{−1}, and those based on diagonalization of a principal axis method Hamiltonian matrix and on the extended internal axis method resulted in V 3 ranging from 180 to 100 cm^{−1}, depending on the isotopic species studied. All the measurements were done by using a pulsed nozzle Fourier transform microwave spectrometer, and the spectral assignments were made with the aid of the Stark effect, which yielded the dipole moment to be 1.730 (10) D. Transitions in higher energy states of the SiH4 internal rotation were observed, clearly resolved from the main lines, when the carrier gas was replaced from Ar to Ne.

Angular and energy distributions of fragment ions in dissociative double photoionization of acetylene molecules in the 31.950.0 eV photon energy range
View Description Hide DescriptionThe twobody dissociation reactions of the dication C2H2 ^{+2}, initiated via double ionization of acetylene molecules by photons in the energy range 31.950.0 eV, have been studied by coupling photoelectronphotoionphotoion coincidence and ion imaging techniques. The angular distributions and kinetic energy of product ions, measured in the 31.950.0 eV energy range, exhibit significant differences for the three leading dissociation reactions with respect to a previous investigation carried out at a fixed energy of 39.0 eV, providing thus new information on the dynamical evolution of the system. The analysis of the results indicates that such dissociation reactions occur with a different mechanism. In particular, the symmetric dissociation in two CH^{+} ions is characterized by different dynamics, and the anisotropy of the angular distribution of ionic products increases with photon energy in a more pronounced way than the other two reactions. Moreover, the kinetic energy distribution of the symmetric dissociation reaction exhibits several components that change with photon energy. The new experimental findings cast light on the microscopic evolution of the system and can provide a laboratory reference for new theoretical calculations on specific features of the multidimensional potential energy surface, namely, the structure, energy and symmetry of dication states, the electronic state of dissociation products, energy barriers and their dependence on the geometry of the intermediate state.