Volume 138, Issue 6, 14 February 2013

While evaporating solvent is a widely used technique to assemble nanosized objects into desired superstructures, there has been limited work on how the assembled structures are affected by the physical aspects of the process. We present large scale molecular dynamics simulations of the evaporationinduced assembly of nanoparticles suspended in a liquid that evaporates in a controlled fashion. The quality of the nanoparticle crystal formed just below the liquid/vapor interface is found to be better at relatively slower evaporation rates, as less defects and grain boundaries appear. This trend is understood as the result of the competition between the accumulation and diffusion times of nanoparticles at the liquid/vapor interface. When the former is smaller, nanoparticles are deposited so fast at the interface that they do not have sufficient time to arrange through diffusion, which leads to the prevalence of defects and grain boundaries. Our results have important implications in understanding assembly of nanoparticles and colloids in nonequilibrium liquid environments.
 ARTICLES

 Theoretical Methods and Algorithms

Calculating excited state properties using KohnSham density functional theory
View Description Hide DescriptionThe accuracy of excited states calculated with KohnSham density functional theory using the maximum overlap method has been assessed for the calculation of adiabatic excitation energies, excited state structures, and excited state harmonic and anharmonic vibrational frequencies for openshell singlet excited states. The computed KohnSham adiabatic excitation energies are improved significantly by post selfconsistent field spinpurification, but remain too low compared with experiment with a larger error than timedependent density functional theory. Excited state structures and vibrational frequencies are also improved by spinpurification. The structures show a comparable accuracy to timedependent density functional theory, while the harmonic vibrational frequencies are found to be more accurate for the majority of vibrational modes. The computed harmonic vibrational frequencies are also further improved by perturbative anharmonic corrections, suggesting a good description of the potential energy surface. Overall, excited state KohnSham density functional theory is shown to provide an efficient method for the calculation of excited state structures and vibrational frequencies in openshell singlet systems and provides a promising technique that can be applied to study large systems.

Reduced atomic pairinteraction design (RAPID) model for simulations of proteins
View Description Hide DescriptionIncreasingly, theoretical studies of proteins focus on large systems. This trend demands the development of computational models that are fast, to overcome the growing complexity, and accurate, to capture the physically relevant features. To address this demand, we introduce a protein model that uses allatom architecture to ensure the highest level of chemical detail while employing effective pair potentials to represent the effect of solvent to achieve the maximum speed. The effective potentials are derived for amino acid residues based on the condition that the solventfree model matches the relevant pairdistribution functions observed in explicit solvent simulations. As a test, the model is applied to alanine polypeptides. For the chain with 10 amino acid residues, the model is found to reproduce properly the native state and its population. Small discrepancies are observed for other folding properties and can be attributed to the approximations inherent in the model. The transferability of the generated effective potentials is investigated in simulations of a longer peptide with 25 residues. A minimal set of potentials is identified that leads to qualitatively correct results in comparison with the explicit solvent simulations. Further tests, conducted for multiple peptide chains, show that the transferable model correctly reproduces the experimentally observed tendency of polyalanines to aggregate into βsheets more strongly with the growing length of the peptide chain. Taken together, the reported results suggest that the proposed model could be used to succesfully simulate folding and aggregation of small peptides in atomic detail. Further tests are needed to assess the strengths and limitations of the model more thoroughly.

Aminoaciddependent mainchain torsionenergy terms for protein systems
View Description Hide DescriptionMany commonly used force fields for protein systems such as AMBER, CHARMM, GROMACS, OPLS, and ECEPP have aminoacidindependent forcefield parameters for mainchain torsionenergy terms. Here, we propose a new type of aminoaciddependent torsionenergy terms in the force fields. As an example, we applied this approach to AMBER ff03 force field and determined new aminoaciddependent parameters for ψ (NC^{α}CN) and ζ (C^{β}C^{α}CN) angles for each amino acid by using our optimization method, which is one of the knowledgebased approach. In order to test the validity of the new forcefield parameters, we then performed folding simulations of αhelical and βhairpin peptides, using the optimized force field. The results showed that the new forcefield parameters gave structures more consistent with the experimental implications than the original AMBER ff03 force field.

An efficient method for calculating dynamical hyperpolarizabilities using realtime timedependent density functional theory
View Description Hide DescriptionIn this paper we present a timedomain timedependent density functional theory (TDDFT) approach to calculate frequencydependent polarizability and hyperpolarizabilities. In this approach, the electronic degrees of freedom are propagated within the density matrix based TDDFT framework using the efficient modified midpoint and unitary transformation algorithm. We use monochromatic waves as external perturbations and apply the finite field method to extract various orders of the timedependent dipole moment. By fitting each order of timedependent dipole to sinusoidal waves with harmonic frequencies, one can obtain the corresponding (hyper)polarizability tensors. This approach avoids explicit Fourier transform and therefore does not require long simulation time. The method is illustrated with application to the optically active organic molecule paranitroaniline, of which the frequencydependent polarizability α(−ω; ω), secondharmonic generation β(−2ω; ω, ω), optical rectification β(0; −ω, ω), thirdharmonic generation γ(−3ω; ω, ω, ω), and degenerate fourwave mixing γ(−ω; ω, ω, −ω) are calculated.

Trapping of diffusing particles by clusters of absorbing disks on a reflecting wall with disk centers on sites of a square lattice
View Description Hide DescriptionA simple approximate formula is derived for the rate constant that describes steadystate flux of diffusing particles through a cluster of perfectly absorbing disks on the otherwise reflecting flat wall, assuming that the disk centers occupy neighboring sites of a square lattice. A distinctive feature of trapping by a disk cluster is that disks located at the cluster periphery shield the disks in the center of the cluster. This competition of the disks for diffusing particles makes it impossible to find an exact analytical solution for the rate constant in the general case. To derive the approximate formula, we use a recently suggested approach [A. M. Berezhkovskii, L. Dagdug, V. A. Lizunov, J. Zimmerberg, and S. M. Bezrukov, J. Chem. Phys.136, 211102 (2012)], which is based on the replacement of the disk cluster by an effective uniform partially absorbing spot. The formula shows how the rate constant depends on the size and shape of the cluster. To check the accuracy of the formula, we compare its predictions with the values of the rate constant obtained from Brownian dynamics simulations. The comparison made for 18 clusters of various shapes and sizes shows good agreement between the theoretical predictions and numerical results.

Gaussianbased multiconfiguration timedependent Hartree: A twolayer approach. I. Theory
View Description Hide DescriptionWe describe a novel twolayer variant of the Gaussianbased multiconfiguration timedependent Hartree (GMCTDH) approach which improves on the performance and convergence properties of quantum propagation based on variationally evolving frozen Gaussians (FGs). While the standard scheme uses factorizable multidimensional FGs, the present approach combines these into flexible, MCTDHlike singleparticle functions. At the same time, the expensive variational evolution of the Gaussian parameters is reduced to lowdimensional subspaces. As a result, the novel scheme significantly alleviates the current bottleneck to accurate propagation in GMCTDH and its variational multiconfigurational Gaussian (vMCG) variant. Since the firstlayer singleparticle functions are chosen to be orthogonal, the present approach can be straightforwardly combined with existing multilayer MCTDH schemes.

Explicitly correlated atomic orbital basis second order Møller–Plesset theory
View Description Hide DescriptionThe scope of problems treatable by ab initio wavefunction methods has expanded greatly through the application of local approximations. In particular, atomic orbital (AO) based wavefunction methods have emerged as powerful techniques for exploiting sparsity and have been applied to biomolecules as large as 1707 atoms [S. A. Maurer, D. S. Lambrecht, D. Flaig, and C. Ochsenfeld, J. Chem. Phys.136, 144107 (Year: 2012)]10.1063/1.3693908. Correlated wavefunction methods, however, converge notoriously slowly to the basis set limit and, excepting the use of large basis sets, will suffer from a severe basis set incompleteness error (BSIE). The use of larger basis sets is prohibitively expensive for AO basis methods since, for example, secondorder MøllerPlesset perturbation theory (MP2) scales linearly with the number of atoms, but still scales as in the number of functions per atom. Explicitly correlated F12 methods have been shown to drastically reduce BSIE for even modestly sized basis sets. In this work, we therefore explore an atomic orbital based formulation of explicitly correlated MP2F12 theory. We present working equations for the new method, which produce results identical to the widely used molecular orbital (MO) version of MP2F12 without resorting to a delocalized MO basis. We conclude with a discussion of several possible approaches to a priori screening of contraction terms in our method and the prospects for a linear scaling implementation of AOMP2F12. The discussion includes concrete examples involving noble gas dimers and linear alkane chains.

Highdensity correlation energy expansion of the onedimensional uniform electron gas
View Description Hide DescriptionWe show that the expression of the highdensity (i.e., smallr _{ s }) correlation energy per electron for the onedimensional uniform electron gas can be obtained by conventional perturbation theory and is of the form ε_{c}(r _{ s }) = −π^{2}/360 + 0.00845 r _{ s } + …, where r _{ s } is the average radius of an electron. Combining these new results with the lowdensity correlation energy expansion, we propose a localdensity approximation correlation functional, which deviates by a maximum of 0.1 mhartree compared to the benchmark diffusion Monte Carlo calculations.
 Advanced Experimental Techniques

^{14}N overtone NMR spectra under magic angle spinning: Experiments and numerically exact simulations
View Description Hide DescriptionIt was recently shown that high resolution ^{14}N overtone NMR spectra can be obtained directly under magic angle spinning (MAS) conditions [L. A. O’Dell and C. I. Ratcliffe, Chem. Phys. Lett.514, 168 (Year: 2011)]10.1016/j.cplett.2011.08.030. Preliminary experimental results showed narrowed powder pattern widths, a frequency shift that is dependent on the MAS rate, and an apparent absence of spinning sidebands, observations which appeared to be inconsistent with previous theoretical treatments. Herein, we reproduce these effects using numerically exact simulations that take into account the full nuclear spin Hamiltonian. Under sample spinning, the ^{14}N overtone signal is split into five (0, ±1, ±2) overtone sidebands separated by the spinning frequency. For a powder sample spinning at the magic angle, the +2ω_{r} sideband is dominant while the others show significantly lower signal intensities. The resultant MAS powder patterns show characteristic quadrupolar lineshapes from which the ^{14}N quadrupolar parameters and isotropic chemical shift can be determined. Spinning the sample at other angles is shown to alter both the shapes and relative intensities of the five overtone sidebands, with MAS providing the benefit of averaging dipolar couplings and shielding anisotropy. To demonstrate the advantages of this experimental approach, we present the ^{14}N overtone MAS spectrum obtained from Lhistidine, in which powder patterns from all three nitrogen sites are clearly resolved.

Short range order in bimetallic nanoalloys: An extended Xray absorption fine structure study
View Description Hide DescriptionPartial coordination numbers measured by extended Xray absorption fine structure (EXAFS) spectroscopy have been used for decades to resolve between different compositional motifs in bulk and nanoscale bimetallic alloys. Due to the ensembleaveraging nature of EXAFS, the values of the coordination numbers in nanoparticles cannot be simply interpreted in terms of the degree of alloying or segregation if the compositional distribution is broad. We demonstrate that a Cowley short range order parameter is an objective measure of either the segregation tendency (e.g., a coreshell type) or the degree of randomness (in homogeneous nanoalloys). This criterion can be used even in the case when the clusters are random but have broad compositional distributions. All cases are illustrated using the analyses of EXAFS data obtained in three different nanoscale bimetallic systems: Pt(core)Pd(shell), Pd(core)Pt(shell), and PtPd random alloy.
 Atoms, Molecules, and Clusters

Photoinduced electron detachment of protein polyanions in the VUV range
View Description Hide DescriptionBiomolecular polyanions mainly relax by electron emission after UV excitation. Here, we study photodetachment of protein polyanions in the 6–16 eV VUV range by coupling a linear quadrupole ion trap with a synchrotron beamline. Gasphase VUV action spectra of electrosprayproduced multiply deprotonated insulin (5.6 kDa) and myoglobin (16.7 kDa) proteins are reported, which significantly increases the amount of data available on the optical response of proteins in the VUV. The influence of the protein charge and oxidation state upon the electron detachment efficiency is discussed. For small protein such as insulin, it appears that higher charge states produce higher detachment yields. Investigations on oxidized species show that the nature of the groups bearing the negative charges has an influence on the yields. For larger proteins, comparison of two forms of myoglobin clearly indicate that the threedimensional structure does not impact much on the shape and the magnitude of the photodetachment spectra, in spite of a slight shift for the first electronic excited states.

Development of a moleculardynamicsbased clusterheatcapacity model for study of homogeneous condensation in supersonic watervapor expansions
View Description Hide DescriptionSupersonic expansions to vacuum produce clusters of sufficiently small size that properties such as heat capacities and latent heat of evaporation cannot be described by bulk vapor thermodynamic values. In this work the MonteCarlo CanonicalEnsemble (MCCE) method was used to provide potential energies and constantvolume heat capacities for small water clusters. The cluster structures obtained using the wellknown simple point charge model were found to agree well with earlier simulations using more rigorous potentials. The MCCE results were used as the starting point for molecular dynamics simulations of the evaporation rate as a function of cluster temperature and size which were found to agree with unimolecular dissociation theory and classical nucleation theory. The heat capacities and latent heat obtained from the MCCE simulations were used in directsimulation MonteCarlo of two experiments that measured Rayleigh scattering and terminal dimer mole fraction of supersonic waterjet expansions. Watercluster temperature and size were found to be influenced by the use of kinetic rather than thermodynamic heatcapacity and latentheat values as well as the nucleation model.

Lowest triplet (n, π*) electronic state of acrolein: Determination of structural parameters by cavity ringdown spectroscopy and quantumchemical methods
View Description Hide DescriptionThe cavity ringdown absorption spectrum of acrolein (propenal, CH_{2}=CH—CH=O) was recorded near 412 nm, under bulkgas conditions at room temperature and in a freejet expansion. The measured spectral region includes the band of the T _{1}(n, π*) ← S _{0} system. We analyzed the rotational contour by using the STROTA computer program [R. H. Judge et al. , J. Chem. Phys.103, 5343 (Year: 1995)]10.1063/1.470569, which incorporates an asymmetric rotor Hamiltonian for simulating and fitting singlettriplet spectra. We used the program to fit T _{1}(n, π*) inertial constants to the roomtemperature contour. The determined values (cm^{−1}), with 2σ confidence intervals, are A = 1.662 ± 0.003, B = 0.1485 ± 0.0006, C = 0.1363 ± 0.0004. Linewidth analysis of the jetcooled spectrum yielded a value of 14 ± 2 ps for the lifetime of isolated acrolein molecules in the T _{1}(n, π*), v = 0 state. We discuss the observed lifetime in the context of previous computational work on acrolein photochemistry. The spectroscopically derived inertial constants for the T _{1}(n, π*) state were used to benchmark a variety of computational methods. One focus was on complete active space methods, such as complete active space selfconsistent field (CASSCF) and secondorder perturbation theory with a CASSCF reference function (CASPT2), which are applicable to excited states. We also examined the equationofmotion coupledcluster and timedependent density function theory excitedstate methods, and finally unrestricted groundstate techniques, including unrestricted density functional theory and unrestricted coupledcluster theory with single and double and perturbative triple excitations. For each of the above methods, we or others [O. S. Bokareva et al. , Int. J. Quantum Chem.108, 2719 (Year: 2008)]10.1002/qua.21803 used a triple zetaquality basis set to optimize the T _{1}(n, π*) geometry of acrolein. We find that the multiconfigurational methods provide the best agreement with fitted inertial constants, while the economical unrestricted PerdewBurkeErnzerhof exchangecorrelation hybrid functional (UPBE0) technique performs nearly as well.

Zerofield splitting in nickel(II) complexes: A comparison of DFT and multiconfigurational wavefunction calculations
View Description Hide DescriptionThe zerofield splitting (ZFS) is an important quantity in the electron spin Hamiltonian for S = 1 or higher. We report calculations of the ZFS in some six and fivecoordinated nickel(II) complexes (S = 1), using different levels of theory within the framework of the ORCA program package [F. Neese, Wiley Interdiscip. Rev.: Comput. Mol. Sci.2, 73 (Year: 2012)]10.1002/wcms.81. We compare the highend ab initio calculations (complete active space selfconsistent field and nelectron valence state perturbation theory), making use of both the secondorder perturbation theory and the quasidegenerate perturbation approach, with density functional theory (DFT) methods using different functionals. The pattern of results obtained at the ab initio levels is quite consistent and in reasonable agreement with experimental data. The DFT methods used to calculate the ZFS give very strongly functionaldependent results and do not seem to function well for our systems.

A multireference perturbation study of the NN stretching frequency of transazobenzene in nπ* excitation and an implication for the photoisomerization mechanism
View Description Hide DescriptionA multireference secondorder perturbation theory is applied to calculate equilibrium structures and vibrational frequencies of transazobenzene in the ground and nπ^{*} excited states, as well as the reaction pathways for rotation and inversion mechanism in the nπ^{*} excited state. It is found that the NN stretching frequency exhibits a slight increase at the minimum energy structure in the nπ^{*} state, which is explained by the mixing of the NN stretching mode with the CN symmetric stretching mode. We also calculate the NN stretching frequency at several selected structures along the rotation and inversion pathways in the nπ^{*} state, and show that the frequency decreases gradually along the rotation pathway while it increases by ca. 300 cm^{−1} along the inversion pathway. The frequencies and energy variations along the respective pathways indicate that the rotation pathway is more consistent with the experimental observation of the NN stretching frequency in nπ^{*} excitation.

Density functional theory and global optimization study of Sn_{ m }Pb_{ n } clusters (7 ⩽ m + n ⩽ 12, 0 ⩽ m/(m + n) ⩽ 1)
View Description Hide DescriptionThe global minima of the neutral binary Sn_{ m } Pb _{ n } atomic clusters, 7 ⩽ m + n ⩽ 12, of all the possible stoichiometric ratios have been found using tabu search in descriptor space and density functional theory. The effects of spinorbit coupling on optimized geometries and energies are important. All of the binary clusters form substitution alloys. Apart from the 11atom case, the pure clusters of the same size have the same ground state geometry. The relative energies of the isomers of a cluster depend on, in order of decreasing importance: the overall geometry; the specific sites occupied by the two atom types; and the degree of segregation. The total cohesive energy difference between the lowest energy homotops is typically on the order of 0.02 eV. The mixing/segregation trends are found to be very different depending on the size of the basis set. Calculations generally overestimate the dipole moments. The trends in calculated dipole moments agree with experiment for the leadrich clusters, and to a lesser degree, the tinrich clusters.

Effects of ^{3}He impurities on the superfluid response of the ^{4}He monolayer on a C_{20} molecule
View Description Hide DescriptionThe pathintegral Monte Carlo calculations have been performed to investigate the effects of ^{3}He impurities on structural and superfluid properties of the ^{4}He monolayer on a single C_{20} molecule. According to our previous study, the helium monolayer exhibits different quantum states for different numbers of ^{4}He adatoms and is completed to form a commensurate solid where nanoscale supersolidity can be realized through the activation of mobile vacancy states. We first observe that different structures for different numbers of helium atoms are mostly preserved with the replacement of a few ^{4}He atoms with the same number of ^{3}He atoms, whether the helium layer is a fluid or a solid. However, the substitution of ^{3}He impurities is found to have different effects on the superfluid response of the helium layer, depending on its quantum state. For a partiallyfilled fluid layer the superfluid fraction decreases monotonically with the increasing ^{3}He concentration, which can be understood in terms of the suppression of exchange couplings among ^{4}He atoms due to the presence of ^{3}He impurities. On the other hand, the substitution of a few ^{3}He impurity atoms may increase the superfluid fraction of a nearcomplete monolayer that is in a crystalline solid state. The enhancement of superfluidity in a solid layer is interpreted to be due to interstitial and vacancy defects promoted by larger quantum fluctuations of lighter ^{3}He atoms. This provides strong evidence that the ^{4}He monolayer on C_{20} shows the vacancybased supersolidity near its completion.

Towards a firstprinciples model of Fermi resonance in the alkyl CH stretch region: Application to 1,2diphenylethane and 2,2,2paracyclophane
View Description Hide DescriptionThe spectroscopy of two flexible hydrocarbons, 1,2diphenylethane (DPE) and 2,2,2paracyclophane (TCP) is presented, and a predictive theoretical model for describing the alkyl CH stretch region of these hydrocarbons is developed. Ultraviolet holeburning spectroscopy identified two isomers of DPE and a single conformation of TCP present in the supersonic jet expansion. Through the analysis of the ground state lowfrequency vibronic spectroscopy obtained by dispersed fluorescence, conformational assignments were made for both DPE and TCP. The two isomers of DPE were found to retain the low energy structures of butane, being present in both the gauche and anti structures. TCP forms a C _{2} symmetric structure, differing from the predicted lower energy C _{3} conformation by the symmetry of the ethano bridges (−CH_{2}CH_{2}−) linking the phenyl substituents. Resonant iondip infrared spectroscopy is used to record singleconformation IR spectra of the two conformers of DPE and the single conformer of TCP in the alkyl CH stretch region and in the midIR that covers the CH bend fundamentals. A local mode Hamiltonian that incorporates cubic stretchbend coupling is developed. Its parameters are obtained from density functional theory methods. Full dimensional calculations are compared to those that use reduced dimensional Hamiltonians in which anharmonic CH stretches and scissor modes are Fermi coupled. Excellent agreement is found. Scale factors of select terms in the reduced dimensional Hamiltonian are determined by fitting the theoretical Hamiltonian to the antiDPE spectrum. The scaled Hamiltonian is then used to predict successfully structures for the remaining lower symmetry experimentally determined spectra in the alkyl CH stretch region.
 Liquids, Glasses, and Crystals

Further details on the phase diagram of hard ellipsoids of revolution
View Description Hide DescriptionIn recent work we revisited the phase diagram of hard ellipsoids of revolution (spheroids) by means of replica exchange Monte Carlo simulations. This was done by setting random initial configurations, and allows to confirm the formation of sm2 crystal structures at high densities [P. Pfleiderer and T. Schilling, Phys. Rev. E75, 020402 (Year: 2007)10.1103/PhysRevE.75.020402] for large anisotropies and stretchedfcc for small anisotropies. In this work we employed the same technique but setting the starting cells as sm2 crystal structures having the maximum known packing density [A. Donev, F. H. Stillinger, P. M. Chaikin, and S. Torquato, Phys. Rev. Lett.92, 255506 (Year: 2004)10.1103/PhysRevLett.92.255506]. This procedure yields a very rich behavior for quasispherical oblates and prolates. These systems, from low to high pressures, show the following phases: isotropic fluid, plastic solid, stretchedfcc solid, and sm2 solid. The first three transitions are first order, whereas the last one is a subtle, probably high order transition. This picture is consistent with the fact of having the sm2 structure capable of producing the maximally achievable density.

NMR relaxation study of water dynamics in superparamagnetic ironoxideloaded vesicles
View Description Hide DescriptionSuperparamagnetic iron oxide (SPIO) nanoparticles have been introduced as contrast agents for clinical applications in magnetic resonance imaging. Recently, SPIO has been also used for tracking cells. However, NMR relaxation of water molecules behaves differently in a SPIO solution and SPIOloaded cells. In this study, we used waterinoilinwater double emulsions to mimic cellular environments. The MR relaxation induced by the SPIOloaded vesicles and SPIO solution indicates that T _{2} ^{*} is sensitive to the iron concentration alone, and the behavior was very similar in both SPIOloaded vesicles and SPIO solution. However, T _{2} relaxation of water in SPIOloaded vesicles was faster than that in a SPIO solution. In addition, the contribution of water inside and outside the vesicles was clarified by replacing H_{2}O with D_{2}O, and water inside the vesicles was found to cause a nonlinear iron concentration dependency. The studied dilution revealed that vesicle aggregation undergoes a structural transition upon dilution by a certain amount of water. R _{2} ^{*} relaxation is sensitive to this structural change and shows an obvious nonlinear iron concentration dependency when the SPIO loading is sufficiently high. Random walk simulations demonstrated that in the assumed model, the vesicles aggregate structures causing the differences between R _{2} ^{*} and R _{2} relaxation of water in vesicles in the presence of SPIO particles.