Volume 140, Issue 22, 14 June 2014

Homogeneous water condensation and ice formation in supersonic expansions to vacuum for stagnation pressures from 12 to 1000 mbar are studied using the particlebased EllipsoidalStatistical BhatnagarGrossKrook (ESBGK) method. We find that when condensation starts to occur, at a stagnation pressure of 96 mbar, the increase in the degree of condensation causes an increase in the rotational temperature due to the latent heat of vaporization. The simulated rotational temperature profiles along the plume expansion agree well with measurements confirming the kinetic homogeneous condensation models and the method of simulation. Comparisons of the simulated gas and cluster number densities, cluster size for different stagnation pressures along the plume centerline were made and it is found that the cluster size increase linearly with respect to stagnation pressure, consistent with classical nucleation theory. The sensitivity of our results to cluster nucleation model and latent heat values based on bulk water, specific cluster size, or bulk ice are examined. In particular, the ESBGK simulations are found to be too coarsegrained to provide information on the phase or structure of the clusters formed. For this reason, molecular dynamics simulations of water condensation in a onedimensional free expansion to simulate the conditions in the core of a plume are performed. We find that the internal structure of the clusters formed depends on the stagnation temperature. A larger cluster of average size 21 was tracked down the expansion, and a calculation of its average internal temperature as well as a comparison of its radial distribution functions (RDFs) with values measured for solid amorphous ice clusters lead us to conclude that this cluster is in a solidlike rather than liquid form. In another moleculardynamics simulation at a much lower stagnation temperature, a larger cluster of size 324 and internal temperature 200 K was extracted from an expansion plume and equilibrated to determine its RDF and selfdiffusion coefficient. The value of the latter shows that this cluster is formed in a supercooled liquid state rather than in an amorphous solid state.
 COMMUNICATIONS


Communication: Hetagged vibrational spectra of the SarGlyH^{+} and H^{+}(H_{2}O)_{2,3} ions: Quantifying tag effects in cryogenic ion vibrational predissociation (CIVP) spectroscopy
View Description Hide DescriptionTo assess the degree to which more perturbative, but widely used “tag” species (Ar, H2, Ne) affect the intrinsic band patterns of the isolated ions, we describe the extension of massselective, cryogenic ion vibrational spectroscopy to the very weakly interacting helium complexes of three archetypal ions: the dipeptide SarGlyH^{+} and the small protonated water clusters: H^{+}(H2O)2,3, including the H5O2 ^{+} “Zundel” ion. He adducts were generated in a 4.5 K octopole ion trap interfaced to a doublefocusing, tandem timeofflight photofragmentation mass spectrometer to record massselected vibrational predissociation spectra. The H2 taginduced shift (relative to that by He) on the tagbound NH stretch of the SarGlyH^{+} spectrum is quite small (12 cm^{−1}), while the effect on the floppy H5O2 ^{+} ion is more dramatic (125 cm^{−1}) in going from Ar (or H2) to Ne. The shifts from Ne to He, on the other hand, while quantitatively significant (maximum of 10 cm^{−1}), display the same basic H5O2 ^{+} band structure, indicating that the Hetagged H5O2 ^{+} spectrum accurately represents the delocalized nature of the vibrational zeropoint level. Interestingly, the Hetagged spectrum of H^{+}(H2O)3 reveals the location of the nonbonded OH group on the central H3O^{+} ion to fall between the collective nonbonded OH stretches on the flanking water molecules in a position typically associated with a neutral OH group.

Communication: Chemical functionality of interfacial water enveloping nanoscale structural defects in proteins
View Description Hide DescriptionBuilding upon a nonDebye multiscale treatment of water dielectrics, this work reveals the biochemical role of interfacial water enveloping nanoscale structural defects in soluble proteins, asserting its role as a chemical base. This quasireactant status is already implied by the significant concentration of structural defects in the vicinity of an enzymatically active site, delineating their role as promoters or enhancers of catalytic activity.

Communication: Remarkable electrophilicity of the oxalic acid monomer: An anion photoelectron spectroscopy and theoretical study
View Description Hide DescriptionOur experimental and computational results demonstrate an unusual electrophilicity of oxalic acid, the simplest dicarboxylic acid. The monomer is characterized by an adiabatic electron affinity and electron vertical detachment energy of 0.72 and 1.08 eV (±0.05 eV), respectively. The electrophilicity results primarily from the bonding carboncarbon interaction in the singly occupied molecular orbital of the anion, but it is further enhanced by intramolecular hydrogen bonds. The wellresolved structure in the photoelectron spectrum is reproduced theoretically, based on FranckCondon factors for the vibronic anion → neutral transitions.
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 ARTICLES

 Theoretical Methods and Algorithms

Exponential time differencing methods with Chebyshev collocation for polymers confined by interacting surfaces
View Description Hide DescriptionWe present a fast and accurate numerical method for the selfconsistent field theory calculations of confined polymer systems. It introduces an exponential time differencing method (ETDRK4) based on Chebyshev collocation, which exhibits fourthorder accuracy in temporal domain and spectral accuracy in spatial domain, to solve the modified diffusion equations. Similar to the approach proposed by Hur et al. [Macromolecules45, 2905 (2012)], nonperiodic boundary conditions are adopted to model the confining walls with or without preferential interactions with polymer species, avoiding the use of surface field terms and the mask technique in a conventional approach. The performance of ETDRK4 is examined in comparison with the operator splitting methods with either Fourier collocation or Chebyshev collocation. Numerical experiments show that our exponential time differencing method is more efficient than the operator splitting methods in high accuracy calculations. This method has been applied to diblock copolymers confined by two parallel flat surfaces.

Asymptotic solution of the diffusion equation in slender impermeable tubes of revolution. I. The leadingterm approximation
View Description Hide DescriptionThe anisotropic 3D equation describing the pointlike particles diffusion in slender impermeable tubes of revolution with cross section smoothly depending on the longitudinal coordinate is the object of our study. We use singular perturbations approach to find the rigorous asymptotic expression for the local particles concentration as an expansion in the ratio of the characteristic transversal and longitudinal diffusion relaxation times. The corresponding leadingterm approximation is a generalization of wellknown FickJacobs approximation. This result allowed us to delineate the conditions on temporal and spatial scales under which the FickJacobs approximation is valid. A striking analogy between solution of our problem and the method of innerouter expansions for low Knudsen numbers gas kinetic theory is established. With the aid of this analogy we clarify the physical and mathematical meaning of the obtained results.

Identifying the Hamiltonian structure in linear response theory
View Description Hide DescriptionWe present a unifying framework for linear response eigenvalue equations that encompasses both variational HartreeFock and KohnSham density functional theory as well as nonvariational coupledcluster theory. The joint description is rooted in the socalled Hamiltonian structure of the response kernel matrices, whose properties permit an immediate identification of the wellknown paired eigenvalue spectrum describing a molecule in the isolated state. Recognizing the Hamiltonian structure underlying the equations further enables a generalization to the case of a polarizableembedded molecule treated in variational and, in particular, in nonvariational theories.

Derivation of coarsegrained potentials via multistate iterative Boltzmann inversion
View Description Hide DescriptionIn this work, an extension is proposed to the standard iterative Boltzmann inversion (IBI) method used to derive coarsegrained potentials. It is shown that the inclusion of target data from multiple states yields a less statedependent potential, and is thus better suited to simulate systems over a range of thermodynamic states than the standard IBI method. The inclusion of target data from multiple states forces the algorithm to sample regions of potential phase space that match the radial distribution function at multiple state points, thus producing a derived potential that is more representative of the underlying interactions. It is shown that the algorithm is able to converge to the true potential for a system where the underlying potential is known. It is also shown that potentials derived via the proposed method better predict the behavior of nalkane chains than those derived via the standard IBI method. Additionally, through the examination of alkane monolayers, it is shown that the relative weight given to each state in the fitting procedure can impact bulk system properties, allowing the potentials to be further tuned in order to match the properties of reference atomistic and/or experimental systems.

Temporal crosscorrelation asymmetry and departure from equilibrium in a bistable chemical system
View Description Hide DescriptionThis paper aims at determining sustained reaction fluxes in a nonlinear chemical system driven in a nonequilibrium steady state. The method relies on the computation of crosscorrelation functions for the internal fluctuations of chemical species concentrations. By employing Langevintype equations, we derive approximate analytical formulas for the crosscorrelation functions associated with nonlinear dynamics. Kinetic Monte Carlo simulations of the chemical master equation are performed in order to check the validity of the Langevin equations for a bistable chemical system. The two approaches are found in excellent agreement, except for critical parameter values where the bifurcation between monostability and bistability occurs. From the theoretical point of view, the results imply that the behavior of crosscorrelation functions cannot be exploited to measure sustained reaction fluxes in a specific nonlinear system without the prior knowledge of the associated chemical mechanism and the rate constants.

Identifiability analysis of rotational diffusion tensor and electronic transition moments measured in timeresolved fluorescence depolarization experiment
View Description Hide DescriptionThe subject of this paper is studies of the deterministic identifiability of molecular parameters, such as rotational diffusion tensor components and orientation of electronic transition moments, resulting from the timeresolved fluorescence anisotropy experiment. In the most general case considered, a pair of perpendicularly polarized emissions enables the unique determination of all the rotational diffusion tensor's principal components. The influence of the tensor's symmetry and the associated degeneration of its eigenvalues on the identifiability of the electronic transitions moments is systematically investigated. The analysis reveals that independently of the rotational diffusion tensor's symmetry, the transition moments involved in photoselection and emission processes cannot be uniquely identified without a priori information about their mutual orientation or their orientation with respect to the principal axes of the tensor. Moreover, it is shown that increasing the symmetry of the rotational diffusion tensor deteriorates the degree of the transition moments identifiability. To obtain these results analytically, a novel approach to solve bilinear system of equations for Markov parameters is applied. The effect of the additional information, obtained from fluorescence measurements for different molecular mobilities, to improve the identifiability at various levels of analysis is shown. The effectiveness and reliability of the target analysis method for experimental determination of the molecular parameters is also discussed.

Path integral Liouville dynamics for thermal equilibrium systems
View Description Hide DescriptionWe show a new imaginary time path integral based method—path integral Liouville dynamics (PILD), which can be derived from the equilibrium Liouville dynamics[J. Liu and W. H. Miller, J. Chem. Phys.134, 104101 (2011)] in the Wigner phase space. Numerical tests of PILD with the simple (white noise) Langevin thermostat have been made for two strongly anharmonic model problems. Since implementation of PILD does not request any specific form of the potential energy surface, the results suggest that PILD offers a potentially useful approach for general condensed phase molecular systems to have the two important properties: conserves the quantum canonical distribution and recovers exact thermal correlation functions (of even nonlinear operators, i.e., nonlinear functions of position or momentum operators) in the classical, high temperature, and harmonic limits.

Landau–Zener type surface hopping algorithms
View Description Hide DescriptionA class of surface hopping algorithms is studied comparing two recent Landau–Zener (LZ) formulas for the probability of nonadiabatic transitions. One of the formulas requires a diabatic representation of the potential matrix while the other one depends only on the adiabatic potential energy surfaces. For each classical trajectory, the nonadiabatic transitions take place only when the surface gap attains a local minimum. Numerical experiments are performed with deterministically branching trajectories and with probabilistic surface hopping. The deterministic and the probabilistic approach confirm the affinity of both the LZ probabilities, as well as the good approximation of the reference solution computed by solving the Schrödinger equation via a grid based pseudospectral method. Visualizations of position expectations and superimposed surface hopping trajectories with reference position densities illustrate the effective dynamics of the investigated algorithms.

Fulldimensional diabatic potential energy surfaces including dissociation: The ^{2} E ^{″} state of NO_{3}
View Description Hide DescriptionA scheme to produce accurate fulldimensional coupled diabatic potential energy surfaces including dissociative regions and suitable for dynamical calculations is proposed. The scheme is successfully applied to model the twosheeted surface of the ^{2} E ^{″} state of the NO3 radical. An accurate potential energy surface for the anion ground state is developed as well. Both surfaces are based on highlevel ab initio calculations. The model consists of a diabatic potential matrix, which is expanded to higher order in terms of symmetry polynomials of symmetry coordinates. The choice of coordinates is key for the accuracy of the obtained potential energy surfaces and is discussed in detail. A second central aspect is the generation of reference data to fit the expansion coefficients of the model for which a stochastic approach is proposed. A third ingredient is a new and simple scheme to handle problematic regions of the potential energy surfaces, resulting from the massive undersampling by the reference data unavoidable for highdimensional problems. The final analytical diabatic surfaces are used to compute the lowest vibrational levels of and the photoelectron detachment spectrum of leading to the neutral radical in the ^{2} E ^{″} state by full dimensional multisurface wavepacket propagation for NO3 performed using the MultiConfiguration Time Dependent Hartree method. The achieved agreement of the simulations with available experimental data demonstrates the power of the proposed scheme and the high quality of the obtained potential energy surfaces.

Twostate theory of binned photon statistics for a large class of waiting time distributions and its application to quantum dot blinking
View Description Hide DescriptionA theoretical method is proposed for the calculation of the photon counting probability distribution during a bin time. Twostate fluorescence and steady excitation are assumed. A key feature is a kinetic scheme that allows for an extensive class of stochastic waiting time distribution functions, including power laws, expanded as a sum of weighted decaying exponentials. The solution is analytic in certain conditions, and an exact and simple expression is found for the integral contribution of “bright” and “dark” states. As an application for power law kinetics, theoretical results are compared with experimental intensity histograms from a number of blinking CdSe/ZnS quantum dots. The histograms are consistent with distributions of intensity states around a “bright” and a “dark” maximum. A gap of states is also revealed in the moreorless flat interpeak region. The slope and to some extent the flatness of the interpeak feature are found to be sensitive to the powerlaw exponents. Possible models consistent with these findings are discussed, such as the combination of multiple charging and fluctuating nonradiative channels or the multiple recombination center model. A fitting of the latter to experiment provides constraints on the interaction parameter between the recombination centers. Further extensions and applications of the photon counting theory are also discussed.

Assessment of amide I spectroscopic maps for a gasphase peptide using IRUV doubleresonance spectroscopy and density functional theory calculations
View Description Hide DescriptionThe spectroscopy of amide I vibrations has become a powerful tool for exploring protein structure and dynamics. To help with spectral interpretation, it is often useful to perform molecular dynamics (MD) simulations. To connect spectroscopic experiments to simulations in an efficient manner, several researchers have proposed “maps,” which relate observables in classical MD simulations to quantum spectroscopic variables. It can be difficult to discern whether errors in the theoretical results (compared to experiment) arise from inaccuracies in the MD trajectories or in the maps themselves. In this work, we evaluate spectroscopic maps independently from MD simulations by comparing experimental and theoretical spectra for a single conformation of the αhelical model peptide AcPhe(Ala)5LysH^{+} in the gas phase. Conformationspecific experimental spectra are obtained for the unlabeled peptide and for several singly and doubly ^{13}Clabeled variants using infraredultraviolet doubleresonance spectroscopy, and these spectra are found to be wellmodeled by density functional theory (DFT) calculations at the B3LYP/631G** level. We then compare DFT results for the deuterated and ^{13}C^{18}Olabeled peptide with those from spectroscopic maps developed and used previously by the Skinner group. We find that the maps are typically accurate to within a few cm^{−1} for both frequencies and couplings, having larger errors only for the frequencies of terminal amides.

Choleskydecomposed density MP2 with density fitting: Accurate MP2 and doublehybrid DFT energies for large systems
View Description Hide DescriptionOur recently developed QQRtype integral screening is introduced in our Choleskydecomposed pseudodensities MøllerPlesset perturbation theory of second order (CDDMP2) method. We use the resolutionoftheidentity (RI) approximation in combination with efficient integral transformations employing sparse matrix multiplications. The RICDDMP2 method shows an asymptotic cubic scaling behavior with system size and a small prefactor that results in an early crossover to conventional methods for both small and large basis sets. We also explore the use of local fitting approximations which allow to further reduce the scaling behavior for very large systems. The reliability of our method is demonstrated on test sets for interaction and reaction energies of medium sized systems and on a diverse selection from our own benchmark set for total energies of larger systems. Timings on DNA systems show that fast calculations for systems with more than 500 atoms are feasible using a single processor core. Parallelization extends the range of accessible system sizes on one computing node with multiple cores to more than 1000 atoms in a doublezeta basis and more than 500 atoms in a triplezeta basis.

Analytical solution of the PoissonNernstPlanck equations for an electrochemical system close to electroneutrality
View Description Hide DescriptionSingle charge densities and the potential are used to describe models of electrochemical systems. These quantities can be calculated by solving a system of time dependent nonlinear coupled partial differential equations, the PoissonNernstPlanck equations. Assuming small deviations from the electroneutral equilibrium, the linearized and decoupled equations are solved for a radial symmetric geometry, which represents the interface between a cell and a sensor device. The densities and the potential are expressed by FourierBessels series. The system considered has a ratio between the Debyelength and its geometric dimension on the order of 10^{−4} so the FourierBessel series can be approximated by elementary functions. The time development of the system is characterized by two time constants, τ c and τ g . The constant τ c describes the approach to the stationary state of the total charge and the potential. τ c is several orders of magnitude smaller than the geometrydependent constant τ g , which is on the order of 10 ms characterizing the transition to the stationary state of the single ion densities.

Certification and the potential energy landscape
View Description Hide DescriptionTypically, there is no guarantee that a numerical approximation obtained using standard nonlinear equation solvers is indeed an actual solution, meaning that it lies in the quadratic convergence basin. Instead, it may lie only in the linear convergence basin, or even in a chaotic region, and hence not converge to the corresponding stationary point when further optimization is attempted. In some cases, these nonsolutions could be misleading. Proving that a numerical approximation will quadratically converge to a stationary point is termed certification. In this report, we provide details of how Smale's αtheory can be used to certify numerically obtained stationary points of a potential energy landscape, providing a mathematical proof that the numerical approximation does indeed correspond to an actual stationary point, independent of the precision employed.
 Atoms, Molecules, and Clusters

Exchange interaction between the triplet exciton and the localized spin in copperphthalocyanine
View Description Hide DescriptionTriplet excitonic state in the organic molecule may arise from a singlet excitation and the following intersystem crossing. Especially for a spinbearing molecule, an exchange interaction between the triplet exciton and the original spin on the molecule can be expected. In this paper, such exchange interaction in copperphthalocyanine (CuPc, spin ) was investigated from firstprinciples by using densityfunctional theory within a variety of approximations to the exchange correlation, ranging from localdensity approximation to longrange corrected hybridexchange functional. The magnitude of the computed exchange interaction is in the order of meV with the minimum value (1.5 meV, ferromagnetic) given by the longrange corrected hybridexchange functional CAMB3LYP. This exchange interaction can therefore give rise to a spin coherence with an oscillation period in the order of picoseconds, which is much shorter than the triplet lifetime in CuPc (typically tens of nanoseconds). This implies that it might be possible to manipulate the localized spin on Cu experimentally using optical excitation and intersystem crossing well before the triplet state disappears.

Rotational excitation of HCN by para and orthoH_{2}
View Description Hide DescriptionRotational excitation of the hydrogen cyanide (HCN) molecule by collisions with paraH2( j = 0, 2) and orthoH2( j = 1) is investigated at low temperatures using a quantum time independent approach. Both molecules are treated as rigid rotors. The scattering calculations are based on a highly correlated ab initio 4dimensional (4D) potential energy surface recently published. Rotationally inelastic cross sections among the 13 first rotational levels of HCN were obtained using a pure quantum close coupling approach for total energies up to 1200 cm^{−1}. The corresponding thermal rate coefficients were computed for temperatures ranging from 5 to 100 K. The HCN rate coefficients are strongly dependent on the rotational level of the H2 molecule. In particular, the rate coefficients for collisions with paraH2( j = 0) are significantly lower than those for collisions with orthoH2( j = 1) and paraH2( j = 2). Propensity rules in favor of even Δj transitions were found for HCN in collisions with paraH2( j = 0) whereas propensity rules in favor of odd Δj transitions were found for HCN in collisions with H2( j ⩾ 1). The new rate coefficients were compared with previously published HCNparaH2( j = 0) rate coefficients. Significant differences were found due the inclusion of the H2 rotational structure in the scattering calculations. These new rate coefficients will be crucial to improve the estimation of the HCN abundance in the interstellar medium.

Dipole polarizability of alkalimetal (Na, K, Rb)–alkalineearthmetal (Ca, Sr) polar molecules: Prospects for alignment
View Description Hide DescriptionElectronic openshell groundstate properties of selected alkalimetal–alkalineearthmetal polar molecules are investigated. We determine potential energy curves of the ^{2}Σ^{+} ground state at the coupledcluster singles and doubles with partial triples (CCSD(T)) level of electron correlation. Calculated spectroscopic constants for the isotopes (^{23} Na, ^{39}K, ^{85}Rb)–(^{40}Ca, ^{88}Sr) are compared with available theoretical and experimental results. The variation of the permanent dipole moment (PDM), average dipole polarizability, and polarizability anisotropy with internuclear distance is determined using finitefield perturbation theory at the CCSD(T) level. Owing to moderate PDM (KCa: 1.67 D, RbCa: 1.75 D, KSr: 1.27 D, RbSr: 1.41 D) and large polarizability anisotropy (KCa: 566 a.u., RbCa: 604 a.u., KSr: 574 a.u., RbSr: 615 a.u.), KCa, RbCa, KSr, and RbSr are potential candidates for alignment and orientation in combined intense laser and external static electric fields.