Volume 136, Issue 9, 07 March 2012

The molecular factors that govern interfacialinteractions between a polymer melt and a solid surface remain largely unclear despite significant progress made in the last years. Simulations are increasingly employed to elucidate these features, however, equilibration and sampling with models of long macromolecules in such heterogeneous systems present significant challenges. In this study, we couple the application of preferential sampling techniques with connectivityaltering Monte Carlo algorithms to explore the configurational characteristics of a polyethylene melt in proximity to a surface and a highly curved nanoparticle. Designed algorithms allow efficient sampling at all length scales of large systems required to avoid finitesize effects. Using detailed atomistic models for the polymer and realistic structures for a silicasurface and a fullerene, we find that at the extreme limit where particles are comparable to the polymer Kuhn segment length, curvature penalizes the formation of long train segments. As a result, an increased number of shorter contacts belonging to different chains are made competing with the anticipated decrease of the bound layer thickness with particle size if polymer adsorbed per unit area remained constant. For very small nanoparticles, formation of new train segments cannot compete with the overall reduction of adsorbance which is present irrespective of the enthalpic interactions; a result that demonstrates the need for an accurate description of polymer rigidity at these length scales.
 COMMUNICATIONS


Communication: Epistructural thermodynamics of soluble proteins
View Description Hide DescriptionThe epistructural tension of a solubleprotein is defined as the reversible work per unit area required to span the interfacialsolvent envelope of the proteinstructure. It includes an entropic penalty term to account for losses in hydrogenbonding coordination of interfacial water and is determined by a scalar field that indicates the expected coordination of a test water molecule at any given spatial location. An exhaustive analysis of structurereported monomeric proteins reveals that disulfide bridges required to maintain structural integrity provide the thermodynamic counterbalance to the epistructural tension, yielding a tight linear correlation. Accordingly, deviations from the balance law correlate with the thermal denaturation free energies of proteins under reducing conditions. The picomolaraffinity toxin HsTX1 has the highest epistructural tension, while the metastable cellular form of the human prion protein PrP^{C} represents the least tensionbalanced protein.

Communication: Transition state theory for dissipative systems without a dividing surface
View Description Hide DescriptionTransition state theory is a central cornerstone in reactiondynamics. Its key step is the identification of a dividing surface that is crossed only once by all reactive trajectories. This assumption is often badly violated, especially when the reactive system is coupled to an environment. The calculations made in this way then overestimate the reaction rate and the results depend critically on the choice of the dividing surface. In this Communication, we study the phase space of a stochastically driven system close to an energetic barrier in order to identify the geometric structure unambiguously determining the reactive trajectories, which is then incorporated in a simple rate formula for reactions in condensed phase that is both independent of the dividing surface and exact.
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 ARTICLES

 Theoretical Methods and Algorithms

Continuum limit frozen Gaussian approximation for the reduced thermal density matrix of dissipative systems
View Description Hide DescriptionA continuum limit frozen Gaussian approximation is formulated for the reduced thermal density matrix for dissipative systems. The imaginary time dynamics is obtained from a novel generalized Langevin equation for the system coordinates. The method is applied to study the thermal density in a double well potential in the presence of Ohmiclike friction. We find that the approximation describes correctly the delocalization of the density due to quantization of the vibrations in the well. It also accounts for the friction induced reduction of the tunneling density in the barrier region.

Coarsegrain model of the benzene ring with parasubstituents in the molecule
View Description Hide DescriptionA new twosite coarsegrain model of the benzene ring with substituents in the paraposition is proposed for use with multiscale simulations. The model uses a modified LennardJones potential and introduces an additional shifting parameter to the description of the atomatom interactions. Furthermore, the model separates sets of parameters of VanderWaals interactions into inter and intramolecular. The shifting parameter is specified separately for each pair of atom types for both inter and intramolecular interactions. The model itself consists of two superatoms. It allows for high speed calculations, “remembers” the benzene ring orientation in multiscale simulations, and can be used together with wellknown sets of “united atoms” potentials. This model was tested on pxylene, 1ethyl4methylbenzene, and 1methyl4propylbenzene. Structural properties for all three substances in the fullatomic model, the “united atoms” model, and the suggested coarsegrained model are discussed. The results demonstrate that the local structure derived from the coarsegrained model is very similar to that derived from the “united atoms” model.

A numerical solution of the linear Boltzmann equation using cubic Bsplines
View Description Hide DescriptionA numerical method using cubic Bsplines is presented for solving the linear Boltzmann equation. The collision kernel for the system is chosen as the WignerWilkins kernel. A total of three different representations for the distribution function are presented. Eigenvalues and eigenfunctions of the collision matrix are obtained for various mass ratios and compared with known values. Distribution functions, along with first and second moments, are evaluated for different mass and temperature ratios. Overall it is shown that the method is accurate and well behaved. In particular, moments can be predicted with very few points if the representation is chosen well. This method produces sparse matrices, can be easily generalized to higher dimensions, and can be cast into efficient parallel algorithms.

Response calculations based on an independent particle system with the exact oneparticle density matrix: Excitation energies
View Description Hide DescriptionAdiabatic response timedependent density functional theory (TDDFT) suffers from the restriction to basically an occupied → virtual single excitation formulation. Adiabatic timedependent density matrix functional theory allows to break away from this restriction. Problematic excitations for TDDFT, viz. bondingantibonding, double, charge transfer, and higher excitations, are calculated along the bonddissociation coordinate of the prototype molecules H_{2} and HeH^{+} using the recently developed adiabatic linear response phaseincluding (PI) natural orbital theory (PINO). The possibility to systematically increase the scope of the calculation from excitations out of (strongly) occupied into weakly occupied (“virtual”) natural orbitals to larger ranges of excitations is explored. The quality of the PINO response calculations is already much improved over TDDFT even when the severest restriction is made, to virtually the size of the TDDFT diagonalization problem (only single excitation out of occupied orbitals plus all diagonal doubles). Further marked improvement is obtained with moderate extension to allow for excitation out of the lumo and lumo+1, which become fractionally occupied in particular at longer distances due to leftright correlation effects. In the second place the interpretation of density matrix response calculations is elucidated. The oneparticle reduced density matrix response for an excitation is related to the transition density matrix to the corresponding excited state. The interpretation of the transition density matrix in terms of the familiar excitation character (single excitations, double excitations of various types, etc.) is detailed. The adiabatic PINO theory is shown to successfully resolve the problematic cases of adiabatic TDDFT when it uses a proper PI orbital functional such as the PILS functional.

Opensystem KohnSham density functional theory
View Description Hide DescriptionA simple model for electron transport through molecules is provided by the sourcesink potential (SSP) method [F. Goyer, M. Ernzerhof, and M. Zhuang, J. Chem. Phys.126, 144104 (2007)10.1063/1.2715932]. In SSP, the boundary conditions of having an incoming and outgoing electron current are enforced through complex potentials that are added to the Hamiltonian. Depending on the sign of the imaginary part of the potentials, current density is generated or absorbed. In this way, a finite system can be used to model infinite molecular electronic devices. The SSP has originally been developed for the Hückel method and subsequently it has been extended [F. Goyer and M. Ernzerhof, J. Chem. Phys.134, 174101 (2011)10.1063/1.3581096] to the Hubbard model. Here we present a step towards its generalization for firstprinciples electronic structure theory methods. In particular, drawing on our earlier work, we discuss a new generalized density functional theory for complex nonHermitian Hamiltonians. This theory enables us to combine SSP and KohnSham theory to obtain a method for the description of open systems that exchange current density with their environment. Similarly, the HartreeFock method is extended to the realm of nonHermitian, SSP containing Hamiltonians. As a proof of principle, we present the first applications of complexdensity functionaltheory (CODFT) as well as nonHermitian HartreeFock theory to electron transport through molecules.

Measuring nonadiabaticity of molecular quantum dynamics with quantum fidelity and with its efficient semiclassical approximation
View Description Hide DescriptionWe propose to measure nonadiabaticity of molecular quantum dynamics rigorously with the quantum fidelity between the BornOppenheimer and fully nonadiabaticdynamics. It is shown that this measure of nonadiabaticity applies in situations where other criteria, such as the energy gap criterion or the extent of population transfer, fail. We further propose to estimate this quantum fidelity efficiently with a generalization of the dephasing representation to multiple surfaces. Two variants of the multiplesurface dephasing representation (MSDR) are introduced, in which the nuclei are propagated either with the fewestswitches surface hopping or with the locally mean fielddynamics (LMFD). The LMFD can be interpreted as the Ehrenfest dynamics of an ensemble of nuclear trajectories, and has been used previously in the nonadiabatic semiclassical initial value representation. In addition to propagating an ensemble of classical trajectories, the MSDR requires evaluating nonadiabatic couplings and solving the Schrödinger (or more generally, the quantum Liouvillevon Neumann) equation for a single discrete degree of freedom. The MSDR can be also used in the diabatic basis to measure the importance of the diabatic couplings. The method is tested on three model problems introduced by Tully and on a twosurface model of dissociation of NaI.

Rethinking the application of the first nucleation theorem to particle formation
View Description Hide DescriptionThe critical cluster is the threshold size above which a cluster will be more likely to grow than to evaporate. In field and laboratory measurements of new particle formation, the number of molecules of a given species in the critical cluster is commonly taken to be the slope of the loglog plot of the formation rate versus the concentration of the species. This analysis is based on an approximate form of the first nucleationtheorem, which is derived with the assumption that there are no minima in the free energy surface prior to the maximum at the critical size. However, many atmospherically relevant systems are likely to exhibit such minima, for example, ions surrounded by condensable vapour molecules or certain combinations of acids and bases. We have solved numerically the birthdeath equations for both an electrically neutral onecomponent model system with a local minimum at precritical sizes and an ioninduced case. For the ioninduced case, it is verified that the loglog slope of the nucleation rate versus particle concentration plot gives accurately the difference between the cluster sizes at the free energy maximum and minimum, as is expected from the classical form of the ioninduced nucleation rate. However, the results show that applying the nucleationtheorem to neutral systems with stable prenucleation clusters may lead to erroneous interpretations about the nature of the critical cluster.

Efficient algorithm of the transcorrelated method for periodic systems
View Description Hide DescriptionThe transcorrelated (TC) method is one of the promising wavefunctionbased approaches for the firstprinciples electronic structure calculations. In this method, the manybody wave function is approximated as the JastrowSlater type and oneelectron orbitals in the Slater determinant are optimized with a onebody selfconsistentfield equation such as that in the HartreeFock (HF) method. Although the TC method has yielded good results for both molecules and solids, its computational cost in solidstate calculations, being of order with N _{ k } and N _{ b } the respective numbers of kpoints and bands, has for some years hindered its wide application in condensed matter physics. Although an efficient algorithm was proposed for a Gaussian basis set, that algorithm is not applicable to a planewave basis that is suited to and widely used in solidstate calculations. In this paper, we present a new efficient algorithm of the TC method for the planewave basis or an arbitrary basis function set expanded in terms of plane waves, with which the computational cost of the TC method scales as . This is the same as that of the HF method. We applied the TC method with the new algorithm to obtain converged band structure and cell parameters of some semiconductors.

Rotational excitation of H_{2}O by paraH_{2} from an adiabatically reduced dimensional potential
View Description Hide DescriptionCross sections and rate coefficients for low lying rotational transitions in H_{2}O colliding with parahydrogen pH_{2} are computed using an adiabatic approximation which reduces the dimensional dynamics from a 5D to a 3D problem. Calculations have been performed at the closecoupling level using the recent potential of Valiron et al. [J. Chem. Phys.129, 134306 (2008)10.1063/1.2988314]. A good agreement is found between the reduced adiabatic calculations and the 5D exact calculations, with an impressive time saving and memory gain. This adiabatic reduction of dimensionality seems very promising for scattering studies involving the excitation of a heavy target molecule by a light molecular projectile.
 Advanced Experimental Techniques

Conversion of parahydrogen induced longitudinal twospin order to evenly distributed single spin polarisation by optimal control pulse sequences
View Description Hide DescriptionStrongly enhanced spin polarization in the form of longitudinal spin order can be generated on target molecules by using parahydrogen in a catalyzed hydrogenation reaction. An optimal control algorithm was used to generate radiofrequency pulse sequences which convert the arising longitudinal twospin order into singlespin Zeeman order with high efficiency and distribute it evenly between three coupled spins within the same molecule. The pulses are designed to be very robust towards variations in the B _{0} and B _{1} fields. Furthermore, this strategy is applied to enhance the NMR signal in an ultrafast gradient assisted single excitation twodimensional spectroscopy experiment.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

On the triplet ground state of tetrahedral X_{4} clusters (X = Li, Na, K, Cu)
View Description Hide DescriptionThe lowest electronic state of distorted tetrahedral X_{4}clusters (with X = Li, Na, K, Cu) is studied at coupledcluster level using highquality atomic basis sets. The ground state is found to have a triplet spin symmetry for this kind of geometry and for all the considered atomic species. The equilibrium geometries correspond to JahnTellerdistorted oblate tetrahedra having D _{2d } symmetry, and tetrahedric structures are local minima on the potentialenergy surfaces for the triplet states. Their energies lie between 0.2 eV (for the K_{4}cluster) and 0.9 eV (for Cu_{4}) above the absolute minimum of the corresponding systems, which is a spin singlet having a rhombus geometry.

Low energy (e,2e) measurements of CH_{4} and neon in the perpendicular plane
View Description Hide DescriptionLow energy experimental and theoretical triple differential cross sections for the highest occupied molecular orbital of methane (1t_{2}) and for the 2p atomic orbital of neon are presented and compared. These targets are isoelectronic, each containing 10 electrons and the chosen orbital within each target has pelectron character. Observation of the differences and similarities of the cross sections for these two species hence gives insight into the different scattering mechanisms occurring for atomic and molecular targets. The experiments used perpendicular, symmetric kinematics with outgoing electron energies between 1.5 eV and 30 eV for CH_{4} and 2.5 eV and 25 eV for neon. The experimental data from these targets are compared with theoretical predictions using a distortedwave Born approximation. Reasonably good agreement is seen between the experiment and theory for neon while mixed results are observed for CH_{4}. This is most likely due to approximations of the target orientation made within the model.

Valence and innervalence shell dissociative photoionization of CO in the 26–33 eV range. II. Molecularframe and recoilframe photoelectron angular distributions
View Description Hide DescriptionExperimental and theoretical results for molecularframe photoemission are presented for innervalence shell photoionization of the CO molecule induced by linearly and circularly polarized light. The experimental recoil frame photoelectron angular distributions (RFPADs) obtained from dissociativephotoionizationmeasurements where the velocities of the ionic fragment and photoelectron were detected in coincidence, are compared to RFPADs computed using the multichannel Schwinger configuration interaction method. The formalism for including a finite lifetime of the predissociative ion state is presented for the case of general elliptically polarized light, to obtain the RFPAD rather than the molecular frame photoelectron angular distribution (MFPAD), which would be obtained with the assumption of instantaneous dissociation. We have considered photoionization of CO for the photon energies of 26.0 eV, 29.5 eV, and 32.5 eV. A comparison of experimental and theoretical RFPADs allows us to identify the ionic states detected in the experimental studies. In addition to previously identified states, we found evidence for the 2 ^{2}Δ state with an ionization potential of 25.3 eV and ^{2}Σ^{+} states with ionization potentials near 32.5 eV. A comparison of the experimental and theoretical RFPADs permits us to estimate predissociative lifetimes of 0.25–1 ps for some of the ion states. Consideration of the MFPADs of a series of ^{2}Π ion states indicates the importance of interchannel coupling at low photoelectron kinetic energy and the limitations of a singlechannel analysis based on the corresponding Dyson orbitals.

Thermal effects on energetics and dynamics in water cluster anions (H_{2}O)_{ n } ^{−}
View Description Hide DescriptionThe electron binding energies and relaxation dynamics of water cluster anions (H_{2}O)_{ n } ^{−} (11 ≤ n ≤ 80) formed in coexpansions with neon were investigated using onephoton and timeresolved photoelectron imaging. Unlike previous experiments with argon, water cluster anions exhibit only one isomer class, the tightly bound isomer I with approximately the same binding energy as clusters formed in argon. This result, along with a decrease in the internal conversion lifetime of excited (H_{2}O)_{ n } ^{−} (25 ≤ n ≤ 40), indicates that clusters are vibrationally warmer when formed in neon. Over the ranges studied, the vertical detachment energies and lifetimes appear to converge to previously reported values.

Infrared spectra of CO_{2}doped hydrogen clusters, (H_{2})_{ N }–CO_{2}
View Description Hide DescriptionClusters of paraH_{2} and/or orthoH_{2} containing a single carbon dioxide molecule are studied by high resolution infrared spectroscopy in the 2300 cm^{−1} region of the CO_{2} ν_{3} fundamental band. The (H_{2})_{ N }–CO_{2} clusters are formed in a pulsed supersonic jet expansion from a cooled nozzle and probed using a rapid scan tunable diode laser. Simple symmetric rotor type spectra are observed with little or no resolved Kstructure, and prominent Qbranch features for orthoH_{2} but not paraH_{2}. Observed rotational constants and vibrational shifts are reported for orthoH_{2} up to N = 7 and paraH_{2} up to N = 15, with the N > 7 assignments only made possible with the help of theoretical simulations. The paraH_{2} cluster with N = 12 shows clear evidence for superfluid effects, in good agreement with theory. The presence of larger clusters with N > 15 is evident in the spectra, but specific assignments are not possible. Mixed para + orthoH_{2} cluster transitions are well predicted by linear interpolation between corresponding pure cluster line positions.

Outer and innervalence satellites of carbon dioxide: Electron momentum spectroscopy compared with symmetryadaptedcluster configuration interaction generalR calculations
View Description Hide DescriptionThe extensive study of outer and innervalence satellites of carbon dioxide by electron momentum spectroscopy is reported. The experiments have been performed using a highsensitivity electron momentum spectrometer employing noncoplanar symmetric geometry at impact energy of about 1200 eV. Binding energy spectrum up to 50 eV, above the first double ionization threshold (∼37.3 eV), is presented. Four main peaks and twelve satellites have been identified including four embedded in the double ionization continuum, among which the two beyond 42 eV are observed for the first time. High accuracy symmetryadaptedcluster configuration interaction generalR calculation with augccpVTZ basis sets has also been performed and the result is in line with the experimental ionization spectrum except the relative intensities for some of the satellites in innervalence region. The experimental momentum profiles for both the main ionization transitions and satellites have been obtained and compared with theoretical calculations by HF and B3LYP methods with 6311++G* and augccpVTZ basis sets. Through comparison, the detailed assignments of the satellite bands have been achieved and the pole strengths for the relevant shakeup transitions are determined experimentally for the first time.

A new analytical potential energy surface for the singlet state of He_{2}H^{+}
View Description Hide DescriptionThe analytic potential energy surface (APES) for the exchange reaction of HeH^{+} (X^{1}Σ^{+}) + He at the lowest singlet state 1^{1}A^{/} has been built. The APES is expressed as AguadoPaniagua function based on the manybody expansion. Using the adaptive nonlinear leastsquares algorithm, the APES is fitted from 15 682 ab initio energy points calculated with the multireference configuration interaction calculation with a large daugccpV5Z basis set. To testify the new APES, we calculate the integral cross sections for He + H^{+}He (v = 0, 1, 2, j = 0) → HeH^{+} + He by means of quasiclassical trajectory and compare them with the previous result in literature.

Exact quantum scattering study of the H + HS reaction on a new ab initio potential energy surface H_{2}S (^{3} A ^{ ″ })
View Description Hide DescriptionWe present an exact quantum dynamical study and quasiclassical trajectory(QCT) calculations for the exchange and abstraction processes for the H + HS reaction. These calculations were based on a newly constructed highquality potential energy surface for the lowest triplet state of H_{2}S (^{3} A ^{″}). The ab initio singlepoint energies were computed using complete active space selfconsistent field and multireference configuration interaction method with a basis set of augccpV5Z. The timedependent wave packet (TDWP) method was used to calculate the total reaction probabilities and integral cross sections over the collision energy (E _{col}) range of 0.0−2.0 eV for the reactant HS initially at the ground state and the first vibrationally excited state. It was found that the initial vibrational excitation of HS enhances both abstraction and exchange processes. In addition, a good agreement is found between QCT and TDWP reaction probabilities at the total momentum J = 0 as a function of collision energy for the H + HS (v = 0, j = 0) reaction.