Volume 140, Issue 15, 21 April 2014

We report computer simulations of an excess electron in various structural motifs of polyethylene at room temperature, including lamellar and interfacial regions between amorphous and lamellae, as well as nanometresized voids. Electronic properties such as density of states, mobility edges, and mobilities are computed on the different phases using a block Lanczos algorithm. Our results suggest that the electronic density of states for a heterogeneous material can be approximated by summing the single phase density of states weighted by their corresponding volume fractions. Additionally, a quantitative connection between the localized states of the excess electron and the local atomic structure is presented.
 COMMUNICATIONS


Communication: A benchmarkquality, fulldimensional ab initio potential energy surface for ArHOCO
View Description Hide DescriptionA fulldimensional, global ab initio potential energy surface (PES) for the ArHOCO system is presented. The PES consists of a previous intramolecular ab initio PES for HOCO [J. Li, C. Xie, J. Ma, Y. Wang, R. Dawes, D. Xie, J. M. Bowman, and H. Guo, J. Phys. Chem. A116, 5057 (2012)], plus a new permutationally invariant interaction potential based on fitting 12 432 UCCSD(T)F12a/aVDZ counterpoisecorrected energies. The latter has a total rms fitting error of about 25 cm^{−1} for fitted interaction energies up to roughly 12 000 cm^{−1}. Two additional fits are presented. One is a novel very compact permutational invariant representation, which contains terms only involving the Aratom distances. The rms fitting error for this fit is 193 cm^{−1}. The other fit is the widely used pairwise one. The pairwise fit to the entire data set has an rms fitting error of 427 cm^{−1}. All of these potentials are used in preliminary classical trajectory calculations of energy transfer with a focus on comparisons with the results using the benchmark potential.

Communication: Disordersuppressed vibrational relaxation in vapordeposited highdensity amorphous ice
View Description Hide DescriptionWe apply twodimensional infrared spectroscopy to differentiate between the two polyamorphous forms of glassy water, lowdensity (LDA) and highdensity (HDA) amorphous ices, that were obtained by slow vapor deposition at 80 and 11 K, respectively. Both the vibrational lifetime and the bandwidth of the 1–2 transition of the isolated OD stretch vibration of HDO in H2O exhibit characteristic differences when comparing hexagonal (Ih), LDA, and HDA ices, which we attribute to the different local structures – in particular the presence of interstitial waters in HDA ice – that cause different delocalization lengths of intermolecular phonon degrees of freedom. Moreover, temperature dependent measurements show that the vibrational lifetime closely follows the structural transition between HDA and LDA phases.
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 ARTICLES

 Theoretical Methods and Algorithms

The rigorous stochastic matrix multiplication scheme for the calculations of reduced equilibrium density matrices of open multilevel quantum systems
View Description Hide DescriptionUnderstanding the roles of the temporary and spatial structures of quantum functional noise in open multilevel quantum molecular systems attracts a lot of theoretical interests. I want to establish a rigorous and general framework for functional quantum noises from the constructive and computational perspectives, i.e., how to generate the random trajectories to reproduce the kernel and path ordering of the influence functional with effective Monte Carlo methods for arbitrary spectral densities. This construction approach aims to unify the existing stochastic models to rigorously describe the temporary and spatial structure of Gaussian quantum noises. In this paper, I review the Euclidean imaginary time influence functional and propose the stochastic matrix multiplication scheme to calculate reduced equilibrium density matrices (REDM). In addition, I review and discuss the FeynmanVernon influence functional according to the Gaussian quadratic integral, particularly its imaginary part which is critical to the rigorous description of the quantum detailed balance. As a result, I establish the conditions under which the influence functional can be interpreted as the average of exponential functional operator over realvalued Gaussian processes for open multilevel quantum systems. I also show the difference between the local and nonlocal phonons within this framework. With the stochastic matrix multiplication scheme, I compare the normalized REDM with the Boltzmann equilibrium distribution for open multilevel quantum systems.

Optimized coordinates in vibrational coupled cluster calculations
View Description Hide DescriptionThe use of variationally optimized coordinates, which minimize the vibrational selfconsistent field (VSCF) ground state energy with respect to orthogonal transformations of the coordinates, has recently been shown to improve the convergence of vibrational configuration interaction (VCI) towards the exact full VCI [K. Yagi, M. Keçeli, and S. Hirata, J. Chem. Phys.137, 204118 (2012)]. The present paper proposes an incorporation of optimized coordinates into the vibrational coupled cluster (VCC), which has in the past been shown to outperform VCI in approximate calculations where similar restricted state spaces are employed in VCI and VCC. An embarrassingly parallel algorithm for variational optimization of coordinates for VSCF is implemented and the resulting coordinates and potentials are introduced into a VCC program. The performance of VCC in optimized coordinates (denoted ocVCC) is examined through pilot applications to water, formaldehyde, and a series of water clusters (dimer, trimer, and hexamer) by comparing the calculated vibrational energy levels with those of the conventional VCC in normal coordinates and VCI in optimized coordinates. For water clusters, in particular, ocVCC is found to gain orders of magnitude improvement in the accuracy, exemplifying that the combination of optimized coordinates localized to each monomer with the sizeextensive VCC wave function provides a supreme description of systems consisting of weakly interacting subsystems.

Can the ring polymer molecular dynamics method be interpreted as real time quantum dynamics?
View Description Hide DescriptionThe ring polymer molecular dynamics (RPMD) method has gained popularity in recent years as a simple approximation for calculating real time quantum correlation functions in condensed media. However, the extent to which RPMD captures real dynamical quantum effects and why it fails under certain situations have not been clearly understood. Addressing this issue has been difficult in the absence of a genuine justification for the RPMD algorithm starting from the quantum Liouville equation. To this end, a new and exact path integral formalism for the calculation of real time quantum correlation functions is presented in this work, which can serve as a rigorous foundation for the analysis of the RPMD method as well as providing an alternative derivation of the well established centroid molecular dynamics method. The new formalism utilizes the cyclic symmetry of the imaginary time path integral in the most general sense and enables the expression of Kubotransformed quantum time correlation functions as that of physical observables preaveraged over the imaginary time path. Upon filtering with a centroid constraint function, the formulation results in the centroid dynamics formalism. Upon filtering with the position representation of the imaginary time path integral, we obtain an exact quantum dynamics formalism involving the same variables as the RPMD method. The analysis of the RPMD approximation based on this approach clarifies that an explicit quantum dynamical justification does not exist for the use of the ring polymer harmonic potential term (imaginary time kinetic energy) as implemented in the RPMD method. It is analyzed why this can cause substantial errors in nonlinear correlation functions of harmonic oscillators. Such errors can be significant for general correlation functions of anharmonic systems. We also demonstrate that the short time accuracy of the exact path integral limit of RPMD is of lower order than those for finite discretization of path. The present quantum dynamics formulation also serves as the basis for developing new quantum dynamical methods that utilize the cyclic nature of the imaginary time path integral.

Determination of the Eckart moleculefixed frame by use of the apparatus of quaternion algebra
View Description Hide DescriptionThe problem of determining the Eckart moleculefixed frame for an arbitrary molecule with nuclei displaced from the equilibrium positions is considered. The solution of the problem is formulated by minimizing the sum of massweighted squared deviations (MWSD) of the nuclei of a displaced configuration from the nuclei of the equilibrium configuration. A mathematical proof of the equivalence of Eckart conditions and the minimum of MWSD is given. It is shown that the extrema of the sum of MWSD coincide with eigenvalues of a special 4 × 4 symmetric matrix. Its minimal eigenvalue corresponds to the desired solution, and the respective eigenvector can be treated as the quaternion containing the necessary information for rotating the original coordinate system and aligning its axes with the moleculefixed coordinate system. A detailed scheme for an efficient numerical implementation of the method is provided, and a numerical example is given.

Modeling the adsorption of short alkanes in the zeolite SSZ13 using “van der Waals” DFT exchange correlation functionals: Understanding the advantages and limitations of such functionals
View Description Hide DescriptionThe inclusion of nonlocal interactions is one of the large challenges in density functional theory. Very promising methods are the vdWDF2 and BEEFvdW functionals, which combine a semilocal approximation for exchange interactions and a nonlocal correlation expression. In this work we apply those functionals to model the adsorption of short alkanes in the zeolite SSZ13. Even though results for energetics are improved with respect to other vdWDF based methods, we still find a comparatively large error compared to highlevel calculations. These errors result from approximations in the determination of the dielectric function and of the van der Waals kernel. The insights presented in this work will help to understand the performance not only of vdWDF2 and BEEFvdW, but all vdWDF based functionals in various chemically or physically important systems.

On equivalence of high temperature series expansion and coupling parameter series expansion in thermodynamic perturbation theory of fluids
View Description Hide DescriptionThe coupling parameter series expansion and the high temperature series expansion in the thermodynamic perturbation theory of fluids are shown to be equivalent if the interaction potential is pairwise additive. As a consequence, for the class of fluids with the potential having a hardcore repulsion, if the hardsphere fluid is chosen as reference system, the terms of coupling parameter series expansion for radial distribution function, direct correlation function, and Helmholtz free energy follow a scaling law with temperature. The scaling law is confirmed by application to squarewell fluids.

Exploration of zerothorder wavefunctions and energies as a first step toward intramolecular symmetryadapted perturbation theory
View Description Hide DescriptionNoncovalent interactions occur between and within all molecules and have a profound impact on structural and electronic phenomena in chemistry, biology, and material science. Understanding the nature of inter and intramolecular interactions is essential not only for establishing the relation between structure and properties, but also for facilitating the rational design of molecules with targeted properties. These objectives have motivated the development of theoretical schemes decomposing intermolecular interactions into physically meaningful terms. Among the various existing energy decomposition schemes, SymmetryAdapted Perturbation Theory (SAPT) is one of the most successful as it naturally decomposes the interaction energy into physical and intuitive terms. Unfortunately, analogous approaches for intramolecular energies are theoretically highly challenging and virtually nonexistent. Here, we introduce a zerothorder wavefunction and energy, which represent the first step toward the development of an intramolecular variant of the SAPT formalism. The proposed energy expression is based on the Chemical Hamiltonian Approach (CHA), which relies upon an asymmetric interpretation of the electronic integrals. The orbitals are optimized with a nonhermitian Fock matrix based on two variants: one using orbitals strictly localized on individual fragments and the other using canonical (delocalized) orbitals. The zerothorder wavefunction and energy expression are validated on a series of prototypical systems. The computed intramolecular interaction energies demonstrate that our approach combining the CHA with strictly localized orbitals achieves reasonable interaction energies and basis set dependence in addition to producing intuitive energy trends. Our zerothorder wavefunction is the primary step fundamental to the derivation of any perturbation theory correction, which has the potential to truly transform our understanding and quantification of nonbonded intramolecular interactions.

Finite barrier corrections to the PGH solution of Kramers' turnover theory
View Description Hide DescriptionKramers [Physica7, 284 (1940)], in his seminal paper, derived expressions for the rate of crossing a barrier in the underdamped limit of weak friction and the moderate to strong friction limit. The challenge of obtaining a uniform expression for the rate, valid for all damping strengths is known as Kramers turnover theory. Two different solutions have been presented. Mel'nikov and Meshkov [J. Chem. Phys.85, 1018 (1986)] (MM) considered the motion of the particle, treating the friction as a perturbation parameter. Pollak, Grabert, and Hänggi [J. Chem. Phys.91, 4073 (1989)] (PGH), considered the motion along the unstable mode which is separable from the bath in the barrier region. In practice, the two theories differ in the way an energy loss parameter is estimated. In this paper, we show that previous numerical attempts to resolve the quality of the two approaches were incomplete and that at least for a cubic potential with Ohmic friction, the quality of agreement of both expressions with numerical simulation is similar over a large range of friction strengths and temperatures. Mel'nikov [Phys. Rev. E48, 3271 (1993)], in a later paper, improved his theory by introducing finite barrier corrections. In this paper we note that previous numerical tests of the finite barrier corrections were also incomplete. They did not employ the exact rate expression, but a harmonic approximation to it. The central part of this paper, is to include finite barrier corrections also within the PGH formalism. Tests on a cubic potential demonstrate that finite barrier corrections significantly improve the agreement of both MM and PGH theories when compared with numerical simulations.

Distance fluctuation of a single molecule in LennardJones liquid based on generalized Langevin equation and mode coupling theory
View Description Hide DescriptionDistance fluctuation of a single molecule, modeled as an idealized beadspring chain, dissolved in a LennardJones liquid is studied by using a multidimensional generalized Langevin equation, where the friction kernel ζ(t) is calculated from the kinetic mode coupling theory (MCT). Temporal behavior of the distance autocorrelation function shows three typical regimes of time dependence, starting with a constant, followed by a power law of t ^{−α}, and finally an exponential decay. Particular attentions are paid to the time span of the power law regime, which corresponds to anomalous subdiffusion behavior, and the MCT framework enables us to investigate thoroughly how this regime depends on microscopic details such as the beadtosolvent mass ratio M R , chain spring frequency ω, and the chain length N. Interestingly, the exponent α is robust to be 1/2 against the change of these parameters, although the friction kernel ζ(t) shows nontrivial dependence on time. In addition, we find that the starting time of the powerlaw region t 1 scales with Γ^{−1}, with Γ = 4ω^{2}/ζ0 where ζ0 is the zerofrequency friction which decreases rapidly with increasing bead mass. On the other hand, the ending time t 2 is not sensitive to varying ω or ζ0, but it increases with N rapidly before it reaches a constant for N larger than some threshold value. Our work may provide a unified strategy starting from the microscopic level to understand the anomalous subdiffusive behavior regarding large scale conformational change of polymers or proteins.
 Atoms, Molecules, and Clusters

Stateresolved imaging of CO from propenal photodissociation: Signatures of concerted threebody dissociation
View Description Hide DescriptionStateselected DC sliced images of propenal photodissociation show clear signatures of a novel synchronous concerted threebody dissociation of propenal recently proposed by Lee and coworkers to give C2H2 + H2 + CO [S. H. Lee, C. H. Chin, C. Chaudhuri, ChemPhysChem12, 753 (2011)]. Unlike any prior example of a concerted 3body dissociation event, this mechanism involves breaking three distinct bonds and yields 3 distinct molecules. DC sliced images of CO fragments were recorded for a range of rotational levels for both v = 0 and v = 1. The results show formation of two distinct CO product channels having dissimilar translational energy distributions with characteristic rovibrational state distributions. The images for CO (v = 0) show a large contribution of slower CO fragments at lower rotational levels (J = 5–25). This slow component is completely absent from the v = 1 CO images. The images for the higher rotational levels of the v = 0 and v = 1 CO are nearly identical, and this provides a basis for decomposing the two channels for v = 0. The quantum state and translational energy distributions for the slow channel are readily assigned to the 3body dissociation based on the properties of the transition state. The faster CO fragments dominating the higher rotational levels in both v = 0 and v = 1 are attributed to formation of CH3CH + CO, also in agreement with the inferences based on previous nonstateresolved measurements with supporting theoretical calculations.

Farinfrared collisioninduced absorption in rare gas mixtures: Quantum and semiclassical calculations
View Description Hide DescriptionWe compare calculations of the translational collisioninduced spectra and their integrated intensities of both He–Ar and Ne–Ar collisional complexes, using the quantum mechanical and a semiclassical formalism. Advanced potential energy and induced dipole functions are used for the calculations. The quantum method used is as described previously [L. Frommhold, Collisioninduced Absorption in Gases (Cambridge University Press, 1993 and 2006)]. The semiclassical method is based on repeated classical atomatom scattering calculations to simulate an ensemble average; subsequent Fourier transform then renders the binary absorption coefficient as a function of frequency. The problem of classical calculations is the violation of the principle of detailed balance, which may be introduced only artificially in classical calculations. Nevertheless, it is shown that the use of classical trajectories permits a fairly accurate reproduction of the experimental spectra, comparable to the quantum mechanical results at not too low temperatures and for collisional pairs of not too small reduced mass. Inexpensive classical calculations may thus be promising to compute spectra also of molecular pairs, or even of polyatomic collisional pairs with anisotropic intermolecular interactions, for which the quantum approach is still inefficient or impractical.

Accurate nonBornOppenheimer calculations of the complete pure vibrational spectrum of ditritium using allparticle explicitly correlated Gaussian functions
View Description Hide DescriptionVery accurate variational calculations of the complete pure vibrational spectrum of the ditritium (T2) molecule are performed within the framework where the BornOppenheimer approximation is not assumed. After separating out the centerofmass motion from the total laboratoryframe Hamiltonian, T2 becomes a threeparticle problem. States corresponding to the zero total angular momentum, which are pure vibrational states, are spherically symmetric in this framework. The wave functions of these states are expanded in terms of allparticle, onecenter, spherically symmetric explicitly correlated Gaussian functions multiplied by even nonnegative powers of the internuclear distance. In the calculations the total energies, the dissociation energies, and expectation values of some operators dependent on interparticle distances are determined.

A diabatic representation of the two lowest electronic states of Li_{3}
View Description Hide DescriptionUsing the MultiReference Configuration Interaction method, the adiabatic potential energy surfaces of Li3 are computed. The two lowest electronic states are bound and exhibit a conical intersection. By fitting the calculated potential energy surfaces to the cubic E ⊗ ɛ JahnTeller model we extract the effective JahnTeller parameters corresponding to Li3. These are used to set up the transformation matrix which transforms from the adiabatic to a diabatic representation. This diabatization method gives a Hamiltonian for Li3 which is free from singular nonadiabatic couplings and should be accurate for large internuclear distances, and it thereby allows for bound dynamics in the vicinity of the conical intersection to be explored.

Effect of antisymmetric C–H stretching excitation on the dynamics of O(^{1}D) + CH_{4} → OH + CH_{3}
View Description Hide DescriptionThe effect of antisymmetric C–H stretching excitation of CH4 on the dynamics and reactivity of the O(^{1}D) + CH4 → OH + CD3 reaction at the collision energy of 6.10 kcal/mol has been investigated using the crossedbeam and timesliced velocity map imaging techniques. The antisymmetric C–H stretching mode excited CH4 molecule was prepared by direct infrared excitation. From the measured images of the CH3 products with the infrared laser on and off, the product translational energy and angular distributions were derived for both the ground and vibrationally excited reactions. Experimental results show that the vibrational energy of the antisymmetric stretching excited CH4 reagent is channeled exclusively into the vibrational energy of the OH coproducts and, hence, the OH products from the excitedstate reaction are about one vibrational quantum hotter than those from the groundstate reaction, and the product angular distributions are barely affected by the vibrational excitation of the CH4 reagent. The reactivity was found to be suppressed by the antisymmetric stretching excitation of CH4 for all observed CH3 vibrational states. The degree of suppression is different for different CH3 vibrational states: the suppression is about 40%–60% for the ground state and the umbrella mode excited CH3 products, while for the CH3 products with one quantum symmetric stretching mode excitation, the suppression is much less pronounced. In consequence, the vibrational state distribution of the CH3 product from the excitedstate reaction is considerably different from that of the groundstate reaction.

Thermal decomposition of 1,3,3trinitroazetidine (TNAZ): A density functional theory and ab initio study
View Description Hide DescriptionDensity functional theory and ab initio methods are employed to investigate decomposition pathways of 1,3,3trinitroazetidine initiated by unimolecular loss of NO2 or HONO. Geometry optimizations are performed using M06/ccpVTZ and coupledcluster (CC) theory with single, double, and perturbative triple excitations, CCSD(T), is used to calculate accurate singlepoint energies for those geometries. The CCSD(T)/ccpVTZ energies for NO2 elimination by N–N and C–N bond fission are, including zeropoint energy (ZPE) corrections, 43.21 kcal/mol and 50.46 kcal/mol, respectively. The decomposition initiated by transHONO elimination can occur by a concerted Hatom and nitramine NO2 group elimination or by a concerted Hatom and nitroalkyl NO2 group elimination via barriers (at the CCSD(T)/ccpVTZ level with ZPE corrections) of 47.00 kcal/mol and 48.27 kcal/mol, respectively. Thus, at the CCSD(T)/ccpVTZ level, the ordering of these four decomposition steps from energetically most favored to least favored is: NO2 elimination by N–N bond fission, HONO elimination involving the nitramine NO2 group, HONO elimination involving a nitroalkyl NO2 group, and finally NO2 elimination by C–N bond fission.

Rationalizing the role of structural motif and underlying electronic structure in the finite temperature behavior of atomic clusters
View Description Hide DescriptionMelting in finite size systems is an interesting but complex phenomenon. Many factors affect melting and owing to their interdependencies it is a challenging task to rationalize their roles in the phase transition. In this work, we demonstrate how structural motif of the ground state influences melting transition in small clusters. Here, we report a case with clusters of aluminum and gallium having same number of atoms, valence electrons, and similar structural motif of the ground state but drastically different melting temperatures. We have employed BornOppenheimer molecular dynamics to simulate the solidlike to liquidlike transition in these clusters. Our simulations have reproduced the experimental trends fairly well. Further, the detailed analysis of isomers has brought out the role of the ground state structure and underlying electronic structure in the finite temperature behavior of these clusters. For both clusters, isomers accessible before cluster melts have striking similarities and does have strong influence of the structural motif of the ground state. Further, the shape of the heat capacity curve is similar in both the cases but the transition is more spread over for Al 36 which is consistent with the observed isomerization pattern. Our simulations also suggest a way to characterize transition region on the basis of accessibility of the ground state at a specific temperature.

Density functional calculations for structural, electronic, and magnetic properties of gadoliniumoxide clusters
View Description Hide DescriptionGadoliniumoxide clusters in various sizes and stoichiometries have been systematically studied by employing the density functional theory with the generalized gradient approximation. The clusters in bulk stoichiometry are relatively more stable and their binding energies increase with the increasing size. Stoichiometric (Gd2O3) n clusters of n = 1–3 prefer cagelike structures, whereas the clusters of n = 4–30 prefer compact structures layered by wedgelike units and exhibit a rough feature toward the bulklike arrangement with small disorders of atomic positions. The polyhedralcages analogous to carbonfullerenes are stable isomers yet not the minimum energy configurations. Their stabilities can be improved by embedding one oxygen atom or a suitable cage to form coreshell configurations. The mostly favored antiferromagnetic couplings between adjacent Gd atoms are nearly degenerated in energy with their ferromagnetic couplings, resulting in superparamagnetic characters of gadoliniumoxide clusters. The RudermanKittelKasuyaYosida (RKKY)type mechanism together with the superexchangetype mechanism plays cooperation role for the magnetic interactions in clusters. We present, as a function of n, calculated binding energies, ionization potential, electron affinity, and electronic dipole moment.

Mesoscale properties of clay aggregates from potential of mean force representation of interactions between nanoplatelets
View Description Hide DescriptionFacetoface and edgetoedge free energy interactions of Wyoming Namontmorillonite platelets were studied by calculating potential of mean force along their center to center reaction coordinate using explicit solvent (i.e., water) molecular dynamics and free energy perturbation methods. Using a series of configurations, the GayBerne potential was parametrized and used to examine the mesoscale aggregation and properties of platelets that are initially random oriented under isothermalisobaric conditions. Aggregates of clay were defined by geometrical analysis of facetoface proximity of platelets with size distribution described by a lognormal function. The isotropy of the microstructure was assessed by computing a scalar order parameter. The number of platelets per aggregate and anisotropy of the microstructure both increases with platelet plan area. The system becomes more ordered and aggregate size increases with increasing pressure until maximum ordered state at confining pressure of 50 atm. Further increase of pressure slides platelets relative to each other leading to smaller aggregate size. The results show aggregate size of (3–8) platelets for sodiumsmectite in agreement with experiments (3–10). The geometrical arrangement of aggregates affects mechanical properties of the system. The elastic properties of the mesoscale aggregate assembly are reported and compared with nanoindentation experiments. It is found that the elastic properties at this scale are close to the cubic systems. The elastic stiffness and anisotropy of the assembly increases with the size of the platelets and the level of external pressure.