Volume 131, Issue 7, 21 August 2009

Twotemperature models are used to represent the interaction between atoms and free electrons during thermal transients such as radiation damage, laser heating, and cascade simulations. In this paper, we introduce an energyconserving version of an inhomogeneous finite reservoir twotemperature model using a Langevin thermostat to communicate energy between the electronic and atomic subsystems. This energyconserving modification allows the inhomogeneous twotemperature model to be used for longer and larger simulations and simulations of small energy phenomena, without introducing nonphysical energy fluctuations that may affect simulation results. We test this model on the annealing of Frenkel defects. We find that Frenkel defectannealing is largely indifferent to the electronic subsystem, unless the electronic subsystem is very tightly coupled to the atomic subsystem. We also consider radiation damage due to local deposition of heat in two idealized systems. We first consider radiation damage in a large facecenteredcubic LennardJones (LJ) singlecomponent crystal that readily recrystallizes. Second, we consider radiation damage in a large binary glassforming LJ crystal that retains permanent damage. We find that the electronic subsystem parameters can influence the way heat is transported through the system and have a significant impact on the number of defects after the heat deposition event. We also find that the two idealized systems have different responses to the electronic subsystem. The singlecomponent LJ system anneals most rapidly with an intermediate electronion coupling and a high electronic thermal conductivity. If sufficiently damaged, the binary glassforming LJ system retains the least permanent damage with both a high electronion coupling and a high electronic thermal conductivity. In general, we find that the presence of an electronic gas can affect short and long term material annealing.
 ARTICLES

 Theoretical Methods and Algorithms

A statistical theory for selfcondensing vinyl polymerization
View Description Hide DescriptionThe method of statistical mechanics is used to investigate several properties of selfcondensing vinyl polymerization system. Under the framework of mean field theory, two types of canonical partition functions of the system are constructed from viewpoints of functional groups and polymers, and by which the explicit expressions of equilibrium free energy and the law of mass action are obtained. Based on the free energy, the same size distribution function of hyperbranched polymers is derived by two different methods, which is identical with the previous result given by solving the kinetic differential equations. This implies that the two partition functions are consistent with each other. Furthermore, in terms of the size distribution function, the radius of gyration as well as its scaling behavior near the critical point are studied, and the corresponding scaling law is given. As an application, the isothermal compressibility is derived on the basis of equation of state, which indicates that the spatial correlation between monomers increases with the increasing of conversion of the double bonds, and reaches the maximum at the critical point. In addition, it is shown that a usual treatment on the polydispersity index would lead it to infinite, which is not agreement with the true result of 1 at the end of the reaction system. To clarify this fact, we find that the correlation length plays an important role, and then by using asymptotic forms of the size distribution and the second moment, the reasonable result can be carried out.

Highly accurate CCSD(R12) and CCSD(F12) optical response properties using standard triple basis sets
View Description Hide DescriptionCoupledcluster response theory for frequencydependent optical properties within the coupledcluster singlesanddoubles model (CCSD) has been derived and implemented for ansatz 2 of the explicitly correlated CCSD(R12) and CCSD(F12) methods as part of the program package DALTON. The basis set convergence of static dipole moments,polarizabilities, and parallel averages of first and second hyperpolarizabilities has been investigated for Ne, BH, , CO, and BF. The frequencydependent results are presented for the electronic secondharmonic generation of . With triplebasis sets, the CCSD(F12) correlation contributions using ansatz 2 are close to the basis set limits for dipole moments and second hyperpolarizabilities; the CCSD(R12) results are better than the CCSD results obtained with at least quintuplebasis sets for polarizabilities and first hyperpolarizabilities. The exponent of Slatertype correlation factor for CCSD(F12) ground state energy may not be optimal and has to be reexamined for response properties. We also suggest that the remaining oneelectron basis set errors arising within the coupledcluster singles should be reduced by allowing excitations into the auxiliary orbital space.

The calculation of chemical potential of organic solutes in dense liquid phases by using expanded ensemble Monte Carlo simulations
View Description Hide DescriptionIn this work, the chemical potentials of organic compounds in dense liquid phases are calculated by using expanded ensemble Monte Carlo simulations. To make insertion of a solute molecule efficiently, LennardJones size parameters and bond lengths are varied with coupling parameter. A robust adaptive scheme is proposed in order to determine biasing weights during the simulation, which enhances the efficiency and applicability of the expanded ensemble method. Using the proposed simulation technique, chemical potentials of organic molecules in dense liquid phases are obtained from a single run of simulation. The excess chemical potentials of several hydrocarbon molecules including alkanes, benzene, toluene, and ethanol in aqueous phases at infinite dilution as well as in their pure liquid phases are calculated at 298 K and 1 atm, and simulation results are compared with experimental data.

Neural network approach to quantumchemistry data: Accurate prediction of density functional theory energies
View Description Hide DescriptionArtificial neural network (ANN) approach has been applied to estimate the density functional theory(DFT)energy with large basis set using lowerlevel energy values and molecular descriptors. A total of 208 different molecules were used for the ANN training, cross validation, and testing by applying BLYP, B3LYP, and BMK density functionals. Hartree–Fock results were reported for comparison. Furthermore, constitutional molecular descriptor (CD) and quantumchemical molecular descriptor (QD) were used for building the calibration model. The neural network structure optimization, leading to four to five hidden neurons, was also carried out. The usage of several lowlevel energy values was found to greatly reduce the prediction error. An expected error, mean absolute deviation, for ANN approximation to DFTenergies was . In addition, the comparison of the different density functionals with the basis sets and the comparison of multiple linear regression results were also provided. The CDs were found to overcome limitation of the QD. Furthermore, the effective ANN model for DFT/ and DFT/energy estimation was developed, and the benchmark results were provided.

Nested Markov chain Monte Carlo sampling of a density functional theory potential: Equilibrium thermodynamics of dense fluid nitrogen
View Description Hide DescriptionAn optimized variant of the nested Markov chain Monte Carlo method [J. Chem. Phys.130, 164104 (2009)] is applied to fluid . In this implementation of , isothermalisobaric ensemble sampling on the basis of a pair potential (the “reference” system) is used to enhance the efficiency of sampling based on Perdew–Burke–Ernzerhof density functional theory with a basis set (, the “full” system). A long sequence of Monte Carlo steps taken in the reference system is converted into a trial step taken in the full system; for a good choice of reference potential, these trial steps have a high probability of acceptance. Using decorrelated samples drawn from the reference distribution, the pressure and temperature of the full system are varied such that its distribution overlaps maximally with that of the reference system. Optimized pressures and temperatures then serve as input parameters for sampling of dense fluid over a wide range of thermodynamic conditions. The simulation results are combined to construct the Hugoniot of nitrogen fluid, yielding predictions in excellent agreement with experiment.

On the variational computation of a large number of vibrational energy levels and wave functions for mediumsized molecules
View Description Hide DescriptionIn a recent publication [J. Chem. Phys.127, 084102 (2007)], the nearly variational DEWE approach (DEWE denotes Discrete variable representation of the Watson Hamiltonian using the Eckart frame and an Exact inclusion of a potential energy surface expressed in arbitrarily chosen coordinates) was developed to compute a large number of (ro)vibrational eigenpairs for mediumsized semirigid molecules having a single welldefined minimum. In this publication, memory, CPU, and hard disk usage requirements of DEWE, and thus of any DEWEtype approach, are carefully considered, analyzed, and optimized. Particular attention is paid to the sparse matrixvector multiplication, the most expensive part of the computation, and to ratedetermining steps in the iterative Lanczos eigensolver, including spectral transformation, reorthogonalization, and restart of the iteration. Algorithmic improvements are discussed in considerable detail. Numerical results are presented for the vibrational band origins of the and isotopologues of the methane molecule. The largest matrix handled on a personal computer during these computations is of the size of . The best strategy for determining vibrational eigenpairs depends largely on the actual details of the required computation. Nevertheless, for a usual scenario requiring a large number of the lowest eigenpairs of the Hamiltonian matrix the combination of the thickrestart Lanczos method, shiftfold filtering, and periodic reorthogonalization appears to result in the computationally most feasible approach.

Matrix method calculation of the Kerr effect transient and ac stationary responses of arbitrary shaped macromolecules
View Description Hide DescriptionA new and simple matrix method of evaluating the Kerr effect transient and ac stationary responses of rigid polar and polarizable particles (macromolecules) of arbitrary shape undergoing the noninertial anisotropic rotational diffusion in the presence of an external electric field is presented. The matrix calculations are accomplished by solving the corresponding coupled differentialrecurrence equations for the statistical moments (ensemble averages of the Wigner functions). The results so obtained are in agreement with previously available solutions for various particular cases and are amenable to comparison with experiment.

Pitfalls of choosing an order parameter for rare event calculations
View Description Hide DescriptionThe mechanism of rare events in complex systems can be found by sampling dynamical paths that connect stable states. To calculate a rate using transition paths, an order parameter is required to describe the progress of the reaction and to distinguish the initial and final states. In this work, we compare two implementations of transition path sampling for Langevin paths, one for which paths are sampled in configuration space and the other in the space of the random variables that describe the thermostat. These two approaches are found to give different rates for the rearrangement of a sevenparticle cluster despite the fact that both are formally exact. The difference is understood in terms of how efficiently the methods sample states along the order parameter. The more efficient approach takes the system to unexpected states that are allowed by a poor choice of order parameter. While transition path sampling is formally correct, we show how mistakes can be made when the system escapes to unknown states along an order parameter represented in terms of collective variables.

Chain fluids: Contrasts of theoretical and simulation approaches, and comparison with experimental alkane properties
View Description Hide DescriptionIn this work, we undertake a fundamental comparison of analogous lattice and continuum integral equationtheories, with both held accountable to the results from Monte Carlo simulation and real experimental data on short chain molecules. Each integral equation method is applied to determine the system’s microscopic intermolecular sitesite distributions and the corresponding bulk thermodynamic properties. These properties and those from the MC simulations are then fitted to corresponding data on alkanes. Thus, in sidebyside comparisons we cover a number of fundamental contrasts: theory versus simulation, latticebased theory versus continuumbased theory, and thermodynamic properties of model chain molecules versus the actual experimental properties of hydrocarbons. The observed behavior of the modeling methods is compared in terms of both the experimentally accessible physical properties (e.g., and coexistence properties) and the more fundamental underlying quantities, such as free energies and model internal energies. We also discuss the various options for model parametrization and subsequent impact on the predicted physical properties. The results from this work are used (alone, with no additional fitting) in the article which follows, wherein we predict the experimental properties of alkane mixtures.

Fluid mixtures: Contrasts of theoretical and simulation approaches, and comparison with experimental alkane properties
View Description Hide DescriptionIn this work we compare lattice and continuum versions of the same theory, as derived in the previous paper (Paper I), to predict the behavior of simple alkane mixtures. In the course of doing this we use characteristic parameters obtained for the pure alkane fluids; no fits of mixture properties are involved. Our two sets of predictions are tested against experimental data and against new Monte Carlo simulation results. The experimental properties of interest include mixed pressurevolumetemperature surfaces, as well as a variety of coexistence diagrams characterizing mixed system liquidvapor equilibria. We contrast the performance of the lattice and continuum approaches and discuss the results in the context of underlying model approximations as derived in Paper I.

Study of linear and nonlinear optical properties of dendrimers using density matrix renormalization group method
View Description Hide DescriptionWe have used the density matrix renormalization group (DMRG) method to study the linear and nonlinear optical responses of first generation nitrogen based dendrimers with donor acceptor groups. We have employed Pariser–Parr–Pople Hamiltonian to model the interacting electrons in these systems. Within the DMRG method we have used an innovative scheme to target excited states with large transition dipole to the ground state. This method reproduces exact optical gaps and polarization in systems where exact diagonalization of the Hamiltonian is possible. We have used a correction vector method which tacitly takes into account the contribution of all excited states, to obtain the ground state polarizibility, first hyperpolarizibility, and two photon absorption cross sections. We find that the lowest optical excitations as well as the lowest excited triplet states are localized. It is interesting to note that the first hyperpolarizibility saturates more rapidly with system size compared to linear polarizibility unlike that of linear polyenes.

Bendtwiststretch model for coarse elastic network simulation of biomolecular motion
View Description Hide DescriptionThe empirical harmonic potential function of elasticnetwork models (ENMs) is augmented by three and fourbody interactions as well as by a parameterfree connection rule. In the new bendtwiststretch (BTS) model the complexity of the parametrization is shifted from the spatial level of detail to the potential function, enabling an arbitrary coarse graining of the network. Compared to distance cutoffbased Hookean springs, the approach yields a more stable parametrization of coarsegrained ENMs for biomolecular dynamics. Traditional ENMs give rise to unbounded zerofrequency vibrations when (pseudo)atoms are connected to fewer than three neighbors. A large cutoff is therefore chosen in an ENM (about twice the average nearestneighbor distance), resulting in many falsepositive connections that reduce the spatial detail that can be resolved. More importantly, the required threeneighbor connectedness also limits the coarse graining, i.e., the network must be dense, even in the case of lowresolution structures that exhibit few spatial features. The new BTS model achieves such coarse graining by extending the ENM potential to include threeand fouratom interactions (bending and twisting, respectively) in addition to the traditional twoatom stretching. Thus, the BTS model enables reliable modeling of any threedimensional graph irrespective of the atom connectedness. The additional potential terms were parametrized using continuum elastic theory of elastic rods, and the distance cutoff was replaced by a competitive Hebb connection rule, setting all free parameters in the model. We validate the approach on a carbonalpha representation of adenylate kinase and illustrate its use with electron microscopy maps of E. coliRNA polymerase, E. coli ribosome, and eukaryotic chaperonin containing Tcomplex polypeptide 1, which were difficult to model with traditional ENMs. For adenylate kinase, we find excellent reproduction ( overlap) of the ENM modes and factors when BTS is applied to the carbonalpha representation as well as to coarser descriptions. For the volumetric maps, coarse BTS yields similar motions (70%–90% overlap) to those obtained from significantly denser representations with ENM. Our Pythonbased algorithms of ENM and BTS implementations are freely available.

A simple model for the treatment of imaginary frequencies in chemical reaction rates and molecular liquids
View Description Hide DescriptionA simple model is presented for treating local imaginary frequencies that are important in the study of quantum effects in chemical reactions and various dynamical processes in molecular liquids. It significantly extends the range of accuracy of conventional local harmonic approximations (LHAs) used in the linearized semiclassical initial value representation/classical Wigner approximation for real time correlation functions. The key idea is realizing that a local Gaussian approximation (LGA) for the momentum distribution (from the Wigner function involving the Boltzmann operator) can be a good approximation even when a LHA for the potential energy surface fails. The model is applied here to two examples where imaginary frequencies play a significant role: the chemical reaction rate for a linear model of the reaction and an analogous asymmetric barrier—a case where the imaginary frequency of the barrier dominates the process—and for momentum autocorrelation functions in liquid parahydrogen at two thermal state points (25 and 14 K under nearly zero external pressure). We also generalize the LGA model to the Feynman–Kleinert approximation.

Nonlinear kinetics of fast relaxation in solutions with short and lengthy micelles
View Description Hide DescriptionAn analytical treatment of the nonlinear kinetic equations for fast relaxation of coexisting short and lengthy micelles in surfactantsolutions is presented. The kinetic equations can be written as a hierarchical set of differential equations for the moments of the aggregation number distribution function of micelles. It is shown that the moment equations can be successively integrated. As examples of the general approach, particular cases of short spherical micelles, lengthy cylindrical micelles, and coexisting short and lengthy micelles have been considered and compared to the results of linear kinetic theory of micellar fast relaxation. The results show that there is a strong interplay between coexisting short and lengthy micelles, even in the case when the total number of surfactant molecules aggregated in short micelles is small in comparison with that in lengthy micelles.

A selfconsistent renormalized jellium approach for calculating structural and thermodynamic properties of charge stabilized colloidal suspensions
View Description Hide DescriptionAn approach is proposed which allows to selfconsistently calculate the structural and the thermodynamic properties of highly charged aqueous colloidalsuspensions. The method is based on the renormalized jellium model with the background charge distribution related to the colloidcolloid correlation function. The theory is used to calculate the correlation functions and the effective colloidal charges for suspensions containing additional monovalent electrolyte. The predictions of the theory are in excellent agreement with Monte Carlo simulations.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Twophoton photodissociation dynamics of via the electronic state
View Description Hide DescriptionPhotodissociationdynamics of via the state by twophoton absorption have been investigated using the Hatom Rydberg tagging timeofflight technique. The action spectrum of the transition band has been measured. The predissociation lifetime of the state is determined to be about 13.5 fs. The quantum stateresolved OH product translational energy distributions and angular distributions have also been measured. By carefully simulating these distributions, quantum state distributions of the OH product as well as the stateresolved angular anisotropy parameters were determined. The most important pathway of the dissociation via the state leads to the highly rotationally excited products. Vibrationally excited products (up to ) and electronically excited have also been observed. The branching ratios are determined to be 17.9% at 244.540 nm and 19.9% at 244.392 nm , which are considerably smaller than the value predicted by the theory. These discrepancies are attributed to the nonadiabatic coupling effect between the and surfaces at the bent geometry.

Rate coefficient of CN formation through radiative association: A theoretical study of quantum effects
View Description Hide DescriptionRadiative association of CN is simulated using a quantum dynamical as well as a semiclassical approach. A comparison of the resulting energyresolved cross sections reveals striking quantum effects that are due to shape resonances. These, in turn, arise because of states that are quasibound by the centrifugal barrier. The quantal rate coefficient for temperatures from 40 to 1900 K has been computed using the Breit–Wigner theory to account for the resonances. Comparison with the results obtained by Singh and Andreazza [Astrophys. J.537, 261 (2000)] shows that the semiclassical method, which completely omits the shape resonances, is accurate to within 25% above room temperature. At lower temperatures the contribution from the shape resonances to the radiative association rate is more significant.

Are isomers of the vinyl cyanide ion missing links for interstellar pyrimidine formation?
View Description Hide DescriptionIn the interstellar medium(ISM) there are many regions where the formation of molecules is kinetically driven rather than thermochemically, which can lead to the formation of many isomers even though some may be fairly higher in energy relative to the molecular global minimum. Recent laboratory experiments where noble gas cations are reacted with pyrimidine favored the formation of , but the molecular structure(s) of this fragment was not determined. Microscopic reversibility means that pyrimidine could form under interstellar conditions should the required reactant be detected in the ISM. Hence could be a strong candidate for involvement in the formation of heterocyclic biomolecules such as pyrimidine in the ISM. In this study, we have investigated the low energy isomers of the acrylonitrile ion using density functional theory as well as high levels of ab initiotheory, namely, the singles and doubles coupledcluster theory that includes a perturbational correction for connected triple excitations, denoted as CCSD(T). An automated stochastic search procedure, Kick, has been employed to find isomers on the ground state doublet potential energy surface. Several new structures, along with all the previously reported minima, have been found. The global minimum is energetically much lower than either , the acrylonitrile ion, or , the most likely intermediate of the reaction between and HCN. These isomers are connected to the global minimum via several transition states and intermediates. The results indicate that not only the global minimum but also several higher energy isomers of the ion could be important in interstellar pyrimidine formation. The isomeric molecules have the necessary CCNC backbone needed for the reaction with HCN to form the cyclic pyrimidine framework. The structural and rotational parameters of all the isomers studied in this work have been predicted at the CCSD(T) level of theory with the anticipation that it will expedite their laboratory as well as astronomical identification.

Anisotropic collisioninduced Raman scattering by the Kr:Xe gas mixture
View Description Hide DescriptionWe report anisotropic collisioninduced Raman scattering intensities by the Kr–Xe atomic pair recorded in a gas mixture of Kr and Xe at room temperature. We compare them to quantummechanical calculations on the basis of modern incremental polarizability models of either ab initio postHartree–Fock or density functional theory methods.
 Condensed Phase Dynamics, Structure, and Thermodynamics: Spectroscopy, Reactions, and Relaxation

An asymmetry model for the highly viscous flow
View Description Hide DescriptionThe shear flow is modeled in terms of local structural rearrangements. Most of these rearrangements are strongly asymmetric, because the embedding matrix tends to be elastically adapted to the initial state and to have a marked elastic misfit with regard to the final state. As one approaches the Maxwell time, the asymmetry becomes time dependent, thus enabling the system to leave the initial state. The model explains the Kohlrausch behavior at the main peak in terms of the interaction between different local structural rearrangements.