Volume 133, Issue 13, 07 October 2010

The photodissociation dynamics of via the state by twophoton excitation has been investigated using the H atom Rydberg tagging timeofflight technique. The rotational resolved action spectrum of the transition band has been measured. The line widths show a pronounced dependence on the parent rotational excitation in the state. The quantum state resolved OH product translational energy distributions and angular distributions have also been obtained. By carefully simulating these distributions, quantum state distributions of the OH product as well as the stateresolved angular anisotropy parameters were determined. The experimental results confirm the variation of two competitive predissociation pathways. A heterogeneous predissociation channel is mediated by rotational coupling to the state associated with the axis , and a homogeneous pathway arises from purely electronic coupling to the state. We have also obtained the branching ratios of the and products, and related these to the and pathways. The branching ratios display a strong dependence.
 ARTICLES

 Theoretical Methods and Algorithms

Generalized principle of corresponding states and the scale invariant meanfield approach
View Description Hide DescriptionIn this paper we apply the relations between the critical points of the LennardJones fluids and lattice gas model found in [V. L. Kulinskii, J. Phys. Chem. B114, 2852 (2010)] to other shortranged potentials like Buckingham and the Miepotentials. The estimates for the corresponding critical point loci correlate quite satisfactory with the available numerical data for these potentials. The explanation for the correlation between the value of the second virial coefficient at the critical temperature and the particle volume found in [G. A. Vliegenthart and H. N. W. Lekkerkerker, J. Chem. Phys.112, 5364 (2000)] is proposed. The connection of the stability of the liquid phase with the short range character of the potentials is discussed on the basis of the global isomorphism approach.

Biased diffusion in tubes formed by spherical compartments
View Description Hide DescriptionWe study the effect of the driving force on Brownian motion of a point particle in a tube formed by identical spherical compartments, which create periodic entropy potential for the motion along the tube axis. The focus is on (i) the effective mobility and diffusion coefficient of the particle as functions of the driving force, (ii) localization of the particle in the central part of the tube induced by the driving force, and (iii) transit time of the particle between the openings connecting neighboring compartments. Some of the results at very small and large driving force are obtained analytically, while the majority of the results are obtained from Brownian dynamics simulations.

Magnetohydrodynamic effects on a charged colloidal sphere with arbitrary doublelayer thickness
View Description Hide DescriptionAn analytical study is presented for the magnetohydrodynamic(MHD) effects on a translating and rotating colloidal sphere in an arbitrary electrolyte solution prescribed with a general flow field and a uniform magnetic field at a steady state. The electric double layer surrounding the charged particle may have an arbitrary thickness relative to the particle radius. Through the use of a simple perturbation method, the Stokes equations modified with an electric force term, including the Lorentz force contribution, are dealt by using a generalized reciprocal theorem. Using the equilibrium doublelayer potential distribution from solving the linearized Poisson–Boltzmann equation, we obtain closedform formulas for the translational and angular velocities of the spherical particle induced by the MHD effects to the leading order. It is found that the MHD effects on the particle movement associated with the translation and rotation of the particle and the ambient fluid are monotonically increasing functions of , where is the Debye screening parameter and is the particle radius. Any pure rotational Stokes flow of the electrolyte solution in the presence of the magnetic field exerts no MHD effect on the particle directly in the case of a very thick double layer. The MHD effect caused by the pure straining flow of the electrolyte solution can drive the particle to rotate, but it makes no contribution to the translation of the particle.

Efficient calculation of temperature dependence of solidphase free energies by overlap sampling coupled with harmonically targeted perturbation
View Description Hide DescriptionWe examine a method for computing the change in free energy with temperature of a crystalline solid. In the method, the freeenergy difference between nearby temperatures is calculated via overlapsampling freeenergyperturbation with Bennett’s optimization. Coupled to this is a harmonically targeted perturbation that displaces the atoms in a manner consistent with the temperature change, such that for a harmonic system, the freeenergy difference would be recovered with no error. A series of such perturbations can be assembled to bridge larger gaps in temperature. We test this harmonically targeted temperature perturbation (HTTP) method through the application to the inversepower soft potential, , over a range of temperatures up to the melting condition. Three exponent values (, 9, and 6) for the potential are studied with different crystal structures, specifically facecentered cubic (fcc), bodycentered cubic (bcc), and hexagonal close packing. Absolute free energies (classical only) for each system are obtained by implementing the series to nearzero temperature, where the harmonic model becomes very accurate. The HTTP method is shown to provide very precise results, with errors in the free energy smaller than two parts in . An analysis of the thermodynamic stability of the various structures in the infinitesystem limit confirms previous findings. In particular, for and 9, the fcc structure is stable for all temperatures up to melting, and for , the bcc crystal becomes stable relative to fcc for temperatures above . The effects of vacancies and other defects are not considered in the analysis.

Propertyoptimized Gaussian basis sets for molecular response calculations
View Description Hide DescriptionWith recent advances in electronic structure methods, firstprinciples calculations of electronic response properties, such as linear and nonlinear polarizabilities, have become possible for molecules with more than 100 atoms. Basis set incompleteness is typically the main source of error in such calculations since traditional diffuse augmented basis sets are too costly to use or suffer from near linear dependence. To address this problem, we construct the first comprehensive set of propertyoptimized augmented basis sets for elements H–Rn except lanthanides. The new basis sets build on the Karlsruhe segmented contracted basis sets of splitvalence to quadruplezeta valence quality and add a small number of moderately diffuse basis functions. The exponents are determined variationally by maximization of atomic Hartree–Fock polarizabilities using analytical derivative methods. The performance of the resulting basis sets is assessed using a set of 313 molecular static Hartree–Fock polarizabilities. The mean absolute basis set errors are 3.6%, 1.1%, and 0.3% for propertyoptimized basis sets of splitvalence, triplezeta, and quadruplezeta valence quality, respectively. Density functional and secondorder Møller–Plesset polarizabilities show similar basis set convergence. We demonstrate the efficiency of our basis sets by computing static polarizabilities of icosahedral fullerenes up to using hybrid density functional theory.

Uncoupled multireference statespecific Mukherjee’s coupled cluster method with triexcitations
View Description Hide DescriptionWe have developed the uncoupled version of multireference Mukherjee’s coupled cluster method with connected triexcitations. The method has been implemented in ACES II program package. The agreement between the uncoupled and the standard version of Mukherjee’s multireference coupled cluster method has been reported previously at the singles and doubles level by Das et al. [J. Mol. Struct.: THEOCHEM79, 771 (2006); Chem. Phys.349, 115 (2008)]. The aim of this article is to investigate this method further, in order to establish how its performance changes with the size of the basis set, size of the model space, multireference character of different molecules, and inclusion of connected triple excitations. Assessment of the new method has been performed on the singlet methylene, potential energy curve of fluorine molecule, and third electronic state of oxygen molecule.

A theoretical investigation on the honeycomb potential fluid
View Description Hide DescriptionA local selfconsistent Ornstein–Zernike (OZ) integral equation theory (IET) is proposed to provide a rapid route for obtaining thermodynamic and structural information for any thermodynamically stable or metastable state points in the bulk phase diagram without recourse to traditional thermodynamic integration, and extensive Monte Carlo simulations are performed on a recently proposed honeycomb potential in three dimensions to test the theory’s reliability. The simulated quantities include radial distribution function (rdf) and excess internal energy,pressure, excess chemical potential, and excess Helmholtz free energy. It is demonstrated that (i) the theory reproduces the rdf very satisfactorily only if the bulk state does not enter deep into a two phases coexistence region; (ii) the excess internal energy is the only one of the four thermodynamic quantities investigated amenable to the most accurate prediction by the present theory, and the simulated pressure is somewhat overestimated by the theoretical calculations, but the deviation tends to vanish along with rising of the temperature; (iii) using the structural functions from the present local selfconsistent OZ IET, a previously derived local expression, due to the present author, achieves even a higher accuracy in calculating for the excess chemical potential than the exact virial pressure formula for the pressure, and the resulting excess Helmholtz free energy is in surprisingly same with the simulation results due to offset of the errors. Based on the above observations, it is suggested that it may be a good procedure to integrate the theoretical excess internal energy along the isochors to get the excess Helmholtz free energy, which is then fitted to a polynomial to be used for calculation of all of other thermodynamic quantities in the framework of the OZ IET.

Constrainedpairing meanfield theory. IV. Inclusion of corresponding pair constraints and connection to unrestricted Hartree–Fock theory
View Description Hide DescriptionOur previously developed constrainedpairing meanfieldtheory (CPMFT) is shown to map onto an unrestricted Hartree–Fock (UHF) type method if one imposes a corresponding pair constraint to the correlation problem that forces occupation numbers to occur in pairs adding to one. In this new version, CPMFT has all the advantages of standard independent particle models (orbitals and orbital energies, to mention a few), yet unlike UHF, it can dissociate polyatomic molecules to the correct groundstate restricted openshell Hartree–Fock atoms or fragments.

Memory effects in nonadiabatic molecular dynamics at metal surfaces
View Description Hide DescriptionWe study the effect of temporal correlation in a Langevin equation describing nonadiabaticdynamics at metal surfaces. For a harmonic oscillator, the Langevin equation preserves the quantum dynamics exactly and it is demonstrated that memory effects are needed in order to conserve the ground state energy of the oscillator. We then compare the result of Langevin dynamics in a harmonic potential with a perturbative master equation approach and show that the Langevin equation gives a better description in the nonperturbative range of high temperatures and large friction. Unlike the master equation, this approach is readily extended to anharmonic potentials. Using density functional theory, we calculate representative Langevin trajectories for associative desorption of from Ru(0001) and find that memory effects lower the dissipation of energy. Finally, we propose an ab initio scheme to calculate the temporal correlation function and dynamical friction within density functional theory.

Knowledgebased probabilistic representations of branching ratios in chemical networks: The case of dissociative recombinations
View Description Hide DescriptionExperimental data about branching ratios for the products of dissociative recombination of polyatomic ions are presently the unique information source available to modelers of natural or laboratory chemical plasmas. Yet, because of limitations in the measurement techniques, data for many ions are incomplete. In particular, the repartition of hydrogen atoms among the fragments of hydrocarbons ions is often not available. A consequence is that proper implementation of dissociative recombination processes in chemical models is difficult, and many models ignore invaluable data. We propose a novel probabilistic approach based on Dirichlettype distributions, enabling modelers to fully account for the available information. As an application, we consider the production rate of radicals through dissociative recombination in an ionospheric chemistry model of Titan, the largest moon of Saturn. We show how the complete scheme of dissociative recombination products derived with our method dramatically affects these rates in comparison with the simplistic Hloss mechanism implemented by default in all recent models.

Including quantum decoherence in surface hopping
View Description Hide DescriptionIn this paper we set up a method called overlap decoherence correction (ODC) to take into account the quantum decoherenceeffect in a surface hopping framework. While keeping the standard surface hopping approach based on independent trajectories, our method allows to account for quantum decoherence by evaluating the overlap between frozen Gaussian wavepackets, the time evolution of which is obtained in an approximate way. The ODC scheme mainly depends on the parameter , which is the Gaussian width of the wavepackets. The performance of the ODC method is tested versus full quantum calculations on three model systems, and by comparison with full multiple spawning (FMS) results for the decay in the azobenzene molecule.

Overcoming barriers in trajectory space: Mechanism and kinetics of rare events via Wang–Landau enhanced transition path sampling
View Description Hide DescriptionWithin the framework of transition path sampling (TPS), activation energies can be computed as path ensemble averages without a priori information about the reaction mechanism [C. Dellago and P. G. Bolhuis, Mol. Simul.30, 795 (2004)]. Activation energies computed for different conditions can then be used to determine by numerical integration the rate constant for a system of interest from the rate constant known for a reference system. However, in systems with complex potential energy surfaces, multiple reaction pathways may exist making ergodic sampling of trajectory space difficult. Here, we present a combination of TPS with the Wang–Landau (WL) flathistogram algorithm for an efficient sampling of the transition path ensemble. This method, denoted by WLTPS, has the advantage that from one single simulation, activation energies at different temperatures can be determined even for systems with multiple reaction mechanisms. The proposed methodology for rate constant calculations does not require the knowledge of the reaction coordinate and is generally applicable to Arrhenius and nonArrhenius processes. We illustrate the applicability of this technique by studying a twodimensional toy system consisting of a triatomic molecule immersed in a fluid of repulsive soft disks. We also provide an expression for the calculation of activation volumes from path averages such that the pressure dependence of the rate constant can be obtained by numerical integration.

A simultaneous probability density for the intracule and extracule coordinates
View Description Hide DescriptionWe introduce the intex density , which combines both the intracular and extracular coordinates to yield a simultaneous probability density for the position of the centerofmass radius and relative separation of electron pairs. One of the principle applications of the intex density is to investigate the origin of the recently observed secondary Coulomb hole. The Hartree–Fock (HF) intex densities for the helium atom and heliumlike ions are symmetric functions that may be used to prove the isomorphism , where is the intracule density and is the extracule density. This is not true of the densities that we have constructed from explicitly correlated wave functions. The difference between these asymmetric functions and their symmetric HF counterparts produces a topologically rich intex correlation hole. From the intex hole distributions , we conclude that the probability of observing an electron pair with a very large interelectronic separation increases with the inclusion of correlationonly when their centerofmass radius is close to half of their separation.

Quantum mechanics based force field for carbon (QMFFCx) validated to reproduce the mechanical and thermodynamics properties of graphite
View Description Hide DescriptionAs assemblies of graphene sheets, carbon nanotubes, and fullerenes become components of new nanotechnologies, it is important to be able to predict the structures and properties of these systems. A problem has been that the level of quantum mechanics practical for such systems (density functional theory at the PBE level) cannot describe the London dispersion forces responsible for interaction of the graphene planes (thus graphite falls apart into graphene sheets). To provide a basis for describing these London interactions, we derive the quantum mechanics based force field for carbon (QMFFCx) by fitting to results from density functional theory calculations at the M062X level, which demonstrates accuracies for a broad class of molecules at short and medium range intermolecular distances. We carried out calculations on the dehydrogenated coronene (C24) dimer, emphasizing two geometries: paralleldisplaced X (close to the observed structure in graphite crystal) and PDY (the lowest energy transition state for sliding graphene sheets with respect to each other). A third, eclipsed geometry is calculated to be much higher in energy. The QMFFCx force field leads to accurate predictions of available experimental mechanical and thermodynamics data of graphite (lattice vibrations, elastic constants, Poisson ratios, lattice modes, phonon dispersion curves, specific heat, and thermal expansion). This validates the use of M062X as a practical method for development of new first principles based generations of QMFF force fields.

Analysis of the quantumclassical Liouville equation in the mapping basis
View Description Hide DescriptionThe quantumclassical Liouville equation provides a description of the dynamics of a quantum subsystem coupled to a classical environment. Representing this equation in the mapping basis leads to a continuous description of discrete quantum states of the subsystem and may provide an alternate route to the construction of simulation schemes. In the mapping basis the quantumclassical Liouville equation consists of a Poisson bracket contribution and a more complex term. By transforming the evolution equation, termbyterm, back to the subsystem basis, the complex term (excess coupling term) is identified as being due to a fraction of the back reaction of the quantum subsystem on its environment. A simple approximation to quantumclassical Liouville dynamics in the mapping basis is obtained by retaining only the Poisson bracket contribution. This approximate mapping form of the quantumclassical Liouville equation can be simulated easily by Newtonian trajectories. We provide an analysis of the effects of neglecting the presence of the excess coupling term on the expectation values of various types of observables. Calculations are carried out on nonadiabatic population and quantum coherencedynamics for curve crossing models. For these observables, the effects of the excess coupling term enter indirectly in the computation and good estimates are obtained with the simplified propagation.

Manyelectron selfinteraction and spin polarization errors in local hybrid density functionals
View Description Hide DescriptionErrors for systems with noninteger occupation have been connected to common failures of density functionals. Previously, global hybrids and pure density functionals have been investigated for systems with noninteger charge and noninteger spin state. Local hybrids have not been investigated for either of those systems to the best of our knowledge. This study intends to close this gap. We investigate systems with noninteger charge to assess the manyelectron selfinteraction error and systems with noninteger spin state to assess the spin polarization error of recently proposed local hybrids and their rangeseparated variants. We find that longrange correction is very important to correct for manyelectron selfinteraction error in cations, whereas most fullrange local hybrids seem to be sufficient for anions, where longrangecorrected density functionals tend to overcorrect. On the other hand, while all hitherto proposed longrangecorrected density functionals show large spin polarization errors, the Perdew–Staroverov–Tao–Scuseria (PSTS) functional performs best of all local hybrids in this case and shows an outstanding behavior for the dependence of the energy on the spin polarization.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Quantum stateselected photodissociation dynamics of : Twophoton dissociation via the electronic state
View Description Hide DescriptionThe photodissociation dynamics of via the state by twophoton excitation has been investigated using the H atom Rydberg tagging timeofflight technique. The rotational resolved action spectrum of the transition band has been measured. The line widths show a pronounced dependence on the parent rotational excitation in the state. The quantum state resolved OH product translational energy distributions and angular distributions have also been obtained. By carefully simulating these distributions, quantum state distributions of the OH product as well as the stateresolved angular anisotropy parameters were determined. The experimental results confirm the variation of two competitive predissociation pathways. A heterogeneous predissociation channel is mediated by rotational coupling to the state associated with the axis , and a homogeneous pathway arises from purely electronic coupling to the state. We have also obtained the branching ratios of the and products, and related these to the and pathways. The branching ratios display a strong dependence.

The applicability of threedimensional aromaticity in Zintl analogues
View Description Hide DescriptionThreedimensional aromaticity is shown to play a role in the stability of deltahedral Zintl clusters and here we examine the connection between aromaticity and stability. In order to gain further insight, we have studied Zintl analogs comprised of bismuthdopedtin clusters with photoelectron spectroscopy and theoretical methods. To assign aromaticity, we examine the ring currents induced around the cage by using the nucleus independent chemical shift. In the current study, is a stable cluster and fits aromatic criteria, while is found to fit antiaromatic criteria and has reduced stability. The more stable clusters exhibit an aromatic character which originates from weakly interacting states and bonding orbitals parallel to the surface of the cluster, while nonbonding lone pairs perpendicular to the surface of the cluster account for antiaromaticity and reduced stability. The effect of threedimensional aromaticity on the electronic structure does not result in degeneracies, so the resulting variations in stability are smaller than those seen in conventional aromaticity.

Application of smooth exterior scaling method to study the time dependent dynamics of in intense laser field
View Description Hide DescriptionA study of the multiphotondissociation of in intense laser field using the smooth exterior scaling method to calculate resonance states is presented. This method is very attractive as it does not disturb the interaction region. The wave functions calculated with this method provide indisputable proof in support of the mechanisms of the different phenomena happening during photodissociation.Wave functions corresponding to the “vibrationally trapped” (bondhardening) states are found. A unequivocal mechanism for “bondsoftening” is provided. It is observed that with an increase in intensity, the lifetime of low vibrational level increases. The mechanism for this novel phenomenon is also explained.

Nitrous oxide dimer: A new potential energy surface and rovibrational spectrum of the nonpolar isomer
View Description Hide DescriptionThe spectrum of nitrous oxide dimer was investigated by constructing new potential energy surfaces using coupledcluster theory and solving the rovibrational Schrödinger equation with a Lanczos algorithm. Two fourdimensional (rigid monomer) global ab initiopotential energy surfaces (PESs) were made using an interpolating moving leastsquares (IMLS) fitting procedure specialized to describe the interaction of two linear fragments. The first exploratory fit was made from 1646 CCSD(T)/3ZaP energies. Isomeric minima and connecting transition structures were located on the fitted surface, and the energies of those geometries were benchmarked using complete basis set (CBS) extrapolations, counterpoise (CP) corrections, and explicitly correlated (F12b) methods. At the geometries tested, the explicitly correlated F12b method produced energies in close agreement with the estimated CBS limit. A second fit to 1757 data at the CCSD(T)F12b/VTZF12 level was constructed with an estimated fitting error of less than . The second surface has a global nonpolar Oin minimum, two Tshaped Nin minima, and two polar minima. Barriers between these minima are small and some wave functions have amplitudes in several wells. Lowlying rovibrational wave functions and energy levels up to about were computed on the F12b PES using a discrete variable representation/finite basis representation method. Calculated rotational constants and intermolecular frequencies are in very close agreement with experiment.