Volume 132, Issue 7, 21 February 2010

We discuss the electrochemicalreactions at the oxygen electrode of an aprotic Liair battery. Using density functional theory to estimate the free energy of intermediates during the discharge and charge of the battery, we introduce a reactionfree energy diagram and identify possible origins of the overpotential for both processes. We also address the question of electron conductivity through the electrode and show that in the presence of Li vacancies becomes a conductor.
 COMMUNICATIONS


Communications: Elementary oxygen electrode reactions in the aprotic Liair battery
View Description Hide DescriptionWe discuss the electrochemicalreactions at the oxygen electrode of an aprotic Liair battery. Using density functional theory to estimate the free energy of intermediates during the discharge and charge of the battery, we introduce a reactionfree energy diagram and identify possible origins of the overpotential for both processes. We also address the question of electron conductivity through the electrode and show that in the presence of Li vacancies becomes a conductor.
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 ARTICLES

 Theoretical Methods and Algorithms

The diffusive finite state projection algorithm for efficient simulation of the stochastic reactiondiffusion master equation
View Description Hide DescriptionWe have developed a computational framework for accurate and efficient simulation of stochastic spatially inhomogeneous biochemical systems. The new computational method employs a fractional step hybrid strategy. A novel formulation of the finite state projection (FSP) method, called the diffusive FSP method, is introduced for the efficient and accurate simulation of diffusive transport. Reactions are handled by the stochastic simulation algorithm.

Multireference study of spinorbit coupling in the hydrides of the 6pblock elements using the model core potential method
View Description Hide DescriptionCareful spinorbit multireference studies were carried out for the late pblock elements Tl, Pb, Bi, Po, At, and Rn and their hydrides using the model core potentials developed in the present work. The model core potentials were designed to treat the scalarrelativistic and spinorbit coupling effects at the Douglas–Kroll level. The variational stability of the spinorbit coupling operator was discussed in terms of the relativistic kinematic operators and depicted graphically. A detailed analysis of the spinorbit multireference dissociation curves of the 6p element hydrides as well as of their atomic spectra allowed to establish the accuracy of the model core potentials with respect to allelectron calculations to be within several mÅ for , meV (ceV) for at the correlation level of configuration interaction (multireference perturbation theory), for , and about for the lowlying atomic and molecular term and level energies. These values are expected to be the maximum error limits for the model core potentials of all the block elements . Furthermore, a good agreement with experiment requires that many terms be coupled in the spinorbit coupling calculations. A timing study of Tl and TlH computations indicates that the model core potentials lead to 20fold (6fold) speedup at the level of configuration interaction (multireference perturbation theory) calculations.

Full implementation and benchmark studies of Mukherjee’s statespecific multireference coupledcluster ansatz
View Description Hide DescriptionThe statespecific multireference coupledcluster (SSMRCC) ansatz developed by Mukherjee and coworkers [J. Chem. Phys.110, 6171 (1999)] has been implemented by means of stringbased techniques. The implementation is general and allows for using arbitrary complete active spaces of any spin multiplicity and arbitrarily high excitations in the cluster operators. Several test calculations have been performed for single and multiplebond dissociations of molecular systems. Our experience shows that convergence problems are encountered when solving the working equations of the SSMRCC in the case the weight of one or more reference functions tends to take on very small values. This is system specific and cannot yet be handled in a blackbox fashion. The problem can be obviated by either dropping all the cluster amplitudes from the corresponding model functions with coefficients below a threshold or by a regularization procedure suggested by Tikhonov or a combination of both. In the current formulation the SSMRCC is not invariant with respect to transformation of active orbitals among themselves. This feature has been extensively explored to test the degree of accuracy of the computed energies with both pseudocanonical and localized active orbitals. The performance of the method is assessed by comparing the results with the corresponding full configuration interaction (CI) values with the same set of orbitals (correlated and frozen). Relative efficacies of CI methods such as MRCI singles and doubles with the same active space and sizeextensivity corrected ones such as MR averaged coupled pair functional and MR averaged quadratic CC have also been studied. Allied fullfledged CC methods have also been employed to see their relative performance visàvis the SSMRCC. These latter methods are the completeactivespaceinspired singlereference (SR) CC based SS theory and the singleroot MR Brillouin–Wigner CC. Our benchmark results indicate that the performance of the SSMRCC is generally quite good for localized active orbitals. The performance with the pseudocanonical orbitals, however, is sometimes not as satisfactory as for the localized orbitals.

Cholesky decomposition within local multireference singles and doubles configuration interaction
View Description Hide DescriptionA local multireference singles and doubles configuration interaction method in which Cholesky vectors are used in place of conventional twoelectron integrals has been developed (CDLMRSDCI). To reduce the overall cost associated with our linear scaling LMRSDCI method presented earlier [T. S. Chwee et al., J. Chem. Phys.128, 224106 (2008)], we adopt a twopronged approach. First, localized orthogonal virtual orbitals, introduced by Subotnik et al. [J. Chem. Phys.123, 114108 (2005)], are substituted for nonorthogonal projected atomic orbitals. This obviates the need for contraction with overlap matrices and simplifies our working formalism. In addition, we restructure the ratelimiting step of our LMRSDCI algorithm to be driven by the search for twoelectron integrals instead of configuration state functions. The shift necessitates a flexible way of processing the fourindexed twoelectron integrals, which is facilitated by use of twoindexed Cholesky vectors. Our restructured LMRSDCI method is an order of magnitude faster and has greatly reduced storage requirements so that we are able to apply it to molecules containing up to 50 heavy atoms. However, generation of the Cholesky vectors and their subsequent transformation to the molecular orbital (MO) basis is not linear scaling. Together with assembling the MO integrals from the Cholesky vectors, these now constitute the ratelimiting steps in our method.

Longlasting molecular alignment: Fact or fiction?
View Description Hide DescriptionIt has been suggested that appropriate periodic sequences of laser pulses can maintain molecular alignment for arbitrarily long times [J. Ortigoso, Phys. Rev. Lett.93, 073001 (2004)]. These aligned states are found among the cyclic eigenstates of truncated matrix representations of the oneperiod time propagator . However, long time localization of periodic driven systems depends on the nature of the spectrum of their exact propagator; if it is continuous, eigenstates of finitebasis propagators cease to be cyclic, in the long time limit, under the exact time evolution. We show that, for very weak laser intensities, the evolution operator of the system has a point spectrum for most laser frequencies, but for the laser powers needed to create aligned wave packets it is unknown if has a point spectrum or a singular continuous spectrum. For this regime, we obtain error bounds on the exact time evolution of rotational wave packets that allow us to determine that truncated aligned cyclic states do not lose their alignment for millions of rotational periods when they evolve under the action of the exact time propagator.

Decoherence and quantumclassical dynamics in a dissipative bath
View Description Hide DescriptionThe dynamics of a mixed quantumclassical system, in which the classical subsystem interacts with a dissipative bath, is investigated. This description of the dynamics will be appropriate if the details of the bath dynamics are unimportant but its presence plays an important role in the dissipation of energy to the environment. In this dynamical description, which can be simulated employing an ensemble of stochastic surfacehopping trajectories, the strength of the dissipation is controlled by a friction coefficient. We show that if decoherence, whose effects are controlled by the bath friction, is sufficiently rapid, the equation of motion can be reduced to a master equation. Thus, decoherence and the validity of master equationmodels may be explored as a function of bath friction. We use this framework to study the mechanism of decoherence in a simple modelnonadiabatic chemical reaction.

Perturbative triples corrections in statespecific multireference coupled cluster theory
View Description Hide DescriptionWe formulated and implemented a perturbative triples correction for the statespecific multireference coupled cluster approach with singles and doubles suggested by Mukherjee and coworkers, MkMRCCSD [Mol. Phys.94, 157 (1998)]. Our derivation of the energy correction [MkMRCCSD(T)] is based on a constrained search for stationary points of the MkMRCC energy functional together with a perturbative expansion with respect to the appearing triples cluster operator. The MkMRCCSD(T) approach derived in this way consists in (1) a correction to the offdiagonal matrix elements of the effective Hamiltonian which is unique to coupled cluster methods based on the Jeziorski–Monkhorst ansatz, and (2) an asymmetric energy correction to the diagonal elements of the effective Hamiltonian. The MkMRCCSD(T) correction is obtained from the MkMRCCSD(T) method by approximating the singles and doubles Lagrange multipliers with the corresponding cluster amplitudes. We investigate the performance of the MkMRCCSD(T) method by applying it to the potential energy curve of the model and and the geometry and harmonic vibrational frequencies of ozone. Computation of the energy difference between the mono and bicyclic forms of the 2,6pyridyne diradical illustrates the potential of MkMRCCSD(T) as a tool for the study of realistic chemical problems requiring multireference zerothorder wave functions.

A new analytical potential energy surface for the adsorption system CO/Cu(100)
View Description Hide DescriptionElectronic structure data and analytical representations of the potential energy surface for the adsorption of carbon monoxide on a crystalline copper Cu(100) substrate are reviewed. It is found that a previously published and widely used analytical hypersurface for this process [J. C. Tully, M. Gomez, and M. HeadGordon, J. Vac. Sci. Technol. A11, 1914 (1993)] represents rather poorly the data obtained from a slab type calculation of the electronic structure. A new, global analytical representation of the potential energy surface for this process is derived via a nonlinear adjustment of parameters. It is more general and fits qualitatively better the electronic structure data. Key characteristic elements of the new surface are the “top” equilibrium adsorption site in the perpendicular arrangement Cu–C–O with Cu–C and C–O distances of 184 and 115 pm, the desorption energy of 0.76 eV and the barrier for lateral diffusion of 33 meV, including approximative corrections for the variation of zero point energy. Anharmonic vibrational fundamentals and overtones are also calculated from six dimensional variational calculations. All these values agree equally well or better with experimental data than previous published theoretical data within estimated uncertainties. The analytical representation is compact and robust, and may be used to describe other adsorption processes of diatomic molecules, including dissociative chemisorption.

Accurate ab initio potential energy curve of . I. Nonrelativistic full configuration interaction valence correlation by the correlation energy extrapolation by intrinsic scaling method
View Description Hide DescriptionThe recently introduced method of correlationenergy extrapolation by intrinsic scaling is used to calculate the nonrelativistic electron correlations in the valence shell of the molecule at 24 internuclear distances along the ground state potential energy curve from 0.9 to 6 Å, the equilibrium distance being 1.207 52 Å. Using Dunning’s correlationconsistent triple and quadruplezeta basis sets, the full configuration interaction energies are determined, with an accuracy of about 0.3 mhartree, by successively generating up to sextuple excitations with respect to multiconfigurational reference functions that strongly change along the reaction path. The energies of the reference functions and those of the correlationenergies with respect to these reference functions are then extrapolated to their complete basis set limits.

Comparing geometric and kinetic cluster algorithms for molecular simulation data
View Description Hide DescriptionThe identification of metastable states of a molecule plays an important role in the interpretation of molecular simulation data because the freeenergysurface, the relative populations in this landscape, and ultimately also the dynamics of the molecule under study can be described in terms of these states. We compare the results of three different geometriccluster algorithms (neighbor algorithm, Kmedoids algorithm, and commonnearestneighbor algorithm) among each other and to the results of a kinetic cluster algorithm. First, we demonstrate the characteristics of each of the geometriccluster algorithms using five twodimensional data sets. Second, we analyze the molecular dynamics data of a heptapeptide in methanol—a molecule that exhibits a distinct folded state, a structurally diverse unfolded state, and a fast folding/unfolding equilibrium—using both geometric and kinetic cluster algorithms. We find that geometricclustering strongly depends on the algorithm used and that the density based commonnearestneighbor algorithm is the most robust of the three geometriccluster algorithms with respect to variations in the input parameters and the distance metric. When comparing the geometriccluster results to the metastable states of the heptapeptide as identified by kinetic clustering, we find that in most cases the folded state is identified correctly but the overlap of geometricclusters with further metastable states is often at best approximate.

Fluid phase coexistence and critical behavior from simulations in the restricted Gibbs ensemble
View Description Hide DescriptionThe symmetrical restricted Gibbs ensemble (RGE) is a version of the Gibbs ensemble in which particles are exchanged between two boxes of fixed equal volumes. It has recently come to prominence because—when combined with specialized algorithms—it provides for the study of nearcoexistence density fluctuations in highly sizeasymmetric binary mixtures. Hitherto, however, a detailed framework for extracting accurate estimates of critical point and coexistence curve parameters from RGE density fluctuations has been lacking. Here we address this problem by exploiting an exact link between the RGE density fluctuations and those of the grand canonical ensemble. In the subcritical region we propose and test a simple method for obtaining accurate estimates of coexistence densities. In the critical region we identify an observable that serves as a finite system size estimator for the critical point parameters, and present a finitesize scaling theory that allows extrapolation to the thermodynamic limit.

Combining ab initio quantum mechanics with a dipolefield model to describe acid dissociation reactions in water: Firstprinciples free energy and entropy calculations
View Description Hide DescriptionWe introduce a novel approach to compute dissociationfree energy and entropy values in simulations that employ a density functional theory description of the acidic moiety and of the solvent. The approach consists of utilizing an alchemical transformation of a weak acid ACOOH into the strong acid BCOOH, which makes it practical to employ alchemical free energy perturbation methods in the context of ab initiomolecular dynamics simulations. The present alchemical transformation circumvents the need to tackle changes in the total number of electrons and atoms by replacing the chemical residue responsible for the change in acidity with an easily tunable external effective potential. Our investigation demonstrates that (1) a simple but effective class of external potentials that control acidity changes in the acetic/trifluoroacetic acid series can be achieved by replacing the methyl and trifluoromethyl substituents by screened dipoles. Using this dipolefield/quantummechanics (DF/QM) approach one can predict gasphase geometries, protondissociation energies, total dipole moments, and water binding energies in good agreement with fullQM values. (2) The resulting alchemical perturbation calculations are stable and well converged and allow one to compute absolute values whose accuracy is limited primarily by the exchangecorrelation functional employed: (fullQM calculation), 3.7 (exp); (DF/QM calculation), 0.5 (exp); (DF/QM calculation), 4.7 (exp); 3) Our DF/QM model predicts that the difference in acidity between H–COOH and is dominated by solvententropy effects, in excellent agreement with experimental observations. The calculated difference between the dissociation energies of these acids is while the experimental value is .
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Dipole oscillator strength distributions with improved highenergy behavior: Dipole sum rules and dispersion coefficients for Ne, Ar, Kr, and Xe revisited
View Description Hide DescriptionThe construction of the dipole oscillator strength distribution (DOSD) from theoretical and experimental photoabsorption cross sections combined with constraints provided by the Kuhn–Reiche–Thomas sum rule and molar refractivity data is a wellestablished technique that has been successfully applied to more than 50 species. Such DOSDs are insufficiently accurate at large photonenergies. A novel iterative procedure is developed that rectifies this deficiency by using the highenergy asymptotic behavior of the dipole oscillator strength density as an additional constraint. Pilot applications are made for the neon, argon, krypton, and xenon atoms. The resulting DOSDs improve the agreement of the predicted and sum rules with ab initio calculations while preserving the accuracy of the remainder of the moments. Our DOSDs exploit new and more accurate experimental data. Improved estimates of dipole properties for these four atoms and of dipoledipole and tripledipole dispersion coefficients for the interactions among them are reported.

Rotation of methane and silane molecules in He droplets
View Description Hide DescriptionThis work studies the renormalization of the molecular moments of inertia in liquid helium. For this purpose we have measured the rotationalvibrational spectra of the modes of a series of homologous light spherical top molecules such as , , , and in He droplets. The spectra were fitted to an empirical gas phase Hamiltonian, yielding a set of spectroscopic constants. We found that the additional moment of inertia, , scales approximately as square of . This is in agreement with the theoretical model which assigns to coupling of molecular rotation with vibration of He in the molecular vicinity. Our results also indicate a large increase in the effective centrifugal distortion constants, which is another manifestation of the interaction of the molecular rotors with the He environment. Finally, the mechanism of the relaxation of rotational energy in liquid helium is discussed.

The ground state van der Waals potentials of the strontium dimer and strontium raregas complexes
View Description Hide DescriptionThe entire ground state potential energy curve of the strontium dimer is accurately described by the Tang–Toennies potential model defined by the three dispersion coefficients and two well parameters. The predicted vibrational frequency, anharmonicity, and vibrationrotation coupling constant are in excellent agreement with experiment. The reduced potential is almost identical to that of and , providing further evidence to the conjecture that the van der Waals dimer potentials of group IIA and group IIB elements have the same shape, which is different from that of raregas dimers. The potentials of SrRG complexes are generated by the same potential model with its parameters calculated with combining rules. These potentials are shown to have the same shape which is between that of the strontium and raregas dimers.

Modeling disequilibrium in gas ensembles: How quantum state populations evolve under multicollision conditions; , CO, , and
View Description Hide DescriptionThe method of Marsh and McCaffery [J. Chem. Phys.117, 503 (2002)] is used to quantify how rovibrational populations and mode temperatures change as an ensemble of CO molecules, initially excited to , evolves to thermal equilibrium in a bath gas. The bath gases considered are Ar, , , and CO all at 300 K with the diatomics in their (0;8) rovibrational states. Ensembles generally contain 1000 molecules, 10% of which are excited CO molecules. State (v;j) populations and mode temperatures of and bath molecules are calculated for successive collisions to 1000 or more. We find that relaxation to local thermodynamic equilibrium occurs in distinct phases that vary widely in rate of cooling. There is especially fast vibrationvibration (VV) exchange in mixtures that is largely decoupled from rotation and translation. Several aspects of ensemble behavior may be rationalized using concepts established in quantum state resolved single collision studies. We demonstrate the existence of a simultaneous energy quasiresonant, angular momentum conserving, low VV process that can cause either ultrafast relaxation or up pumping of the kind seen in a number of experiments.

Intensityresolved IR multiple photon ionization and fragmentation of
View Description Hide DescriptionThe sequential absorption of multiple infrared (IR) photons by isolated gasphase species can lead to their dissociation and/or ionization. Using the newly constructed “FreeElectron Laser for IntraCavity Experiments” (FELICE) beam line at the FELIX facility, neutral molecules have been exposed to an extremely high number of for a total time duration of up to . At wavelengths around , resonant with allowed IR transitions of , ionization and extensive fragmentation of the fullerenes are observed. The resulting photofragment distributions are attributed to absorption in fragmentation products formed once is excited to internal energies at which fragmentation or ionization takes place within the duration of the laser pulse. The high IR intensities available combined with the large interaction volume permit spatially resolved detection of the ions inside the laser beam, thereby disentangling the contributions from different IR intensities. The use of spatial imaging reveals intensity dependent mass distributions that are substantially narrower than what has been observed previously, indicating rather narrow energy distributions. A simple rateequation modeling of the excitation process supports the experimental observations.

Electron scattering at high momentum transfer from methane: Analysis of line shapes
View Description Hide DescriptionThe measurement of the energy distribution of keV electrons backscattered elastically from molecules reveals one or more peaks. These peaks are at nonzero energy loss and have an intrinsic width. The usual interpretation of these measurements is attractively simple and assumes billiardballtype collisions between the electron and a specific atom in the molecule, and the scattering atom is assumed to behave as a free particle. The peak position is then related to the mass of the scattering atom, and its width is a Compton profile of the momentum distribution of this atom in the molecule. Here we explore the limits of the validity of this picture for the case of electrons scattering from methane. The biggest discrepancy is found for electrons scattering from carbon. For electrons scattering from hydrogen the effects are substantial at relatively low incoming energies and appear to decrease with increasing momentum transfer. The discrepancy is analyzed in terms of the force the atom experiences near the equilibrium position.

Accurate ab initio potential energy curve of . II. Corevalence correlations, relativistic contributions, and vibrationrotation spectrum
View Description Hide DescriptionIn the first paper of this series, a very accurate ab initio potential energy curve of the ground state of has been determined in the approximation that all valence shell electron correlations were calculated at the complete basis set limit. In the present study, the corrections arising from core electron correlations and relativity effects, viz., spinorbit coupling and scalar relativity, are determined and added to the potential energy curve. From the 24 points calculated on this curve, an analytical expression in terms of eventempered Gaussian functions is determined and, from it, the vibrational and rotational energy levels are calculated by means of the discrete variable representation. We find 42 vibrational levels. Experimental data (from the Schumann–Runge band system) only yield the lowest 36 levels due to significant reduction in the transition intensities of higher levels. For the 35 term values G(v), the mean absolute deviation between theoretical and experimental data is . The dissociation energy with respect to the lowest vibrational energy is calculated within of the experimental value of . The theoretical crossing between the state and the state is found to occur at 2.22 Å and the spinorbit coupling in this region is analyzed.