Volume 140, Issue 12, 28 March 2014

The effects of Li2CO3 like species originating from reactions between CO2 and Li2O2 at the cathode of nonaqueous Liair batteries were studied by density functional theory (DFT) and galvanostatic chargedischarge measurements. Adsorption energies of CO2 at various nucleation sites on a stepped Li2O2 surface were determined and even a low concentration of CO2 effectively blocks the step nucleation site and alters the Li2O2 shape due to Li2CO3 formation. Nudged elastic band calculations show that once CO2 is adsorbed on a step valley site, it is effectively unable to diffuse and impacts the Li2O2 growth mechanism, capacity, and overvoltages. The charging processes are strongly influenced by CO2 contamination, and exhibit increased overvoltages and increased capacity, as a result of poisoning of nucleation sites: this effect is predicted from DFT calculations and observed experimentally already at 1% CO2. Large capacity losses and overvoltages are seen at higher CO2 concentrations.
 COMMUNICATIONS


Communication: The influence of CO_{2} poisoning on overvoltages and discharge capacity in nonaqueous LiAir batteries
View Description Hide DescriptionThe effects of Li2CO3 like species originating from reactions between CO2 and Li2O2 at the cathode of nonaqueous Liair batteries were studied by density functional theory (DFT) and galvanostatic chargedischarge measurements. Adsorption energies of CO2 at various nucleation sites on a stepped Li2O2 surface were determined and even a low concentration of CO2 effectively blocks the step nucleation site and alters the Li2O2 shape due to Li2CO3 formation. Nudged elastic band calculations show that once CO2 is adsorbed on a step valley site, it is effectively unable to diffuse and impacts the Li2O2 growth mechanism, capacity, and overvoltages. The charging processes are strongly influenced by CO2 contamination, and exhibit increased overvoltages and increased capacity, as a result of poisoning of nucleation sites: this effect is predicted from DFT calculations and observed experimentally already at 1% CO2. Large capacity losses and overvoltages are seen at higher CO2 concentrations.

Communication: Different behavior of Young's modulus and fracture strength of CeO_{2}: Density functional theory calculations
View Description Hide DescriptionIn this Communication, we use density functional theory (DFT) to examine the fracture properties of ceria (CeO2), which is a promising electrolyte material for lowering the working temperature of solid oxide fuel cells. We estimate the stressstrain curve by fitting the energy density calculated by DFT. The calculated Young's modulus of 221.8 GPa is of the same order as the experimental value, whereas the fracture strength of 22.7 GPa is two orders of magnitude larger than the experimental value. Next, we combine DFT and Griffith theory to estimate the fracture strength as a function of a crack length. This method produces an estimated fracture strength of 0.467 GPa, which is of the same order as the experimental value. Therefore, the fracture strength is very sensitive to the crack length, whereas the Young's modulus is not.

Communication: Selfinteraction correction with unitary invariance in density functional theory
View Description Hide DescriptionStandard spindensity functionals for the exchangecorrelation energy of a manyelectron ground state make serious selfinteraction errors which can be corrected by the PerdewZunger selfinteraction correction (SIC). We propose a sizeextensive construction of SIC orbitals which, unlike earlier constructions, makes SIC computationally efficient, and a true spindensity functional. The SIC orbitals are constructed from a unitary transformation that is explicitly dependent on the noninteracting oneparticle density matrix. When this SIC is applied to the local spindensity approximation, improvements are found for the atomization energies of molecules.

Communication: Resolving the threebody contribution to the lattice energy of crystalline benzene: Benchmark results from coupledcluster theory
View Description Hide DescriptionCoupledcluster theory including single, double, and perturbative triple excitations [CCSD(T)] has been applied to trimers that appear in crystalline benzene in order to resolve discrepancies in the literature about the magnitude of nonadditive threebody contributions to the lattice energy. The present results indicate a nonadditive threebody contribution of 0.89 kcal mol^{−1}, or 7.2% of the revised lattice energy of −12.3 kcal mol^{−1}. For the trimers for which we were able to compute CCSD(T) energies, we obtain a sizeable difference of 0.63 kcal mol^{−1} between the CCSD(T) and MP2 threebody contributions to the lattice energy, confirming that threebody dispersion dominates over threebody induction. Taking this difference as an estimate of threebody dispersion for the closer trimers, and adding an AxilrodTellerMuto estimate of 0.13 kcal mol^{−1} for longrange contributions yields an overall value of 0.76 kcal mol^{−1} for threebody dispersion, a significantly smaller value than in several recent studies.

Communication: Comparing ab initio methods of obtaining effective U parameters for closedshell materials
View Description Hide DescriptionThe density functional theory (DFT)+U method is an efficient and effective way to calculate the groundstate properties of strongly correlated transition metal compounds, with the effective U parameters typically determined empirically. Two ab initio methods have been developed to compute the U parameter based on either constrained DFT (CDFT) or unrestricted HartreeFock (UHF) theory. Previous studies have demonstrated the success of both methods in typical openshell materials such as FeO and NiO. In this Communication we report numerical instability issues that arise for the CDFT method when applied to closedshell transition metals, by using ZnO and Cu 2O as examples. By contrast, the UHF method behaves much more robustly for both closed and openshell materials, making it more suitable for treating closedshell transition metals, as well as main group elements.
 Top

 ARTICLES

 Theoretical Methods and Algorithms

Approximate treatment of semicore states in GW calculations with application to Au clusters
View Description Hide DescriptionWe address the treatment of transition metal atoms in GW electronicstructure calculations within the planewave pseudopotential formalism. The contributions of s and p semicore electrons to the selfenergy, which are essential to grant an acceptable accuracy, are dealt with using a recently proposed scheme whereby the exchange components are treated exactly at the G0W0 level, whereas a suitable approximation to the correlation components is devised. This scheme is benchmarked for small gold nanoclusters, resulting in ionization potentials, electron affinities, and density of states in very good agreement with those obtained from calculations where s and p semicore states are treated as valence orbitals, and allowing us to apply this same scheme to clusters of intermediate size, Au 20 and Au 32, that would be otherwise very difficult to deal with.

Coupled cluster channels in the homogeneous electron gas
View Description Hide DescriptionWe discuss diagrammatic modifications to the coupled cluster doubles (CCD) equations, wherein different groups of terms out of rings, ladders, crossedrings, and mosaics can be removed to form approximations to the coupled cluster method, of interest due to their similarity with various types of random phase approximations. The finite uniform electron gas (UEG) is benchmarked for 14 and 54electron systems at the complete basis set limit over a wide density range and performance of different flavours of CCD is determined. These results confirm that rings generally overcorrelate and ladders generally undercorrelate; mosaicsonly CCD yields a result surprisingly close to CCD. We use a recently developed numerical analysis [J. J. Shepherd and A. Grüneis, Phys. Rev. Lett.110, 226401 (2013)] to study the behaviours of these methods in the thermodynamic limit. We determine that the mosaics, on forming the Brueckner onebody Hamiltonian, open a gap in the effective oneparticle eigenvalues at the Fermi energy. Numerical evidence is presented which shows that methods based on this renormalisation have convergent energies in the thermodynamic limit including mosaiconly CCD, which is just a renormalised MP2. All other methods including only a single channel, namely, ladderonly CCD, ringonly CCD, and crossedringonly CCD, appear to yield divergent energies; incorporation of mosaic terms prevents this from happening.

Two algorithms to compute projected correlation functions in molecular dynamics simulations
View Description Hide DescriptionAn explicit derivation of the MoriZwanzig orthogonal dynamics of observables is presented and leads to two practical algorithms to compute exactly projected observables (e.g., random noise) and projected correlation function (e.g., memory kernel) from a molecular dynamics trajectory. The algorithms are then applied to study the diffusive dynamics of a tagged particle in a LennardJones fluid, the properties of the associated random noise, and a decomposition of the corresponding memory kernel.

A magnetic gradient induced force in NMR restricted diffusion experiments
View Description Hide DescriptionWe predict that the phase cancellation of a precessing magnetisation field carried by a diffusing species in a bounded geometry under certain nuclear magnetic resonance pulsed magnetic field gradient sequences results in a small force over typically micrometre length scales. Our calculations reveal that the total magnetisation energy in a pore under the influence of a pulsed gradient will be distancedependent thus resulting in a force acting on the boundary. It is shown that this effect of the magnetisation of diffusing particles will appear as either an attractive or repulsive force depending on the geometry of the pore and magnetic properties of the material. A detailed analysis is performed for the case of a pulsed gradient spinecho experiment on parallel planes. It is shown that the force decays exponentially in terms of the spinspin relaxation. The proof is based on classical electrodynamics. An application of this effect to soft matter is suggested.

Theoretical volume profiles as a tool for probing transition states: Folding kinetics
View Description Hide DescriptionThe mechanism by which conformational changes, particularly folding and unfolding, occur in proteins and other biopolymers has been widely discussed in the literature. Molecular dynamics (MD) simulations of protein folding present a formidable challenge since these conformational changes occur on a time scale much longer than what can be afforded at the current level of computational technology. Transition state (TS) theory offers a more economic description of kinetic properties of a reaction system by relating them to the properties of the TS, or for flexible systems, the TS ensemble (TSE). The application of TS theory to protein folding is limited by ambiguity in the definition of the TSE for this process. We propose to identify the TSE for conformational changes in flexible systems by comparison of its experimentally determined volumetric property, known as the volume of activation, to the structurespecific volume profile of the process calculated using MD. We illustrate this approach by its successful application to unfolding of a model chain system.

Global solutions of restricted openshell HartreeFock theory from semidefinite programming with applications to strongly correlated quantum systems
View Description Hide DescriptionWe present a density matrix approach for computing global solutions of restricted openshell HartreeFock theory, based on semidefinite programming (SDP), that gives upper and lower bounds on the HartreeFock energy of quantum systems. While wave function approaches to HartreeFock theory yield an upper bound to the HartreeFock energy, we derive a semidefinite relaxation of HartreeFock theory that yields a rigorous lower bound on the HartreeFock energy. We also develop an upperbound algorithm in which HartreeFock theory is cast as a SDP with a nonconvex constraint on the rank of the matrix variable. Equality of the upper and lowerbound energies guarantees that the computed solution is the globally optimal solution of HartreeFock theory. The work extends a previously presented method for closedshell systems [S. Veeraraghavan and D. A. Mazziotti, Phys. Rev. A89, 010502–R (2014)]. For strongly correlated systems the SDP approach provides an alternative to the locally optimized HartreeFock energies and densities with a certificate of global optimality. Applications are made to the potential energy curves of , CN, , and .

Including screening in van der Waals corrected density functional theory calculations: The case of atoms and small molecules physisorbed on graphene
View Description Hide DescriptionThe Density Functional Theory (DFT)/van der WaalsQuantum Harmonic OscillatorWannier function (vdWQHOWF) method, recently developed to include the vdW interactions in approximated DFT by combining the quantum harmonic oscillator model with the maximally localized Wannier function technique, is applied to the cases of atoms and small molecules (X=Ar, CO, H2, H2O) weakly interacting with benzene and with the ideal planar graphene surface. Comparison is also presented with the results obtained by other DFT vdWcorrected schemes, including PBE+D, vdWDF, vdWDF2, rVV10, and by the simpler Local Density Approximation (LDA) and semilocal generalized gradient approximation approaches. While for the Xbenzene systems all the considered vdWcorrected schemes perform reasonably well, it turns out that an accurate description of the Xgraphene interaction requires a proper treatment of manybody contributions and of shortrange screening effects, as demonstrated by adopting an improved version of the DFT/vdWQHOWF method. We also comment on the widespread attitude of relying on LDA to get a rough description of weakly interacting systems.

Goaloriented sensitivity analysis for lattice kinetic Monte Carlo simulations
View Description Hide DescriptionIn this paper we propose a new class of coupling methods for the sensitivity analysis of high dimensional stochastic systems and in particular for lattice Kinetic Monte Carlo (KMC). Sensitivity analysis for stochastic systems is typically based on approximating continuous derivatives with respect to model parameters by the mean value of samples from a finite difference scheme. Instead of using independent samples the proposed algorithm reduces the variance of the estimator by developing a strongly correlated“coupled” stochastic process for both the perturbed and unperturbed stochastic processes, defined in a common state space. The novelty of our construction is that the new coupled process depends on the targeted observables, e.g., coverage, Hamiltonian, spatial correlations, surface roughness, etc., hence we refer to the proposed method as goaloriented sensitivity analysis. In particular, the rates of the coupled Continuous Time Markov Chain are obtained as solutions to a goaloriented optimization problem, depending on the observable of interest, by considering the minimization functional of the corresponding variance. We show that this functional can be used as a diagnostic tool for the design and evaluation of different classes of couplings. Furthermore, the resulting KMC sensitivity algorithm has an easy implementation that is based on the Bortz–Kalos–Lebowitz algorithm's philosophy, where events are divided in classes depending on level sets of the observable of interest. Finally, we demonstrate in several examples including adsorption, desorption, and diffusion Kinetic Monte Carlo that for the same confidence interval and observable, the proposed goaloriented algorithm can be two orders of magnitude faster than existing coupling algorithms for spatial KMC such as the Common Random Number approach. We also provide a complete implementation of the proposed sensitivity analysis algorithms, including various spatial KMC examples, in a supplementary MATLAB source code.

Adaptive tworegime method: Application to front propagation
View Description Hide DescriptionThe Adaptive TwoRegime Method (ATRM) is developed for hybrid (multiscale) stochastic simulation of reactiondiffusion problems. It efficiently couples detailed Brownian dynamics simulations with coarser latticebased models. The ATRM is a generalization of the previously developed TwoRegime Method [Flegg et al. , J. R. Soc., Interface9, 859 (2012)] to multiscale problems which require a dynamic selection of regions where detailed Brownian dynamics simulation is used. Typical applications include a front propagation or spatiotemporal oscillations. In this paper, the ATRM is used for an indepth study of front propagation in a stochastic reactiondiffusion system which has its meanfield model given in terms of the Fisher equation [R. Fisher, Ann. Eugen.7, 355 (1937)]. It exhibits a travelling reaction front which is sensitive to stochastic fluctuations at the leading edge of the wavefront. Previous studies into stochastic effects on the Fisher wave propagation speed have focused on latticebased models, but there has been limited progress using offlattice (Brownian dynamics) models, which suffer due to their high computational cost, particularly at the high molecular numbers that are necessary to approach the Fisher meanfield model. By modelling only the wavefront itself with the offlattice model, it is shown that the ATRM leads to the same Fisher wave results as purely offlattice models, but at a fraction of the computational cost. The error analysis of the ATRM is also presented for a morphogen gradient model.

Mechanochemical coupling in BelousovZhabotinskii reactions
View Description Hide DescriptionMechanochemical coupling has been recently recognised as an important effect in various systems as chemical reactivity can be controlled through an applied mechanical loading. Namely, BelousovZhabotinskii reactions in polymer gels exhibit selfsustained oscillations and have been identified to be reasonably controllable and definable to the extent that they can be harnessed to perform mechanical work at specific locations. In this paper, we use our theoretical work of nonlinear mechanochemical coupling and investigate the possibility of providing an explanation of phenomena found in experimental research by means of this theory. We show that mechanotransduction occurs as a response to both static and dynamic mechanical stimulation, e.g., volume change and its rate, as observed experimentally and discuss the difference of their effects on oscillations. Plausible values of the quasistoichiometric parameter f of Oregonator model are estimated together with its dependence on mechanical stimulation. An increase in static loading, e.g., pressure, is predicted to have stimulatory effect whereas dynamic loading, e.g., rate of volume change, is predicted to be stimulatory only up to a certain threshold. Further, we offer a physically consistent explanation of the observed phenomena why some BelousovZhabotinskii gels require an additional mechanical stimulation to show emergence of oscillation or why “revival” of oscillations in BelousovZhabotinskii reactions is possible together with indications for further experimental setups.

Electronic quantum effects mapped onto nonBornOppenheimer nuclear paths: Nonclassical surmounting over potential barriers and trapping above the transition states due to nonadiabatic pathbranching
View Description Hide DescriptionWe develop the pathbranching representation for nonadiabatic electron wavepacket dynamics [T. Yonehara and K. Takatsuka, J. Chem. Phys.132, 244102 (2010)] so as to treat dynamics in an energy range comparable to the barrier height of adiabatic potential energy curves. With this representation two characteristic chemical reaction dynamics are studied, in which an incident nuclear wavepacket encounters a potential barrier, on top of which lies another nonadiabatically coupled adiabatic potential curve: (1) Dynamics of initial paths coming into the nonadiabatic interaction region with energy lower than the barrier height. They branch into two pieces (and repeat branching subsequently), the upper counterparts of which can penetrate into a classically inaccessible high energy region and eventually branch back to the product region on the ground state curve. This is so to say surmounting the potential barrier via nonadiabatically coupled excited state, and phenomenologically looks like the socalled deep tunneling. (2) Dynamics of classical paths whose initial energies are a little higher than the barrier but may be lower than the bottom of the excited state. They can undergo branching and some of those components are trapped on top of the potential barrier, being followed by the population decay down to the lower state flowing both to product and reactant sites. Such expectations arising from the pathbranching representation are numerically confirmed with full quantum mechanical wavepacket dynamics. This phenomenon may be experimentally observed as timedelayed pulses of wavepacket trains.

Gaussian approximations for stochastic systems with delay: Chemical Langevin equation and application to a Brusselator system
View Description Hide DescriptionWe present a heuristic derivation of Gaussian approximations for stochastic chemical reaction systems with distributed delay. In particular, we derive the corresponding chemical Langevin equation. Due to the nonMarkovian character of the underlying dynamics, these equations are integrodifferential equations, and the noise in the Gaussian approximation is coloured. Following on from the chemical Langevin equation, a further reduction leads to the linearnoise approximation. We apply the formalism to a delay variant of the celebrated Brusselator model, and show how it can be used to characterise noisedriven quasicycles, as well as noisetriggered spiking. We find surprisingly intricate dependence of the typical frequency of quasicycles on the delay period.

Timedependent potentialfunctional embedding theory
View Description Hide DescriptionWe introduce a timedependent potentialfunctional embedding theory (TDPFET), in which atoms are grouped into subsystems. In TDPFET, subsystems can be propagated by different suitable timedependent quantum mechanical methods and their interactions can be treated in a seamless, firstprinciples manner. TDPFET is formulated based on the timedependent quantum mechanics variational principle. The action of the total quantum system is written as a functional of the timedependent embedding potential, i.e., a potentialfunctional formulation. By exploiting the RungeGross theorem, we prove the uniqueness of the timedependent embedding potential under the constraint that all subsystems share a common embedding potential. We derive the integral equation that such an embedding potential needs to satisfy. As proofofprinciple, we demonstrate TDPFET for a Na 4 cluster, in which each Na atom is treated as one subsystem and propagated by timedependent KohnSham density functional theory (TDDFT) using the adiabatic local density approximation (ALDA). Our results agree well with a direct TDDFT calculation on the whole Na 4 cluster using ALDA. We envision that TDPFET will ultimately be useful for studying ultrafast quantum dynamics in condensed matter, where key regions are solved by highly accurate timedependent quantum mechanics methods, and unimportant regions are solved by faster, less accurate methods.

Adaptive multiconfigurational wave functions
View Description Hide DescriptionA method is suggested to build simple multiconfigurational wave functions specified uniquely by an energy cutoff Λ. These are constructed from a model space containing determinants with energy relative to that of the most stable determinant no greater than Λ. The resulting ΛCI wave function is adaptive, being able to represent both singlereference and multireference electronic states. We also consider a more compact wave function parameterization (Λ+SDCI), which is based on a small ΛCI reference and adds a selection of all the singly and doubly excited determinants generated from it. We report two heuristic algorithms to build ΛCI wave functions. The first is based on an approximate prescreening of the full configuration interaction space, while the second performs a breadthfirst search coupled with pruning. The ΛCI and Λ+SDCI approaches are used to compute the dissociation curve of N2 and the potential energy curves for the first three singlet states of C2. Special attention is paid to the issue of energy discontinuities caused by changes in the size of the ΛCI wave function along the potential energy curve. This problem is shown to be solvable by smoothing the matrix elements of the Hamiltonian. Our last example, involving the Cu 2 core, illustrates an alternative use of the ΛCI method: as a tool to both estimate the multireference character of a wave function and to create a compact model space to be used in subsequent highlevel multireference coupled cluster computations.
 Advanced Experimental Techniques

Mechanism of dilutespinexchange in solidstate NMR
View Description Hide DescriptionIn the stationary, aligned samples used in oriented sample (OS) solidstate NMR, ^{1}H^{1}H homonuclear dipolar couplings are not attenuated as they are in magic angle spinning solidstate NMR; consequently, they are available for participation in dipolar couplingbased spinexchange processes. Here we describe analytically the pathways of ^{15}N^{15}N spinexchange mediated by ^{1}H^{1}H homonuclear dipolar couplings. The mixedorder protonrelay mechanism can be differentiated from the third spin assisted recoupling mechanism by setting the ^{1}H to an offresonance frequency so that it is at the “magic angle” during the spinexchange interval in the experiment, since the “magic angle” irradiation nearly quenches the former but only slightly attenuates the latter. Experimental spectra from a single crystal of Nacetyl leucine confirm that this protonrelay mechanism plays the dominant role in ^{15}N^{15}N dilutespinexchange in OS solidstate NMR in crystalline samples. Remarkably, the “forbidden” spinexchange condition under “magic angle” irradiation results in ^{15}N^{15}N crosspeaks intensities that are comparable to those observed with onresonance irradiation in applications to proteins. The mechanism of the proton relay in dilutespinexchange is crucial for the design of polarization transfer experiments.