Volume 136, Issue 6, 14 February 2012

The structural and energetic properties of purely siliceous, proton, and Cu and Coexchanged chabazite have been studied using periodic densityfunctional (DFT) calculations with both conventional gradientcorrected exchangecorrelation functionals and hybrid functionals mixing exact (i.e., HartreeFock) and DFT exchange. Spinpolarized and fixedmoment calculations have been performed to determine the equilibrium and excited spinconfigurations of the metalexchanged chabazites. For the purely siliceous chabazite, hybrid functionals predict a slightly more accurate cell volume and lattice geometry. For isolated Al/Si substitution sites, gradientcorrected functionals predict that the lattice distortion induced by the substitution preserves the local tetrahedral symmetry, whereas hybrid functionals lead to a distorted Al coordination with two short and two long AlO bonds. Hybrid functionals yield a stronger cationframework binding that conventional functionals in metalexchanged zeolites, they favor shorter cationoxygen bonds and eventually also a higher coordination of the cation. Both types of functionals predict the same spin in the groundstate. The structural optimization of the excited spinstates shows that the formation of a highspin configuration leads to a strong lattice relaxation and a weaker cationframework bonding. For both Cu and Coexchanged chabazite, the prediction of a preferred location of the cation in a sixmembered ring of the zeolite agrees with experiment, but the energy differences between possible cation locations and the lattice distortion induced by the Al/Si substitution and the bonding of the cation depends quite significantly on the choice of the functional. All functionals predict similar energy differences for excited spin states. Spinexcitations are shown to be accompanied by significant changes in the cation coordination, which are more pronounced with hybrid functionals. The consequences of electronic spectra and chemical reactivity are analyzed in the following papers.
 COMMUNICATIONS


Communication: Angleresolved thermal dissociative sticking of CH_{4} on Pt(111): Further indication that rotation is a spectator to the gassurface reaction dynamics
View Description Hide DescriptionEffusive molecular beam measurements of angleresolved thermal dissociative sticking coefficients for CH_{4} impinging on a Pt(111) surface, at a temperature of 700 K, are reported and compared to theoretical predictions. The reactivity falls off steeply as the molecular angle of incidence increases away from the surface normal. Successful modeling of the thermal dissociative sticking behavior, consistent with existent CH_{4} supersonic molecular beamexperiments involving rotationally cold molecules, required that rotation be treated as a spectator degree of freedom.

Communication: Thermodynamics of condensed matter with strong pressureenergy correlations
View Description Hide DescriptionWe show that for any liquid or solid with strong correlation between its NVT virial and potentialenergy equilibrium fluctuations, the temperature is a product of a function of excess entropy per particle and a function of density, T = f(s)h(ρ). This implies that (1) the system's isomorphs (curves in the phase diagram of invariant structure and dynamics) are described by h(ρ)/T = Const., (2) the densityscaling exponent is a function of density only, and (3) a Grüneisentype equation of state applies for the configurational degrees of freedom. For strongly correlating atomic systems one has h(ρ) = ∑_{ n } C _{ n }ρ^{ n/3} in which the only nonzero terms are those appearing in the pair potential expanded as v(r) = ∑_{ n } v _{ n } r ^{−n }. Molecular dynamics simulations of LennardJones type systems confirm the theory.
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 ARTICLES

 Theoretical Methods and Algorithms

Accurate thermochemistry from a parameterized coupledcluster singles and doubles model and a local pair natural orbital based implementation for applications to larger systems
View Description Hide DescriptionWe have recently introduced a parameterized coupledcluster singles and doubles model (pCCSD(α, β)) that consists of a bivariate parameterization of the CCSD equations and is inspired by the coupled electron pair approximations. In our previous work, it was demonstrated that the pCCSD(−1, 1) method is an improvement over CCSD for the calculation of geometries, harmonic frequencies, and potential energy surfaces for single bondbreaking. In this paper, we find suitable pCCSD parameters for applications in reactionthermochemistry and thermochemical kinetics. The motivation is to develop an accurate and economical methodology that, when coupled with a robust local correlation framework based on localized pair natural orbitals, is suitable for largescale thermochemical applications for sizeable molecular systems. It is demonstrated that the original pCCSD(−1, 1) method and several other pCCSD methods are a significant improvement upon the standard CCSD approach and that these methods often approach the accuracy of CCSD(T) for the calculation of reaction energies and barrier heights. We also show that a local version of the pCCSD methodology, implemented within the local pair natural orbital (LPNO) based CCSD code in ORCA, is sufficiently accurate for widescale chemical applications. The LPNO based methodology allows us for routine applications to intermediate sized (20–100 atoms) molecular systems and is a significantly more accurate alternative to MP2 and density functional theory for the prediction of reaction energies and barrier heights.

Revised selfconsistent continuum solvation in electronicstructure calculations
View Description Hide DescriptionThe solvation model proposed by Fattebert and Gygi [J. Comput. Chem.23, 662 (2002)10.1002/jcc.10069] and Scherlis et al. [J. Chem. Phys.124, 074103 (2006)10.1063/1.2168456] is reformulated, overcoming some of the numerical limitations encountered and extending its range of applicability. We first recast the problem in terms of induced polarization charges that act as a direct mapping of the selfconsistent continuum dielectric; this allows to define a functional form for the dielectric that is well behaved both in the highdensity region of the nuclear charges and in the lowdensity region where the electronic wavefunctions decay into the solvent. Second, we outline an iterative procedure to solve the Poisson equation for the quantum fragment embedded in the solvent that does not require multigrid algorithms, is trivially parallel, and can be applied to any Bravais crystallographic system. Last, we capture some of the nonelectrostatic or cavitation terms via a combined use of the quantum volume and quantum surface [M. Cococcioni, F. Mauri, G. Ceder, and N. Marzari, Phys. Rev. Lett.94, 145501 (2005)10.1103/PhysRevLett.94.145501] of the solute. The resulting selfconsistent continuum solvation model provides a very effective and compact fit of computational and experimental data, whereby the static dielectric constant of the solvent and one parameter allow to fit the electrostatic energy provided by the polarizable continuum model with a mean absolute error of 0.3 kcal/mol on a set of 240 neutral solutes. Two parameters allow to fit experimental solvation energies on the same set with a mean absolute error of 1.3 kcal/mol. A detailed analysis of these results, broken down along different classes of chemical compounds, shows that several classes of organic compounds display very high accuracy, with solvation energies in error of 0.30.4 kcal/mol, whereby larger discrepancies are mostly limited to selfdissociating species and strong hydrogenbondforming compounds.

A neural network potentialenergy surface for the water dimer based on environmentdependent atomic energies and charges
View Description Hide DescriptionUnderstanding the unique properties of water still represents a significant challenge for theory and experiment. Computer simulations by molecular dynamics require a reliable description of the atomic interactions, and in recent decades countless water potentials have been reported in the literature. Still, most of these potentials contain significant approximations, for instance a frozen internal structure of the individual water monomers.Artificial neural networks (NNs) offer a promising way for the construction of very accurate potentialenergysurfaces taking all degrees of freedom explicitly into account. These potentials are based on electronic structure calculations for representative configurations, which are then interpolated to a continuous energy surface that can be evaluated many orders of magnitude faster. We present a fulldimensional NN potential for the water dimer as a first step towards the construction of a NN potential for liquid water. This manybody potential is based on environmentdependent atomic energy contributions, and longrange electrostatic interactions are incorporated employing environmentdependent atomic charges. We show that the potential and derived properties like vibrational frequencies are in excellent agreement with the underlying reference densityfunctional theory calculations.

Coherent control and timedependent density functional theory: Towards creation of wave packets by ultrashort laser pulses
View Description Hide DescriptionExplicitly timedependent density functional theory (TDDFT) is a formally exact theory, which can treat very large systems. However, in practice it is used almost exclusively in the adiabatic approximation and with standard ground state functionals. Therefore, if combined with coherent controltheory, it is not clear which control tasks can be achieved reliably, and how this depends on the functionals. In this paper, we continue earlier work in order to establish rules that answer these questions. Specifically, we look at the creation of wave packets by ultrashort laser pulses that contain several excited states. We find that (i) adiabatic TDDFT only works if the system is not driven too far from the ground state, (ii) the permanent dipole moments involved should not differ too much, and (iii) these results are independent of the functional used. Additionally, we find an artifact that produces fluencedependent excitation energies.

Transienttime correlation function applied to mixed shear and elongational flows
View Description Hide DescriptionThe transienttime correlation function (TTCF) method is used to calculate the nonlinear response of a homogeneous atomic fluid close to equilibrium. The TTCF response of the pressure tensor subjected to a timeindependent planar mixed flow of shear and elongation is compared to directly averaged nonequilibrium molecular dynamics (NEMD) simulations. We discuss the consequence of noise in simulations with a small rate of deformation. The generalized viscosity for planar mixed flow is also calculated with TTCF. We find that for small rates of deformation, TTCF is far more efficient than direct averages of NEMD simulations. Therefore, TTCF can be applied to fluids with deformation rates which are much smaller than those commonly used in NEMD simulations. Ultimately, TTCF applied to molecular systems is amenable to direct comparison between NEMD simulations and experiments and so in principle can be used to study the rheology of polymer melts in industrial processes.

Critical lines for an unequal size of molecules in a binary gasliquid mixture around the van Laar point using the combination of the Tompa model and the van der Waals equation
View Description Hide DescriptionWe combine the modified Tompa model with the van der Waals equation to study critical lines for an unequal size of molecules in a binary gasliquid mixture around the van Laar point. The van Laar point is coined by Meijer and it is the only point at which the mathematical double point curve is stable. It is the intersection of the tricritical point and the double critical end point. We calculate the critical lines as a function of x _{1} and x _{2}, the density of type I molecules and the density of type II molecules for various values of the system parameters; hence the global phase diagrams are presented and discussed in the densitydensity plane. We also investigate the connectivity of critical lines at the van Laar point and its vicinity and discuss these connections according to the Scott and van Konynenburg classifications. It is also found that the critical lines and phase behavior are extremely sensitive to small modifications in the system parameters.

Calculations of nonlinear response properties using the intermediate state representation and the algebraicdiagrammatic construction polarization propagator approach: Twophoton absorption spectra
View Description Hide DescriptionAn earlier proposed approach to molecular response functions based on the intermediate state representation (ISR) of polarization propagator and algebraicdiagrammatic construction (ADC) approximations is for the first time employed for calculations of nonlinear response properties. The twophoton absorption (TPA) spectra are considered. The hierarchy of the first and secondorder ADC/ISR computational schemes, ADC(1), ADC(2), ADC(2)x, and ADC(3/2), is tested in applications to H2O, HF, and C2H4 (ethylene). The calculated TPA spectra are compared with the results of coupled cluster (CC) models and timedependent densityfunctional theory (TDDFT) calculations, using the results of the CC3 model as benchmarks. As a more realistic example, the TPA spectrum of C8H10 (octatetraene) is calculated using the ADC(2)x and ADC(2) methods. The results are compared with the results of TDDFT method and earlier calculations, as well as to the available experimental data. A prominent feature of octatetraene and other polyene molecules is the existence of lowlying excited states with increased double excitation character. We demonstrate that the twophoton absorption involving such states can be adequately studied using the ADC(2)x scheme, explicitly accounting for interaction of doubly excited configurations. Observed peaks in the experimental TPA spectrum of octatetraene are assigned based on our calculations.

Markov processes follow from the principle of maximum caliber
View Description Hide DescriptionMarkovmodels are widely used to describe stochastic dynamics. Here, we show that Markovmodels follow directly from the dynamical principle of maximum caliber (Max Cal). Max Cal is a method of deriving dynamical models based on maximizing the path entropy subject to dynamical constraints. We give three different cases. First, we show that if constraints (or data) are given in the form of singlet statistics (average occupation probabilities), then maximizing the caliber predicts a timeindependent process that is modeled by identical, independently distributed random variables. Second, we show that if constraints are given in the form of sequential pairwise statistics, then maximizing the caliber dictates that the kinetic process will be Markovian with a uniform initial distribution. Third, if the initial distribution is known and is not uniform we show that the only process that maximizes the path entropy is still the Markov process. We give an example of how Max Cal can be used to discriminate between different dynamical models given data.

An excited state paired interacting orbital method
View Description Hide DescriptionA new method for analyzing and visualizing the molecular excited states, named “excited state paired interacting orbital (EPIO),” is proposed. The method is based both on the paired interacting orbital (PIO) proposed by Fujimoto and Fukui [J. Chem. Phys.60, 572 (1974)] and the natural transition orbital (NTO) by Martin [J. Chem. Phys.118, 4775 (2003)10.1063/1.1558471]. Within the PIO method, orbital interactions between the two fragmented molecules are represented practically only by a few pairs of fragment orbitals. The NTO method is a means of finding a compact orbital representation for the electronic transitions in the excited states. With the method, electronic transitions are expressed by a few particlehole orbital pairs and a clear picture on the electronic transitions is obtained. EPIO method is designed to have both properties of the preceding two methods: electronic transitions in composite molecular systems can be expressed with a few pairs of EPIOs which are constructed with fragmented molecular orbitals (MOs). Excited state characters, such as charge transfer and local excitations, are analyzed by using EPIOs with their generation probabilities. Thus, the present method gives us clear information on the composition of MOs which play an important role in the molecular excitation processes, e.g., optical processes.

Vibronic coupling simulations for linear and nonlinear optical processes: Simulation results
View Description Hide DescriptionA vibronic coupling model based on timedependent wavepacket approach is applied to simulate linear optical processes, such as onephoton absorbance and resonance Raman scattering, and nonlinear optical processes, such as twophoton absorbance and resonance hyperRaman scattering, on a series of small molecules. Simulations employing both the longrange corrected approach in density functional theory and coupled cluster are compared and also examined based on available experimental data. Although many of the small molecules are prone to anharmonicity in their potential energy surfaces, the harmonic approach performs adequately. A detailed discussion of the nonCondon effects is illustrated by the molecules presented in this work. Linear and nonlinear Raman scattering simulations allow for the quantification of interference between the FranckCondon and HerzbergTeller terms for different molecules.

Vibronic coupling simulations for linear and nonlinear optical processes: Theory
View Description Hide DescriptionA comprehensive vibronic coupling model based on the timedependent wavepacket approach is derived to simulate linear optical processes, such as onephoton absorbance and resonance Raman scattering, and nonlinear optical processes, such as twophoton absorbance and resonance hyperRaman scattering. This approach is particularly well suited for combination with firstprinciples calculations. Expressions for the FranckCondon terms, and nonCondon effects via the HerzbergTeller coupling approach in the independentmode displaced harmonic oscillator model are presented. The significance of each contribution to the different spectral types is discussed briefly.

Density functional theory guided Monte Carlo simulations: Application to melting of Na_{13}
View Description Hide DescriptionWe present a density functional theory(DFT) based Monte Carlo simulation method in which a simple energy function gets fitted onthefly to DFT energies and gradients. The fitness of the energy function gets tested periodically using the classical importance function technique [R. Iftimie, D. Salahub, D. Wei, and J. Schofield, J. Chem. Phys.113, 4852 (2000)]. The function is updated to fit the DFT energies and gradients of the most recent structures visited whenever it fails to achieve a preset accuracy. In this way, we effectively break down the problem of fitting the entire potential energy surface (PES) into many easier problems, which are to fit small local regions of the PES. We used the scaled Morse potential empirical function to guide a DFTMonte Carlo simulation of Na_{13} at various temperatures. The use of empirical function guide produced a computational speedup of about 7 in our test system without affecting the quality of the results.

Firstorder phase transitions in repulsive rigid kmers on twodimensional lattices
View Description Hide DescriptionIn a previous paper [F. Romá, A. J. RamirezPastor, and J. L. Riccardo, Phys. Rev. B72, 035444 (2005)], the critical behavior of repulsive rigid rods of length k (kmers) on a square lattice at half coverage has been studied by using Monte Carlo(MC) simulations. The obtained results indicated that (1) the phase transition occurring in the system is a secondorder phase transition for all adsorbate sizes k; and (2) the universality class of the transition changes from 2D Isingtype for monomers (k = 1) to an unknown universality class for k ≥ 2. In the present work, we revisit our previous results together with further numerical evidences, resulting from new extensive MC simulations based on an efficient exchange algorithm and using highperformance computational capabilities. In contrast to our previous conclusions (1) and (2), the new numerical calculations clearly support the occurrence of a firstorder phase transition for k ≥ 2. In addition, a similar scenario was found for kmers adsorbed on the triangular lattice at coverage k/(2k+1).

Survival of interacting Brownian particles in crowded onedimensional environment
View Description Hide DescriptionWe investigate a diffusive motion of a system of interacting Brownian particles in quasionedimensional micropores. In particular, we consider a semiinfinite 1D geometry with a partially absorbing boundary and the hardcore interparticle interaction. Due to the absorbing boundary the number of particles in the pore gradually decreases. We present the exact analytical solution of the problem. Our procedure merely requires the knowledge of the corresponding singleparticle problem. First, we calculate the simultaneous probability density of having still a definite number (N − k) of surviving particles at definite coordinates. Focusing on an arbitrary tagged particle, we derive the exact probability density of its coordinate. Second, we present a complete probabilistic description of the emerging escape process. The survival probabilities for the individual particles are calculated, the first and the second moments of the exit times are discussed. Generally speaking, although the original interparticle interaction possesses a pointlike character, it induces entropic repulsive forces which, e.g., push the leftmost (rightmost) particle towards (opposite) the absorbing boundary thereby accelerating (decelerating) its escape. More importantly, as compared to the reference problem for the noninteracting particles, the interaction changes the dynamical exponents which characterize the longtime asymptotic dynamics. Interesting new insights emerge after we interpret our model in terms of (a) diffusion of a single particle in a Ndimensional space, and (b) order statistics defined on a system of Nindependent, identically distributed random variables.

Farfromequilibrium processes without net thermal exchange via energy sorting
View Description Hide DescriptionMany important processes at the microscale require farfromequilibrium conditions to occur, as in the functioning of mesoscopic bioreactors, nanoscopic rotors, and nanoscale mass conveyors. Achieving such conditions, however, is typically based on energy inputs that strongly affect the thermal properties of the environment and the controllability of the system itself. Here, we present a general class of farfromequilibrium processes that suppress the net thermal exchange with the environment by maintaining the MaxwellBoltzmann velocity distribution intact. This new phenomenon, referred to as ghost equilibrium, results from the statistical cancellation of superheated and subcooled nonequilibrated degrees of freedom that are autonomously generated through a microscale energy sorting process. We provide general conditions to observe this phenomenon and study its implications for manipulating energy at the microscale. The results are applied explicitly to two mechanistically different cases, an ensemble of rotational dipoles and a gas of trapped particles, which encompass a great variety of common situations involving both rotational and translational degrees of freedom.

A generalized gradient approximation for exchange derived from the model potential of van Leeuwen and Baerends
View Description Hide DescriptionThe common way to obtain energies from KohnSham exchange potentials is by using the LevyPerdew virial relation. For potentials that are not functional derivatives (i.e., nearly all model exchange potentials in existence), this approach leads to energy expressions that lack translational and rotational invariance. We propose a method for constructing potentialbased energy functionals that are free from these artifacts. It relies on the same lineintegration technique that gives rise to the LevyPerdew relation, but uses density scaling instead of coordinate scaling. The method is applicable to any exchange or correlation potential that depends on the density explicitly, and correctly recovers the parent energy functional from a functional derivative. To illustrate our approach we develop a properly invariant generalized gradient approximation for exchange starting from the model potential of van Leeuwen and Baerends.

Statetostate reaction probabilities within the quantum transition state framework
View Description Hide DescriptionRigorous quantum dynamics calculations of reaction rates and initial stateselected reaction probabilities of polyatomic reactions can be efficiently performed within the quantum transition state concept employing flux correlation functions and wave packet propagation utilizing the multiconfigurational timedependent Hartree approach. Here, analytical formulas and a numerical scheme extending this approach to the calculation of statetostate reaction probabilities are presented. The formulas derived facilitate the use of three different dividing surfaces: two dividing surfaces located in the product and reactant asymptotic region facilitate full state resolution while a third dividing surface placed in the transition state region can be used to define an additional flux operator. The eigenstates of the corresponding thermal flux operator then correspond to vibrational states of the activated complex. Transforming these states to reactant and product coordinates and propagating them into the respective asymptotic region, the full scattering matrix can be obtained. To illustrate the new approach, test calculations study the D + H_{2}(ν, j) → HD(ν′, j′) + H reaction for J = 0.
 Advanced Experimental Techniques

Electromagnetically induced transparency spectroscopy
View Description Hide DescriptionWe propose a method based on the electromagnetically induced transparency (EIT) phenomenon for the detection of molecules which exist as a small minority in the presence of a majority of absorbers. The EIT effect we employ effectively eliminates the absorption of the majority species in the spectral region where it overlaps with the absorption of the minority species. The method can also be used to enhance localmodes transitions which overlap spectrally with a background of other localmodes transitions of the same molecule. The general theory is applied to the case of sparse and congested background spectra within the same molecule and to the recording of the spectra of isotopomers (of chlorine and methanol) that are in minority relative to other isotopomers which constitute the majority of molecules present.