Volume 129, Issue 18, 14 November 2008
 ARTICLES

 Theoretical Methods and Algorithms

Coarsegrained kinetic Monte Carlo models: Complex lattices, multicomponent systems, and homogenization at the stochastic level
View Description Hide DescriptionOnlattice kinetic Monte Carlo(KMC) simulations have extensively been applied to numerous systems. However, their applicability is severely limited to relatively short time and length scales. Recently, the coarsegrained MC (CGMC) method was introduced to greatly expand the reach of the lattice KMC technique. Herein, we extend the previous spatial CGMC methods to multicomponent species and/or site types. The underlying theory is derived and numerical examples are presented to demonstrate the method. Furthermore, we introduce the concept of homogenization at the stochastic level over all site types of a spatially coarsegrained cell. Homogenization provides a novel coarsening of the number of processes, an important aspect for complex problems plagued by the existence of numerous microscopic processes (combinatorial complexity). As expected, the homogenized CGMC method outperforms the traditional KMC method on computational cost while retaining good accuracy.

Power spectra for both interrupted and perennial aging processes
View Description Hide DescriptionWe study the power spectrum of a random telegraphic noise with the distribution density of waiting times given by , with . The condition violates the ergodic hypothesis, and in this case the adoption of Wiener–Khintchine (WK) theorem for the spectrum evaluation requires some caution. We study this problem theoretically and numerically and we prove that the power spectrum obeys the prescription , with , namely, the noise lives at border between the ergodic and nonergodic condition. We study sequences with the finite length . In the case the adoption of WK theorem is made legitimate by two different kinds of truncation effects: the physical and observationinduced effect. In the former case is truncated at and ensures the condition of interrupted aging. In this case, we find that is a number independent of . The latter case, , is more challenging. It was already solved by Margolin and Barkai, who used time asymptotic arguments based on the ergodicity breakdown and obtained , proving that the outofequilibrium nature of the condition is signaled by the decrease of with the increase of . We use a generalized version of the Onsager principle that leads us to the same conclusion from a somewhat more extended view valid also for the transient outofequilibrium case of . We do not limit our treatment to the time asymptotic case, thereby producing a prediction that accounts for the transition from the to the regime, recently observed in an experiment on blinking quantum dots. Our theoretical approach allows us to discuss some other recent experiments on molecular intermittent fluorescence and affords indications that should help to assess whether the spectrum is determined by the or by the condition.

Comparison of interaction potentials of liquid water with respect to their consistency with neutron diffraction data of pure heavy water
View Description Hide DescriptionA number of interaction potential models for liquid water are scrutinized from the point of view of their compatibility with results of neutron diffractionexperiments on pure heavy water. For the quantitative assessment a protocol developed recently [L. Pusztai et al., Chem. Phys. Lett.457, 96 (2008)] using the reverse Monte Carlo method has been applied. The approach combines the experimental total scattering structure factor (tssf) and partial radial distribution functions (prdfs) from molecular dynamics simulations in a single structural model (particle configuration). Goodnessoffit values to the three (O–O, O–H, and H–H) simulated prdfs and to the experimental tssf provided an unbiased measure characterizing the level of consistency between various interaction potentials and diffractionexperiments. Out of the sets of prdfs investigated here, corresponding to SPCE, BJH, ST2, POL3, TIP4P, TIP4P2005, TTMF3, and ENCS interaction potentials, the ones from the TIP4P2005 potential proved to be the most consistent with the experimental neutronweighted tssf of heavy water. More importantly, it is shown that none of the above interaction potentials are seriously inconsistent with the measured structure factor at ambient conditions.

An inversion technique for the calculation of embedding potentials
View Description Hide DescriptionA new embedding method to include local correlation in large systems is proposed. In this method the density of the whole system, calculated via density functional theory approaches, is partitioned in two pieces, one corresponding to the subsystem of interest and the rest to the environment. In the second step, an embedding potential is obtained iteratively using as a driving force the selfrepulsion due to the density difference, in a similar form as proposed by Zhao et al. [Phys. Rev. A50, 2138 (1994)], to obtain the “exact” exchangecorrelation functional. Such potential is added to the Fock equation to build the localized molecular orbitals which are further used to include the local electronic correlation in the subsystem of interest. This method is an alternative to the previous DFTbased embedding methods first proposed by Wesolowski and Washell [J. Phys. Chem.97, 8050 (1993)] and after enhanced by Govind et al. [J. Chem. Phys.110, 7677 (1999)] and adapted to metal extended systems, which use density functionals to describe the kinetic energy contribution to the embedding potential, whose precise form has been largely treated in the literature and its crucial role is discussed here. The method is applied to hydrogen chains and its van der Waals interaction with . The results obtained are in very good agreement with exact calculations performed on the whole system, which demonstrates that the method proposed is a very promising route to introduce correlation in large systems.

Multireference statespecific Mukherjee’s coupled cluster method with noniterative triexcitations
View Description Hide DescriptionWe have formulated and implemented the multireference Mukherjee’s coupled cluster method with connected singles, doubles, and perturbative triples [MR MkCCSD(T)] in the ACES II program package. Assessment of the new method has been performed on the first three electronic states of the oxygen molecule and on the automerization barrier of cyclobutadiene, where a comparison with other multireference CC treatments and with experimental data where available. The MR MkCCSD(T) method seems to be a promising candidate for an accurate, yet computationally tractable, treatment of systems where the static correlation plays an important role.

Coarse moleculardynamics analysis of an ordertodisorder transformation of a krypton monolayer on graphite
View Description Hide DescriptionThe thermally induced ordertodisorder transition of a monolayer of krypton (Kr) atoms adsorbed on a graphitesurface is studied based on a coarse moleculardynamics (CMD) approach for the bracketing and location of the transition onset. A planar order parameter is identified as a coarse variable, , that can describe the macroscopic state of the system. Implementation of the CMD method enables the construction of the underlying effective freeenergy landscapes from which the transition temperature, , is predicted. The CMD prediction of is validated by comparison with predictions based on conventional moleculardynamics (MD) techniques. The conventional MD computations include the temperature dependence of the planar order parameter, the specific heat, the Kr–Kr pair correlation function, the mean square displacement and corresponding diffusion coefficient, as well as the equilibrium probability distribution function of Kratom coordinates. Our findings suggest that the thermally induced ordertodisorder transition at the conditions examined in this study appears to be continuous. The CMD implementation provides substantial computational gains over conventional MD.

A linearscaling spectralelement method for computing electrostatic potentials
View Description Hide DescriptionA new linearscaling method is presented for the fast numerical evaluation of the electronic Coulomb potential. Our approach uses a simple realspace partitioning of the system into cubic cells and a spectralelement representation of the density in a tensorial basis of highorder Chebyshev polynomials.Electrostaticinteractions between nonneighboring cells are described using the fast multipole method. The remaining nearfield interactions are computed in the tensorial basis as a sum of differential contributions by exploiting the numerical lowrank separability of the Coulomb operator. The method is applicable to arbitrary charge densities, avoids the Poisson equation, and does not involve the solution of any systems of linear equations. Above all, an adaptive resolution of the Chebyshev basis in each cell facilitates the accurate and efficient treatment of molecular systems. We demonstrate the performance of our implementation for quantum chemistry with benchmark calculations on the noble gas atoms, longchain alkanes, and diamond fragments. We conclude that the spectralelement method can be a competitive tool for the accurate computation of electrostatic potentials in largescale molecular systems.

Optimized auxiliary basis sets for explicitly correlated methods
View Description Hide DescriptionAuxiliary basis sets for use in explicitly correlated MP2F12 and CCSDF12 methods, in which three and fourelectron integrals are approximated as products of twoelectron integrals through the resolution of the identity (RI), have been optimized for the elements H, B–Ne, and Al–Ar. Fully matched to the recently constructed orbital basis sets, these new auxiliary basis sets result in very small RI errors, as exemplified by the calculated atomization energies of 42 molecules at the MP2F12 level. Their utility in calculating smooth potential energy surfaces is also demonstrated in calculations of the spectroscopicproperties of several diatomic molecules.

Asymmetric oscillations during phase separation under continuous cooling: A simple model
View Description Hide DescriptionWe investigate the phase separation of binary mixtures under continuous cooling using the Cahn–Hilliard equation including the effect of gravity. In our simple model,sedimentation is accounted for by instantaneously “removing” droplets from the supersaturated mixture into the coexisting phase once the droplets have reached a defined maximum size. Our model predicts an oscillatory variation of turbidity. Depending on the composition, either both phases oscillate (symmetric oscillations) or only one of the phases oscillates (asymmetric oscillations). In the asymmetric case, dropletsedimentation from the majority phase into the minority phase reduces supersaturation in the minority phase. This inhibits droplet formation in the minority phase. The cooling rate dependence of the period agrees with experimental results.

Reliability of rangeseparated hybrid functionals for describing magnetic coupling in molecular systems
View Description Hide DescriptionThe performance of the Heyd–Scuseria–Ernzerhorf (HSE) and single parameter longrange corrected Perdew–Burke–Ernzerhorf rangeseparated hybrids for predicting magnetic coupling constants has been investigated for a broad set of magnetic molecular systems for which accurate experimental data exist. The set includes the H–He–H model system, two organic diradicals with different magnetic behaviors, and a series of Cu dinuclear complexes with a broad range of magnetic coupling values. Both HSE and provide a significant improvement to standard hybrids such as the wellknown hybrid Becke3parameters exchange with Lee–Yang–Parr correlation (B3LYP) functional. Nevertheless, the performance of these two rangeseparated hybrid functionals is different: HSE overestimates antiferromagnetic and ferromagnetic interactions in Cu dinuclear complexes (although significantly less than B3LYP), whereas treats ferro and antiferromagnetic couplings on a much more balanced way. The increased accuracy of suggests that the inclusion of 100% Hartree–Fock exchange considered in the definition of this longrange corrected hybrid functional has important consequences for an accurate description of exchange and correlation effects on the electronic structure of open shell systems. On the other hand, HSE, which was developed with periodic systems in mind, also performs quite well (and better than B3LYP) thus opening the possibility of magnetic coupling studies in metal oxides and other challenging solids.

Effects of anharmonicity on diffusivecontrolled symmetric electron transfer rates: From the weak to the strong electronic coupling regions
View Description Hide DescriptionThe approach for the diffusivecontrolled electron transfer rates [W. Zhu and Y. Zhao, J. Chem. Phys.126, 184105 (2007)], which is modeled after the Sumi–Marcus theory, is applied to symmetric electrontransfer reactions in a solvent environment with anharmonic potential functions. The electrontransfer rates are evaluated using the quantum matrix theory for dealing with the intramolecular vibrational motions and imaginarytime split operator technique for solving the diffusive equations, thereby taking explicit account of the weaktostrong electronic couplings. The effect of anharmonicity for both the solvent and intramolecular vibrational degrees of freedom are investigated. It is found that the anharmonicity of the intramolecular modes always enhances the rate while the solvent anharmonicity decreases the rate, compared with the harmonic modes. The possible mechanisms have been clarified.

Dynamic electronic response of a quantum dot driven by timedependent voltage
View Description Hide DescriptionWe present a comprehensive theoretical investigation on the dynamic electronic response of a noninteracting quantum dotsystem to various forms of timedependent voltage applied to the single contact lead. Numerical simulations are carried out by implementing a recently developed hierarchical equations of motion formalism [J. S. Jin et al., J. Chem. Phys.128, 234703 (2008)], which is formally exact for a fermionic system interacting with grand canonical fermionic reservoirs, in the presence of arbitrary timedependent applied chemical potentials. The dynamical characteristics of the transient transport current evaluated in both linear and nonlinearresponse regimes are analyzed, and the equivalent classic circuit corresponding to the coupled dotlead system is also discussed.

Coreexcitation energy calculations with a longrange corrected hybrid exchangecorrelation functional including a shortrange Gaussian attenuation (LCgauBOP)
View Description Hide DescriptionWe report the calculations of coreexcitation energies of firstrow atoms using the timedependent density functional theory(DFT) and the longrange correction (LC) scheme for exchangecorrelation functionals, including LCBOP, Coulombattenuated method BLYP, and our recently developed LCgauBOP method, which includes a flexible portion of shortrange Hartree–Fock (HF) exchange through the inclusion of a Gaussian function in the LC scheme. We show that the LC scheme completely fails to improve the poor accuracy of conventional generalized gradient approximation functionals, while the LCgau scheme gives an accuracy which is an order of magnitude better than BLYP and significantly better than B3LYP. A reoptimization of the two parameters controlling the inclusion of shortrange HF exchange in the LCgau method enables the errors to be reduced to the order of 0.1 eV which is competitive with the best DFT methods we are aware of. This reparametrization does not affect the LC scheme and therefore maintains the high accuracy of predicted reaction barrier heights. Moreover, while there is some loss in accuracy in thermochemical predictions compared to the previously optimized LCgauBOP, rms errors in the atomization energies over the G2 test set are found to be comparable to B3LYP. Finally, we attempt to rationalize the success of the LC and LCgau schemes in terms of the wellknown selfinteraction error (SIE) of conventional functionals. To estimate the role of the SIE, we examine the total energy calculations for systems with a fractional number of electrons, not only in the highest occupied molecular orbital but also in the characterized core orbital. Our conclusion is that the inclusion of shortrange HF exchange in LCtype functionals can significantly alleviate the problems of the SIE in the core region. In particular, we confirm that the absence of the SIE diagnostics in the core orbital energies correlates with the accurate prediction of coreexcitation energies using the newly optimized LCgau approach.

A revised electronic Hessian for approximate timedependent density functional theory
View Description Hide DescriptionTimedependent density functional theory (TDDFT) at the generalized gradient level of approximation (GGA) has shown systematic errors in the calculated excitation energies. This is especially the case for energies representing electron transitions between two separated regions of space or between orbitals of different spatial extents. It will be shown that these limitations can be attributed to the electronic ground state Hessian . Specifically, we shall demonstrate that the Hessian can be used to describe changes in energy due to small perturbations of the electron density , but it should not be applied to oneelectron excitations involving the density rearrangement of a full electron charge. This is in contrast to Hartree–Fock theory where has a trust region that is accurate for both small perturbations and oneelectron excitations. The large trust radius of can be traced back to the complete cancellation of Coulomb and exchange terms in Hartree–Fock (HF) theory representing selfinteraction (complete selfinteraction cancellation, CSIC). On the other hand, it is shown that the small trust radius for can be attributed to the fact that CSIC is assumed for GGA in the derivation of although GGA (and many other approximate DFT schemes) exhibits incomplete selfinteraction cancellation (ISIC). It is further shown that one can derive a new matrix with the same trust region as by taking terms due to ISIC properly into account. Further, with TDDFT based on , energies for statetostate transitions represented by a oneelectron excitation are approximately calculated as . Here is the energy difference between the ground state Kohn–Sham Slater determinant and the energy of a Kohn–Sham Slater determinant where has been replaced by . We make use of the new Hessian in two numerical applications involving chargetransfer excitations. It is concluded that higher than second order response theory (involving ISIC terms) must be used in approximate TDDFT, in order to describe chargetransfer excitations.

Use of an enhanced bulk diffusionbased algorithm for phase separation of a ternary mixture
View Description Hide DescriptionPhase separation kinetics of twodimensional ternary mixtures have been studied by means of a Monte Carlo approach. Standard Kawasaki kinetics are impractical to study the late stages of the segregation process at deep quenches. An extension of the accelerated algorithm for binary mixtures proposed by Marko and Barkema [Phys. Rev. E52, 2522 (1995)] is presented to overcome this problem in a threecomponent system discretized with two coupled lattices. We study the domain growth and the scaling behavior over a wide range of quench depths. Computer performances of the Kawasaki and the accelerated schemes are compared.

Uniformly convergent tuple augmented polarized basis sets for complete basis set extrapolations. I. Selfconsistent field energies
View Description Hide DescriptionWe present a sequence of tuple augmented polarized basis sets designed for extrapolations of both selfconsistent field (SCF) and correlation energies to the complete basis set (CBS) limit. These basis sets are formulated to give consistent errors throughout the Periodic Table (e.g., a consistent of error for the 2ZaP SCF energy and a consistent of error for the 6ZaP SCF energy). The SCF energy exhibits systematic convergence to the CBS limit: . A single parameter, , describes the 2ZaP through 6ZaP errors of H through Xe within 10%. The SCF rms basis set truncation errors of H through Xe are , , , , and for 2ZaP, 3ZaP, 4ZaP, 5ZaP, and 6ZaP, respectively. Linear extrapolations of the (2,3)ZaP, (3,4)ZaP, (4,5)ZaP, and (5,6)ZaP calculations (all with ) reduce these errors by an order of magnitude to , , , and , respectively. A test set of 34 atoms, ions, and molecules gives similar results, and the associated test set of 25 chemical energy differences also gives comparable absolute accuracy. However, the cancellation of errors between reactant and product is lost by extrapolation. As a result, these chemical energy differences show a more modest twotofourfold improvement with extrapolation.

Investigation of charge transport in mercaptosuccinic acidpassivated gold clusters
View Description Hide DescriptionInvestigation of electric chargetransport in welldried thin films of mercaptosuccinic acidprotected gold clusters having different cluster core sizes by a fourprobe methodology revealed a novel behavior of metalliclike to semiconductor crossover with an increase in temperature. The systems were found comprising of minor metallic and major insulating networks. At low temperatures, the monolayerprotected clusters (MPCs) were found to show a metalliclike nature with a linear increase in resistivity with an increase in temperature. The temperature coefficient of resistivity decreases and approaches that of bulk gold with an increase in the size of the cluster cores of the MPCs. This behavior was correlated with the phonon softening mechanism to the electron scattering and was explained by a simple model with a spherical layer lattice vibration. High temperature region was marked by a sharp decrease in resistivity due to thermally activated nearest neighbor electron hopping process, which follows either Arrhenius or Abeles activation models. We believe that this is the first report showing a maximum in the resistivity of any MPC with temperature as also describing the effect of phonon softening on temperature coefficient of resistivity from chargetransportmeasurements.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

A laboratory and theoretical study of silicon hydroxide SiOH
View Description Hide DescriptionThe rotational spectrum of the triatomic free radical SiOH in its ground electronic state has been observed in a supersonic molecular beam by Fourier transform microwave spectroscopy. The fundamental transition has been detected for normal SiOH and for three rare isotopic species: , , and SiOD. The same transition has also been observed in two of three excited vibrational states, and , for the most abundant species. Precise spectroscopic constants, including those that describe the effective spin doubling and hydrogen hyperfine structure, have been derived for each isotopic species or vibrational state. To complement the laboratory work, theoretical calculations of the structure, dipole moment, and energies of the and lowlying states have also been undertaken at the coupled cluster level of theory. In agreement with theoretical predictions, we conclude from the hyperfine constants that SiOH is a best described as a type radical, with the unpaired electron localized on a orbital on the silicon atom. Assuming a bond angle of , the Si–O bond length is and the O–H bond length is .

Theoretical prediction of ion (, Ne, Ar, Kr, and Xe)
View Description Hide DescriptionAb initio quantum chemical methods have been employed to investigate the structure, stability, charge redistribution, and harmonic vibrational frequencies of rare gas (, Ne, Ar, Kr, and Xe) containing ion. The Rg atoms are inserted in between the H and C atoms of ion and the geometries are optimized for minima as well as transition state using second order Møller–Plesset perturbation theory,density functional theory, and coupledcluster theory [CCSD(T)] methods. The ions are found to be metastable and exhibit a linear structure at the minima position and show a nonlinear structure at the transition state. The predicted ion is unstable with respect to the twobody dissociation channel leading to the global minima on the singlet potential surface. The binding energies corresponding to this channel are , , , , and for , , , , and ions, respectively, at CCSD(T) method. However, with respect to other twobody dissociation channel, , the ions are found to be stable and have positive energies except for at the same level of theory. The computed binding energies for this channel are 15.0, 28.8, 29.5, and for , , , and ions, respectively. Very high positive threebody dissociation energies are found for and dissociation channels. It indicates the existence of a very strong bonding between Rg and H atoms in ions. The predicted ions dissociate into global minima, , via a transition state involving H–Rg–C bending mode. The barrier heights for the transition states are 22.7, 10.1, 13.1, and for He, Ar, Kr, and Xe containing ions, respectively. The computed twobody dissociation energies are comparable to that of the experimentally observed mixed cations such as , , and in an electron bombardment matrix isolation technique. Thus cations may also be possible to prepare and characterize similar to the mixed cations in low temperature matrix isolation technique.

Solvation of in clusters. I. Structures and spectroscopic properties
View Description Hide DescriptionWe present a theoretical study of solvation in an argon matrix for to a few tens. We use a model based on an explicit description of valence electron interaction with and Ar cores by means of core polarization pseudopotential. The electronic structure determination is thus reduced to a oneelectron problem, which can be handled efficiently. We investigate the ground state geometry and related optical absorption of clusters. For , the lowest energy isomers are obtained by aggregation of Ar atoms at one single extremity of , leading to moderate perturbation of the optical transition. For , the Ar atoms aggregate at both extremities. This structural change is associated with a strong blueshift of the first optical transition , which reveals the confinement of the excited state. The energy spectrum is so strongly perturbed that the state becomes higher than the states. The closure of the first solvation shell is observed at . Above this size, the second solvation shell develops. Its structure is dominated by a pentagonal organization around the molecular axis. The optical transitions vary smoothly with and the and states are no longer inverted, though the first optical transition remains strongly blueshifted.