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Showing papers in "Journal of Chemical Physics in 2006"


Journal ArticleDOI
TL;DR: This work reexamines the effect of the exchange screening parameter omega on the performance of the Heyd-Scuseria-Ernzerhof (HSE) screened hybrid functional and recommends a new version of HSE with the screened parameter omega=0.11 bohr(-1) for further use.
Abstract: This work reexamines the effect of the exchange screening parameter ω on the performance of the Heyd-Scuseria-Ernzerhof (HSE) screened hybrid functional. We show that variation of the screening parameter influences solid band gaps the most. Other properties such as molecular thermochemistry or lattice constants of solids change little with ω. We recommend a new version of HSE with the screening parameter ω=0.11bohr−1 for further use. Compared to the original implementation, the new parametrization yields better thermochemical results and preserves the good accuracy for band gaps and lattice constants in solids.

4,625 citations



Journal ArticleDOI
TL;DR: The new local density functional, called M06-L, is designed to capture the main dependence of the exchange-correlation energy on local spin density, spin density gradient, and spin kinetic energy density, and it is parametrized to satisfy the uniform-electron-gas limit.
Abstract: We present a new local density functional, called M06-L, for main-group and transition element thermochemistry, thermochemical kinetics, and noncovalent interactions. The functional is designed to capture the main dependence of the exchange-correlation energy on local spin density, spin density gradient, and spin kinetic energy density, and it is parametrized to satisfy the uniform-electron-gas limit and to have good performance for both main-group chemistry and transition metal chemistry. The M06-L functional and 14 other functionals have been comparatively assessed against 22 energetic databases. Among the tested functionals, which include the popular B3LYP, BLYP, and BP86 functionals as well as our previous M05 functional, the M06-L functional gives the best overall performance for a combination of main-group thermochemistry, thermochemical kinetics, and organometallic, inorganometallic, biological, and noncovalent interactions. It also does very well for predicting geometries and vibrational frequencies. Because of the computational advantages of local functionals, the present functional should be very useful for many applications in chemistry, especially for simulations on moderate-sized and large systems and when long time scales must be addressed. © 2006 American Institute of Physics. DOI: 10.1063/1.2370993

4,154 citations


Journal ArticleDOI
TL;DR: The uniformity with which B2-PLYP improves for a wide range of chemical systems emphasizes the need of (virtual) orbital-dependent terms that describe nonlocal electron correlation in accurate exchange-correlation functionals.
Abstract: A new hybrid density functional for general chemistry applications is proposed. It is based on a mixing of standard generalized gradient approximations GGAs for exchange by Becke B and for correlation by Lee, Yang, and Parr LYP with Hartree-Fock HF exchange and a perturbative second-order correlation part PT2 that is obtained from the Kohn-Sham GGA orbitals and eigenvalues. This virtual orbital-dependent functional contains only two global parameters that describe the mixture of HF and GGA exchange ax and of the PT2 and GGA correlation c, respectively. The parameters are obtained in a least-squares-fit procedure to the G2/97 set of heat of formations. Opposed to conventional hybrid functionals, the optimum ax is found to be quite large 53% with c=27% which at least in part explains the success for many problematic molecular systems compared to conventional approaches. The performance of the new functional termed B2-PLYP is assessed by the G2/97 standard benchmark set, a second test suite of atoms, molecules, and reactions that are considered as electronically very difficult including transition-metal compounds, weakly bonded complexes, and reaction barriers and comparisons with other hybrid functionals of GGA and meta-GGA types. According to many realistic tests, B2-PLYP can be regarded as the best general purpose density functional for molecules e.g., a mean absolute deviation for the two test sets of only 1.8 and 3.2 kcal/mol compared to about 3 and 5 kcal/mol, respectively, for the best other density functionals. Very importantly, also the maximum and minium errors outliers are strongly reduced by about 10‐20 kcal/mol. Furthermore, very good results are obtained for transition state barriers but unlike previous attempts at such a good description, this definitely comes not at the expense of equilibrium properties. Preliminary calculations of the equilibrium bond lengths and harmonic vibrational frequencies for diatomic molecules and transition-metal complexes also show very promising results. The uniformity with which B2-PLYP improves for a wide range of chemical systems emphasizes the need of virtual orbital-dependent terms that describe nonlocal electron correlation in accurate exchange-correlation functionals. From a practical point of view, the new functional seems to be very robust and it is thus suggested as an efficient quantum chemical method of general purpose. © 2006 American Institute of Physics. DOI: 10.1063/1.2148954

2,704 citations


Journal ArticleDOI
TL;DR: An efficient and reliable methodology for crystal structure prediction, merging ab initio total-energy calculations and a specifically devised evolutionary algorithm, which allows one to predict the most stable crystal structure and a number of low-energy metastable structures for a given compound at any P-T conditions without requiring any experimental input.
Abstract: We have developed an efficient and reliable methodology for crystal structure prediction, merging ab initio total-energy calculations and a specifically devised evolutionary algorithm. This method allows one to predict the most stable crystal structure and a number of low-energy metastable structures for a given compound at any P-T conditions without requiring any experimental input. Extremely high (nearly 100%) success rate has been observed in a few tens of tests done so far, including ionic, covalent, metallic, and molecular structures with up to 40 atoms in the unit cell. We have been able to resolve some important problems in high-pressure crystallography and report a number of new high-pressure crystal structures (stable phases: epsilon-oxygen, new phase of sulphur, new metastable phases of carbon, sulphur and nitrogen, stable and metastable phases of CaCO3). Physical reasons for the success of this methodology are discussed.

1,945 citations


Journal ArticleDOI
TL;DR: A detailed comparison of the performance of the HSE03 and PBE0 functionals for a set of archetypical solid state systems is presented, indicating that the hybrid functionals indeed often improve the description of these properties, but in several cases the results are not yet on par with standard gradient corrected functionals.
Abstract: Hybrid Fock exchange/density functional theory functionals have shown to be very successful in describing a wide range of molecular properties. For periodic systems, however, the long-range nature of the Fock exchange interaction and the resultant large computational requirements present a major drawback. This is especially true for metallic systems, which require a dense Brillouin zone sampling. Recently, a new hybrid functional [HSE03, J. Heyd, G. E. Scuseria, and M. Ernzerhof, J. Chem. Phys. 118, 8207 (2003)] that addresses this problem within the context of methods that evaluate the Fock exchange in real space was introduced. We discuss the advantages the HSE03 functional brings to methods that rely on a reciprocal space description of the Fock exchange interaction, e.g., all methods that use plane wave basis sets. Furthermore, we present a detailed comparison of the performance of the HSE03 and PBE0 functionals for a set of archetypical solid state systems by calculating lattice parameters, bulk moduli, heats of formation, and band gaps. The results indicate that the hybrid functionals indeed often improve the description of these properties, but in several cases the results are not yet on par with standard gradient corrected functionals. This concerns in particular metallic systems for which the bandwidth and exchange splitting are seriously overestimated.

1,875 citations


Journal ArticleDOI
TL;DR: This long-range-corrected hybrid, here denoted LC-omegaPBE, is remarkably accurate for a broad range of molecular properties, such as thermochemistry, barrier heights of chemical reactions, bond lengths, and most notably, description of processes involving long- range charge transfer.
Abstract: Common approximate exchange-correlation functionals suffer from self-interaction error, and as a result, their corresponding potentials have incorrect asymptotic behavior. The exact asymptote can be imposed by introducing range separation into the exchange component and replacing the long-range portion of the approximate exchange by the Hartree-Fock counterpart. The authors show that this long-range correction works particularly well in combination with the short-range variant of the Perdew-Burke-Ernzerhof (PBE) exchange functional. This long-range-corrected hybrid, here denoted LC-ωPBE, is remarkably accurate for a broad range of molecular properties, such as thermochemistry, barrier heights of chemical reactions, bond lengths, and most notably, description of processes involving long-range charge transfer.

1,555 citations


Journal ArticleDOI
TL;DR: A remarkably simple approximate effective potential is found that closely resembles the Talman-Shadwick potential in atoms and depends only on total densities and requires no two-electron integrals.
Abstract: The optimized effective potential (OEP) for exchange was introduced some time ago by Sharp and Horton [Phys. Rev. 90, 317 (1953)] and by Talman and Shadwick [Phys. Rev. A 14, 36 (1976)]. The integral equation for the OEP is difficult to solve, however, and a variety of approximations have therefore been proposed. These are explicitly orbital dependent and require the same two-electron integrals as Hartree-Fock theory. We have found a remarkably simple approximate effective potential that closely resembles the Talman-Shadwick potential in atoms. It depends only on total densities and requires no two-electron integrals.

1,198 citations


Journal ArticleDOI
TL;DR: PCM-TDDFT is shown to be successful in supporting the analysis of experimental data with useful insights for a better understanding of photophysical and photochemical pathways in solution.
Abstract: In this paper we present the theory and implementation of analytic derivatives of time-dependent density functional theory (TDDFT) excited states energies, both in vacuo and including solvent effects by means of the polarizable continuum model. The method is applied to two case studies: p-nitroaniline and 4-(dimethyl)aminobenzonitrile. For both molecules PCM-TDDFT is shown to be successful in supporting the analysis of experimental data with useful insights for a better understanding of photophysical and photochemical pathways in solution.

1,160 citations


Journal ArticleDOI
TL;DR: A new flexible simple point-charge water model was derived by optimizing bulk diffusion and dielectric constants to the experimental values via the equilibrium bond length and angle and extensive comparisons of thermodynamic, structural, and kinetic properties indicate that the new model is much improved over the standard SPC model and its overall performance is comparable to or even better than the extended SPC models.
Abstract: In order to introduce flexibility into the simple point-charge (SPC) water model, the impact of the intramolecular degrees of freedom on liquid properties was systematically studied in this work as a function of many possible parameter sets. It was found that the diffusion constant is extremely sensitive to the equilibrium bond length and that this effect is mainly due to the strength of intermolecular hydrogen bonds. The static dielectric constant was found to be very sensitive to the equilibrium bond angle via the distribution of intermolecular angles in the liquid: A larger bond angle will increase the angle formed by two molecular dipoles, which is particularly significant for the first solvation shell. This result is in agreement with the work of Hochtl et al. [J. Chem. Phys. 109, 4927 (1998)]. A new flexible simple point-charge water model was derived by optimizing bulk diffusion and dielectric constants to the experimental values via the equilibrium bond length and angle. Due to the large sensitivities, the parametrization only slightly perturbs the molecular geometry of the base SPC model. Extensive comparisons of thermodynamic, structural, and kinetic properties indicate that the new model is much improved over the standard SPC model and its overall performance is comparable to or even better than the extended SPC model.

1,001 citations


Journal ArticleDOI
TL;DR: The model is extended to include higher-order dispersion coefficients C(8) and C(10) and performs very well for prediction of intermonomer separations and binding energies of 45 van der Waals complexes, with minimal computational cost.
Abstract: We have previously demonstrated that the dipole moment of the exchange hole can be used to derive intermolecular C6 dispersion coefficients [J. Chem. Phys. 122, 154104 (2005)]. This was subsequently the basis for a novel post-Hartree-Fock model of intermolecular interactions [J. Chem. Phys. 123, 024101 (2005)]. In the present work, the model is extended to include higher-order dispersion coefficients C8 and C10. The extended model performs very well for prediction of intermonomer separations and binding energies of 45 van der Waals complexes. In particular, it performs twice as well as basis-set extrapolated MP2 theory for dispersion-bound complexes, with minimal computational cost.

Journal ArticleDOI
TL;DR: A general class of hybrid density functionals with decomposition of the exchange component into short-range and long-range parts with a great degree of flexibility in choosing the mixing parameters in range-separated hybrids is considered.
Abstract: We consider a general class of hybrid density functionals with decomposition of the exchange component into short-range and long-range parts. The admixture of Hartree-Fock (HF) exchange is controlled by three parameters: short-range mixing, long-range mixing, and range separation. We study how the variation of these parameters affects the accuracy of hybrid functionals for thermochemistry and kinetics. For the density functional component of the hybrids, we test three nonempirical approximations: local spin-density approximation, generalized gradient approximation (GGA), and meta-GGA. We find a great degree of flexibility in choosing the mixing parameters in range-separated hybrids. For the studied properties, short-range and long-range HF exchange seem to have a similar effect on the errors. One may choose to treat the long-range portion of the exchange by HF to recover the correct asymptotic behavior of the exchange potential and improve the description of density tail regions. If this asymptote is not important, as in solids, one may use screened hybrids, where long-range HF exchange is excluded. Screened hybrids retain most of the benefits of global hybrids but significantly reduce the computational cost in extended systems.

Journal ArticleDOI
TL;DR: The FSP is utilized to solve two examples taken from the field of systems biology, and comparisons are made between the FSP, the SSA, and tau leaping algorithms.
Abstract: This article introduces the finite state projection (FSP) method for use in the stochastic analysis of chemically reacting systems. One can describe the chemical populations of such systems with probability density vectors that evolve according to a set of linear ordinary differential equations known as the chemical master equation (CME). Unlike Monte Carlo methods such as the stochastic simulation algorithm (SSA) or tau leaping, the FSP directly solves or approximates the solution of the CME. If the CME describes a system that has a finite number of distinct population vectors, the FSP method provides an exact analytical solution. When an infinite or extremely large number of population variations is possible, the state space can be truncated, and the FSP method provides a certificate of accuracy for how closely the truncated space approximation matches the true solution. The proposed FSP algorithm systematically increases the projection space in order to meet prespecified tolerance in the total probability density error. For any system in which a sufficiently accurate FSP exists, the FSP algorithm is shown to converge in a finite number of steps. The FSP is utilized to solve two examples taken from the field of systems biology, and comparisons are made between the FSP, the SSA, and tau leaping algorithms. In both examples, the FSP outperforms the SSA in terms of accuracy as well as computational efficiency. Furthermore, due to very small molecular counts in these particular examples, the FSP also performs far more effectively than tau leaping methods.

Journal ArticleDOI
TL;DR: The favorable scaling properties of PCM-TD-DFT models in both SS and LR variants and their availability in effective quantum mechanical codes pave the route for the computation of reliable spectroscopic properties of large molecules of technological and/or biological interest in their natural environments.
Abstract: An effective state specific (SS) model for the inclusion of solvent effects in time dependent density functional theory (TD-DFT) computations of excited electronic states has been developed and coded in the framework of the so-called polarizable continuum model (PCM). Different relaxation time regimes can be treated thus giving access to a number of different spectroscopic properties together with solvent relaxation energies of paramount relevance in electron transfer processes. SS and conventional linear response (LR) models have been compared for two benchmark systems (coumarin 153 and formaldehyde in different solvents) and in the limiting simple case of a dipolar solute embedded in a spherical cavity. The results point out the complementarity of LR and SS approaches and the advantages of the latter model especially for polar solvents. The favorable scaling properties of PCM-TD-DFT models in both SS and LR variants and their availability in effective quantum mechanical codes pave the route for the computation of reliable spectroscopic properties of large molecules of technological and/or biological interest in their natural environments.

Journal ArticleDOI
TL;DR: A simple analytic model for the optical properties of gold is proposed, which includes a minimum set of parameters necessary to represent the complex dielectric function of gold in the visible and near-uv regions.
Abstract: A simple analytic model for the optical properties of gold is proposed. The model includes a minimum set of parameters necessary to represent the complex dielectric function of gold in the visible and near-uv regions. Explicit values for the parameters to reproduce the Johnson and Christy data [Phys. Rev. B 6, 4370 (1972)] on the optical properties of gold are provided.

Journal ArticleDOI
TL;DR: A computational technique is proposed which combines the string method with a sampling technique to determine minimum free energy paths and captures the mechanism of transition in that it allows to determine the committor function for the reaction and, in particular, the transition state region.
Abstract: A computational technique is proposed which combines the string method with a sampling technique to determine minimum free energy paths. The technique only requires to compute the mean force and another conditional expectation locally along the string, and therefore can be applied even if the number of collective variables kept in the free energy calculation is large. This is in contrast with other free energy sampling techniques which aim at mapping the full free energy landscape and whose cost increases exponentially with the number of collective variables kept in the free energy. Provided that the number of collective variables is large enough, the new technique captures the mechanism of transition in that it allows to determine the committor function for the reaction and, in particular, the transition state region. The new technique is illustrated on the example of alanine dipeptide, in which we compute the minimum free energy path for the isomerization transition using either two or four dihedral angles as collective variables. It is shown that the mechanism of transition can be captured using the four dihedral angles, but it cannot be captured using only two of them.

Journal ArticleDOI
TL;DR: After identifying the sufficient condition for functionals to be free from SIE, the focus on the symptoms and investigate the performance of most popular functionals, which show that these functionals suffer from many-electron SIE.
Abstract: One of the most important challenges in density functional theory (DFT) is the proper description of fractional charge systems relating to the self-interaction error (SIE). Traditionally, the SIE has been formulated as a one-electron problem, which has been addressed in several recent functionals. However, these recent one-electron SIE-free functionals, while greatly improving the description of thermochemistry and reaction barriers in general, still exhibit many of the difficulties associated with SIE. Thus we emphasize the need to surpass this limit and shed light on the many-electron SIE. After identifying the sufficient condition for functionals to be free from SIE, we focus on the symptoms and investigate the performance of most popular functionals. We show that these functionals suffer from many-electron SIE. Finally, we give a SIE classification of density functionals.

Journal ArticleDOI
TL;DR: An improved procedure for estimating the largest value for tau that is consistent with theory and more accurate, easier to code, and faster to execute than the currently used procedure is presented.
Abstract: The tau-leaping method of simulating the stochastic time evolution of a well-stirred chemically reacting system uses a Poisson approximation to take time steps that leap over many reaction events. Theory implies that tau leaping should be accurate so long as no propensity function changes its value “significantly” during any time step τ. Presented here is an improved procedure for estimating the largest value for τ that is consistent with this condition. This new τ-selection procedure is more accurate, easier to code, and faster to execute than the currently used procedure. The speedup in execution will be especially pronounced in systems that have many reaction channels.

Journal ArticleDOI
TL;DR: A new computational thermochemistry protocol for first- and second-row main-group systems, to be known as W4 theory, is proposed, and its computational cost is not insurmountably higher than that of the earlier W3 theory, while performance is markedly superior.
Abstract: In an attempt to improve on our earlier W3 theory [A. D. Boese et al., J. Chem. Phys. 120, 4129 (2004)] we consider such refinements as more accurate estimates for the contribution of connected quadruple excitations (T4), inclusion of connected quintuple excitations (T5), diagonal Born-Oppenheimer corrections (DBOC), and improved basis set extrapolation procedures. Revised experimental data for validation purposes were obtained from the latest version of the Active Thermochemical Tables thermochemical network. The recent CCSDT(Q) method offers a cost-effective way of estimating T4, but is insufficient by itself if the molecule exhibits some nondynamical correlation. The latter considerably slows down basis set convergence for T4, and anomalous basis set convergence in highly polar systems makes two-point extrapolation procedures unusable. However, we found that the CCSDTQ−CCSDT(Q) difference converges quite rapidly with the basis set, and that the formula 1.10[CCSDT(Q)∕cc-pVTZ+CCSDTQ∕cc-pVDZ-CCSDT(Q)∕...

Journal ArticleDOI
TL;DR: One of the pairwise electrostatic interaction methods investigated, the damped shifted force method, shows a remarkable ability to reproduce the energetic and dynamic characteristics exhibited by simulations employing lattice summation techniques.
Abstract: We investigate pairwise electrostatic interaction methods and show that there are viable computationally efficient (O(N)) alternatives to the Ewald summation for typical modern molecular simulations. These methods are extended from the damped and cutoff-neutralized Coulombic sum originally proposed by Wolf et al. [J. Chem. Phys. 110, 8255 (1999)]. One of these, the damped shifted force method, shows a remarkable ability to reproduce the energetic and dynamic characteristics exhibited by simulations employing lattice summation techniques. Comparisons were performed with this and other pairwise methods against the smooth particle-mesh Ewald summation to see how well they reproduce the energetics and dynamics of a variety of molecular simulations.

Journal ArticleDOI
TL;DR: The all-electron results with quadruple zeta valence basis sets validate semilocal density-functional theory as the workhorse of computational TM chemistry and confirms TPSS as a general purpose functional that works throughout the periodic table.
Abstract: We investigate the performance of contemporary semilocal and hybrid density functionals for bond energetics, structures, dipole moments, and harmonic frequencies of 3d transition-metal (TM) compounds by comparison with gas-phase experiments. Special attention is given to the nonempirical metageneralized gradient approximation (meta-GGA) of Tao, Perdew, Staroverov, and Scuseria (TPSS) [Phys. Rev. Lett. 91, 146401 (2003)], which has been implemented in TURBOMOLE for the present work. Trends and error patterns for classes of homologous compounds are analyzed, including dimers, monohydrides, mononitrides, monoxides, monofluorides, polyatomic oxides and halogenides, carbonyls, and complexes with organic pi ligands such as benzene and cyclopentadienyl. Weakly bound systems such as Ca(2), Mn(2), and Zn(2) are discussed. We propose a reference set of reaction energies for benchmark purposes. Our all-electron results with quadruple zeta valence basis sets validate semilocal density-functional theory as the workhorse of computational TM chemistry. Typical errors in bond energies are substantially larger than in (organic) main group chemistry, however. The Becke-Perdew'86 [Phys. Rev. A 38, 3098 (1988); Phys. Rev. B 33, 8822 (1986)] GGA and the TPSS meta-GGA have the best price/performance ratio, while the TPSS hybrid functional achieves a slightly lower mean absolute error in bond energies. The popular Becke three-parameter hybrid B3LYP underbinds significantly and tends to overestimate bond distances; we give a possible explanation for this. We further show that hybrid mixing does not reduce the width of the error distribution on our reference set. The error of a functional for the s-d transfer energy of a TM atom does not predict its error for TM bond energies and bond lengths. For semilocal functionals, self-interaction error in one- and three-electron bonds appears to be a major source of error in TM reaction energies. Nevertheless, TPSS predicts the correct ground-state symmetry in the vast majority of cases and rarely fails qualitatively. This further confirms TPSS as a general purpose functional that works throughout the periodic table. We also give workstation timing comparisons for the 645-atom protein crambin.

Journal ArticleDOI
TL;DR: A novel approach to study the formation and relaxation of excited states in solution is presented within the integral equation formalism version of the polarizable continuum model that introduces a state-specific solvent response and is further generalized within a time dependent formalism.
Abstract: In this paper a novel approach to study the formation and relaxation of excited states in solution is presented within the integral equation formalism version of the polarizable continuum model. Such an approach uses the excited state relaxed density matrix to correct the time dependent density functional theory excitation energies and it introduces a state-specific solvent response, which can be further generalized within a time dependent formalism. This generalization is based on the use of a complex dielectric permittivity as a function of the frequency, e(ω). The approach is here presented in its theoretical formulation and applied to the various steps involved in the formation and relaxation of electronic excited states in solvated molecules. In particular, vertical excitations (and emissions), as well as time dependent Stokes shift and complete relaxation from vertical excited states back to ground state, can be obtained as different applications of the same theory. Numerical results on two molecular systems are reported to better illustrate the features of the model.

Journal ArticleDOI
TL;DR: The results for the melting temperature from the direct coexistence simulations of this work are in agreement with those obtained previously by us from free energy calculations.
Abstract: In this work we present an implementation for the calculation of the melting point of ice Ih from direct coexistence of the solid-liquid interface. We use molecular dynamics simulations of boxes containing liquid water and ice in contact. The implementation is based on the analysis of the evolution of the total energy along NpT simulations at different temperatures. We report the calculation of the melting point of ice Ih at 1 bar for seven water models: SPC/E, TIP4P, TIP4P-Ew, TIP4P/ice, TIP4P/2005, TIP5P, and TIP5P-E. The results for the melting temperature from the direct coexistence simulations of this work are in agreement within the statistical uncertainty with those obtained previously by us from free energy calculations. By taking into account the results of this work and those of our free energy calculations, recommended values of the melting point of ice Ih at 1 bar for the above mentioned water models are provided. © 2006 American Institute of Physics. DOI: 10.1063/1.2183308

Journal ArticleDOI
TL;DR: A novel method is presented whereby the parameters quantifying the conductivity of an ionomer can be extracted from the phenomenon of electrode polarization in the dielectric loss and tan delta planes.
Abstract: A novel method is presented whereby the parameters quantifying the conductivity of an ionomer can be extracted from the phenomenon of electrodepolarization in the dielectric loss and tan δ planes. Mobile ion concentrations and ion mobilities were determined for a poly(ethylene oxide)-based sulfonated ionomer with Li + , Na + , and Cs + cations. The validity of the model was confirmed by examining the effects of sample thickness and temperature. The Vogel-Fulcher-Tammann (VFT)-type temperature dependence of conductivity was found to arise from the Arrhenius dependence of ion concentration and VFT behavior of mobility. The ion concentration activation energy was found to be 25.2, 23.4, and 22.3 ± 0.5 kJ ∕ mol for ionomers containing Li + , Na + , and Cs + , respectively. The theoretical binding energies were also calculated and found to be ∼ 5 kJ ∕ mol larger than the experimental activation energies, due to stabilization by coordination with polyethylene glycol segments. Surprisingly, the fraction of mobile ions was found to be very small, < 0.004 % of the cations in the Li + ionomer at 20 ° C .

Journal ArticleDOI
TL;DR: The desideratum of "many-electronSelf-interaction-corrected (SIC) semilocal approximations are exact for one-electrons systems and also reduce the spurious fractional charge q.
Abstract: Semilocal density functional approximations for the exchange-correlation energy can improperly dissociate a neutral molecule XY (Y≠X) to fractionally charged fragments X+q⋯Y−q with an energy significantly lower than X0⋯Y0. For example, NaCl can dissociate to Na+0.4⋯Cl−0.4. Generally, q is positive when the lowest-unoccupied orbital energy of atom Y0 lies below the highest-occupied orbital energy of atom X0. The first 24 open sp-shell atoms of the Periodic Table can form 276 distinct unlike pairs XY, and in the local spin density approximation 174 of these display fractional-charge dissociation. Finding these lowest-energy solutions with standard quantum chemistry codes, however, requires special care. Self-interaction-corrected (SIC) semilocal approximations are exact for one-electron systems and also reduce the spurious fractional charge q. The original SIC of Perdew and Zunger typically reduces q to 0. A scaled-down SIC with better equilibrium properties sometimes fails to reduce q all the way to 0. The...

Journal ArticleDOI
TL;DR: This work presents a detailed theoretical and experimental account of the effects of pore radii and electrolyte concentration on the current-voltage and current-concentration curves for nanopore fixed charges and mobile charges confined in the reduced volume of the inside solution.
Abstract: Modern track-etching methods allow the preparation of membranes containing a single charged conical nanopore that shows high ionic permselectivity due to the electrical interactions of the surface pore charges with the mobile ions in the aqueous solution. The nanopore has potential applications in electrically assisted single-particle detection, analysis, and separation of biomolecules. We present a detailed theoretical and experimental account of the effects of pore radii and electrolyte concentration on the current-voltage and current-concentration curves. The physical model used is based on the Nernst-Planck and Poisson equations. Since the validity of continuum models for the description of ion transport under different voltages and concentrations is recognized as one of the main issues in the modeling of future applications, special attention is paid to the fundamental understanding of the electrical interactions between the nanopore fixed charges and the mobile charges confined in the reduced volume of the inside solution.

Journal ArticleDOI
TL;DR: A new approach for calculating reaction coordinates in complex systems based on transition path sampling and likelihood maximization is presented, which requires fewer trajectories than a single iteration of existing procedures and applies to both low and high friction dynamics.
Abstract: We present a new approach for calculating reaction coordinates in complex systems. The new method is based on transition path sampling and likelihood maximization. It requires fewer trajectories than a single iteration of existing procedures, and it applies to both low and high friction dynamics. The new method screens a set of candidate collective variables for a good reaction coordinate that depends on a few relevant variables. The Bayesian information criterion determines whether additional variables significantly improve the reaction coordinate. Additionally, we present an advantageous transition path sampling algorithm and an algorithm to generate the most likely transition path in the space of collective variables. The method is demonstrated on two systems: a bistable model potential energy surface and nucleation in the Ising model. For the Ising model of nucleation, we quantify for the first time the role of nuclei surface area in the nucleation reaction coordinate. Surprisingly, increased surface area increases the stability of nuclei in two dimensions but decreases nuclei stability in three dimensions.

Journal ArticleDOI
TL;DR: In this article, the authors provide a theoretical framework to understand the phenomenology and statistics of single molecule signals arising in surface enhanced Raman scattering (SERS) under the presence of so-called electromagnetic hot spots.
Abstract: We provide the theoretical framework to understand the phenomenology and statistics of single molecule (SM) signals arising in surface enhanced Raman scattering (SERS) under the presence of so-called electromagnetic hot spots. We show that most characteristics of the SM-SERS phenomenon can be tracked down to the presence of a tail-like (power law) distribution of enhancements and we propose a specific model for it. We analyze, in the light of this, the phenomenology of SM-SERS and show how the different experimental manifestations of the effect reported in the literature can be analyzed and understood under a unified "universal" framework with a minimum set of parameters.


Journal ArticleDOI
TL;DR: In this paper, the authors present three algorithms for calculating rate constants and sampling transition paths for rare events in simulations with stochastic dynamics, which do not require a priori knowledge of the phase-space density and are suitable for equilibrium or nonequilibrium systems in stationary state.
Abstract: We present three algorithms for calculating rate constants and sampling transition paths for rare events in simulations with stochastic dynamics. The methods do not require a priori knowledge of the phase-space density and are suitable for equilibrium or nonequilibrium systems in stationary state. All the methods use a series of interfaces in phase space, between the initial and final states, to generate transition paths as chains of connected partial paths, in a ratchetlike manner. No assumptions are made about the distribution of paths at the interfaces. The three methods differ in the way that the transition path ensemble is generated. We apply the algorithms to kinetic Monte Carlo simulations of a genetic switch and to Langevin dynamics simulations of intermittently driven polymer translocation through a pore. We find that the three methods are all of comparable efficiency, and that all the methods are much more efficient than brute-force simulation.