Showing papers in "Journal of Chemical Physics in 2010"

A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu

Abstract: The method of dispersion correction as an add-on to standard Kohn-Sham density functional theory (DFT-D) has been refined regarding higher accuracy, broader range of applicability, and less empiricism. The main new ingredients are atom-pairwise specific dispersion coefficients and cutoff radii that are both computed from first principles. The coefficients for new eighth-order dispersion terms are computed using established recursion relations. System (geometry) dependent information is used for the first time in a DFT-D type approach by employing the new concept of fractional coordination numbers (CN). They are used to interpolate between dispersion coefficients of atoms in different chemical environments. The method only requires adjustment of two global parameters for each density functional, is asymptotically exact for a gas of weakly interacting neutral atoms, and easily allows the computation of atomic forces. Three-body nonadditivity terms are considered. The method has been assessed on standard benchmark sets for inter- and intramolecular noncovalent interactions with a particular emphasis on a consistent description of light and heavy element systems. The mean absolute deviations for the S22 benchmark set of noncovalent interactions for 11 standard density functionals decrease by 15%-40% compared to the previous (already accurate) DFT-D version. Spectacular improvements are found for a tripeptide-folding model and all tested metallic systems. The rectification of the long-range behavior and the use of more accurate C(6) coefficients also lead to a much better description of large (infinite) systems as shown for graphene sheets and the adsorption of benzene on an Ag(111) surface. For graphene it is found that the inclusion of three-body terms substantially (by about 10%) weakens the interlayer binding. We propose the revised DFT-D method as a general tool for the computation of the dispersion energy in molecules and solids of any kind with DFT and related (low-cost) electronic structure methods for large systems.

Continuous surface charge polarizable continuum models of solvation. I. General formalism

Abstract: Continuum solvation models are appealing because of the simplified yet accurate description they provide of the solvent effect on a solute, described either by quantum mechanical or classical methods. The polarizable continuum model (PCM) family of solvation models is among the most widely used, although their application has been hampered by discontinuities and singularities arising from the discretization of the integral equations at the solute-solvent interface. In this contribution we introduce a continuous surface charge (CSC) approach that leads to a smooth and robust formalism for the PCM models. We start from the scheme proposed over ten years ago by York and Karplus and we generalize it in various ways, including the extension to analytic second derivatives with respect to atomic positions. We propose an optimal discrete representation of the integral operators required for the determination of the apparent surface charge. We achieve a clear separation between “model” and “cavity” which, together with simple generalizations of modern integral codes, is all that is required for an extensible and efficient implementation of the PCM models. Following this approach we are now able to introduce solvent effects on energies, structures, and vibrational frequencies (analytical first and second derivatives with respect to atomic coordinates), magnetic properties (derivatives with respect of magnetic field using GIAOs), and in the calculation more complex properties like frequency-dependent Raman activities, vibrational circular dichroism, and Raman optical activity.

Property-optimized gaussian basis sets for molecular response calculations.

Abstract: With recent advances in electronic structure methods, first-principles calculations of electronic response properties, such as linear and nonlinear polarizabilities, have become possible for molecules with more than 100 atoms. Basis set incompleteness is typically the main source of error in such calculations since traditional diffuse augmented basis sets are too costly to use or suffer from near linear dependence. To address this problem, we construct the first comprehensive set of property-optimized augmented basis sets for elements H–Rn except lanthanides. The new basis sets build on the Karlsruhe segmented contracted basis sets of split-valence to quadruple-zeta valence quality and add a small number of moderately diffuse basis functions. The exponents are determined variationally by maximization of atomic Hartree–Fock polarizabilities using analytical derivative methods. The performance of the resulting basis sets is assessed using a set of 313 molecular static Hartree–Fock polarizabilities. The mean...

Nonlocal van der Waals density functional: The simpler the better

Abstract: We devise a nonlocal correlation energy functional that describes the entire range of dispersion interactions in a seamless fashion using only the electron density as input. The new functional is considerably simpler than its predecessors of a similar type. The functional has a tractable and robust analytic form that lends itself to efficient self-consistent implementation. When paired with an appropriate exchange functional, our nonlocal correlation model yields accurate interaction energies of weakly-bound complexes, not only near the energy minima but also far from equilibrium. Our model exhibits an outstanding precision at predicting equilibrium intermonomer separations in van der Waals complexes. It also gives accurate covalent bond lengths and atomization energies. Hence the functional proposed in this work is a computationally inexpensive electronic structure tool of broad applicability.

A reactive molecular dynamics simulation of the silica-water interface

Abstract: We report our study of a silica-water interface using reactive molecular dynamics. This first-of-its-kind simulation achieves length and time scales required to investigate the detailed chemistry of the system. Our molecular dynamics approach is based on the ReaxFF force field of van Duin et al. [J. Phys. Chem. A 107, 3803 (2003)]. The specific ReaxFF implementation (SERIALREAX) and force fields are first validated on structural properties of pure silica and water systems. Chemical reactions between reactive water and dangling bonds on a freshly cut silica surface are analyzed by studying changing chemical composition at the interface. In our simulations, reactions involving silanol groups reach chemical equilibrium in approximately 250 ps. It is observed that water molecules penetrate a silica film through a proton-transfer process we call "hydrogen hopping," which is similar to the Grotthuss mechanism. In this process, hydrogen atoms pass through the film by associating and dissociating with oxygen atoms within bulk silica, as opposed to diffusion of intact water molecules. The effective diffusion constant for this process, taken to be that of hydrogen atoms within silica, is calculated to be 1.68 x 10(-6) cm(2)/s. Polarization of water molecules in proximity of the silica surface is also observed. The subsequent alignment of dipoles leads to an electric potential difference of approximately 10.5 V between the silica slab and water.

Communications: Elementary oxygen electrode reactions in the aprotic Li-air battery

Abstract: We discuss the electrochemical reactions at the oxygen electrode of an aprotic Li-air battery. Using density functional theory to estimate the free energy of intermediates during the discharge and charge of the battery, we introduce a reaction free energy diagram and identify possible origins of the overpotential for both processes. We also address the question of electron conductivity through the Li(2)O(2) electrode and show that in the presence of Li vacancies Li(2)O(2) becomes a conductor.

Communications: Survival of the fittest: accelerating convergence in full configuration-interaction quantum Monte Carlo.

Abstract: We provide a very simple adaptation of our recently published quantum Monte Carlo algorithm in full configuration-interaction (Slater determinant) spaces which dramatically reduces the number of walkers required to achieve convergence. A survival criterion is imposed for newly spawned walkers. We define a set of initiator determinants such that progeny of walkers spawned from such determinants onto unoccupied determinants are able to survive, while the progeny of walkers not in this set can survive only if they are spawned onto determinants which are already occupied. The set of initiators is originally defined to be all determinants constructable from a subset of orbitals, in analogy with complete-active spaces. This set is dynamically updated so that if a noninitiator determinant reaches an occupation larger than a preset limit, it becomes an initiator. The new algorithm allows sign-coherent sampling of the FCI space to be achieved with relatively few walkers. Using the N2 molecule as an illustration, w...

Spotlight on ionic liquids

Abstract: Ionic liquids are an emerging class of materials with a diverse and extraordinary set of properties. Understanding the origins of these properties and how they can be controlled by design to serve valuable practical applications presents a wide array of challenges and opportunities to the chemical physics and physical chemistry community. We highlight here some of the significant progress already made and future research directions in this exciting area.

On Koopmans' theorem in density functional theory.

Abstract: This paper clarifies why long-range corrected (LC) density functional theory gives orbital energies quantitatively. First, the highest occupied molecular orbital and the lowest unoccupied molecular orbital energies of typical molecules are compared with the minus vertical ionization potentials (IPs) and electron affinities (EAs), respectively. Consequently, only LC exchange functionals are found to give the orbital energies close to the minus IPs and EAs, while other functionals considerably underestimate them. The reproducibility of orbital energies is hardly affected by the difference in the short-range part of LC functionals. Fractional occupation calculations are then carried out to clarify the reason for the accurate orbital energies of LC functionals. As a result, only LC functionals are found to keep the orbital energies almost constant for fractional occupied orbitals. The direct orbital energy dependence on the fractional occupation is expressed by the exchange self-interaction (SI) energy through the potential derivative of the exchange functional plus the Coulomb SI energy. On the basis of this, the exchange SI energies through the potential derivatives are compared with the minus Coulomb SI energy. Consequently, these are revealed to be cancelled out only by LC functionals except for H, He, and Ne atoms.

Basis set consistent revision of the S22 test set of noncovalent interaction energies

Abstract: The S22 test set of interaction energies for small model complexes [Phys. Chem. Chem. Phys. 8, 1985 (2006)] has been very valuable for benchmarking new and existing methods for noncovalent interactions. However, the basis sets utilized to compute the CCSD(T) interaction energies for some of the dimers are insufficient to obtain converged results. Here we consistently extrapolate all CCSD(T)/complete basis set (CBS) interaction energies using larger basis sets for the CCSD(T) component of the computation. The revised values, which we designate S22A, represent the most accurate results to date for this set of dimers. The new values appear to be within a few hundredths of 1 kcal mol−1 of the true CCSD(T)/CBS limit at the given geometries, but the former S22 values are off by as much as 0.6 kcal mol−1 compared to the revised values. Because some of the most promising methods for noncovalent interactions are already achieving this level of agreement (or better) compared to the S22 data, more accurate benchmark values would clearly be helpful. The MP2, SCS-MP2, SCS-CCSD, SCS(MI)-MP2, and B2PLYP-D methods have been tested against the more accurate benchmark set. The B2PLYP-D method outperforms all other methods tested here, with a mean average deviation of only 0.12 kcal mol−1. However, the consistent, slight underestimation of the interaction energies computed by the SCS-CCSD method (an overall mean absolute deviation and mean deviation of 0.24 and −0.23 kcal mol−1, respectively) suggests that the SCS-CCSD method has the potential to become even more accurate with a reoptimization of its parameters for noncovalent interactions.

Assessment of TD-DFT methods and of various spin scaled CIS(D) and CC2 versions for the treatment of low-lying valence excitations of large organic dyes

Abstract: We present an extension of our previously published benchmark set for low-lying valence transitions of large organic dyes [L. Goerigk et al., Phys. Chem. Chem. Phys.11, 4611 (2009)]. The new set comprises in total 12 molecules, including two charged species and one with a clear charge-transfer transition. Our previous study on TD-DFT methods is repeated for the new test set with a larger basis set. Additionally, we want to shed light on different spin-scaled variants of the configuration interaction singles with perturbative doubles correction [CIS(D)] and the approximate coupled cluster singles and doubles method (CC2). Particularly for CIS(D) we want to clarify, which of the proposed versions can be recommended. Our results indicate that an unpublished SCS-CIS(D) variant, which is implemented into the TURBOMOLE program package, shows worse results than the original CIS(D) method, while other modified versions perform better. An SCS-CIS(D) version with a parameterization, that has already been used in an application by us recently [L. Goerigk and S. Grimme, ChemPhysChem9, 2467 (2008)], yields the best results. Another SCS-CIS(D) version and the SOS-CIS(D) method [Y. M. Rhee and M. Head-Gordon, J. Phys. Chem. A111, 5314 (2007)] perform very similar, though. For the electronic transitions considered herein, there is no improvement observed when going from the original CC2 to the SCS-CC2 method but further adjustment of the latter seems to be beneficial. Double-hybrid density functionals belong to best methods tested here. Particularly B2GP-PLYP provides uniformly good results for the complete set and is considered to be close to chemical accuracy within an ab initiotheory of color. For conventional hybrid functionals, a Fock-exchange mixing parameter of about 0.4 seems to be optimum in TD-DFT treatments of large chromophores. A range-separated functional such as, e.g., CAM-B3LYP seems also to be promising.

Widom line and the liquid-liquid critical point for the TIP4P/2005 water model.

Abstract: The Widom line and the liquid-liquid critical point of water in the deeply supercooled region are investigated via computer simulation of the TIP4P/2005 model. The Widom line has been calculated as the locus of compressibility maxima. It is quite close to the experimental homogeneous nucleation line and, in the region studied, it is almost parallel to the curve of temperatures of maximum density at fixed pressure. The critical temperature is determined by examining which isotherm has a region with flat slope. An interpolation in the Widom line gives the rest of the critical parameters. The computed critical parameters are T(c)=193 K, p(c)=1350 bar, and ρ(c)=1.012 g/cm(3). Given the performance of the model for the anomalous properties of water and for the properties of ice phases, the calculated critical parameters are probably close to those of real water.

Including quantum decoherence in surface hopping.

Abstract: In this paper we set up a method called overlap decoherence correction (ODC) to take into account the quantum decoherence effect in a surface hopping framework. While keeping the standard surface hopping approach based on independent trajectories, our method allows to account for quantum decoherence by evaluating the overlap between frozen Gaussian wavepackets, the time evolution of which is obtained in an approximate way. The ODC scheme mainly depends on the parameter σ, which is the Gaussian width of the wavepackets. The performance of the ODC method is tested versus full quantum calculations on three model systems, and by comparison with full multiple spawning (FMS) results for the S(1)→S(0) decay in the azobenzene molecule.

The shear viscosity of rigid water models

Abstract: In this work, the shear viscosity at ambient conditions of several water models (SPC/E, TIP4P, TIP5P, and TIP4P/2005) is evaluated using the Green–Kubo formalism. The performance of TIP4P/2005 is excellent, that of SPC/E and TIP5P is more or less acceptable, whereas TIP4P and especially TIP3P give a poor agreement with experiment. Further calculations have been carried out for TIP4P/2005 to provide a wider assessment of its performance. In accordance with experimental data, TIP4P/2005 predicts a minimum in the shear viscosity for the 273 K isotherm, a shift in the minimum toward lower pressures at 298 K, and its disappearance at 373 K.

Small angle neutron scattering from 1-alkyl-3-methylimidazolium hexafluorophosphate ionic liquids ([C(n)mim][PF(6)], n=4, 6, and 8).

Abstract: The presence of local anisotropy in the bulk, isotropic, and ionic liquid phases-leading to local mesoscopic inhomogeneity-with nanoscale segregation and expanding nonpolar domains on increasing the length of the cation alkyl-substituents has been proposed on the basis of molecular dynamics (MD) simulations. However, there has been little conclusive experimental evidence for the existence of intermediate mesoscopic structure between the first/second shell correlations shown by neutron scattering on short chain length based materials and the mesophase structure of the long chain length ionic liquid crystals. Herein, small angle neutron scattering measurements have been performed on selectively H/D-isotopically substituted 1-alkyl-3-methylimidazolium hexafluorophosphate ionic liquids with butyl, hexyl, and octyl substituents. The data show the unambiguous existence of a diffraction peak in the low-Q region for all three liquids which moves to longer distances (lower Q), sharpens, and increases in intensity with increasing length of the alkyl substituent. It is notable, however, that this peak occurs at lower values of Q (longer length scale) than predicted in any of the previously published MD simulations of ionic liquids, and that the magnitude of the scattering from this peak is comparable with that from the remainder of the amorphous ionic liquid. This strongly suggests that the peak arises from the second coordination shells of the ions along the vector of alkyl-chain substituents as a consequence of increasing the anisotropy of the cation, and that there is little or no long-range correlated nanostructure in these ionic liquids.

Excited state dynamics in solid and monomeric tetracene: The roles of superradiance and exciton fission

Abstract: The excited state dynamics in polycrystalline thin films of tetracene are studied using both picosecond fluorescence and femtosecond transient absorption. The solid-state results are compared with those obtained for monomeric tetracene in dilute solution. The room temperature solid-state fluorescence decays are consistent with earlier models that take into account exciton-exciton annihilation and exciton fission but with a reduced delayed fluorescence lifetime, ranging from 20–100 ns as opposed to 2 μs or longer in single crystals. Femtosecond transient absorption measurements on the monomer in solution reveal several excited state absorption features that overlap the ground state bleach and stimulated emission signals. On longer timescales, the initially excited singlet state completely decays due to intersystem crossing, and the triplet state absorption superimposed on the bleach is observed, consistent with earlier flash photolysis experiments. In the solid-state, the transient absorption dynamics are ...

Communications: Accurate and efficient approximations to explicitly correlated coupled-cluster singles and doubles, CCSD-F12

Abstract: We propose a novel explicitly correlated coupled-cluster singles and doubles method CCSD(F12∗), which retains the accuracy of CCSD-F12 while the computational costs are only insignificantly larger than those for a conventional CCSD calculation.

Density fitting and Cholesky decomposition approximations in symmetry-adapted perturbation theory: Implementation and application to probe the nature of π-π interactions in linear acenes

Abstract: Density fitting (DF) approximations have been used to increase the efficiency of several quantum mechanical methods. In this work, we apply DF and a related approach, Cholesky decomposition (CD), to wave function-based symmetry-adapted perturbation theory (SAPT). We also test the one-center approximation to the Cholesky decomposition. The DF and CD approximations lead to a dramatic improvement in the overall computational cost of SAPT, while introducing negligible errors. For typical target accuracies, the Cholesky basis needed is noticeably smaller than the DF basis (although the cost of constructing the Cholesky vectors is slightly greater than that of constructing the three-index DF integrals). The SAPT program developed in this work is applied to the interactions between acenes previously studied by Grimme [Angew. Chem., Int. Ed. 47, 3430 (2008)], expanding the cases studied by adding the pentacene dimer. The SAPT decomposition of the acene interactions provides a more realistic picture of the interac...

Efficient stochastic thermostatting of path integral molecular dynamics.

Abstract: The path integral molecular dynamics (PIMD) method provides a convenient way to compute the quantum mechanical structural and thermodynamic properties of condensed phase systems at the expense of introducing an additional set of high frequency normal modes on top of the physical vibrations of the system. Efficiently sampling such a wide range of frequencies provides a considerable thermostatting challenge. Here we introduce a simple stochastic path integral Langevin equation (PILE) thermostat which exploits an analytic knowledge of the free path integral normal mode frequencies. We also apply a recently developed colored noise thermostat based on a generalized Langevin equation (GLE), which automatically achieves a similar, frequency-optimized sampling. The sampling efficiencies of these thermostats are compared with that of the more conventional Nose–Hoover chain (NHC) thermostat for a number of physically relevant properties of the liquid water and hydrogen-in-palladium systems. In nearly every case, the new PILE thermostat is found to perform just as well as the NHC thermostat while allowing for a computationally more efficient implementation. The GLE thermostat also proves to be very robust delivering a near-optimum sampling efficiency in all of the cases considered. We suspect that these simple stochastic thermostats will therefore find useful application in many future PIMD simulations.

Energy variational analysis of ions in water and channels: Field theory for primitive models of complex ionic fluids

Abstract: Ionic solutions are mixtures of interacting anions and cations. They hardly resemble dilute gases of uncharged noninteracting point particles described in elementary textbooks. Biological and electrochemical solutions have many components that interact strongly as they flow in concentrated environments near electrodes, ion channels, or active sites of enzymes. Interactions in concentrated environments help determine the characteristic properties of electrodes, enzymes, and ion channels. Flows are driven by a combination of electrical and chemical potentials that depend on the charges, concentrations, and sizes of all ions, not just the same type of ion. We use a variational method EnVarA (energy variational analysis) that combines Hamilton’s least action and Rayleigh’s dissipation principles to create a variational field theory that includes flow, friction, and complex structure with physical boundary conditions. EnVarA optimizes both the action integral functional of classical mechanics and the dissipation functional. These functionals can include entropy and dissipation as well as potential energy. The stationary point of the action is determined with respect to the trajectory of particles. The stationary point of the dissipation is determined with respect to rate functions (such as velocity). Both variations are written in one Eulerian (laboratory) framework. In variational analysis, an “extra layer” of mathematics is used to derive partial differential equations. Energies and dissipations of different components are combined in EnVarA and Euler–Lagrange equations are then derived. These partial differential equations are the unique consequence of the contributions of individual components. The form and parameters of the partial differential equations are determined by algebra without additional physical content or assumptions. The partial differential equations of mixtures automatically combine physical properties of individual (unmixed) components. If a new component is added to the energy or dissipation, the Euler–Lagrange equations change form and interaction terms appear without additional adjustable parameters. EnVarA has previously been used to compute properties of liquid crystals, polymer fluids, and electrorheological fluids containing solid balls and charged oil droplets that fission and fuse. Here we apply EnVarA to the primitive model of electrolytes in which ions are spheres in a frictional dielectric. The resulting Euler–Lagrange equations include electrostatics and diffusion and friction. They are a time dependent generalization of the Poisson–Nernst–Planck equations of semiconductors, electrochemistry, and molecular biophysics. They include the finite diameter of ions. The EnVarA treatment is applied to ions next to a charged wall, where layering is observed. Applied to an ion channel, EnVarA calculates a quick transient pile-up of electric charge, transient and steady flow through the channel, stationary “binding” in the channel, and the eventual accumulation of salts in “unstirred layers” near channels. EnVarA treats electrolytes in a unified way as complex rather than simple fluids. Ad hoc descriptions of interactions and flow have been used in many areas of science to deal with the nonideal properties of electrolytes. It seems likely that the variational treatment can simplify, unify, and perhaps derive and improve those descriptions.

Correlation consistent basis sets for molecular core-valence effects with explicitly correlated wave functions: The atoms B–Ne and Al–Ar

Abstract: Correlation consistent basis sets have been optimized for accurately describing core-core and core-valence correlation effects with explicitly correlated F12 methods. The new sets, denoted cc-pCVnZ-F12 (n=D, T, Q) and aug-cc-pC(F12)VnZ (n=D, T, Q, 5), were developed by augmenting the cc-pVnZ-F12 and aug-cc-pVnZ families of basis sets with additional functions whose exponents were optimized based on the difference between all-electron and valence-electron correlation energies. The number of augmented functions added is fewer, in general, than in the standard cc-pCVnZ and cc-pwCVnZ families of basis sets. Optimal values of the geminal Slater exponent for use with these basis sets in MP2-F12 calculations are presented and are also recommended for CCSD-F12b calculations. Auxiliary basis sets for use in the resolution of the identity approximation in explicitly correlated calculations have also been optimized and matched to the new cc-pCVnZ-F12 series of orbital basis sets. The cc-pCVnZ-F12 basis sets, along with the new auxiliary sets, were benchmarked in CCSD(T)-F12b calculations of spectroscopic properties on a series of homo- and heteronuclear first and second row diatomic molecules. Comparing the effects of correlating the outer core electrons in these molecules with those from conventional CCSD(T) at the complete basis set limit, which involved calculations with new cc-pCV6Z basis sets for the second row elements that were also developed in the course of this work, it is observed that the F12 values are reasonably well converged already at just the triple-zeta level.

Fast computation of molecular random phase approximation correlation energies using resolution of the identity and imaginary frequency integration

Abstract: The random phase approximation (RPA) is an increasingly popular post-Kohn–Sham correlation method, but its high computational cost has limited molecular applications to systems with few atoms. Here we present an efficient implementation of RPA correlation energies based on a combination of resolution of the identity (RI) and imaginary frequency integration techniques. We show that the RI approximation to four-index electron repulsion integrals leads to a variational upper bound to the exact RPA correlation energy if the Coulomb metric is used. Auxiliary basis sets optimized for second-order Moller–Plesset (MP2) calculations are well suitable for RPA, as is demonstrated for the HEAT [A. Tajti et al., J. Chem. Phys. 121, 11599 (2004)] and MOLEKEL [F. Weigend et al., Chem. Phys. Lett. 294, 143 (1998)] benchmark sets. Using imaginary frequency integration rather than diagonalization to compute the matrix square root necessary for RPA, evaluation of the RPA correlation energy requires O(N4 log N) operations an...

Density fitting of intramonomer correlation effects in symmetry-adapted perturbation theory

Abstract: Symmetry-adapted perturbation theory (SAPT) offers insight into the nature of intermolecular interactions. In addition, accurate energies can be obtained from the wave function-based variant of SAPT provided that intramonomer electron correlation effects are included. We apply density-fitting (DF) approximations to the intramonomer correlation corrections in SAPT. The introduction of this approximation leads to an improvement in the computational cost of SAPT by reducing the scaling of certain SAPT terms, reducing the amount of disk I/O, and avoiding the explicit computation of certain types of MO integrals. We have implemented all the intramonomer correlation corrections to SAPT through second-order under the DF approximation. Additionally, leading third-order terms are also implemented. The accuracy of this truncation of SAPT is tested against the S22 test set of Hobza and co-workers [Phys. Chem. Chem. Phys. 8, 1985 (2006)]. When the intramonomer corrections to dispersion are included in SAPT, a mean ab...

Adsorption of small aromatic molecules on the (111) surfaces of noble metals: A density functional theory study with semiempirical corrections for dispersion effects

Abstract: The adsorption of benzene, thiophene, and pyridine on the (111) surface of gold and copper have been studied using density functional theory (DFT). Adsorption geometries and energies as well as the nature of bonding have been analyzed and compared to experimental results. Dispersion effects between neighboring molecules and between molecules and the surface have been taken into account via a semiempirical C(6)R(-6) approach. The C(6) coefficients for metal atoms have been deduced using both atomic properties and a hybrid QM:QM approach. Whereas the pure DFT calculations underestimate the adsorption energies significantly, a good agreement with experimental results is obtained using the DFT-D method based on the QM:QM hybrid approach.

Benchmarks of electronically excited states: basis set effects on CASPT2 results.

Abstract: Vertical excitation energies and one-electron properties are computed for the valence excited states of 28 medium-sized organic benchmark molecules using multistate multiconfigurational second-order perturbation theory (MS-CASPT2) and the augmented correlation-consistent aug-cc-pVTZ basis set. They are compared with previously reported MS-CASPT2 results obtained with the smaller TZVP basis. The basis set extension from TZVP to aug-cc-pVTZ causes rather minor and systematic shifts in the vertical excitation energies that are normally slightly reduced (on average by 0.11 eV for the singlets and by 0.09 eV for the triplets), whereas the changes in the calculated oscillator strengths and dipole moments are somewhat more pronounced on a relative scale. These basis set effects at the MS-CASPT2 level are qualitatively and quantitatively similar to those found at the coupled cluster level for the same set of benchmark molecules. The previously proposed theoretical best estimates (TBE-1) for the vertical excitation energies for 104 singlet and 63 triplet excited states of the benchmark molecules are upgraded by replacing TZVP with aug-cc-pVTZ data that yields a new reference set (TBE-2). Statistical evaluations of the performance of density functional theory (DFT) and semiempirical methods lead to the same ranking and very similar quantitative results for TBE-1 and TBE-2, with slightly better performance measures with respect to TBE-2. DFT/MRCI is most accurate among the investigated DFT-based approaches, while the OMx methods with orthogonalization corrections perform best at the semiempirical level.

Crystal structure prediction using the minima hopping method

Abstract: A structure prediction method is presented based on the minima hopping method. To escape local minima, moves on the configurational enthalpy surface are performed by variable cell shape molecular dynamics. To optimize the escape steps the initial atomic and cell velocities are aligned to low curvature directions of the current local minimum. The method is applied to both silicon crystals and well-studied binary Lennard-Jones mixtures. For the latter new putative ground state structures are presented. It is shown that a high success rate is achieved and a reliable prediction of unknown ground state structures is possible.

Two- and three-body interatomic dispersion energy contributions to binding in molecules and solids

Abstract: We present numerical estimates of the leading two- and three-body dispersion energy terms in van der Waals interactions for a broad variety of molecules and solids. The calculations are based on London and Axilrod-Teller-Muto expressions where the required interatomic dispersion energy coefficients, C(6) and C(9), are computed "on the fly" from the electron density. Inter- and intramolecular energy contributions are obtained using the Tang-Toennies (TT) damping function for short interatomic distances. The TT range parameters are equally extracted on the fly from the electron density using their linear relationship to van der Waals radii. This relationship is empiricially determined for all the combinations of He-Xe rare gas dimers, as well as for the He and Ar trimers. The investigated systems include the S22 database of noncovalent interactions, Ar, benzene and ice crystals, bilayer graphene, C(60) dimer, a peptide (Ala(10)), an intercalated drug-DNA model [ellipticine-d(CG)(2)], 42 DNA base pairs, a protein (DHFR, 2616 atoms), double stranded DNA (1905 atoms), and 12 molecular crystal polymorphs from crystal structure prediction blind test studies. The two- and three-body interatomic dispersion energies are found to contribute significantly to binding and cohesive energies, for bilayer graphene the latter reaches 50% of experimentally derived binding energy. These results suggest that interatomic three-body dispersion potentials should be accounted for in atomistic simulations when modeling bulky molecules or condensed phase systems.

Exact nonadditive kinetic potentials for embedded density functional theory

Abstract: We describe an embedded density functional theory (DFT) protocol in which the nonadditive kinetic energy component of the embedding potential is treated exactly. At each iteration of the Kohn–Sham equations for constrained electron density, the Zhao–Morrison–Parr constrained search method for constructing Kohn–Sham orbitals is combined with the King-Handy expression for the exact kinetic potential. We use this formally exact embedding protocol to calculate ionization energies for a series of three- and four-electron atomic systems, and the results are compared to embedded DFT calculations that utilize the Thomas–Fermi (TF) and the Thomas–Fermi–von Weisacker approximations to the kinetic energy functional. These calculations illustrate the expected breakdown due to the TF approximation for the nonadditive kinetic potential, with errors of 30%–80% in the calculated ionization energies; by contrast, the exact protocol is found to be accurate and stable. To significantly improve the convergence of the new protocol, we introduce a density-based switching function to map between the exact nonadditive kinetic potential and the TF approximation in the region of the nuclear cusp, and we demonstrate that this approximation has little effect on the accuracy of the calculated ionization energies. Finally, we describe possible extensions of the exact protocol to perform accurate embedded DFT calculations in large systems with strongly overlapping subsystem densities.

Accurate frozen-density embedding potentials as a first step towards a subsystem description of covalent bonds.

Abstract: The frozen-density embedding (FDE) scheme [Wesolowski and Warshel, J. Phys. Chem. 97, 8050 (1993)] relies on the use of approximations for the kinetic-energy component vT[ρ1,ρ2] of the embedding potential. While with approximations derived from generalized-gradient approximation kinetic-energy density functional weak interactions between subsystems such as hydrogen bonds can be described rather accurately, these approximations break down for bonds with a covalent character. Thus, to be able to directly apply the FDE scheme to subsystems connected by covalent bonds, improved approximations to vT are needed. As a first step toward this goal, we have implemented a method for the numerical calculation of accurate references for vT. We present accurate embedding potentials for a selected set of model systems, in which the subsystems are connected by hydrogen bonds of various strength (water dimer and F–H–F−), a coordination bond (ammonia borane), and a prototypical covalent bond (ethane). These accurate potent...

Crystal nucleation of hard spheres using molecular dynamics, umbrella sampling, and forward flux sampling: A comparison of simulation techniques

Abstract: Over the last number of years several simulation methods have been introduced to study rare events such as nucleation. In this paper we examine the crystal nucleation rate of hard spheres using three such numerical techniques: molecular dynamics, forward flux sampling, and a Bennett–Chandler-type theory where the nucleation barrier is determined using umbrella sampling simulations. The resulting nucleation rates are compared with the experimental rates of Harland and van Megen [Phys. Rev. E 55, 3054 (1997)], Sinn et al. [Prog. Colloid Polym. Sci. 118, 266 (2001)], Schatzel and Ackerson [Phys. Rev. E 48, 3766 (1993)], and the predicted rates for monodisperse and 5% polydisperse hard spheres of Auer and Frenkel [Nature 409, 1020 (2001)]. When the rates are examined in units of the long-time diffusion coefficient, we find agreement between all the theoretically predicted nucleation rates, however, the experimental results display a markedly different behavior for low supersaturation. Additionally, we examined the precritical nuclei arising in the molecular dynamics, forward flux sampling, and umbrella sampling simulations. The structure of the nuclei appears independent of the simulation method, and in all cases, the nuclei contains on average significantly more face-centered-cubic ordered particles than hexagonal-close-packed ordered particles.