Volume 135, Issue 19, 21 November 2011

A numerical scheme based upon established hydrodynamic and elastic considerations is introduced and used to predict the intermediate scattering function for lipid bilayer membranes. The predictions span multiple wavelength regimes, including those studied by dynamic light scattering (DLS; microns) and neutron spinecho (NSE) spectroscopy (10–100 nm). The results validate a recent theory specific to the NSE regime and expose slight inaccuracies associated with the theoretical results available in the DLS regime. The assumptions that underlie both our numerical methods and the related theoretical predictions are reviewed in detail to explain when certain results can be applied to experiment and where caution must be exercised.
 COMMUNICATIONS


Communication: Standard surface hopping predicts incorrect scaling for Marcus’ goldenrule rate: The decoherence problem cannot be ignored
View Description Hide DescriptionWe evaluate the accuracy of Tully's surface hopping algorithm for the spinboson model for the case of a small diabatic coupling parameter (V). We calculate the transition rates between diabatic surfaces, and we compare our results to the expected Marcus rates. We show that standard surface hopping yields an incorrect scaling with diabatic coupling (linear in V), which we demonstrate is due to an incorrect treatment of decoherence. By modifying standard surface hopping to include decoherence events, we recover the correct scaling (∼V ^{2}).

Communication: A global hybrid generalized gradient approximation to the exchangecorrelation functional that satisfies the secondorder densitygradient constraint and has broad applicability in chemistry
View Description Hide DescriptionWe extend our recent SOGGA11 approximation to the exchangecorrelation functional to include a percentage of HartreeFock exchange. The new functional, called SOGGA11X, has better overall performance for a broad chemical database than any previously available global hybrid generalized gradient approximation, and in addition it satisfies an extra physical constraint in that it is correct to second order in the densitygradient.
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 ARTICLES

 Theoretical Methods and Algorithms

Phase diagram of hard tetrahedra
View Description Hide DescriptionAdvancements in the synthesis of faceted nanoparticles and colloids have spurred interest in the phase behavior of polyhedral shapes. Regular tetrahedra have attracted particular attention because they prefer local symmetries that are incompatible with periodicity. Two dense phases of regular tetrahedra have been reported recently. The densest known tetrahedron packing is achieved in a crystal of triangular bipyramids (dimers) with a packing density of 4000/4671 ≈ 85.63%. In simulation a dodecagonal quasicrystal is observed; its approximant, with periodic tiling (3.4.3^{2}.4), can be compressed to a packing fraction of 85.03%. Here, we show that the quasicrystal approximant is more stable than the dimer crystal for packing densities below 84% using Monte Carlo computer simulations and free energy calculations. To carry out the free energy calculations, we use a variation of the FrenkelLadd method for anisotropic shapes and thermodynamic integration. The enhanced stability of the approximant can be attributed to a network substructure, which maximizes the free volume (and hence the wiggle room) available to the particles and facilitates correlated motion of particles, which further contributes to entropy and leads to diffusion for packing densities below 65%. The existence of a solidsolidtransition between structurally distinct phases not related by symmetry breaking – the approximant and the dimer crystal – is unusual for hard particle systems.

Basis set convergence of the coupledcluster correction, : Best practices for benchmarking noncovalent interactions and the attendant revision of the S22, NBC10, HBC6, and HSG databases
View Description Hide DescriptionIn benchmarkquality studies of noncovalent interactions, it is common to estimate interaction energies at the complete basis set (CBS) coupledcluster through perturbative triples [CCSD(T)] level of theory by adding to CBS secondorder perturbation theory (MP2) a “coupledcluster correction,” , evaluated in a modest basis set. This work illustrates that commonly used basis sets such as 631G*(0.25) can yield large, even wrongly signed, errors for that vary significantly by binding motif. Doubleζ basis sets show more reliable results when used with explicitly correlated methods to form a correction, yielding a mean absolute deviation of 0.11 kcal mol^{−1} for the S22 test set. Examining the coupledcluster correction for basis sets up to sextupleζ in quality reveals that converges monotonically only beyond a turning point at tripleζ or quadrupleζ quality. In consequence, CBS extrapolation of corrections before the turning point, generally CBS (augccpVDZ,augccpVTZ), are found to be unreliable and often inferior to augccpVTZ alone, especially for hydrogenbonding systems. Using the findings of this paper, we revise some recent benchmarks for noncovalent interactions, namely the S22, NBC10, HBC6, and HSG test sets. The maximum differences in the revised benchmarks are 0.080, 0.060, 0.257, and 0.102 kcal mol^{−1}, respectively.

A distancedependent parameterization of the extended Hubbard model for conjugated and aromatic hydrocarbons derived from stretched ethene
View Description Hide DescriptionThe Hubbard model, which is widely used in physics but is mostly unfamiliar to chemists, provides an attractive yet simple model for chemistry beyond the self consistent field molecular orbital approximation. The Hubbard model adds an effective electronelectron repulsion when two electrons occupy the same atomic orbital to the familiar Hückel Hamiltonian. Thus it breaks the degeneracy between excited singlet and triplet states and allows an explicit treatment of electroncorrelation. We show how to evaluate the parameters of the model from highlevel ab initio calculations on twoatom fragments and then to transfer the parameters to large molecules and polymers where accurate ab initio calculations are difficult or impossible. The recently developed MSRASPT2 method is used to generate accurate potential energy curves for ethene as a function of carboncarbon bond length, which are used to parameterize the model for conjugated hydrocarbons. Test applications to several conjugated/aromatic molecules show that even though the model is very simple, it is capable of reasonably accurate predictions for bond lengths, and predicts molecular excitation energies in reasonable agreement with those from the MSRASPT2 method.

Potentialfunctional embedding theory for molecules and materials
View Description Hide DescriptionWe introduce a potentialfunctional embedding theory by reformulating a recently proposed densitybased embedding theory in terms of functionals of the embedding potential. This potentialfunctional based theory completes the dual problem in the context of embedding theory for which densityfunctional embedding theory has existed for two decades. With this potentialfunctional formalism, it is straightforward to solve for the unique embedding potential shared by all subsystems. We consider charge transfer between subsystems and discuss how to treat fractional numbers of electrons in subsystems. We show that one is able to employ different energy functionals for different subsystems in order to treat different regions with theories of different levels of accuracy, if desired. The embedding potential is solved for by directly minimizing the total energy functional, and we discuss how to efficiently calculate the gradient of the total energy functional with respect to the embedding potential. Forces are also derived, thereby making it possible to optimize structures and account for nuclear dynamics. We also extend the theory to spinpolarized cases. Numerical examples of the theory are given for some homo and heteronuclear diatomic molecules and a more complicated test of a sixhydrogenatom chain. We also test our theory in a periodic bulk environment with calculations of basic properties of bulk NaCl, by treating each atom as a subsystem. Finally, we demonstrate the theory for water adsorption on the MgO(001)surface.

Accurate potential energy surfaces with a DFT+ approach
View Description Hide DescriptionWe introduce an improvement to the Hubbard U augmented density functional approach known as DFT+U that incorporates variations in the value of selfconsistently calculated, linearresponse U with changes in geometry. This approach overcomes the one major shortcoming of previous DFT+U studies, i.e., the use of an averaged Hubbard U when comparing energies for different points along a potential energy surface is no longer required. While DFT+U is quite successful at providing accurate descriptions of localized electrons (e.g., d or f) by correcting selfinteraction errors of standard exchange correlation functionals, we show several diatomic molecule examples where this positiondependent DFT+ provides a significant two to fourfold improvement over DFT+U predictions, when compared to accurate correlated quantum chemistry and experimental references. DFT+ reduces errors in binding energies, frequencies, and equilibrium bond lengths by applying the linearresponse, positiondependent at each configuration considered. This extension is most relevant where variations in U are large across the points being compared, as is the case with covalent diatomic molecules such as transitionmetal oxides. We thus provide a tool for deciding whether a standard DFT+U approach is sufficient by determining the strength of the dependence of U on changes in coordinates. We also apply this approach to larger systems with greater degrees of freedom and demonstrate how DFT+ may be applied automatically in relaxations, transitionstate finding methods, and dynamics.

Spinadapted openshell timedependent density functional theory. III. An even better and simpler formulation
View Description Hide DescriptionThe recently proposed spinadapted timedependent density functional theory (STDDFT) [Z. Li and W. Liu, J. Chem. Phys.133, 064106 (2010)]10.1063/1.3463799 resolves the spincontamination problem in describing singly excited states of high spin openshell systems. It is an extension of the standard restricted openshell KohnShambased TDDFT which can only access those excited states due to singletcoupled single excitations. It is also far superior over the unrestricted KohnShambased TDDFT (UTDDFT) which suffers from severe spin contamination for those excited states due to tripletcoupled single excitations. Nonetheless, the accuracy of STDDFT for high spin openshell systems is still inferior to TDDFT for wellbehaved closedshell systems. The reason can be traced back to the violation of the spin degeneracy conditions (SDC) by approximate exchangecorrelation (XC) functionals. Noticing that spinadapted random phase approximation (SRPA) can indeed maintain the SDC by virtue of the WignerEckart theorem, a hybrid ansatz combining the good of STDDFT and SRPA can immediately be envisaged. The resulting formalism, dubbed as XTDDFT, is free of spin contamination and can also be viewed as a SRPA correction to the XC kernel of UTDDFT. Compared with STDDFT, XTDDFT leads to much improved results for the lowlying excited states of, e.g., , yet with much reduced computational cost. Therefore, XTDDFT can be recommended for routine calculations of excited states of high spin openshell systems.

On the entropy of relaxing deterministic systems
View Description Hide DescriptionIn this paper, we revisit Gibbs’ second (unresolved) paradox, namely the constancy of the finegrained Gibbs entropy for autonomous Hamiltonian systems. We compare and contrast the different roles played by dissipation and entropy both at equilibrium where dissipation is identically zero and away from equilibrium where entropy cannot be defined and seems unnecessary in any case. Away from equilibrium dissipation is a powerful quantity that can always be defined and that appears as the central argument of numerous exact theorems: the fluctuation, relaxation, and dissipation theorems and the newly derived Clausius inequality.

Differential geometry based solvation model. III. Quantum formulation
View Description Hide DescriptionSolvation is of fundamental importance to biomolecular systems. Implicit solventmodels, particularly those based on the PoissonBoltzmann equation for electrostaticanalysis, are established approaches for solvation analysis. However, ad hoc solventsolute interfaces are commonly used in the implicit solventtheory. Recently, we have introduced differential geometry based solvation models which allow the solventsolute interface to be determined by the variation of a total free energy functional. Atomic fixed partial charges (point charges) are used in our earlier models, which depends on existing molecular mechanical force field software packages for partial charge assignments. As most force field models are parameterized for a certain class of molecules or materials, the use of partial charges limits the accuracy and applicability of our earlier models. Moreover, fixed partial charges do not account for the charge rearrangement during the solvation process. The present work proposes a differential geometry based multiscale solvation model which makes use of the electron density computed directly from the quantum mechanical principle. To this end, we construct a new multiscale total energy functional which consists of not only polar and nonpolar solvation contributions, but also the electronic kinetic and potential energies. By using the EulerLagrange variation, we derive a system of three coupled governing equations, i.e., the generalized PoissonBoltzmann equation for the electrostatic potential, the generalized LaplaceBeltrami equation for the solventsolute boundary, and the KohnSham equations for the electronic structure. We develop an iterative procedure to solve three coupled equations and to minimize the solvation free energy. The present multiscale model is numerically validated for its stability, consistency and accuracy, and is applied to a few sets of molecules, including a case which is difficult for existing solvation models. Comparison is made to many other classic and quantum models. By using experimental data, we show that the present quantum formulation of our differential geometry based multiscale solvation model improves the prediction of our earlier models, and outperforms some explicit solvation model.

Dispersion interactions in densityfunctional theory: An adiabaticconnection analysis
View Description Hide DescriptionWe present an analysis of the dispersion interaction energy and forces in densityfunctional theory from the point of view of the adiabatic connection between the Kohn–Sham noninteracting and fully interacting systems. Accurate coupledcluster singlesdoublesperturbativetriples [CCSD(T)] densities are computed for the helium dimer and used to construct the exchangecorrelation potential of Kohn–Sham theory, showing agreement with earlier results presented for the Hartree–Fock–Kohn–Sham method [M. Allen and D. J. Tozer, J. Chem. Phys.117, 11113 (2002)10.1063/1.1522715]. The accuracy of the methodology utilized to determine these solutions is checked by calculation of the Hellmann–Feynman forces based on the Kohn–Sham densities, which are compared with analytic CCSD(T) forces. To ensure that this comparison is valid in a finite atomicorbital basis set, we employ floating Gaussian basis functions throughout and all results are counterpoise corrected. The subtle chargerearrangement effects associated with the dispersion interaction are highlighted as the origin of a large part of the dispersion force. To recover the exchangecorrelation components of the interaction energy, adiabatic connections are constructed for the supermolecular system and for its constituent atoms; subtraction of the resulting adiabaticconnection curves followed by integration over the interaction strength recovers the exchangecorrelation contribution relevant to the densityfunctional description of the dispersion interaction. The results emphasize the longranged, dynamically correlated nature of the dispersion interaction between closedshell species. An alternative adiabaticconnection path is also explored, where the electronic interactions are introduced in a manner that emphasizes the range of the electronic interactions, highlighting their purely longranged nature, consistent with the success of rangeseparated hybrid approaches in this context.

Replica exchange and expanded ensemble simulations as Gibbs sampling: Simple improvements for enhanced mixing
View Description Hide DescriptionThe widespread popularity of replica exchange and expanded ensemble algorithms for simulating complex molecular systems in chemistry and biophysics has generated much interest in discovering new ways to enhance the phase space mixing of these protocols in order to improve sampling of uncorrelated configurations. Here, we demonstrate how both of these classes of algorithms can be considered as special cases of Gibbs sampling within a Markov chain Monte Carlo framework. Gibbs sampling is a wellstudied scheme in the field of statistical inference in which different random variables are alternately updated from conditional distributions. While the update of the conformational degrees of freedom by Metropolis Monte Carlo or molecular dynamics unavoidably generates correlated samples, we show how judicious updating of the thermodynamic state indices—corresponding to thermodynamic parameters such as temperature or alchemical coupling variables—can substantially increase mixing while still sampling from the desired distributions. We show how state update methods in common use can lead to suboptimal mixing, and present some simple, inexpensive alternatives that can increase mixing of the overall Markov chain, reducing simulation times necessary to obtain estimates of the desired precision. These improved schemes are demonstrated for several common applications, including an alchemical expanded ensemble simulation, parallel tempering, and multidimensional replica exchange umbrella sampling.

Asymmetric stochastic localization in geometry controlled kinetics
View Description Hide DescriptionWe consider the motion of Brownian particles confined in a twodimensional symmetric bilobal enclosure with uneven cross section. Varying cross section of the confinement results in an effective entropic potential in reduced dimension. By employing two external noise forces, one additive and another multiplicative along x direction, we demonstrate that a correlation between them causes a symmetry breaking of entropic stability, i.e., a difference in relative stability of two lobes. This leads to an asymmetric localization of population in the stationary state. A twostate model is proposed to explain the asymmetric localization of population due to entropic diffusion.

The effect of a mechanical force on quantum reaction rate: Quantum Bell formula
View Description Hide DescriptionThe purpose of this note is to derive a quantummechanical analog of Bell's formula, which describes the sensitivity of a chemical reaction to a mechanical pulling force. According to this formula, the reaction rate depends exponentially on the force f, i.e., k( f ) ∼ exp( f / f _{ c }), where the force scale f _{ c } is estimated as the thermal energy k _{ B } T divided by a distance a between the reactant and transition states along the pulling coordinate. Here I use instanton theory to show that, at low temperatures where quantum tunneling is dominant, this force scale becomes f _{ c } ∼ ℏω/a (in the limit where frictional damping is absent) or f _{ c } ∼ ℏτ^{−1}/a (in the strong damping limit). Here ω is a characteristic vibration frequency along the pulling coordinate and τ is a characteristic relaxation time in the reactant state. That is, unlike the classical case where f _{ c } is unaffected by dissipation, this force scale becomes friction dependent in the quantum limit. I further derive higherorder corrections in the force dependence of the rate, describe generalizations to many degrees of freedom, and discuss connection to other quantum rate theories.

Binary systems from quantum cluster equilibrium theory
View Description Hide DescriptionAn extension of the quantum cluster equilibrium theory to treat binary mixtures is introduced in this work. The necessary equations are derived and a possible implementation is presented. In addition an alternative sampling procedure using widely available experimental data for the quantum cluster equilibrium approach is suggested and tested. An illustrative example, namely, the binary mixture of water and dimethyl sulfoxide, is given to demonstrate the new approach. A basic cluster set is introduced containing the relevant cluster motifs. The populations computed by the quantum cluster equilibrium approach are compared to the experimental data. Furthermore, the excess Gibbs free energy is computed and compared to experiments as well.

Direct perturbation theory in terms of energy derivatives: Scalarrelativistic treatment up to sixth order
View Description Hide DescriptionA formulation of sixthorder direct perturbation theory (DPT) to treat relativistic effects in quantumchemical calculations is presented in the framework of derivative theory. Detailed expressions for DPT6 are given at the Hartree–Fock level in terms of the third derivative of the energy with respect to the relativistic perturbation parameter defined as . They were implemented for the computation of scalarrelativistic energy corrections. The convergence of the scalarrelativistic DPT expansion is studied for energies and firstorder properties such as dipole moment and electricfield gradient within the series of the hydrogen halides (HX, X = F, Cl, Br, I, and At). Comparison with spinfree Dirac–Coulomb calculations indicates that the DPT series exhibits a smooth and monotonic convergence. The rate of convergence, however, depends on the charge of the involved nuclei and significantly slows down for heavyelement compounds.
 Advanced Experimental Techniques

Novel coherent twodimensional optical spectroscopy probes of chirality exchange and fluctuations in molecules
View Description Hide DescriptionWe demonstrate how stochastic transitions between molecular configurations with opposite senses of chirality may be probed by 2D optical signals with specific pulse polarization configurations. The thirdorder optical response of molecular dimers (such as biphenyls) with dynamical axial chirality is calculated to order of k ^{2} in the wavevector of light. Spectroscopic signatures of equilibrium chirality fluctuations are predicted for three dynamical models (OrnsteinUhlenbeck, twostate jump, and diffusion in double well) of the dihedral angle that controls the chirality.

Sum frequency generationcompressive sensing microscope
View Description Hide DescriptionA new sum frequency generation imaging microscope using a novel sampling theory, compressive sensing (CS), has been developed for surface studies. CS differentiates itself from the conventional sampling methods by collecting fewer measurements than the traditional methods to reconstruct a high quality image. Pseudorandom patterns were applied to a light modulator and reflected the sum frequency (SF) signal generated from the sample into a photomultiplier tube detector. The image of the sample was reconstructed using sparsity preserving algorithms from the SF signal. The influences of the number of CS testingpatterns applied and the number of SF pulses acquired for each pattern on the quality of the images was investigated and a comparison of the image quality with the traditional raster scan was made at varying resolutions for a goldpatterned Si surface. Our results demonstrate the CS technique achieved 16 times the pixel density beyond the resolution where the raster scan strategy lost its ability to image the sample due to the dilution of the SF signal below the detection limit of the detector.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Molecularbeam study of the ammonia–noble gas systems: Characterization of the isotropic interaction and insights into the nature of the intermolecular potential
View Description Hide DescriptionWe report new high resolution molecular beam experiments aimed at characterizing the intermolecular interaction in the NH_{3}–Ng (Ng = He, Ne, Ar, Kr, Xe) weakly bound complexes. Integral cross section data are obtained over a sufficiently wide velocity range and with rotationally hot NH_{3} molecules to produce (except for the NH_{3}–He case) a well resolved “glory” quantum interference pattern. Data analysis, carried out by employing a recently proposed potential model, allows unique information on the absolute scale of the intermolecular interaction to be obtained both at long range and at the equilibrium distance. An extensive and internally consistent comparison with the behavior of the corresponding Kr–Ng systems is exploited in order to identify those cases where an interaction component due to charge transfer effects provides an appreciable intermolecular bond stabilization that is clearly distinct from and must be added to the standard van der Waals plus induction picture. The results of the present investigation extend the phenomenology of perturbative charge transfer effects in gas phase complexes involving hydrogenated molecules.

Cross sections and rate constants for OH + H_{2} reaction on three different potential energy surfaces for rovibrationally excited reagents
View Description Hide DescriptionA systematic study of the reagent rovibrational excitations in H_{2} + OH reaction is presented on three different potential energy surfaces using the multiconfiguration timedependent Hartree method. An exact form of the kinetic energy operator including Coriolis coupling has been used. Coupled channel results on WDSE surface for vibrational excitation of H_{2} produce very large cross sections in accordance with the previous approximate results. The rate constant obtained for H_{2}(v = 1) at 300 K on the YZCL2 surface shows an excellent agreement with the most recent experimental result. Quantum dynamical results for rovibrational excitation of reagents obtained on the WSLFH surface show similar behavior to previous quasiclassical trajectory studies. The integral cross sections obtained for excited reagent rotations exhibit contrasting trends on the three surfaces. The effects are explained considering the different orientations of the transition state structure and the individual surface characteristics.