Volume 134, Issue 6, 14 February 2011

We report the combined results of computational and x ray scattering studies of amorphous methyltributylammonium bis(trifluoromethylsulfonyl)amide as a function of temperature. These studies included the temperature range for the normal isotropic liquid, a deeply supercooled liquid and the glass. The low q peaks in the range from 0.3 to 1.5 Å^{−1} in the structure function of this liquid can be properly accounted for by correlations between first and second nearest neighbors. The lowest q peak can be assigned to real space correlations between ions of the same charge, while the second peak arises mostly from nearest neighbors of opposite charge. Peaks at larger q values are mostly intramolecular in nature. While our simulated structure functions provide an excellent match to our experimental results and our experimental findings agree with previous studies reported for this liquid, the prior interpretation of the experimental data in terms of an interdigitated smectic A phase is not supported by our simulations. In this work, we introduce a set of general theoretical partitions of real and reciprocal space correlations that allow for unambiguous analysis of all intra and interionic contributions to the structure function and coherent scattering intensity. We find that the intermolecular contributions to the x ray scattering intensity are dominated by the anions and cross terms between cations and anions for this ionic liquid.
 COMMUNICATIONS


Communication: Accurate determination of sidechain torsion angle χ_{1} in proteins: Phenylalanine residues
View Description Hide DescriptionQuantitative sidechain torsion angle χ_{1} determinations of phenylalanine residues in Desulfovibrio vulgaris flavodoxin are carried out using exclusively the correlation between the experimental vicinal coupling constants and theoretically determined Karplus equations. Karplus coefficients for nine vicinal coupling related with the torsion angle χ_{1} were calculated using the B3LYP functional and basis sets of different size. Optimized χ_{1} angles are in outstanding agreement with those previously reported by employing x ray and NMR measurements.
 Top

 ARTICLES

 Theoretical Methods and Algorithms

Constrained active space unrestricted meanfield methods for controlling spincontamination
View Description Hide DescriptionWe have recently proposed a novel approach for obtaining highspin restricted openshell Hartree–Fock wave functions by imposing constraints on the unrestricted Hartree–Fock (UHF) method [T. Tsuchimochi and G. E. Scuseria, J. Chem. Phys. 133, 141102 (2010)]. We here extend these ideas to the case where the constraints are released in an active space but imposed elsewhere. If the active space is properly chosen, our constrained UHF (CUHF) method greatly benefits from a controlled brokensymmetry effect while avoiding the massive spin contamination of traditional UHF. We also revisit and apply Lwdin's projection operator to CUHF and obtain multireference wave functions with moderate computational cost. We report singlet–triplet energy splittings showing that our constrained scheme outperforms fully unrestricted methods. This constrained approach can be readily used in spin density functional theory with similar favorable effects.

Alkane adsorption in Naexchanged chabazite: The influence of dispersion forces
View Description Hide DescriptionThe importance of dispersion forces for the correct description of the adsorption of short alkanes in Naexchanged and purely siliceous chabazite has been investigated at different levels of theory: (i) standard densityfunctional (DFT) calculations using the Perdew, Burke, and Ernzerhof (PBE) exchange–correlation functional in the generalized gradient approximation, (ii) dispersion corrections based on empirical force fields according to Grimme [J. Computat. Chem.134, 1463 (2004)– PBEd], (iii) calculations based on the van der Waals density functional (vdWDF) proposed by Dion et al.[Phys. Rev. Lett.92, 246401 (2004)], and (iv) using the random phase approximation (RPA) in combination with the adiabaticconnection fluctuationdissipation theorem (RPAACFDT), using wavefunctions calculated at the DFT and Hartree–Fock (HF) levels. A full relaxation of the adsorbate–zeolite complex was performed at the PBE, PBEd, and vdWDF levels. RPA and RPAHF energies were calculated for the optimized configurations. A critical analysis of the results shows that the most accurate description is achieved at the RPA level with HF exchange energies, while both PBEd and vdWDF overestimate the strength of the interaction with the acid site.

The accuracy of dipole moments from spincomponent scaled CC2 in ground and electronically excited states
View Description Hide DescriptionThe accuracy of dipole moments calculated from wave function methods based on secondorder perturbation theory is investigated in the ground and electronically excited states. Results from the approximate coupledcluster singlesanddoubles model, CC2, Møller–Plesset perturbation theory, MP2, and the algebraic diagrammatic construction through secondorder, ADC(2), are discussed together with the spincomponent scaled and the scaled oppositespin variants of these methods. The computed dipole moments show a very good correlation with data from highresolution spectroscopy. Compared to the unscaled methods, the spincomponent scaling increases the accuracy of the results and improves the robustness of the calculations. An accuracy about 0.2 to 0.1 D in the ground state and about 0.3 to 0.2 D in the electronically excited states can be achieved with these approaches.

Basis set construction for molecular electronic structure theory: Natural orbital and Gauss–Slater basis for smooth pseudopotentials
View Description Hide DescriptionA simple yet general method for constructing basis sets for molecular electronic structure calculations is presented. These basis sets consist of atomic natural orbitals from a multiconfigurational selfconsistent field calculation supplemented with primitive functions, chosen such that the asymptotics are appropriate for the potential of the system. Primitives are optimized for the homonuclear diatomic molecule to produce a balanced basis set. Two general features that facilitate this basis construction are demonstrated. First, weak coupling exists between the optimal exponents of primitives with different angular momenta. Second, the optimal primitive exponents for a chosen system depend weakly on the particular level of theory employed for optimization. The explicit case considered here is a basis set appropriate for the Burkatzki–Filippi–Dolg pseudopotentials. Since these pseudopotentials are finite at nuclei and have a Coulomb tail, the recently proposed Gauss–Slater functions are the appropriate primitives. Double and triplezeta bases are developed for elements hydrogen through argon. These new bases offer significant gains over the corresponding Burkatzki–Filippi–Dolg bases at various levels of theory. Using a Gaussian expansion of the basis functions, these bases can be employed in any electronic structure method. Quantum Monte Carlo provides an added benefit: expansions are unnecessary since the integrals are evaluated numerically.

Convergence of vibrational angular momentum terms within the Watson Hamiltonian
View Description Hide DescriptionVibrational angular momentum terms within the Watson Hamiltonian are often considered negligible or are approximated by the zeroth order term of an expansion of the inverse of the effective moment of inertia tensor. A multimode expansion of this tensor up to second order has been used to study the impact of first and second order terms on the vibrational transitions of N_{2}H_{2} and HBeH_{2}BeH. Comparison with experimental data is provided. The expansion of the tensor can be exploited to introduce efficient prescreening techniques.

Bottomup coarsegraining of a simple graphene model: The blob picture
View Description Hide DescriptionThe coarsegraining of a simple allatom 2D microscopic model of graphene, in terms of “blobs” described by center of mass variables, is presented. The equations of motion of the coarsegrained variables take the form of dissipative particle dynamics (DPD). The coarsegrained conservative forces and the friction of the DPD model are obtained via a bottomup procedure from molecular dynamics (MD) simulations. The separation of timescales for blobs of 24 and 96 carbon atoms is sufficiently pronounced for the Markovian assumption, inherent to the DPD model, to provide satisfactory results. In particular, the MD velocity autocorrelation function of the blobs is well reproduced by the DPD model, provided that the effect of friction and noise is taken into account. However, DPD crosscorrelations between neighbor blobs show appreciable discrepancies with respect to the MD results. Possible extensions to mend these discrepancies are briefly outlined.

Treecodebased generalized Born method
View Description Hide DescriptionWe have developed a treecodebased O(Nlog N) algorithm for the generalized Born (GB) implicit solvation model. Our treecodebased GB (tGB) is based on the GBr6 [J. Phys. Chem. B111, 3055 (2007)], an analytical GB method with a pairwise descreening approximation for the R6 volume integral expression. The algorithm is composed of a cutoff scheme for the effective Born radii calculation, and a treecode implementation of the GB charge–charge pair interactions. Test results demonstrate that the tGB algorithm can reproduce the vdW surface based Poisson solvation energy with an average relative error less than 0.6% while providing an almost linearscaling calculation for a representative set of 25 proteins with different sizes (from 2815 atoms to 65456 atoms). For a typical system of 10k atoms, the tGB calculation is three times faster than the direct summation as implemented in the original GBr6 model. Thus, our tGB method provides an efficient way for performing implicit solvent GB simulations of larger biomolecular systems at longer time scales.

Geometric phase for collinear conical intersections. I. Geometric phase angle and vector potentials
View Description Hide DescriptionWe present a method for properly treating collinear conical intersections in triatomic systems. The general vector potential (gauge theory) approach for including the geometric phase effects associated with collinear conical intersections in hyperspherical coordinates is presented. The current study develops an introductory method in the treatment of collinear conical intersections by using the phase angle method. The geometric phase angle, η, in terms of purely internal coordinates is derived using the example of a spinaligned quartet lithium triatomic system. A numerical fit and thus an analytical form for the associated vector potentials are explicitly derived for this triatomic A _{3} system. The application of this methodology to AB _{2} and ABC systems is also discussed.

A general set of order parameters for molecular crystals
View Description Hide DescriptionCrystallization is fundamental to many aspects of physics and chemistry in addition to being of technological relevance, for example, in the chemical, food, and pharmaceutical industries. However, the design of crystalline materials and crystallization processes is often challenging due to the many variables that can influence the process. As a part of an effort to gain a molecularlevel understanding of the way molecules aggregate and organize themselves into crystal structures, in this work we present a new method to construct order parameters suitable for the study of crystallization and polymorph transformations in molecular systems. Our order parameters can be systematically defined for complex systems using information that can be obtained from simple molecular dynamics simulations of the crystals. We show how to construct the order parameters for the study of three different systems: the formation of αglycine crystals in solution, the crystallization of benzene from the melt, and the polymorph transformation of terephthalic acid. Finally, we suggest how these order parameters could be used to study order–disorder transitions in molecular systems.

Implementation of Lees–Edwards periodic boundary conditions for direct numerical simulations of particle dispersions under shear flow
View Description Hide DescriptionA general methodology is presented to perform direct numerical simulations of particle dispersions in a shear flow with Lees–Edwards periodic boundary conditions. The Navier–Stokes equation is solved in oblique coordinates to resolve the incompatibility of the fluid motions with the sheared geometry, and the force coupling between colloidal particles and the host fluid is imposed by using a smoothed profile method. The validity of the method is carefully examined by comparing the present numerical results with experimental viscosity data for particle dispersions in a wide range of volume fractions and shear rates including nonlinear shearthinning regimes.

Accurate and efficient algorithm for Bader charge integration
View Description Hide DescriptionWe propose an efficient, accurate method to integrate the basins of attraction of a smooth function defined on a general discrete grid and apply it to the Bader charge partitioning for the electron charge density. Starting with the evolution of trajectories in space following the gradient of charge density, we derive an expression for the fraction of space neighboring each grid point that flows to its neighbors. This serves as the basis to compute the fraction of each grid volume that belongs to a basin (Bader volume) and as a weight for the discrete integration of functions over the Bader volume. Compared with other gridbased algorithms, our approach is robust, more computationally efficient with linear computational effort, accurate, and has quadratic convergence. Moreover, it is straightforward to extend to nonuniform grids, such as from a meshrefinement approach, and can be used to both identify basins of attraction of fixed points and integrate functions over the basins.

Twodimensional replica exchange approach for peptide–peptide interactions
View Description Hide DescriptionThe replica exchange molecular dynamics (REMD) method has emerged as a standard approach for simulating proteins and peptides with rugged underlying free energy landscapes. We describe an extension to the original methodology—here termed umbrellasampling REMD (UREMD)—that offers specific advantages in simulating peptide–peptide interactions. This method is based on the use of two dimensions in the replica cascade, one in temperature as in conventional REMD, and one in an umbrella sampling coordinate between the center of mass of the two peptides that aids explicit exploration of the complete association–dissociation reaction coordinate. To mitigate the increased number of replicas required, we pursue an approach in which the temperature and umbrella dimensions are linked at only fully associated and dissociated states. Coupled with the reweighting equations, the UREMD method aids accurate calculations of normalized free energy profiles and structural or energetic measures as a function of interpeptide separation distance. We test the approach on two families of peptides: a series of designed tetrapeptides that serve as minimal models for amyloidfibril formation, and a fragment of a classic leucine zipper peptide and its mutant. The results for these systems are compared to those from conventional REMD simulations, and demonstrate good convergence properties, low statistical errors, and, for the leucine zippers, an ability to sample nearnative structures.

Doublehybrid densityfunctional theory made rigorous
View Description Hide DescriptionWe provide a rigorous derivation of a class of doublehybrid approximations, combining Hartree–Fock exchange and secondorder Møller–Plesset correlation with a semilocal exchangecorrelation density functional. These doublehybrid approximations contain only one empirical parameter and use a densityscaled correlation energy functional. Neglecting density scaling leads to a oneparameter version of the standard doublehybrid approximations. We assess the performance of these doublehybrid schemes on representative test sets of atomization energies and reaction barrier heights, and we compare to other hybrid approximations, including rangeseparated hybrids. Our best oneparameter doublehybrid approximation, called 1DHBLYP, roughly reproduces the two parameters of the standard B2PLYP or B2GPPLYP doublehybrid approximations, which shows that these methods are not only empirically close to an optimum for general chemical applications but are also theoretically supported.

Direct perturbation theory in terms of energy derivatives: Fourthorder relativistic corrections at the Hartree–Fock level
View Description Hide DescriptionIn this work, the quantumchemical treatment of relativistic effects by means of direct perturbation theory is extended from its lowest order, DPT2, to the next higher order, DPT4. The required theory is given in terms of energy derivatives with the DPT4 energy correction defined as the corresponding second derivative with respect to the relativistic perturbation parameter λ_{rel} = c ^{2} and c as the speed of light. To facilitate the implementation in standard quantumchemical program packages, a general formulation of DPT starting from a nonrelativistic Lagrangian is developed, thereby expanding both wave function and operators in terms of λ_{rel}. The corresponding expressions, which incorporate in an additive manner scalarrelativistic and spinorbit contributions, are given at the Hartree–Fock level and have been implemented in the CFOUR program package using the available analytic secondderivative techniques. The accuracy of the DPT4 corrections at the HF level is investigated by comparison with rigorous fourcomponent calculations. Scalarrelativistic and spinorbit contributions are analyzed individually and the importance of the various terms to those corrections is discussed. Furthermore, the basisset dependence of the computed DPT4 corrections is investigated.

Pair correlation function of softsphere fluids
View Description Hide DescriptionA closedform analytic formula for the radial distribution function (RDF) or g(r) of inverse power fluids is proposed. The RDF is expressed as a sum of separate component functions, one monotonic and a series of exponentially damped oscillatory functions. Unlike previous treatments in the literature, this formula does not rely on patching different functional forms at arbitrary crossover distances. This expression, which we refer to as g _{ M }(r), yields the expected asymptotic behavior at large distance and reproduces the main features of the RDF generated by molecular dynamics (MD) simulations. The g _{ M } is applied to the soft n = 4 inverse power fluid, and it is shown that in this case seven or fewer terms are sufficient to represent accurately the MDgenerated RDF over the entire fluid domain. The relative contributions of the separate terms of the g _{ M } as a function of density are analyzed and discussed. The key role played by the monotonic component function and two oscillatory terms is demonstrated. The origin of the crossover from the oscillatory to the monotonic behavior is shown to be the same as that recently proposed by Evans and Henderson [R. Evans and J. R. Henderson, J. Phys.: Condens. Matter21, 474220 (2009)] for the dispersion interactions.

Extended hydrodynamic approach to quantumclassical nonequilibrium evolution. I. Theory
View Description Hide DescriptionA mixed quantumclassical formulation is developed for a quantum subsystem in strong interaction with an Nparticle environment, to be treated as classical in the framework of a hydrodynamic representation. Starting from the quantum Liouville equation for the Nparticle distribution and the corresponding reduced singleparticle distribution, exact quantum hydrodynamicequations are obtained for the momentum moments of the singleparticle distribution coupled to a discretized quantum subsystem. The quantumclassical limit is subsequently taken and the resulting hierarchy of equations is further approximated by various closure schemes. These include, in particular, (i) a Grad–Hermitetype closure, (ii) a Gaussian closure at the level of a quantumclassical local Maxwellian distribution, and (iii) a dynamical density functional theory approximation by which the hydrodynamic pressure term is replaced by a free energy functional derivative. The latter limit yields a mixed quantumclassical formulation which has previously been introduced by I. Burghardt and B. Bagchi, Chem. Phys.134, 343 (2006).

Very accurate potential energy curve of the LiH molecule
View Description Hide DescriptionWe present very accurate calculations of the groundstate potential energy curve (PEC) of the LiH molecule performed with allelectron explicitly correlated Gaussian functions with shifted centers. The PEC is generated with the variational method involving simultaneous optimization of all Gaussians with an approach employing the analytical first derivatives of the energy with respect to the Gaussian nonlinear parameters (i.e., the exponents and the coordinates of the shifts). The LiH internuclear distance is varied between 1.8 and 40 bohrs. The absolute accuracy of the generated PEC is estimated as not exceeding 0.3 cm^{−1}. The adiabatic corrections for the four LiH isotopologues, i.e., ^{7}LiH, ^{6}LiH, ^{7}LiD, and ^{6}LiD, are also calculated and added to the LiH PEC. The aforementioned PECs are then used to calculate the vibrational energies for these systems. The maximum difference between the computed and the experimental vibrational transitions is smaller than 0.9 cm^{−1}. The contribution of the adiabatic correction to the dissociation energy of ^{7}LiH molecule is 10.7 cm^{−1}. The magnitude of this correction shows its importance in calculating the LiH spectroscopic constants. As the estimated contribution of the nonadiabatic and relativistic effects to the ground statedissociation energy is around 0.3 cm^{−1}, their inclusion in the LiH PEC calculation seems to be the next most important contribution to evaluate in order to improve the accuracy achieved in this work.

Dynamics of fluid mixtures in nanospaces
View Description Hide DescriptionA multicomponent extension of our recent theory of simple fluids [U. M. B. Marconi and S. Melchionna, J. Chem. Phys.131, 014105 (2009)] is proposed to describe miscible and immiscible liquid mixtures under inhomogeneous, nonsteady conditions typical of confined fluid flows. We first derive from a microscopic level the evolution equations of the phase space distribution function of each component in terms of a set of selfconsistent fields, representing both body forces and viscous forces (forces dependent on the density distributions in the fluid and on the velocity distributions). Second, we numerically solve the resulting governing equations by means of the lattice Boltzmann method, whose implementation contains novel features with respect to existing approaches. Our model incorporates hydrodynamicflow, diffusion, surface tension, and the possibility for global and local viscosity variations. We validate our model by studying the bulk viscosity dependence of the mixture on concentration, packing fraction, and size ratio. Finally, we consider inhomogeneous systems and study the dynamics of mixtures in slits of molecular thickness and relate structural and flow properties.

Comparison of the experimental, semiexperimental and ab initio equilibrium structures of acetylene: Influence of relativisitic effects and of the diagonal Born–Oppenheimer corrections
View Description Hide DescriptionThe equilibrium structure of acetylene (also named ethyne) has been reinvestigated to resolve the small discrepancies noted between different determinations. The size of the system as well as the large amount of available experimental data provides the quite unique opportunity to check the magnitude and relevance of various contributions to equilibrium structure as well as to verify the accuracy of experimental results. With respect to pure theoretical investigation, quantumchemical calculations at the coupledcluster level have been employed together with extrapolation to the basis set limit, consideration of higher excitations in the cluster operator, inclusion of core correlation effects as well as relativistic and diagonal Born–Oppenheimer corrections. In particular, it is found that the extrapolation to the complete basis set limit, the inclusion of higher excitations in the electroniccorrelation treatment and the relativistic corrections are of the same order of magnitude. It also appears that a basis set as large as a core–valence quintuplezeta set is required for accurately accounting for the innershell correlation contribution. From a pure experimental point of view, the equilibrium structure has been determined using very accurate rotational constants recently obtained by a “global analysis” (that is to say that all nonnegligible interactions are explicitely included in the Hamiltonian matrix) of rovibrational spectra. Finally, a semiexperimental equilibrium structure (where the equilibrium rotational constants are obtained from the experimental ground state rotational constants and computed rovibrational corrections) has been obtained from the available experimental groundstaterotational constants for ten isotopic species corrected for computed vibrational corrections. Such a determination led to the revision of the groundstaterotational constants of two isotopologues, thus showing that structural determination is a good method to identify errors in experimental rotational constants. The three structures are found in a very good agreement, and our recommended values are r _{CC} = 120.2958(7) pm and r _{CH} = 106.164(1) pm.