Volume 133, Issue 10, 14 September 2010

We report the results from Mayersampling Monte Carlo calculations of the virial coefficients of the unitedatom TraPPEUA model of normal alkanes. For alkane chain lengths from to 20 (where is the number of carbon atoms), results are given for the virial coefficients , , and ; results for are given for chains up to length ; and results for are given for chains of length , 3, and 4. In all cases, values are given for temperatures ranging from 200 K to 2000 K in 20–50 K increments. The values are used to calculate the equation of state for butane and the pressuredensity behavior is compared to experimental data at 350 and 550 K. Critical points are calculated for all systems and compared to simulation data previously taken for the same molecular model, and to experiment. The comparison with temperature is very good (within 1.5% for all chain lengths up to ), while the critical density is underestimated by about 5%–15% and the critical pressure is given within about 10%. The convergence behavior of the virial equation of state as applied across the alkane series is well characterized by corresponding states, meaning that the accuracy at a given density relative to the critical density does not deteriorate with increasing chain length.
 ARTICLES

 Theoretical Methods and Algorithms

Virial coefficients of model alkanes
View Description Hide DescriptionWe report the results from Mayersampling Monte Carlo calculations of the virial coefficients of the unitedatom TraPPEUA model of normal alkanes. For alkane chain lengths from to 20 (where is the number of carbon atoms), results are given for the virial coefficients , , and ; results for are given for chains up to length ; and results for are given for chains of length , 3, and 4. In all cases, values are given for temperatures ranging from 200 K to 2000 K in 20–50 K increments. The values are used to calculate the equation of state for butane and the pressuredensity behavior is compared to experimental data at 350 and 550 K. Critical points are calculated for all systems and compared to simulation data previously taken for the same molecular model, and to experiment. The comparison with temperature is very good (within 1.5% for all chain lengths up to ), while the critical density is underestimated by about 5%–15% and the critical pressure is given within about 10%. The convergence behavior of the virial equation of state as applied across the alkane series is well characterized by corresponding states, meaning that the accuracy at a given density relative to the critical density does not deteriorate with increasing chain length.

Improving upon for potential energy surfaces: models
View Description Hide DescriptionWe consider classes of noniterative (coupled cluster singles and doubles with noniterative triples and quadruples) for bond breaking including approximations based on . All methods are applied to the standard tests for the treatment of potential energy curves for small molecules (HF, , , , and ) where unambiguous comparison to full configuration interaction exists. Depending on the nature of the electron correlation substantial improvements are obtained at the same cost over CCSD(T).

Rung 3.5 density functionals
View Description Hide DescriptionThis work proposes a new term on the “Jacob’s ladder” of approximate exchangecorrelation functionals in Kohn–Sham density functional theory. In these Rung 3.5 functionals, the exchangecorrelation energy density at a point depends linearly (rather than quadratically) on the nonlocal Kohn–Sham oneparticle density matrix in a finite neighborhood around the point. These functionals are intermediate in complexity between the semilocal approximations of Rungs 1–3, and fully nonlocal Rung 4 approximations such as global hybrids. Rung 3.5 functionals built on the model for exchange in [B. G. Janesko, J. Chem. Phys.131, 234111 (2009)] predict molecular thermochemistry and kinetics with accuracy intermediate between their “parent” semilocal functional and the corresponding global hybrid. The best Rung 3.5 functional presented here gives mean absolute errors of 5.7 kcal/mol for G3/99 thermochemistry, 5.2 kcal/mol for HTBH38/04 hydrogentransfer reaction barriers, and 5.7 kcal/mol for NHTBH38/04 nonhydrogentransfer reaction barriers, while incorporating only two empirical parameters.

Energy variational analysis of ions in water and channels: Field theory for primitive models of complex ionic fluids
View Description Hide DescriptionIonic 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 pileup 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.

Basis set dependence of the doubly hybrid XYG3 functional
View Description Hide DescriptionIn the present study, we investigated the basis set dependence of XYG3, a newly developed doubly hybrid functional [Y. Zhang, X. Xu, and W. A. Goddard III, Proc. Natl. Acad. Sci. U.S.A.106, 4963 (2009)], in prediction of (1) heats of formation (HOFs), (2) bond dissociation enthalpies (BDEs), (3) reaction barrier heights (RBHs), and (4) nonbonded interactions (NBIs). We used basis sets of triplezeta quality starting from with increasing completeness of the polarization functions to the largest Popletype basis set and found that there was a continued improvement with larger basis sets. We showed that while HOF predictions were prone to basis set deficiencies, the basis set dependences in calculating BDEs, RBHs, and NBIs were mild. All of them converged fast with the increase of basis set size. We extended XYG3 to propose the XYG3o functional which was specifically optimized for a particular basis set in order to enhance its performance when using basis set of moderate size. With the basis set, XYG3o led to MADs of 2.56 kcal/mol for HOFs of the G3/99 set, 1.17 kcal/mol for BDEs of the BDE92/07 set, 1.11 kcal/mol for RBHs of the NHTBH38/04 and HTBH38/04 sets, and 0.40 kcal/mol for NBIs of the NCIE31/05 set, being comparable to those obtained by using XYG3/.

Musings on thermostats
View Description Hide DescriptionIn 2005, Bright et al. gave numerical evidence that among the family of time reversible deterministic thermostats known as thermostats, the conventional thermostat proposed by Hoover and Evans is the only thermostat that is capable of generating an equilibrium state. Using the recently discovered relaxation theorem, we give a mathematical proof that this is true.

Efficient evaluation of triple excitations in symmetryadapted perturbation theory via secondorder Møller–Plesset perturbation theory natural orbitals
View Description Hide DescriptionAn accurate description of dispersion interactions is required for reliable theoretical studies of many noncovalent complexes. This can be obtained with the wave functionbased formulation of symmetryadapted perturbation theory (SAPT) provided that the contribution of triple excitations to dispersion is included. Unfortunately, this triples dispersion correction limits the applicability of SAPT due to its scaling. The efficiency of the evaluation of this correction can be greatly improved by removing virtual orbitals from the computation. The error incurred from truncating the virtual space is reduced if secondorder Møller–Plesset perturbation theory (MP2) natural orbitals are used in place of the canonical Hartree–Fock molecular orbitals that are typically used. This approximation is further improved if the triples correction to dispersion is scaled to account for the smaller virtual space. If virtual MP2 natural orbitals are removed according to their occupation numbers, in practice, roughly half of the virtual orbitals can be removed (with the augccpVDZ basis set) with negligible errors if the remaining triples dispersion contribution is scaled. This typically leads to speedups of 15–20 times for the cases considered here. By combining the truncated virtual space with the frozen core approximation, the triples correction can be evaluated approximately 50 times faster than the canonical computation. These approximations cause less than 1% error (or at most ) for the cases considered. Truncation of greater fractions of the virtual space is possible for larger basis sets (leading to speedups of over 40 times before additional speedups from the frozen core approximation).

New closed Newton–Cotes type formulae as multilayer symplectic integrators
View Description Hide DescriptionIn this paper, we introduce new integrators of Newton–Cotes type and investigate the connection between these new methods, differential methods, and symplectic integrators. From the literature, we can see that several one step symplectic integrators have been obtained based on symplectic geometry. However, the investigation of multistep symplectic integrators is very poor. In this paper, we introduce a new numerical method of closed Newton–Cotes type and we write it as a symplectic multilayer structure. We apply the symplectic schemes in order to solve Hamilton’s equations of motion which are linear in position and momentum. We observe that the Hamiltonian energy of the system remains almost constant as integration proceeds.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Magic and hot giant fullerenes formed inside ion irradiated weakly bound clusters
View Description Hide DescriptionWe find that the most stable fullerene isomers, , form efficiently in closeto central collisions between keV atomic ions and weakly bound clusters of more than 15 molecules. We observe extraordinarily high yields of and marked preferences for and . Larger evensize carbon molecules, , follow a smooth lognormal (statistical) intensity distribution. Measurements of kinetic energies indicate that mainly are formed by coalescence reactions between small carbon molecules and , while with are due to selfassembly (of small molecules) and shrinking hot giant fullerenes.

A new ab initio potential energy surface and microwave and infrared spectra for the complex
View Description Hide DescriptionWe report a new threedimensional potential energy surface for including the normal mode for the antisymmetric stretching vibration of the molecule. The potential energies were calculated using the supermolecular method at the coupledcluster singles and doubles level with noniterative inclusion of connected triples [CCSD(T)], using a large basis set supplemented with midpoint bond functions. Two vibrationally averaged potentials with at both the ground and the first vibrational excited states were generated from the integration of the threedimensional potential over the coordinate. Each potential was found to have a Tshaped global minimum and two equivalent linear local minima. The radial DVR/angular FBR method and the Lanczos algorithm are applied to calculate the rovibrational energy levels. Comparison with the available observed values showed an overall excellent agreement for the microwave and infrared spectra. The calculated band origin shifts were found to be 0.1306 and for and , respectively, which are very close to the experimental values of 0.1303 and .

Mechanism for the abiotic synthesis of uracil via UVinduced oxidation of pyrimidine in pure ices under astrophysical conditions
View Description Hide DescriptionThe UV photoirradiation of pyrimidine in pure ices has been explored using secondorder Møller–Plesset perturbation theory and density functional theory methods, and compared with experimental results. Mechanisms studied include those starting with neutral pyrimidine or cationic pyrimidine radicals, and reacting with OH radical. The ab initio calculations reveal that the formation of some key species, including the nucleobase uracil, is energetically favored over others. The presence of one or several water molecules is necessary in order to abstract a proton which leads to the final products. Formation of many of the photoproducts in UVirradiated ice mixtures was established in a previous experimental study. Among all the products, uracil is predicted by quantum chemical calculations to be the most favored, and has been identified in experimental samples by two independent chromatography techniques. The results of the present study strongly support the scenario in which prebiotic molecules, such as the nucleobase uracil, can be formed under abiotic processes in astrophysically relevant environments, namely in condensed phase on the surface of icy, cold grains before being delivered to the telluric planets, like Earth.

Theoretical predictions of trends in spectroscopic properties of gold containing dimers of the 6p and 7p elements and their adsorption on gold
View Description Hide DescriptionFully relativistic, fourcomponent density functional theory electronic structure calculations were performed for the MAu dimers of the 7p elements, 113 through 118, and their 6p homologs, Tl through Rn. It was shown that the M–Au bond strength should decrease from the 6p to 7p homologs in groups 13 and 14, while it should stay about the same in groups 15 through 17 and even increase in group 18. This is in contrast with the decreasing trend in the M–M bond strength in groups 15 through 17. The reason for these trends is increasingly important relativistic effects on the np AOs of these elements, particularly their large spinorbit splitting. Trends in the adsorption energies of the heaviest elements and their homologs on gold are expected to be related to those in the binding energies of MAu, while sublimationenthalpies are closely connected to the binding energies of the MM dimers. Lack of a correlation between the MAu and MM binding energies means that no correlation can also be expected between adsorptionenthalpies on gold and sublimationenthalpies in groups 15 through 17. No linear correlation between these quantities is established in the row of the 6p elements, as well as no one is expected in the row of the 7p elements.

An “adiabatichinderedrotor” treatment allows para to be treated as if it were spherical
View Description Hide DescriptionIn para–{molecule} interactions, the common assumption that para may be treated as a spherical particle is often substantially in error. For example, quantum mechanical eigenvalues on a full fourdimensional (4D) potential energy surface for para –{linear molecule} species often differ substantially from those calculated from the corresponding twodimensional (2D) surface obtained by performing a simple spherical average over the relative orientations of the moiety. However, use of an “adiabatichinderedrotor” approximation can yield an effective 2D surface whose spectroscopic properties are an order of magnitude closer to those yielded by a full 4D treatment.

Longrange dispersion coefficients for Li, , and interacting with the rare gases
View Description Hide DescriptionThe longrange dispersion coefficients for the ground and excited states of Li, , and interacting with the He, Ne, Ar, Kr, and Xe atoms in their ground states are determined. The variational Hylleraas method is used to determine the necessary lists of multipole matrix elements for He, Li, , and , while pseudooscillator strength distributions are used for the heavier rare gases. Some single electron calculations using a semiempirical Hamiltonian are also performed for Li and and found to give dispersion coefficients in good agreement with the Hylleraas calculations. Polarizabilities are given for some of the Li and states and the recommended polarizability including both finitemass and relativistic effects was 0.192 486 a.u. The impact of finitemass effects upon the dispersion coefficients has been given for some selected interatomic interactions.
 Condensed Phase Dynamics, Structure, and Thermodynamics: Spectroscopy, Reactions, and Relaxation

Melting and freezing lines for a mixture of charged colloidal spheres with spindletype phase diagram
View Description Hide DescriptionWe have measured the phase behavior of a binary mixture of likecharged colloidal spheres with a size ratio of and a charge ratio of as a function of particle number density and composition . Under exhaustively deionized conditions, the aqueous suspension forms solid solutions of body centered cubic structure for all compositions. The freezing and melting lines as a function of composition show opposite behavior and open a wide, spindle shaped coexistence region. Lacking more sophisticated treatments, we model the interaction in our mixtures as an effective onecomponent pair energy accounting for number weighted effective charge and screening constant. Using this description, we find that within experimental error the location of the experimental melting points meets the range of melting points predicted for monodisperse, onecomponent Yukawa systems made in several theoretical approaches. We further discuss that a detailed understanding of the exact phase diagram shape including the composition dependent width of the coexistence region will need an extended theoretical treatment.

Paircorrelation properties and momentum distribution of finite number of interacting trapped bosons in three dimensions
View Description Hide DescriptionWe study the ground state paircorrelation properties of a weakly interacting trapped Bose gas in three dimensions by using a correlated manybody method. The use of the van der Waals interaction potential and an external trapping potential shows realistic features. We also test the validity of shapeindependent approximation in the calculation of correlationproperties.

Two hard spheres in a pore: Exact statistical mechanics for different shaped cavities
View Description Hide DescriptionThe partition function of two hard spheres in a hardwall pore is studied, appealing to a graph representation. The exact evaluation of the canonical partition function and the onebody distribution function in three different shaped pores are achieved. The analyzed simple geometries are the cuboidal, cylindrical, and ellipsoidal cavities. Results have been compared with two previously studied geometries; the spherical pore and the spherical pore with a hard core. The search of common features in the analytic structure of the partition functions in terms of their length parameters and their volumes, surface area, edges length, and curvatures is addressed too. A general framework for the exact thermodynamicanalysis of systems with few and many particles in terms of a set of thermodynamic measures is discussed. We found that an exact thermodynamic description is feasible based on the adoption of an adequate set of measures and the search of the free energy dependence on the adopted measure set. A relation similar to the Laplace equation for the fluidvapor interface is obtained, which expresses the equilibrium between magnitudes that in extended systems are intensive variables. This exact description is applied to study the thermodynamic behavior of the two hard spheres in a hardwall pore for the analyzed different geometries. We obtain analytically the external reversible work, the pressure on the wall, the pressure in the homogeneous region, the wallfluid surface tension, the line tension, and other similar properties.

Role of OH radicals in the formation of oxygen molecules following vacuum ultraviolet photodissociation of amorphous solid water
View Description Hide DescriptionPhotodesorption of and from amorphous solidwater at 90 K has been studied following photoexcitation within the first absorption band at 157 nm. Timeofflight and rotational spectra of reveal the translational and internal energy distributions, from which production mechanisms are deduced. Exothermic and endothermic reactions of are proposed as plausible formation mechanisms for . To examine the contribution of the recombination reaction to the formation following 157 nm photolysis of amorphous solidwater, products following 193 nm photodissociation of adsorbed on amorphous solidwater were also investigated.

Demixing of a binary symmetric mixture studied with transition path sampling
View Description Hide DescriptionWe present transition path sampling simulations of the nucleation of the demixing transition in a binary symmetric LennardJones fluid. In this system the demixing transition takes place between two phases of the same density but different compositions. The appropriateness of the reaction coordinate of classical nucleationtheory is examined. Using paths harvested with transition path sampling, we investigate the nucleation mechanism and analyze the properties of critical nuclei obtained by determining the transition state ensemble. Our simulations show that despite the fact that the densities of the coexisting phases are equal, the density of the growing cluster plays a crucial role in the nucleation process: nucleation tends to proceed either via small, compact clusters with densities below that of the metastable fluid or via large clusters with even lower densities.

Excess entropy scaling of dynamic quantities for fluids of dumbbellshaped particles
View Description Hide DescriptionWe use molecular simulation to study the ability of entropy scaling relationships to describe the kinetic properties of two LennardJones dumbbell models. We begin by examining the excess entropy, the key quantity used to correlate dynamic properties within entropy scaling strategies. We compute the thermodynamic excess entropy as well as contributions to the twobody excess entropy stemming from translational and orientational intermolecular correlations. Our results indicate that the total twobody contribution accounts for more than 70% of the thermodynamic excess entropy at all state conditions explored. For the two dumbbell models studied here, the orientational component of the twobody excess entropy dominates at moderate and high fluid densities. We next investigate the relationships between kinetic properties and various contributions to the excess entropy. Four dynamic properties are considered: translational and rotational diffusivities, a characteristic relaxation time for rotational motion, and a collective relaxation time stemming from analysis of the coherent intermediatescattering function. We find that the thermodynamic excess entropy provides the best metric for describing kinetic properties. For each of the dynamic properties considered, reduced data collapse onto a common curve when expressed as a function of the thermodynamic excess entropy. The likelihood of a twobody contribution to the excess entropy serving as a reliable scaling variable is linked to the extent to which it correlates with the thermodynamic excess entropy. The total twobody term contributes significantly to the excess entropy, and therefore this quantity generally serves as a suitable scaling variable.