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.
 COMMUNICATIONS


Communication: Are hydrodynamic models suited for describing the reorientational dynamics of ions in ionic liquids? A case study of methylimidazolium tetra(hexafluoroisopropoxy)aluminates
View Description Hide DescriptionWe report on dielectric relaxation spectra of six homologous ionic liquids (ILs) with tetra(hexafluoroisopropoxy)aluminate as a common anion. The dominating mode on the time scale of several 100 ps mainly results from cation reorientation. Because the viscosities are low and cation modification does not substantially change the viscosity, these ILs are interesting candidates for testing hydrodynamic models of rotational dynamics. The calculated hydrodynamic volumes are extraordinarily low, and roughly agree with values calculated from literature data for ILs with the same cations, but different anions. Comparison with magnetic relaxation data shows that the peculiarities are founded in the rotational dynamics and are not special to dielectric relaxation. Collectively, the observations make a strong case against the applicability of hydrodynamic approaches to the orientational dynamics of ions.

Communication: Simple selfcorrelation corrections to the Ragot–Cortona model of local correlation energy
View Description Hide DescriptionThe Ragot–Cortona or RC model of local correlation energy [J. Chem. Phys.121, 7671 (2004)] improves the standard local approximation in various respects. This letter aims at illustrating the origin of this improvement. To that aim, simple selfinteraction corrected versions of the RC model are implemented, which involve local energy differences only. Several correlation functionals are selected for direct comparison using Hartree–Fock charge densities of atomic ions ( to Ar). One of the selfinteraction corrected versions of the RC model shows surprising improvements over the initial RC model. First, it dramatically improves the atomic correlation energies of atomic ions. Second, the impact on the contribution of the correlation energy to ionization potentials or electron affinities is still more convincing. In both cases, the accuracy achieved is close to or better than a selection of gradientlevel functionals.

Communication: Near edge xray absorption fine structure spectroscopy of aqueous adenosine triphosphate at the carbon and nitrogen Kedges
View Description Hide DescriptionNear edge xray absorption fine structure(NEXAFS)spectroscopy at the nitrogen and carbon Kedges was used to study the hydration of adenosine triphosphate in liquid microjets. The total electron yield spectra were recorded as a function of concentration, , and the presence of sodium,magnesium, and copper ions . Significant spectral changes were observed upon protonation of the adenine ring, but not under conditions that promote stacking, such as high concentration or presence of , indicating that NEXAFS is insensitive to the phenomenon. Intramolecular innersphere association of did create observable broadening of the nitrogen spectrum, whereas outersphere association with did not.

Communication: Explicit construction of functional derivatives in potentialdriven densityfunctional theory
View Description Hide DescriptionWe propose a method for imposing an important exact constraint on model Kohn–Sham potentials, namely, the requirement that they be functional derivatives of functionals of the electron density . In particular, we show that if a model potential involves no ingredients other than , , and , then the necessary and sufficient condition for to be a functional derivative is . Integrability conditions of this type can be used to construct functional derivatives without knowing their parent functionals. This opens up possibilities for developing model exchangecorrelation potentials that do not lead to unphysical effects common to existing approximations. Application of the technique is illustrated with examples.

Communication: Effective spectroscopic Hamiltonian for multiple minima with above barrier motion: Isomerization in
View Description Hide DescriptionWe present a twodimensional potential surface for the isomerization in the hydroperoxyl radical and calculate the vibrational spectrum. We then show that a simple effective spectroscopic fitting Hamiltonian is capable of reproducing large scale vibrational spectral structure above the isomerization barrier. Polyad breaking with multiple resonances is necessary to adequately describe the spectral features of the system. Insight into the dynamical nature of isomerization related to the effective Hamiltonian is gained through classical trajectories on the model potential. Contrary to physical intuition, the bend mode is not a “reaction mode,” but rather isomerization requires excitation in both stretch and bend. The dynamics reveals a Farey tree formed from the 2:1 and 3:1 resonances, corresponding to the resonance coupling terms in the effective Hamiltonian, with the prominent 5:2 feature dividing the tree into parts that we call the 3:1 and 2:1 portions.

Communication: Padé spectrum decomposition of Fermi function and Bose function
View Description Hide DescriptionPadé approximant is exploited for an efficient sumoverpoles decomposition of Fermi and Bose functions. The resulting poles are all pure imaginary and can therefore be used to define Padé frequencies, in analogy with the celebrated Matsubara frequencies. The proposed Padé spectrum decomposition is shown to be equivalent to a truncated continued fraction. It converges significantly faster than other schemes such as the Matsubara expansion at all temperatures. By introducing the characteristic validity length as the measure of approximant, we analyze the convergence properties of different schemes thoroughly. Our results qualify the present scheme the best among all sumoverpoles approaches. Thus, it is of great value in efficient numerical evaluations of integrals involving Fermi/Bose function in various condensedphase matter problems.
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 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.