Volume 132, Issue 16, 28 April 2010

has been proposed as a key entity in lithiumammonia solutions, but its spectral signature has so far proved impossible to distinguish from other species in these solutions. Here we report the first electronic spectrum of in the gas phase, which was recorded using massselective depletion spectroscopy. Strong absorption is observed in the nearinfrared and the band system is assigned to the transition in a nominally tetrahedral complex. However, the vibrational structure is indicative of a substantial Jahn–Teller effect in the excited electronic state. The broad and structured spectrum confirms a recent theoretical prediction that the electronic spectrum of will strongly overlap with the spectrum of the solvated electron in lithiumammonia solutions.
 COMMUNICATIONS


Communications: The electronic spectrum of
View Description Hide Descriptionhas been proposed as a key entity in lithiumammonia solutions, but its spectral signature has so far proved impossible to distinguish from other species in these solutions. Here we report the first electronic spectrum of in the gas phase, which was recorded using massselective depletion spectroscopy. Strong absorption is observed in the nearinfrared and the band system is assigned to the transition in a nominally tetrahedral complex. However, the vibrational structure is indicative of a substantial Jahn–Teller effect in the excited electronic state. The broad and structured spectrum confirms a recent theoretical prediction that the electronic spectrum of will strongly overlap with the spectrum of the solvated electron in lithiumammonia solutions.

Communications: When diffraction rules the stereodynamics of rotationally inelastic collisions
View Description Hide DescriptionFollowing upon our recent work on vector correlations in the Ar–NO collisions [Lemeshko and Friedrich, Phys. Chem. Chem. Phys.12, 1038 (2010)], we compare model results with closecoupling calculations for a range of channels and collision energies for the He–NO system. The striking agreement between the model and exact polarization moments indicates that the stereodynamics of rotationally inelastic atommolecule collisions at thermal energies is governed by diffraction of matter waves from a twodimensional repulsive core of the atommolecule potential. Furthermore, the modelpolarization moments characterizing the He–NO, , He–OH, and He–CaH stereodynamics are found to coalesce into a single, distinctive pattern, which can serve as a “fingerprint” to identify diffractiondriven stereodynamics in future work.

Communications: Investigation of the superatomic character of via its interaction with sulfur atoms
View Description Hide DescriptionWe investigated and clusters with mass spectrometry and photoelectron spectroscopy. We found that is relatively robust when it reacts with sulfur atoms, indicating that it has some superatomic character. However, cannot be simply considered as a superatom when it interacts with sulfur due to the following reasons: ’s icosahedral structure has been distorted slightly by sulfur atoms; the vertical detachment energies and adiabatic detachment energies of and clusters are not significantly different from those of their neighboring clusters; and the charge distributions in and do not necessarily associate with superatomic behavior of .

Communications: Wall free capillarity and pendant drop removal
View Description Hide DescriptionWhen a sessile drop encounters a pendant drop through a hole, it is generally anticipated that they will coalesce and flow downward due to gravity. However, like “wallfree” capillarity, we show that the pendant drop may be sucked up by a sliding drop instantaneously if the radius of the curvature of the former is smaller than that of the later. This phenomenon can be explained by Laplace–Young equation and convective Ostwald ripening. Our results indicate that superhydrophilic perforated surface can be used as an effective way for the removal of small droplets adhering to the inner walls of microchannel systems.
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 ARTICLES

 Theoretical Methods and Algorithms

Accurate frozendensity embedding potentials as a first step towards a subsystem description of covalent bonds
View Description Hide DescriptionThe frozendensity embedding (FDE) scheme [Wesolowski and Warshel, J. Phys. Chem.97, 8050 (1993)] relies on the use of approximations for the kineticenergy component of the embedding potential. While with approximations derived from generalizedgradient approximation kineticenergy density functional weak interactions between subsystems such as hydrogen bonds can be described rather accurately, these approximations break down for bonds with a covalent character. Thus, to be able to directly apply the FDE scheme to subsystems connected by covalent bonds, improved approximations to are needed. As a first step toward this goal, we have implemented a method for the numerical calculation of accurate references for . We present accurate embedding potentials for a selected set of model systems, in which the subsystems are connected by hydrogen bonds of various strength (water dimer and ), a coordination bond (ammonia borane), and a prototypical covalent bond (ethane). These accurate potentials are analyzed and compared to those obtained from popular kineticenergy density functionals.

Improving the density functional theory description of water with selfconsistent polarization
View Description Hide DescriptionWe applied the selfconsistent polarizationdensity functional theory (SCPDFT) to water. SCPDFT requires only minimal parametrization, selfconsistently includes the dispersion interaction neglected by standard DFT functionals, and has a cost similar to standard DFT despite its improved performance. Compared to the DFT functionals BLYP and BLYPD (where the latter contains a simple dispersion correction), SCPDFT yields interactionenergies per molecule and harmonic frequencies of clusters in better agreement with experiment, with errors in the former of only a few tenths of a kcal/mol. BLYP and BLYPD underbind and overbind the clusters, respectively, by up to about 1 kcal/mol. For liquid water, both BLYP and SCPDFT predict radial distribution functions that are similar and overstructured compared to experiment. However, SCPDFT improves over BLYP in predicting the experimental enthalpy of vaporization. A decomposition of the dimer interactionenergy attempts to rationalize the performance of SCPDFT. The SCPDFT approach holds promise as an efficient and accurate method for describing large hydrogenbonded systems, and has the potential to model complex systems with minimal parametrization.

A practical method to avoid zeropoint leak in molecular dynamics calculations: Application to the water dimer
View Description Hide DescriptionWe report the implementation of a previously suggested method to constrain a molecular system to have modespecific vibrational energy greater than or equal to the zeropoint energy in quasiclassical trajectory calculations [J. M. Bowman et al., J. Chem. Phys.91, 2859 (1989); W. H. Miller et al., J. Chem. Phys.91, 2863 (1989)]. The implementation is made practical by using a technique described recently [G. Czakó and J. M. Bowman, J. Chem. Phys.131, 244302 (2009)], where a normalmode analysis is performed during the course of a trajectory and which gives only realvalued frequencies. The method is applied to the water dimer, where its effectiveness is shown by computing mode energies as a function of integration time. Radial distribution functions are also calculated using constrained quasiclassical and standard classical molecular dynamics at low temperature and at 300 K and compared to rigorous quantum path integral calculations.

Structure, properties, and nature of the pyridineXY (X, , Cl, Br) complexes: An ab initio study
View Description Hide DescriptionStructure and properties(energies, electronic, and thermodynamic properties) of complexes pyridineXY (X, , Cl, Br) have been investigated at the MP2/augccpVDZ level. Two types of geometries (halogen bonded and halogen bonded) are observed. In contrast with the previous results on similar furan and thiophene complexes, the halogen bonded structures are more stable and the reasons are discussed. Charge transfer is found to be important in the formation of title system and the possible existing complexes under experimental conditions have been forecasted too. A symmetryadapted perturbation theoryenergy decomposition analysis reveals that the pyridineXY complexes are dominantly inductive in nature.

Vibrational absorption spectra calculated from vibrational configuration interaction response theory using the Lanczos method
View Description Hide DescriptionThe Lanczos method is used to efficiently obtain the linear vibrational response function for all frequencies in an arbitrary interval. The complex part of the response function gives the absorptionspectrum which can subsequently be analyzed. The method provides a way to obtain global information on the absorptionspectrum without explicitly converging all vibrational eigenstates of the system. The tridiagonal Lanczos matrix used to obtain the response functions needs only be constructed once for each operator. Example calculations on cyclopropene and uracil are presented.

The multiscale coarsegraining method. V. Isothermalisobaric ensemble
View Description Hide DescriptionThe multiscale coarsegraining (MSCG) method is a method for determining the effective potential energy function for a coarsegrained (CG) model of a system using the data obtained from molecular dynamics simulation of the corresponding atomically detailed model. The MSCG method, as originally formulated for systems at constant volume, has previously been given a rigorous statistical mechanical basis for the canonical ensemble. Here, we propose and test a version of the MSCG method suitable for the isothermalisobaric ensemble. The method shows how to construct an effective potential energy function for a CG system that generates the correct volume fluctuations as well as correct distribution functions in the configuration space of the CG sites. The formulation of the method requires introduction of an explicitly volume dependent term in the potential energy function of the CG system. The theory is applicable to simulations with isotropic volume fluctuations and cases where both the atomistic and CG models do not have any intramolecular constraints, but it is straightforward to extend the theory to more general cases. The present theory deals with systems that have short ranged interactions. (The extension to Coulombic forces using Ewald methods requires additional considerations.) We test the theory for constant pressure MSCG simulations of a simple model of a solution. We show that both the volume dependent and the coordinate dependent parts of the potential are transferable to larger systems than the one used to obtain these potentials.

The multiscale coarsegraining method. VI. Implementation of threebody coarsegrained potentials
View Description Hide DescriptionMany methodologies have been proposed to build reliable and computationally fast coarsegrained potentials. Typically, these force fields rely on the assumption that the relevant properties of the system under examination can be reproduced using a pairwise decomposition of the effective coarsegrained forces. In this work it is shown that an extension of the multiscale coarsegraining technique can be employed to parameterize a certain class of twobody and threebody force fields from atomistic configurations. The use of explicit threebody potentials greatly improves the results over the more commonly used twobody approximation. The method proposed here is applied to develop accurate onesite coarsegrained water models.

Expectation values in twocomponent relativistic theories
View Description Hide DescriptionWe examined numerically the equivalence between the expectation values calculated by the fourcomponent wave function and those calculated by the twocomponent wave functionsgenerated by the infiniteorder Douglas–Kroll (IODK) transformation. We showed the expectation values and in several closedshell atoms using the socalled picturechanged operators at some levels of approximation. The effect of the twoelectron Coulomb term was also discussed. The numerical results indicated that the accuracy of mainly depends on the level of the wave functions, while that of is affected by the accuracy of both the wave functions and the picturechanged operators. As expected, the picturechanged operators and the IODK wave functionsgenerate essentially equivalent expectation values in comparison with those calculated by the fourcomponent Diractype method.

Fast stochastic simulation of biochemical reaction systems by alternative formulations of the chemical Langevin equation
View Description Hide DescriptionThe Chemical Langevin Equation (CLE), which is a stochastic differential equation driven by a multidimensional Wiener process, acts as a bridge between the discrete stochastic simulation algorithm and the deterministic reaction rate equation when simulating (bio)chemical kinetics. The CLE model is valid in the regime where molecular populations are abundant enough to assume their concentrations change continuously, but stochastic fluctuations still play a major role. The contribution of this work is that we observe and explore that the CLE is not a single equation, but a parametric family of equations, all of which give the same finitedimensional distribution of the variables. On the theoretical side, we prove that as many Wiener processes are sufficient to formulate the CLE as there are independent variables in the equation, which is just the rank of the stoichiometric matrix. On the practical side, we show that in the case where there are pairs of reversible reactions and irreversible reactions there is another, simple formulation of the CLE with only Wiener processes, whereas the standard approach uses . We demonstrate that there are considerable computational savings when using this latter formulation. Such transformations of the CLE do not cause a loss of accuracy and are therefore distinct from model reduction techniques. We illustrate our findings by considering alternative formulations of the CLE for a human ether agogo related gene ion channel model and the Goldbeter–Koshland switch.

Generalized valence bond wave functions in quantum Monte Carlo
View Description Hide DescriptionWe present a technique for using quantum Monte Carlo (QMC) to obtain high quality energy differences. We use generalized valence bond (GVB) wave functions, for an intuitive approach to capturing the important sources of static correlation, without needing to optimize the orbitals with QMC. Using our modifications to Walker branching and Jastrows, we can then reliably use diffusionquantum Monte Carlo to add in all the dynamic correlation. This simple approach is easily accurate to within a few tenths of a kcal/mol for a variety of problems, which we demonstrate for the adiabatic singlettriplet splitting in methylene, the vertical and adiabatic singlettriplet splitting in ethylene, cycloaddition, and bond breaking.

Partitioning of the molecular density matrix over atoms and bonds
View Description Hide DescriptionA doubleindex atomic partitioning of the molecular firstorder density matrix is proposed. Contributions diagonal in the atomic indices correspond to atomic density matrices, whereas offdiagonal contributions carry information about the bonds. The resulting matrices have good localization properties, in contrast to singleindex atomic partitioning schemes of the molecular density matrix. It is shown that the electron density assigned to individual atoms, when derived from the density matrix partitioning, can be made consistent with wellknown partitions of the electron density over atom in the molecule basins, either with sharp or with fuzzy boundaries. The method is applied to a test set of about 50 molecules, representative for various types of chemical binding. A close correlation is observed between the trace of the bond matrices and the shared electron density index.

Effect of an external field on the reversible reaction of a neutral particle and a charged particle in three dimensions. II. Excitedstate reaction
View Description Hide DescriptionThe excitedstate reversible reaction of a neutral particle and a charged particle in an external electric field is studied in three dimensions. This work extends the previous investigation for the groundstatereaction [S. Y. Reigh et al., J. Chem. Phys.129, 234501 (2008)] to the excitedstatereaction with two different lifetimes and quenching. The analytic series solutions for all the fundamental probability density functions are obtained with the help of the diagonal approximation. They are found to be in excellent agreement with the exact numerical solutions of anisotropic diffusionreaction equations. The analytical solutions for reaction rates and survival probabilities are also obtained. We find that the longtime kinetic transition from a powerlaw decrease to an exponential increase can be controlled by the external field strength or excitedstate decay rates or both.

Implementation and assessment of a simple nonlocal van der Waals density functional
View Description Hide DescriptionRecently we developed a nonlocal van der Waals density functional (VV09) that has a simple and wellbehaved analytic form. In this article, we report a selfconsistent implementation of VV09 with an atomcentered basis set. We compute binding energies for a diverse benchmark set and find that VV09 performs well in combination with Hartree–Fock exchange. We compare VV09 with its precursor, discuss likely sources of inaccuracies in both models, and identify some aspects of the methodology where further refinements are desirable.

Automated incremental scheme for explicitly correlated methods
View Description Hide DescriptionAn automated implementation of the incremental scheme for the computation of MP2F12 and CCSD(F12) energies is presented. The numerical accuracy of the approach is explored for a set of 15 chemical reactions using the limiting case of single orbital onesite domains as a worst case scenario. The results are analyzed by the maximum absolute deviation, the mean absolute error, and the root mean square error, with respect to the standard MP2F12 and CCSD(F12) results. It is found that the MP2 reactionenergies are within 1 kcal/mol accuracy at third order of the expansion, whereas the F12 corrections are already sufficiently accurate at second order. For the CCSD(F12) method 1 kcal/mol accuracy is obtained at fourth order.

Accurate calculation and modeling of the adiabatic connection in density functional theory
View Description Hide DescriptionUsing a recently implemented technique for the calculation of the adiabatic connection (AC) of density functional theory(DFT) based on Lieb maximization with respect to the external potential, the AC is studied for atoms and molecules containing up to ten electrons: the helium isoelectronic series, the hydrogen molecule, the beryllium isoelectronic series, the neon atom, and the water molecule. The calculation of AC curves by Lieb maximization at various levels of electronicstructure theory is discussed. For each system, the AC curve is calculated using Hartree–Fock (HF) theory, secondorder Møller–Plesset (MP2) theory,coupledcluster singlesanddoubles (CCSD) theory, and coupledcluster singlesdoublesperturbativetriples [CCSD(T)] theory, expanding the molecular orbitals and the effective external potential in large Gaussian basis sets. The HF AC curve includes a small correlationenergy contribution in the context of DFT, arising from orbital relaxation as the electronelectron interaction is switched on under the constraint that the wave function is always a single determinant. The MP2 and CCSD AC curves recover the bulk of the dynamical correlation energy and their shapes can be understood in terms of a simple energy model constructed from a consideration of the doublesenergy expression at different interaction strengths. Differentiation of this energy expression with respect to the interaction strength leads to a simple twoparameter doubles model (ACD) for the AC integrand (and hence the correlation energy of DFT) as a function of the interaction strength. The structure of the triplesenergy contribution is considered in a similar fashion, leading to a quadratic model for the triples correction to the AC curve (ACT). From a consideration of the structure of a twolevel configurationinteraction (CI) energy expression of the hydrogen molecule, a simple twoparameter CI model (ACCI) is proposed to account for the effects of static correlation on the AC. When parametrized in terms of the same input data, the ACCI model offers improved performance over the corresponding ACD model, which is shown to be the lowestorder contribution to the ACCI model. The utility of the accurately calculated AC curves for the analysis of standard density functionals is demonstrated for the BLYP exchangecorrelation functional and the interactionstrengthinterpolation (ISI) model AC integrand. From the results of this analysis, we investigate the performance of our proposed twoparameter ACD and ACCI models when a simple density functional for the AC at infinite interaction strength is employed in place of information at the fully interacting point. The resulting twoparameter correlation functionals offer a qualitatively correct behavior of the AC integrand with much improved accuracy over previous attempts. The AC integrands in the present work are recommended as a basis for further work, generating functionals that avoid spurious error cancellations between exchange and correlation energies and give good accuracy for the range of densities and types of correlation contained in the systems studied here.

Particle number and probability density functional theory and representability
View Description Hide DescriptionIn Hohenberg–Kohn density functional theory, the energy is expressed as a unique functional of the ground state density : with the internal energy component being universal. Knowledge of the functional by itself, however, is insufficient to obtain the energy: the particle number is primary. By emphasizing this primacy, the energy is written as a nonuniversalfunctional of and probability density: . The set of functions satisfies the constraints of normalization to unity and nonnegativity, exists for each , and defines the probability density or pspace. A particle number and probability densityfunctionaltheory is constructed. Two examples for which the exact energy functionals are known are provided. The concept of representability is introduced, by which it is meant the set of functions that leads to probability densities obtained as the quantummechanical expectation of the probability density operator, and which satisfies the above constraints. We show that the set of functions of space is equivalent to the representable probability density set. We also show via the Harriman and Gilbert constructions that the representable and representable probability density sets are equivalent.