Volume 127, Issue 17, 07 November 2007
 COMMUNICATIONS


Comparing the activation energy of diffusion in bulk and ultrathin fluid films
View Description Hide DescriptionWe have measured the activation energy of translational diffusion for a dissolved fluorescent dye in bulk and within an ultrathin liquid film formed on a solid substrate. The experiments were performed using the singlemolecule sensitive technique of fluorescence correlation spectroscopy. From the temperaturedependent measurements, we have determined that the activation energy for a few nanometer thick fluid film increases by a factor of compared to bulk liquid. The results are confirmed for two distinctly different systems in regard to molecular shape, tetrakis (2ethylhexoxy) silane and hexadecane.

A soft effective segment representation of semidilute polymer solutions
View Description Hide DescriptionA coarsegrained effective segment description of polymer solutions is presented, based on soft, transferable effective interactions between bonded and nonbonded effective segments. The number of segments is chosen such that the segment density does not exceed their overlap threshold, allowing polymer concentrations to be explored deep into the semidilute regime. This quantitative effective segment description is shown to preserve known scaling laws of polymer solutions and provides accurate estimates of amplitudes, while leading to a ordersofmagnitude increase in the simulation efficiency and allowing analytic calculations of structural and thermodynamic properties.
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 ARTICLES

 Theoretical Methods and Algorithms

Optimized effective potentials from electron densities in finite basis sets
View Description Hide DescriptionThe WuYang method for determining the optimized effective potential (OEP) and implicit density functionals from a given electron density is revisited to account for its illposed nature, as recently done for the direct minimization method for OEP’s from a given orbital functional [T. HeatonBurgess, F. A. Bulat, and W. Yang, Phys. Rev. Lett.98, 256401 (2007)]. To address the issues on the general validity and practical applicability of methods that determine the KohnSham (local) multiplicative potential in a finite basis expansion, a new functional is introduced as a regularized version of the original work of Wu and Yang. It is shown that the unphysical, highly oscillatory potentials that can be obtained when unbalanced basis sets are used are the controllable manifestation of the illposed nature of the problem. The new method ensures that well behaved potentials are obtained for arbitrary basis sets.

Exactexchange density functional theory for hyperpolarizabilities
View Description Hide DescriptionTimedependent density functional theory (TDDFT) employing the exactexchange functional (TDDFTx) has been formulated using the optimized effective potential method for the static hyperpolarizabilities, where it reduces to coupledperturbed KohnSham theory. A diagrammatic technique is used to take the functional derivatives for the derivation of the adiabatic second kernel, which is required for the analytical calculation of the static hyperpolarizabilities with DFT. The derived formulas have been implemented using Gaussian basis sets. The structure of the adiabatic exactexchange second kernel is described and numerical examples are presented. It is shown that no current DFT functional satisfies the correct properties of the second kernel. Not surprisingly, TDDFTx, which corrects the selfinteraction error in standard DFT methods and has the correct longrange behavior, provides results close to those of timedependent HartreeFock in the static limit.

Optimized expanded ensembles for simulations involving molecular insertions and deletions. I. Closed systems
View Description Hide DescriptionMonte Carlo simulation methods that involve the insertiondeletion of molecules are of wide spread use for the study of thermophysical behavior of complex systems; e.g., for the estimation of chemical potentials in closedsystem ensembles. In this work, efficient expanded ensemble methods are described to overcome the lack of ergodicity that often plagues such molecular moves, wherein an arbitrary physical parameter is used to gradually couple and decouple a partial molecule to and from the system. In particular, we describe the use of (1) acceptance ratio methods for the robust estimation of freeenergy changes associated with transitions between states of the partial molecule, (2) nonBoltzmann sampling of the probability density of states so that one can achieve either a flat histogram or an optimized histogram based on the maximization of round trips between the bounds, and (3) an approach to select suitable intermediate stages of the parameter that maximizes such round trips. The validity of the advocated methods is demonstrated by their application to two model systems, namely, the solvation of large hard spheres into a fluid of small spheres, and the mesophase formation of a block copolymerhomopolymer mixture.

Optimized expanded ensembles for simulations involving molecular insertions and deletions. II. Open systems
View Description Hide DescriptionIn the Grand Canonical, osmotic, and Gibbs ensembles, chemical potential equilibrium is attained via transfers of molecules between the system and either a reservoir or another subsystem. In this work, the expanded ensemble (EXE) methods described in part I [F. A. Escobedo and F. J. MartínezVeracoechea, J. Chem. Phys.127, 174103 (2007)] of this series are extended to these ensembles to overcome the difficulties associated with implementing such wholemolecule transfers. In EXE, such moves occur via a target molecule that undergoes transitions through a number of intermediate coupling states. To minimize the tunneling time between the fully coupled and fully decoupled states, the intermediate states could be either: (i) sampled with an optimal frequency distribution (the sampling problem) or (ii) selected with an optimal spacing distribution (staging problem). The sampling issue is addressed by determining the biasing weights that would allow generating an optimal ensemble; discretized versions of this algorithm (well suited for small number of coupling stages) are also presented. The staging problem is addressed by selecting the intermediate stages in such a way that a flat histogram is the optimized ensemble. The validity of the advocated methods is demonstrated by their application to two model problems, the solvation of large hard spheres into a fluid of small and large spheres, and the vaporliquid equilibrium of a chain system.

The weak orthogonality functional in explicitly correlated pair theories
View Description Hide DescriptionRecent advances have seen the convergence of the R12 and Gaussian geminal explicitly correlated methods, such that the principal remaining distinction is the way in which the manyelectron integrals are handled. Here we examine the weak orthogonality functional and the resolution of the identity and find that the first, although exact in the limit of infinite basis, introduces a conflict between the physical description of the electronic cusp and the satisfaction of the strong orthogonality constraint. This leads us to propose an improved weak orthogonality functional where the explicitly correlated pair functions are almost orthogonal to the occupied orbitals by construction. For applications where 95%98% accuracy in the total correlation energy is sufficient, we recommend use of the strong orthogonality functional in combination with the resolution of the identity for three and fourelectron integral evaluations.

Breaking bonds with the left eigenstate completely renormalized coupledcluster method
View Description Hide DescriptionThe recently developed [P. Piecuch and M. Wloch, J. Chem. Phys.123, 224105 (2005)] sizeextensive left eigenstate completely renormalized (CR) coupledcluster (CC) singles (S), doubles (D), and noniterative triples (T) approach, termed CRCC(2,3) and abbreviated in this paper as CCL, is compared with the full configuration interaction (FCI) method for all possible types of single bondbreaking reactions between C, H, Si, and Cl (except ) and the double bondbreaking reaction. The CCL method is in excellent agreement with FCI in the entire region for all of the studied single bondbreaking reactions, where and are the bond distance and the equilibrium bond length, respectively. The CCL method recovers the FCI results to within approximately in the region of the , H–Cl, , , , and bonds. The maximum errors are , 1.6, and in the region of the , Cl–Cl, and bonds, respectively, while the discrepancy for the double bondbreaking reaction is 6.6 at . CCL also predicts more accurate relative energies than the conventional CCSD and CCSD(T) approaches, and the predecessor of CRCC(2,3) termed CRCCSD(T).

Nonvariational timedependent multiconfiguration selfconsistent field equations for electronic dynamics in laserdriven molecules
View Description Hide DescriptionA timedependent multiconfiguration selfconsistent field (TDMCSCF) scheme is developed to describe the timeresolved electron dynamics of a laserdriven manyelectron atomic or molecular system, starting directly from the timedependent Schrödinger equation for the system. This nonvariational formulation aims at the full exploitations of concepts, tools, and facilities of existing, welldeveloped quantum chemical MCSCF codes. The theory uses, in particular, a unitary representation of timedependent configuration mixings and orbital transformations. Within a shorttime, or adiabatic approximation, the TDMCSCF scheme amounts to a secondorder splitoperator algorithm involving generically the two noncommuting oneelectron and twoelectron parts of the timedependent electronic Hamiltonian. We implement the scheme to calculate the laserinduced dynamics of the twoelectron molecule described within a minimal basis, and show how electron correlation is affected by the interaction of the molecule with a strong laser field.

Quantum mechanical correlation functions, maximum entropy analytic continuation, and ring polymer molecular dynamics
View Description Hide DescriptionThe maximum entropy analytic continuation (MEAC) and ringpolymermolecular dynamics (RPMD) methods provide complementary approaches to the calculation of real time quantum correlation functions. RPMD becomes exact in the high temperature limit, where the thermal time tends to zero and the ringpolymer collapses to a single classical bead. MEAC becomes most reliable at low temperatures, where exceeds the correlation time of interest and the numerical imaginary time correlation function contains essentially all of the information that is needed to recover the real time dynamics. We show here that this situation can be exploited by combining the two methods to give an improved approximation that is better than either of its parts. In particular, the MEAC method provides an ideal way to impose exact moment (or sum rule) constraints on a prior RPMD spectrum. The resulting scheme is shown to provide a practical solution to the “nonlinear operator problem” of RPMD, and to give good agreement with recent exact results for the shorttime velocity autocorrelation function of liquid parahydrogen. Moreover these improvements are obtained with little extra effort, because the imaginary time correlation function that is used in the MEAC procedure can be computed at the same time as the RPMD approximation to the real time correlation function. However, there are still some problems involving longtime dynamics for which the combination is inadequate, as we illustrate with an example application to the collective density fluctuations in liquid orthodeuterium.

Stringent test of the statistical quasiclassical trajectory model for the exchange reaction: A comparison with rigorous statistical quantum mechanical results
View Description Hide DescriptionA complete formulation of a statistical quasiclassical trajectory (SQCT) model is presented in this work along with a detailed comparison with results obtained with the statistical quantum mechanical (SQM) model for the and reactions. The basic difference between the SQCT and the SQM models lies in the fact that trajectories instead of wave functions are propagated in the entrance and exit channels. Other than this the two formulations are entirely similar and both comply with the principle of detailed balance and conservation of parity.Reaction probabilities, and integral and differential cross sections (DCS’s) for these reactions at different levels of product’s state resolution and from various initial states are shown and discussed. The agreement is in most cases excellent and indicates that the effect of tunneling through the centrifugal barrier is negligible. Some differences are found, however, between state resolved observables calculated by the SQCT and the SQM methods which makes use of the centrifugal sudden (coupled states) approximation (SQMCS). When this approximation is removed and the full close coupling treatment is used in the SQM model (SQMCC), an almost perfect agreement is achieved. This shows that the SQCT is sensitive enough to show the relatively small inaccuracies resulting from the decoupling inherent to the CS approximation. In addition, the effect of ignoring the parity conservation is thoroughly examined. This effect is in general minor except in particular cases such as the DCS from initial rotational state . It is shown, however, that in order to reproduce the sharp forward and backward peaks the conservation of parity has to be taken into account.

Core ionization potentials from selfinteraction corrected KohnSham orbital energies
View Description Hide DescriptionWe propose a simple selfinteraction correction to KohnSham orbital energies in order to apply ground state KohnSham density functional theory to accurate predictions of core electron binding energies and chemical shifts. The proposition is explored through a series of calculations of organic compounds of different sizes and types. Comparison is made versus experiment and the “Sham” method employing separate state optimizations of the ground and core hole states, with the use of the B3LYP functional and different basis sets. A parameter is introduced for a best fitting of computed and experimental ionization potentials. It is found that internal parametrizations in terms of basis set expansions can be well controlled. With a unique and basis set larger than 631G, the core ionization energies (IPs) of the selfinteraction corrected KohnSham calculations fit quite well to the experimental values. Hence, selfinteraction corrected KohnSham calculations seem to provide a promising tool for core IPs that combines accuracy and efficiency.

Relativistic twocomponent formulation of timedependent currentdensity functional theory: Application to the linear response of solids
View Description Hide DescriptionIn this paper we derive the relativistic twocomponent formulation of timedependent currentdensityfunctional theory. To arrive at a twocomponent currentdensity formulation we apply a FoldyWouthuysentype transformation to the timedependent fourcomponent DiracKohnSham equations of relativistic densityfunctional theory. The twocomponent Hamiltonian is obtained as a regular expansion which is gauge invariant at each order of approximation, and to zeroth order it represents the timedependent version of the relativistic zeroth order regular Hamiltonian obtained by van Lenthe et al., for the ground state [J. Chem. Phys.99, 4597 (1993)]. The corresponding zeroth order regular expression for the density is unchanged, whereas the currentdensity operator now comprises a paramagnetic, a diamagnetic, and a spin contribution, similar to the Gordon decomposition of the Dirac four current. The zeroth order current density is directly related to the mean velocity corresponding to the zeroth order Hamiltonian. These density and current density operators satisfy the continuity equation. This zeroth order approximation is therefore consistent and physically realistic. By combining this formalism with the formulation of the linear response of solids within timedependent currentdensity functional theory[Romaniello and de Boeij, Phys. Rev. B71, 155108 (2005)], we derive a method that can treat orbital and spin contributions to the response in a unified way. The effect of spinorbit coupling can now be taken into account. As first test we apply the method to calculate the relativistic effects in the linear response of several metals and nonmetals to a macroscopic electric field. Treatment of spinorbit coupling yields visible changes in the spectra: a smooth onset of the interband transitions in the absorptionspectrum of Au, a sharp onset with peak at about in the absorptionspectrum of W, and a lowfrequency doublet structure in the absorption spectra of ZnTe,CdTe, and HgTe in agreement with experimental results.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Interaction of CO with Kr: Potential energy surface and bound states
View Description Hide DescriptionThe first ab initiopotential energy surface of the Kr–CO complex is developed using single and double excitation coupledcluster theory with noniterative treatment of triple excitations. Mixed basis sets, augccpVQZ for the C and O atoms and augccpVQZPP for the Kr atom, with an additional set of midbond functions are used. The computed interaction energies in 336 configurations are analytically fitted to a twodimensional potential model by a least squares fit. The potential has a minimum of with at an approximate Tshaped geometry . Bound state energies are calculated up to , thus enabling a comprehensive comparison between theory and available experimental data as well as providing detailed guidance for future spectroscopic investigations of higherlying states. The predicted transition frequencies and spectroscopic constants are in good agreement with the experimental results.

New ab initio potential energy surfaces for the reaction
View Description Hide DescriptionWe present the results of new ab initio calculations of the three potential energy surfaces (PESs) which are necessary for a complete description of the reaction. These are the result of highprecision multireference configurationinteraction calculations, with an additional scaling of the external correlation energy. The results of these calculations have been fitted to a multiparameter form for use in subsequent quantum scattering calculations. With a scaling factor of , the calculated exoergicity agrees nearly exactly with experimentally determined values. With a slightly reduced scaling factor of , the fitted PESs give excellent agreement with the position and modulation depth of the transition state resonance observed by Skodje et al. [J. Chem. Phys.112, 4536 (2000)]. This suggests that these new PESs can be used with confidence in the simulation of the reactivity of the ground and excited spinorbit states of the F atom in reactions with .

Lowlying quartet electronic states of nitrogen dioxide
View Description Hide DescriptionThe environmentally active molecule nitrogen dioxide has been systematically studied using high level theoretical methods. The electronic ground state and the lowlying quartet states of have been investigated. Single reference restricted openshell selfconsistent field (SCF), complete active space SCF (CASSCF), spinrestricted (R) and spinunrestricted (U) configuration interaction with single and double excitations (CISD), coupled cluster with single and double excitations (CCSD), CCSD with perturbative triple excitations [CCSD(T)], and internally contracted multireference configuration interaction (ICMRCI) methods along with Dunning’s correlation consistent polarized valence ccpVXZ and augmented ccpVXZ (where ) basis sets were used in this research. At the augccpV5Z/UCCSD(T) level the classical adiabatic excitation energies ( values) of the three lowestlying quartet excited states were predicted to be (, ) for the state, (, ) for the state, and (, ) for the state. The quantum mechanical excitation energies ( values) were determined to be (, ) for the state and (, ) for the state. The lowest quartet linear RennerTeller state gives rise to the state with 112.8° and the state with 124.4° ∠(ONO) bond angles upon bending. The state shows some peculiar behavior. Although CASSCF, RCISD, UCISD, RCCSD, UCCSD, and RCCSD(T) methods predicted the presence of a equilibrium geometry (a double minimum state), SCF, UCCSD(T), and ICMRCI wave functions predicted the structure for the state. The importance of both dynamical and nondynamical correlation treatments for the energy difference between and structures of state is highlighted in this context. The state is predicted to have a very small bond angle of 85.8°. Potential energy diagrams with respect to the bond angles of the ground state and four quartet states are presented.

Phenol revisited: An ab initio study on the photophysics of these clusters at the level of coupled cluster response theory
View Description Hide DescriptionThe state surfaces of the phenolclusters are reexplored at the level of coupled cluster response theory. The global minima for and so obtained are qualitatively different from those reported so far, which were obtained with methods such as configuration interaction singles or complete active space selfconsistent field lacking dynamical electron correlation effects. Furthermore, the minimumenergy points on the conical intersection seams were located in this work. The results of these calculations offer a qualitative explanation for the anomalous photophysical behavior (broad congested absorptionband structure, low quantum yield, short lifetime) of and the observed predissociation of at excess energies beyond , resolving a disagreement between theory and experiment which persisted for almost a decade.

Coupledcluster study of the electronic structure and energetics of tetrasulfur,
View Description Hide DescriptionAb initio electronic structure calculations are reported for . Geometric and energetic parameters are calculated using the singles and doubles coupledcluster method, including a perturbutional correction for connected triple excitation, CCSD(T), together with systematic sequences of correlation consistent basis sets extrapolated to the complete basis set limit. The geometry for the ground state singlet structure of is in good agreement with the microwave structure determined for . There is a lowlying transition state at which interchanges the long S–S bond. has a lowlying triplet state in symmetry which is above the singlet ground state. The S–S bond dissociation energy for into two molecules is predicted to be . The S–S bond energy to form is predicted to be .

Probing molecular conformations in momentum space: The case of pentane
View Description Hide DescriptionA comprehensive study, throughout the valence region, of the electronic structure and electron momentum density distributions of the four conformational isomers of pentane is presented. Theoretical valence ionizationspectra at high electron impact energies ( binding energy) and at azimuthal angles ranging from 0° to 10° in a noncoplanar symmetric kinematical setup are generated according to the results of large scale oneparticle Green’s function calculations of Dyson orbitals and related electron binding energies, using the thirdorder algebraicdiagrammatic construction [ADC(3)] scheme. The results of a focal point analysis (FPA) of relative conformer energies [A. Salam and M. S. Deleuze, J. Chem. Phys.116, 1296 (2002)] and improved thermodynamical calculations accounting for hindered rotations are also employed in order to quantitatively evaluate the abundance of each conformer in the gas phase at room temperature and reliably predict the outcome of experiments on pentane employing high resolution electron momentum spectroscopy. Comparison with available photoelectron measurements confirms the suggestion that, due to entropy effects, the transgauche conformer strongly dominates the conformational mixture characterizing pentane at room temperature. Our simulations demonstrate therefore that experimental measurements of valence ionizationspectra and electron momentum distributions would very consistently and straightforwardly image the topological changes and energy variations that molecular orbitals undergo due to torsion of the carbon backbone. The strongest fingerprints for the most stable conformer are found for the electron momentum distributions associated with ionization channels at the top of the innervalence region, which sensitively image the development of methylenic hyperconjugation in allstaggered alkane chains.

Electron ionization of acetylene
View Description Hide DescriptionRelative partial ionization cross sections and precursor specific relative partial ionization cross sections for fragment ions formed by electron ionization of have been measured using timeofflight mass spectrometry coupled with a 2D ionion coincidence technique. We report data for the formation of , , , , , , , and relative to the formation of , as a function of ionizing electron energy from . While excellent agreement is found between our data and one set of previously published absolute partial ionization cross sections, some discrepancies exist between the results presented here and two other recent determinations of these absolute partial ionization cross sections. We attribute these differences to the loss of some translationally energetic fragment ions in these earlier studies. Our relative precursorspecific partial ionization cross sections enable us, for the first time, to quantify the contribution to the yield of each fragment ion from single, double, and triple ionization. Analysis shows that at double ionization contributes 2% to the total ion yield, increasing to over 10% at an ionizing energy of . From our ionion coincidence data, we have derived branching ratios for charge separating dissociations of the acetylene dication. Comparison of our data to recent ab initio/RRKM calculations suggest that close to the double ionization potential dissociates predominantly on the ground triplet potential energy surface with a much smaller contribution from dissociation via the lowest singlet potential energy surface. Measurements of the kinetic energy released in the fragmentation reactions of have been used to obtain precursor state energies for the formation of product ion pairs, and are shown to be in good agreement with available experimental data and with theory.