Volume 122, Issue 5, 01 February 2005
 COMMUNICATIONS


Chemisorption sites of CO on small gold clusters and transitions from chemisorption to physisorption
View Description Hide DescriptionGold clusters adsorbed with CO, were studied by photoelectron spectroscopy (PES). The first few CO adsorptions were observed to induce significant redshifts to the PES spectra relative to pure gold clusters. For each Au cluster, a critical CO number was observed, beyond which the PES spectra of change very little with increasing n. was shown to correspond exactly to the available low coordination apex sites in each Au cluster. CO first chemisorbs to these sites and additional CO then only physisorbs to the chemisorptionsautrated complexes.
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 ARTICLES

 Theoretical Methods and Algorithms

Gaussian split Ewald: A fast Ewald mesh method for molecular simulation
View Description Hide DescriptionGaussian split Ewald (GSE) is a versatile Ewald mesh method that is fast and accurate when used with both realspace and kspace Poisson solvers. While realspace methods are known to be asymptotically superior to kspace methods in terms of both computational cost and parallelization efficiency, kspace methods such as smooth particlemesh Ewald (SPME) have thus far remained dominant because they have been more efficient than existing realspace methods for simulations of typical systems in the size range of current practical interest. Realspace GSE, however, is approximately a factor of 2 faster than previously described realspace Ewald methods for the level of force accuracy typically required in biomolecular simulations, and is competitive with leading kspace methods even for systems of moderate size. Alternatively, GSE may be combined with a kspace Poisson solver, providing a conveniently tunable kspace method that performs comparably to SPME. The GSE method follows naturally from a uniform framework that we introduce to concisely describe the differences between existing Ewald mesh methods.

van der Waals interactions of polycyclic aromatic hydrocarbon dimers
View Description Hide DescriptionDensity functional theory is in principle exact and includes also longrange interactions, such as the van der Waals interactions. These are, however, part of the exchangecorrelation energy functional that needs to be approximated, and are absent in the local and semilocal standard implementations. Recently a density functional which includes van der Waals interactions for planar systems has been developed [Phys. Rev. Lett. 91, 126402 (2003)], which we show can be extended to provide a treatment of planar molecules. We use this functional to calculate binding distances and energies for dimers of three of the smallest polycyclic aromatic hydrocarbons (PAHs)—naphthalene, anthracene, and pyrene.

Accurate hybrid stochastic simulation of a system of coupled chemical or biochemical reactions
View Description Hide DescriptionThe dynamical solution of a wellmixed, nonlinear stochastic chemical kineticsystem, described by the Master equation, may be exactly computed using the stochastic simulation algorithm. However, because the computational cost scales with the number of reaction occurrences, systems with one or more “fast” reactions become costly to simulate. This paper describes a hybrid stochastic method that partitions the system into subsets of fast and slow reactions, approximates the fast reactions as a continuous Markov process, using a chemical Langevin equation, and accurately describes the slow dynamics using the integral form of the “Next Reaction” variant of the stochastic simulation algorithm. The key innovation of this method is its mechanism of efficiently monitoring the occurrences of slow, discrete events while simultaneously simulating the dynamics of a continuous, stochastic or deterministic process. In addition, by introducing an approximation in which multiple slow reactions may occur within a time step of the numerical integration of the chemical Langevin equation, the hybrid stochastic method performs much faster with only a marginal decrease in accuracy. Multiple examples, including a biological pulse generator and a largescale system benchmark, are simulated using the exact and proposed hybrid methods as well as, for comparison, a previous hybrid stochastic method. Probability distributions of the solutions are compared and the weak errors of the first two moments are computed. In general, these hybrid methods may be applied to the simulation of the dynamics of a system described by stochastic differential, ordinary differential, and Master equations.

The dynamic JahnTeller problem: A new insight from the strong coupling limit
View Description Hide DescriptionCorrect boundary conditions for the dynamic JahnTeller problem are considered explicitly for the first time to obtain approximate analytical solutions in the strong coupling limit. Numerical solutions for the decoupled equations using the finite difference method are also presented. The numerical solutions for the decoupled equations exhibit avoided crossings in the weak coupling region, which explains the oscillating behavior of the solutions obtained by LonguetHiggins et al. for the coupled equations. The obtained analytical energy expressions show improved agreement with the numerical calculations as compared with the previous treatment in which the potentials were assumed to be harmonic. We demonstrate that the pseudorotational energy where is the dimensionless vibronic coupling constant, and total angular momentum: in the conventional strong coupling expression for the vibronic levels of the lower sheet is exact. NonHermitian firstorder perturbation theory gives the energy which is correct up to The asymptotic behavior of the wave function at the origin does not influence the corrected energy up to order of At the same time the treatment of the upper sheet with correct boundary conditions gives solutions which are entirely different from the corresponding Slonczewski’s solutions. Besides, the correct boundary conditions enable us to evaluate the nonadiabatic coupling between the lower and upper potential sheets. The energy correction due to the nonadiabatic coupling is estimated to be of order

Fast centroid molecular dynamics: A forcematching approach for the predetermination of the effective centroid forces
View Description Hide DescriptionA fast centroid molecular dynamics (CMD) methodology is proposed in which the effective centroid forces are predetermined through a forcematching algorithm applied to a standard path integral molecular dynamics simulation. The resulting method greatly reduces the computational cost of generating centroid trajectories, thus extending the applicability of CMD. The method is applied to the study of liquid parahydrogen at two state points and liquid orthodeuterium at one state point. The static and dynamical results are compared to those obtained from full adiabatic CMD simulations and found to be in excellent agreement for all three systems; the transport properties are also compared to experiment and found to have a similar level of agreement.

Finite bias conductance of an Anderson level: A sourceLiouville Hartree–Fock study
View Description Hide DescriptionWe address the problem of stationary conductance through an Anderson spindegenerate level at finite bias. Just as in the Anderson solution, for a finite bias in parameter space (bias, gate voltage, interaction constant, and the couplings to the leads) there exist spinpolarized and nonspinpolarized regions. The transition curve between them is found analytically for the case of symmetric coupling to the left and right leads. We approach the problem by a nonMarkovian sourceLiouville equation where the twobody interaction selfenergies are taken in the Hartree–Fock approximation.

Cubic response functions in timedependent density functional theory
View Description Hide DescriptionWe present densityfunctional theory for timedependent response functions up to and including cubic response. The working expressions are derived from an explicit exponential parametrization of the density operator and the Ehrenfest principle, alternatively, the quasienergy ansatz. While the theory retains the adiabatic approximation, implying that the timedependency of the functional is obtained only implicitly—through the time dependence of the density itself rather than through the form of the exchangecorrelation functionals—it generalizes previous timedependent implementations in that arbitrary functionals can be chosen for the perturbed densities (energy derivatives or response functions). In particular, general density functionals beyond the local density approximation can be applied, such as hybrid functionals with exchange correlation at the generalizedgradient approximation level and fractional exact Hartree–Fock exchange. With our implementation the response of the density can always be obtained using the stated density functional, or optionally different functionals can be applied for the unperturbed and perturbed densities, even different functionals for different response order. As illustration we explore the use of various combinations of functionals for applications of nonlinear optical hyperpolarizabilities of a few centrosymmetric systems; molecular nitrogen, benzene, and the fullerene. Considering that vibrational, solvent, and local field factors effects are left out, we find in general that very good experimental agreement can be obtained for the second dynamic hyperpolarizability of these systems. It is shown that a treatment of the response of the density beyond the local density approximation gives a significant effect. The use of different functional combinations are motivated and discussed, and it is concluded that the choice of higher order kernels can be of similar importance as the choice of the potential which governs the Kohn–Sham orbitals.

Multiconfiguration selfconsistentfield theory based upon the fragment molecular orbital method
View Description Hide DescriptionThe fragment molecular orbital (FMO) method was combined with the multiconfiguration selfconsistentfield (MCSCF) theory. One and twolayer approaches were developed, the former involving all dimer MCSCF calculations and the latter limiting MCSCF calculations to a small part of the system. The accuracy of the two methods was tested using the six electrons in six orbitals complete active space type of MCSCF and singlet spin state for and basis sets); α helices and β strands of Both doubleζ and tripleζ quality basis sets with polarization were found to have very similar accuracy. The error in the correlationenergy was at most 0.000 88 a.u., the error in the gradient of the correlationenergy was at most and the error in the correlation correction to the dipole moment was at most 0.018 D. In addition, vertical singlettriplet electron excitation energies were computed for and the errors were found to be at most 0.02 eV. Approximately linear scaling was observed for the FMObased MCSCF methods. As an example, an FMObased MCSCF calculation with 1262 basis functions took 98 min on one 3.0 GHz Pentium4 node with 1 Gbyte RAM.

Intramolecular energy transfer through charge transfer state in lanthanide compounds: A theoretical approach
View Description Hide DescriptionA theoretical approach for the intramolecular energy transfer process involving the ligandtometal charge transfer (LMCT) state in lanthanide compounds is developed. Considering a twoelectron interaction, both the direct Coulomb and exchange interactions are taken into account, leading to expressions from which selection rules may be derived and transfer rates may be calculated. These selection rules show that the direct Coulomb and exchange mechanisms are complementary, in the same way as obtained in previous works for the case of ligandlanthanide ion energy transfer processes. An important result from numerical estimates is that the channel ligand–LMCT state is by far the dominant case, leading to transfer rates higher than for the channel lanthanide ion–LMCT state by several orders of magnitude. The analysis of the emission quantum yield as a function of the relative energy position of the LMCT state in a typical compound allows the identification of two quenching regions, the most pronounced one occurring close to the lower ligand triplet level.

Coupled cluster methods including triple excitations for excited states of radicals
View Description Hide DescriptionWe report an extension of the coupled cluster iterativetriples model, CC3, to excited states of openshell molecules, including radicals. We define the method for both spinunrestricted Hartree–Fock (UHF) and spinrestricted openshell Hartree–Fock (ROHF) reference determinants and discuss its efficient implementation in the PSI3 program package. The program is streamlined to use at most computational steps and avoids storage of the tripleexcitation amplitudes for both the ground and excitedstate calculations. The excitationenergy program makes use of a Löwdin projection formalism (comparable to that of earlier implementations) that allows computational reduction of the Davidson algorithm to only the single and doubleexcitation space, but limits the calculation to only one excited state at a time. However, a rootfollowing algorithm may be used to compute energies for multiple states of the same symmetry. Benchmark applications of the new methods to the lowest valence state of the allyl radical, lowlying states of the CH and diatomics, and the nitromethyl radical show substantial improvement over ROHF and UHFbased CCSD excitation energies for states with strong doubleexcitation character or cases suffering from significant spin contamination. For the allyl radical, CC3 adiabatic excitation energies differ from experiment by less than 0.02 eV, while for the state of CH, significant errors of more than 0.4 eV remain.

Propagator corrections to adiabatic timedependent densityfunctional theory linear response theory
View Description Hide DescriptionIt has long been known that only oneelectron excitations are available from adiabatic timedependent density functional theory (TDDFT). This is particularly clear in Casida’s formulation of TDDFT linear response theory [M. E. Casida, in Recent Advances in Density Functional Methods, Part I, edited by D. P. Chong (World Scientific, Singapore, 1995), p. 155]. Nevertheless the explicit inclusion of two and higherelectron excitations is necessary for an adequate description of some excited states, notably the first excited singlet states of butadiene and quartet excited states of molecules with a doublet ground state. The equationofmotion superoperator approach is used here to derive a Casidalike propagator equation which can be clearly separated into an adiabatic part and a nonadiabatic part. The adiabatic part is identified as corresponding to Casida’s equation for adiabatic TDDFT linear response theory. This equivalence is confirmed by deriving a general formula which includes the result that Gonze and Scheffler derived to show the equivalence of TDDFT and GörlingLevy adiabatic connection perturbation theory for the exchangeonly optimized effective potential [X. Gonze and M. Scheffler, Phys. Rev. Lett. 82, 4416 (1999)]. The nonadiabatic part explicitly corrects adiabatic TDDFT for two and higherelectron excitations. The “dressed TDDFT” of Maitra, Zhang, Cave, and Burke is obtained as a special case where the ground state is closed shell [N. T. Maitra, F. Zhang, R. J. Cave, and K. Burke, J. Chem. Phys. 120, 5932 (2004)]. The extension of dressed TDDFT to the case where the ground state is an openshell doublet is presented, highlighting the importance of correctly accounting for symmetry in this theory. The extension to other ground state spin symmetries is a straightforward consequence of the present work.

Targeted Car–Parrinello molecular dynamics: Elucidating double proton transfer in formic acid dimer
View Description Hide DescriptionThe targeted molecular dynamics method, making possible the study of rare events, has been assessed in the framework of Car–Parrinello ab initiomolecular dynamics. As a test case, we have studied the staggered–eclipsed rotation of ethane. The technique has subsequently been applied to investigate the nature of double proton transfer in formic acid dimer. The latter is found to follow a concerted transfer mechanism involving an essentially planar transition state. A “funnellike region” of the potential energy surface is identified, where floppy intermolecular modes stiffen upon approaching the transition state.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

An investigation of valence shell orbital momentum profiles of difluoromethane by binary spectroscopy
View Description Hide DescriptionThe electron binding energy spectra and momentum profiles of the valence orbitals of difluoromethane, also known as HFC32 (HFC—hydrofluorocarbon) have been studied by using a high resolution electron momentum spectrometer, at an impact energy of 1200 eV plus the binding energy, and by using symmetric noncoplanar kinematics. The experimental momentum profiles of the outer valence orbitals and inner valence orbital are compared with the theoretical momentum distributions calculated using Hartree–Fock and density functional theory(DFT) methods with various basis sets. In general, the shapes of the experimental momentum distributions are well described by both the Hartree–Fock and DFT calculations when large and diffuse basis sets are used. However, the result also shows that it is hard to choose the different calculations for some orbitals, including the methods and the size of the basis sets employed. The pole strength of the ionization peak from the inner valence orbital is estimated.

Multireference configuration interaction calculations for positronium halides
View Description Hide DescriptionMultireference configuration interaction (MRCI) calculations of the positronium halides, PsF, PsCl, PsBr, and PsI, are carried out, to give positronionization energies, positronium binding energies, and twophoton annihilation rates. All CI calculations consider only valence correlation effect with a frozencore approximation, and use the orbitals with angular momentum up to 8. To incorporate the effects of manybody correlations in the energies and twophoton annihilation rates, the MRCI calculations are repeated with increasing reference configurations, and the full CI limits of these energies and annihilation rates are estimated. The contribution from orbitals having angular momentum greater than 8 to those values is also estimated. Relative to our previous single reference CI calculations, manybody correlation effects significantly increase the positronionization energies, positronium binding energies, and twophoton annihilation rates. The structures of the positronium halides are also discussed.

Theoretical investigation of the dication and the photodouble ionization spectrum of SO
View Description Hide DescriptionHighly correlated ab initio methods were used in order to generate the potential energy curves of the electronic states of the dication and of the electronic ground state of the neutral SO molecule. These curves were used to predict the spectroscopicproperties of this dication and to perform forward calculations of the double photoionizationspectrum of SO. In light of spinorbit calculations, the metastability of this doubly charged ion is discussed: for instance, the rovibrational levels of the and states are found to present relatively long lifetimes. In contrast, the other electronic excited states should predissociate to form and in their electronic ground states. The simulated spectrum shows structures due to transitions between the vibrational level of SO and the vibrational levels below the barrier maximum of 11 of the calculated electronic states. The electronic state of received further treatment: in addition to vibrational bands due to the below barrier energy levels of this electronic state, at least nine continuum resonances were predicted which are responsible for the special shape of the spectrum in this energy region. This work is predictive in nature and should stimulate future experimental investigations dealing with this dication.

Timedependent quantum mechanical wave packet study of the reaction
View Description Hide DescriptionA detailed threedimensional timedependent quantum dynamical study of the reaction is reported for different vibrational states of in its ground rotational state over a range of translational energies on an accurate ab initiopotential energy surface published by Palmieri et al. Plots of reaction probability as a function of total energy E reveal a large number of oscillations indicating the presence of a number of reactive scattering resonances. When averaged over total angular momentumJ, some of the oscillations survive, indicating that they may be amenable to experimental observation. A comparison of our present results with our earlier results on the McLaughlin–Thompson–Joseph–Sathyamurthy surface and the experimental results from different research groups reveal a good deal of agreement as well as some discrepancies between theory and experiment at the level of stateselected gas phase dynamics.

Ab initio potential energy surfaces, total absorption cross sections, and product quantum state distributions for the lowlying electronic states of
View Description Hide DescriptionAdiabatic potential energy surfaces for the six lowest singlet electronic states of and have been computed using an ab initio multireference configuration interaction (MRCI) method and a large orbital basis set (augccpVQZ). The potential energy surfaces display several symmetry related and some nonsymmetry related conical intersections. Total photodissociation cross sections and product rotational state distributions have been calculated for the first ultraviolet absorption band of the system using the adiabatic ab initiopotential energy and transition dipole momentsurfaces corresponding to the lowest three excited electronic states. In the Franck–Condon region the potential energy curves corresponding to these three states lie very close in energy and they all contribute to the absorption cross section in the first ultraviolet band. The total angular momentum is treated correctly in both the initial and final states. The total photodissociationspectra and product rotational distributions are determined for initially in its ground vibrational state (0,0,0) and in the vibrationally excited (0,1,0) (bending) state. The resulting total absorption spectra are in good quantitative agreement with the experimental results over the region of the first ultraviolet absorption band, from 150 to 220 nm. All of the lowest three electronically excited states and have zero transition dipole moments from the ground state in its equilibrium linear configuration. The absorption becomes possible only through the bending motion of the molecule. The absorption dominates the absorption cross section with absorption to the other two electronic states contributing to the shape and diffuse structure of the band. It is suggested that absorption to the bound state makes an important contribution to the experimentally observed diffuse structure in the first ultraviolet absorption band. The predicted product rotational quantum state distribution at 203 nm agrees well with experimental observations.

New CO–CO interaction potential tested by rovibrational calculations
View Description Hide DescriptionA fourdimensional potential energy surface (PES) for the CO dimer consisting of rigid molecules has been calculated, using a scheme that combines density functional theory to describe the monomers and symmetry adapted perturbation theory for the interaction energy (DFTSAPT). The potential is fitted in terms of analytic functions, and the fitted potential is used to compute the lowest rovibrational states of the dimer. The quality of the PES is comparable to that of a previously published surface [G. W. M. Vissers, P. E. S. Wormer, and A. van der Avoird, Phys. Chem. Chem. Phys., 5, 4767 (2003)], which was calculated with the coupled cluster single double and perturbative triples [CCSD(T)] method. It is shown that a weighted average of the DFTSAPT and the CCSD(T) potential gives results that are in very good agreement with experimental data, for both and The relative weight was determined by adjusting the energy gap between the origins of the lowest two stacks of rotational levels of to the measured value.

Photodissociation dynamics of
View Description Hide DescriptionWe report the ionic photoproducts produced following photoexcitation of mass selected cluster ions at 790 and 355 nm. These wavelengths provide single state excitation to two dissociative states, corresponding to the and states of the chromophore. Excitation of these states in leads to production of and respectively. Potential energy curves for the six lowest electronic states of are calculated, together with structures for Translational energy release measurements on photodissociated determine the bond strength to be 1.10±0.04 eV; related measurements characterize the absorption band. Photodissociation product distributions are measured as a function of cluster size following excitation to the and states. The solvent is shown to drive processes such as spinorbit relaxation, charge transfer, recombination, and vibrational relaxation on the ground electronic state. Following excitation to the electronic state, exhibits sizedependent cage fractions remarkably similar to those observed for In contrast, excitation to the state shows extensive trapping in excited states that dominates the recombination behavior for all cluster sizes we investigated. Finally, a pumpprobe experiment on determines the time required for recombination on the ground state following excitation to the state. While the photofragmentation experiments establish 100% recombination in the ground electronic state for this and larger cluster ions, the time required for recombination is found to be ∼5 ns, some three orders of magnitude longer than observed for the analogous cluster ion. Comparisons are made with similar experiments carried out on and cluster ions.