Volume 130, Issue 18, 14 May 2009

Oxygen vacancies on have been proposed to be the catalytically active sites for methanol synthesis on pure ZnO. The charge state and thus the chemical reactivity of such vacancies on this polar Oterminated basal plane of ZnO is expected to be intimately connected to the degree of its hydroxylation in view of its Tasker type(3) unstable character. Here, the interplay between hydrogen adsorption and the thermodynamic stability of O vacancies in various charge states, corresponding formally to , , , , and centers, is investigated using electronic structure calculations. Assuming thermodynamic equilibrium of the defective surface with a hydrogen containing gas phase the thermodynamically most stable O vacancy type is determined as a function of temperature and pressure. For the adsorption of molecules at O vacancy sites it is found that the homolytic process leads to energetically more favorable structures than heterolytic adsorption and hydride formation. By homolytic adsorption and desorption one can switch between , , and or between and , a process which is believed to occur during methanol synthesis. However, the barrier for heterolytic dissociation of at O vacancies is significantly lower compared to homolytic cleavage. Furthermore, the barrier for transforming hydridic hydrogen, i.e., ZnH species, to protonic hydrogen, i.e., OH species together with a reduction of ZnO itself, is quite high. This implies that hydridic species created as a result of heterolytic dissociation might have a long enough lifetime at O vacancies that they will be available for methanol synthesis. ZnH and OH vibrational frequencies have been computed in order to assist future experimental assignments.
 COMMUNICATIONS


Phenomenological local field enhancement factor distributions around electromagnetic hot spots
View Description Hide DescriptionWe propose a general phenomenological description of the enhancement factor distribution for surfaceenhanced Raman scattering(SERS) and other related phenomena exploiting large local field enhancements at hot spots. This description extends naturally the particular case of a single (fixed) hot spot, and it is expected to be “universal” for many classes of common SERS substrates containing a collection of electromagnetic hot spots with varying geometrical parameters. We further justify it from calculations with generalized Mie theory. The description studied here provides a useful starting point for a qualitative (and semiquantitative) understanding of experimental data and, in particular, the analysis of the statistics of singlemolecule SERS events.

 ARTICLES

 Theoretical Methods and Algorithms

Highly multireferenced arynes studied with large active spaces using twoelectron reduced density matrices
View Description Hide DescriptionUsing the activespace twoelectron reduced density matrix (2RDM) method, which scales polynomially with the size of the active space [G. Gidofalvi and D. A. Mazziotti, J. Chem. Phys.129, 134108 (2008)], we were able to use active spaces as large as 24 electrons in 24 orbitals in computing the groundstate energies and properties of highly multireferenced arynes. Because the conventional completeactivespace selfconsistentfield (CASSCF) method scales exponentially with the size of the active space, its application to arynes was mainly limited to active spaces of 12 electrons in 12 orbitals. For these smaller active spaces the activespace 2RDM method accurately reproduces the results of CASSCF. However, we show that the larger active spaces are necessary for describing changes in energies and properties with aryne chain length such as the emergence of polyradical character. Furthermore, the addition of further electron correlation by multireference perturbation theory is demonstrated to be inadequate for removing the limitations of the smaller active spaces.

Development of generalized potentialenergy surfaces using manybody expansions, neural networks, and moiety energy approximations
View Description Hide DescriptionA general method for the development of potentialenergy hypersurfaces is presented. The method combines a manybody expansion to represent the potentialenergysurface with twolayer neural networks (NN) for each body term in the summations. The total number of NNs required is significantly reduced by employing a moiety energy approximation. An algorithm is presented that efficiently adjusts all the coupled NN parameters to the database for the surface. Application of the method to four different systems of increasing complexity shows that the fitting accuracy of the method is good to excellent. For some cases, it exceeds that available by other methods currently in literature. The method is illustrated by fitting large databases of ab initio energies for clusters obtained from density functional theory calculations and for vinyl bromide and all products for dissociation into six open reaction channels (12 if the reverse reactions are counted as separate open channels) that include C–H and C–Br bond scissions, threecenter HBr dissociation, and threecenter dissociation. The vinyl bromide database comprises the ab initio energies of 71 969 configurations computed at MP4(SDQ) level with a basis set for the carbon and hydrogen atoms and Huzinaga’s (4333/433/4) basis set augmented with split outer and orbitals (43321/4321/4) and a polarization orbital with an exponent of 0.5 for the bromine atom. It is found that an expansion truncated after the threebody terms is sufficient to fit the system with a mean absolute testing set error of . Expansions truncated after the fourbody terms for and provide fits whose mean absolute testing set errors are 0.0056 and 0.0212 eV, respectively. For vinyl bromide, a manybody expansion truncated after the fourbody terms provides fitting accuracy with mean absolute testing set errors that range between 0.0782 and 0.0808 eV. These errors correspond to mean percent errors that fall in the range 0.98%–1.01%. Our best result using the present method truncated after the fourbody summation with 16 NNs yields a testing set error that is 20.3% higher than that obtained using a 15dimensional (151401) NN to fit the vinyl bromide database. This appears to be the price of the added simplicity of the manybody expansion procedure.

Secondorder Møller–Plesset perturbation theory applied to extended systems. I. Within the projectoraugmentedwave formalism using a plane wave basis set
View Description Hide DescriptionWe present an implementation of the canonical formulation of secondorder Møller–Plesset (MP2) perturbation theory within the projectoraugmentedwave method under periodic boundary conditions using a plane wave basis set. To demonstrate the accuracy of our approach we show that our result for the atomization energy of a LiH molecule at the level is in excellent agreement with well converged Gaussiantypeorbital calculations. To establish the feasibility of employing MP2 perturbation theory in its canonical form to systems that are periodic in three dimensions we calculated the cohesive energy of bulk LiH.

An accurate density functional theory calculation for electronic excitation energies: The leastsquares support vector machine
View Description Hide DescriptionSupport vector machines (SVMs), as a novel type of learning machine, has been very successful in pattern recognition and function estimation problems. In this paper we introduce leastsquares (LS) SVMs to improve the calculation accuracy of density functional theory. As a demonstration, this combined quantum mechanical calculation with LSSVM correction approach has been applied to evaluate the electronic excitation energies of 160 organic molecules. The newly introduced LSSVM approach reduces the rootmeansquare deviation of the calculated electronic excitation energies of 160 organic molecules from 0.32 to 0.11 eV for the calculation. Thus, the LSSVM correction on top of is a better method to correct electronic excitation energies and can be used as the approximation of experimental results which are impossible to obtain experimentally.

A comparative study of the centroid and ringpolymer molecular dynamics methods for approximating quantum time correlation functions from path integrals
View Description Hide DescriptionThe problems of ergodicity and internal consistency in the centroid and ringpolymer molecular dynamics methods are addressed in the context of a comparative study of the two methods. Enhanced sampling in ringpolymer molecular dynamics (RPMD) is achieved by first performing an equilibrium path integral calculation and then launching RPMD trajectories from selected, stochastically independent equilibrium configurations. It is shown that this approach converges more rapidly than periodic resampling of velocities from a single long RPMD run. Dynamical quantities obtained from RPMD and centroid molecular dynamics (CMD) are compared to exact results for a variety of model systems. Fully converged results for correlations functions are presented for several one dimensional systems and parahydrogen near its triple point using an improved sampling technique. Our results indicate that CMD shows very similar performance to RPMD. The quality of each method is further assessed via a new descriptor constructed by transforming approximate realtime correlation functions from CMD and RPMD trajectories to imaginary time and comparing these to numerically exact imaginary time correlation functions. For parahydrogen near its triple point, it is found that adiabatic CMD and RPMD both have similar error.

A cluster algorithm for Monte Carlo simulation at constant pressure
View Description Hide DescriptionWe propose an efficient algorithm to sample the volume in Monte Carlo simulations in the isobaricisothermal ensemble. The method is designed to be applied in the simulation of hardcore models at high density. The algorithm is based in the generation of clusters of particles. At the volume change step, the distances between pairs of particles belonging to the same cluster do not change. This is done by rescaling the positions of the center of mass of each cluster instead of the position of each individual particle. We have tested the performance of the algorithm by simulating fluid and solid phases of hard spheres, finding that in both cases the algorithm is much more efficient than the standard procedure. Moreover, the efficiency of the method measured in terms of correlation ”time” does not depend on the system size in contrast with the standard method, in which the sampling becomes rapidly inefficient as the system size increases. We have used the procedure to compute with high precision the equation of state of the facecenteredcubic phase of the hard sphere system for different system sizes. Using these results we have estimated the equation of state at the thermodynamic limit. The results are compared to different equations of state proposed in literature.

Competition between structural distortion and magnetic moment formation in fullerene
View Description Hide DescriptionWe investigate the effect of onsite Coulomb interactions on the structural and magnetic ground state of fullerene based on densityfunctionaltheory calculations within the local density approximation (LDA) plus onsite Coulomb corrections . The total energies of the high symmetry and the distorted structures of are calculated for different spin configurations. The ground state configurations are found to depend on the forms of exchangecorrelation potentials and the onsite Coulomb interaction parameter , reflecting the subtle nature of the competition between Jahn–Teller distortion and magnetic instability in the fullerene. While the nonmagnetic state of the distorted structure is robust for small , a magnetic ground state of the undistorted structure emerges for larger than 4 eV when the LDA exchangecorrelation potential is employed.

Semiclassical description of vibrational quantum coherence in a three dimensional cluster: A forwardbackward initial value representation implementation
View Description Hide DescriptionThe semiclassical (SC) initial value representation (IVR) has been applied to describe true quantum coherenceeffects in a complex molecular system in full three dimensional space. The specific quantity considered is the timedependent probability distribution of the vibrational coordinate following photoexcitation of in a rare gas cluster. The “forwardbackward” version of the IVR method is shown to be capable of capturing detailed quantum coherence in this quantity, coherence that cannot be described by a classical Wigner model (which is equivalent to a linearized approximation to the more general SCIVR). Solventeffects on this vibrational quantum coherence have also been investigated for a cluster. A solvent cage consisting of six argon atoms reduces the fraction of iodine molecules that dissociate (an example of the “cage effect”) and also diminishes, but does not entirely eliminate, quantum coherence in the vibrational motion of the molecules that remain undissociated.

On the importance of nuclear quantum motions in near edge xray absorption fine structure spectroscopy of molecules
View Description Hide DescriptionWe report the effects of sampling nuclear quantum motion with path integral molecular dynamics (PIMD) on calculations of the nitrogen edge spectra of two isolated organic molecules. triazine, a prototypical aromatic molecule occupying primarily its vibrational ground state at room temperature, exhibits substantially improved spectral agreement when nuclear quantum effects are included via PIMD, as compared to the spectra obtained from either a single fixednuclei based calculation or from a series of configurations extracted from a classical molecular dynamics trajectory. Nuclear quantum dynamics can accurately explain the intrinsic broadening of certain features. Glycine, the simplest amino acid, is problematic due to large spectral variations associated with multiple energetically accessible conformations at the experimental temperature. This work highlights the sensitivity of near edge xray absorption fine structure(NEXAFS) to quantum nuclear motions in molecules, and the necessity of accurately sampling such quantum motion when simulating their NEXAFSspectra.

Electronpair radial sum and difference density functions
View Description Hide DescriptionFor deeper understanding of electronelectron radial holes, we introduce and discuss electronpair radial sum and difference density functions, which respectively represent the probability densities for the radial sum and difference variables of two electrons. Fundamental properties of the densities and are clarified. The appearance of radial holes given by is shown to have a nontrivial effect on the sum density as well. Numerical illustrations are given for the and states of the helium atom and for the ground state of the lithium atom.

Analytic response theory for the density matrix renormalization group
View Description Hide DescriptionWe propose an analytic response theory for the density matrix renormalization group, whereby response properties correspond to analytic derivatives of density matrix renormalization group observables with respect to the applied perturbations. Both static and frequencydependent response theories are formulated and implemented. We evaluate our pilot implementation by calculating static and frequencydependent polarizabilities of short oligodiacetylenes. The analytic response theory is competitive with dynamical density matrix renormalization group methods and yields significantly improved accuracies when using a small number of density matrix renormalization group states. Strengths and weaknesses of the analytic approach are discussed.

Activation energies of sigmatropic shifts in propene and acetone enolate from the antiHermitian contracted Schrödinger equation
View Description Hide DescriptionThe hydrogen [1,3]sigmatropic shift in propene is predicted by the Woodward–Hoffman rules to occur by an antarafacial pathway, yet the lack of experimental evidence suggests that this pathway is not favorable. Two natural questions arise: (i) can the [1,3]shift be made more favorable by a symmetryforbidden multistep pathway, and (ii) can the energetics be influenced by a substituent on propene? As in many chemical reactions, describing the energetics of these reactions requires a balanced treatment of both singlereference and multireference electron correlations, and yet traditional wave function methods often excel in treating only one kind of correlation. An equitable description of correlation effects, however, can be achieved, at a cost similar to efficient singlereference methods, by computing the twoelectron reduced density matrix (2RDM) from the antiHermitian part of the contracted Schrödinger equation (ACSE) [D. A. Mazziotti, Phys. Rev. Lett.97, 143002 (2006)]. As with the contracted Schrödinger equation, the indeterminacy of the ACSE is removed without the manyelectron wave function by reconstructing the 3RDM from the 2RDM via cumulant theory [D. A. Mazziotti, Chem. Phys. Lett.289, 419 (1998)]. In this paper we apply the ACSE to study sigmatropic shifts in both propene and acetone enolate while extending its formalism to treat doublet spin states. In the basis set the ACSE predicts the activation energy of the trimethylenetopropene rearrangement to be 8.8 kcal/mol while multireference perturbation theory yields a smaller barrier of 2.2 kcal/mol and coupled cluster singlesdoubles predicts a negative barrier. We further find that the [1,3]shift in acetone enolate is more favorable by than the [1,3]shift in propene, which is consistent with a prior theoretical investigation as well as experimental observations of these shifts in 2butanone enolate.

The numerical condition of electron correlation theories when only active pairs of electrons are spinunrestricted
View Description Hide DescriptionThe use of spinunrestriction with highquality correlation theory, such as coupledcluster (CC) methods, is a common practice necessary to obtain highquality potential energy surfaces. While this typically is a useful approach, we find that in the unrestricted limit of ROHF fragments (the unrestricted in active pair orbitals) the CC equations are singular if only the strongly correlated electrons are considered. Unstable amplitudes which do not represent the physics of the problem are easily found and could be unwittingly accepted without inspection. We use stability analysis and the condition number of the CC doubles Jacobian matrix to examine the problem, and present results for several molecular systems with a variety of unrestricted cluster models. Finally a regularization of the CC equations is proposed, using a dynamic penalty function, which allows us to apply CC, and Lagrangian gradient formulas even in the singular limit.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

On the statistical behavior of the reaction: A comparison between quasiclassical trajectory, quantum scattering, and statistical calculations
View Description Hide DescriptionThe dynamics of the reaction on the ground state potential energy surface (PES) is investigated by means of the quasiclassical trajectory method and two statistical methods: phase space theory and statistical quantum method. Preliminary calculations with an exact quantum method are also reported. The quasiclassical trajectory calculations show evidence for a phase space bottleneck inhibiting the intramolecular energy transfer between the O–H and O–O bonds. As a result, the probability of the intermediate complex dissociating back toward the reactants is high, thereby yielding a reaction probability significantly lower than expected for a barrierless and exothermic reaction. The features of the PES, which are the cause of this dynamical effect, are identified. This is essentially the conservation of the equilibrium distance of the O–H bond, hardly changed by a close encounter with an oxygen atom. The statistical calculations, which do not take into account the PES in the complex region, yield a high reaction probability, much larger than the probability calculated from the dynamical methods, both classical and quantum. If the statistical cross sections are corrected by a scaling factor, which corresponds actually to scaling the capture probability, then a good agreement is observed between dynamical and statistical calculations of the product state distributions. The differential cross sections calculated with all the methods show a backwardforward symmetry, with sharp polarization peaks. The complex lifetime is divided into two parts by the bottleneck. During the first part, the system remains trapped in a small region of the phase space and has a high probability to dissociate back toward the reactants. This is a nonstatistical effect due to the PES shape. During the second part, fast intramolecular vibrational energy redistribution takes place, leading to a statistical distribution of energy on the rovibrational states of the products. These findings indicate that the reaction has mixed dynamics, both with statistical and nonstatistical aspects.

A diabatic threestate representation of photoisomerization in the green fluorescent protein chromophore
View Description Hide DescriptionWe give a quantum chemical description of the photoisomerization reaction of green fluorescent protein (GFP) chromophores using a representation over three diabatic states. Photoisomerization leads to nonradiative decay, and competes with fluorescence in these systems. In the protein, this pathway is suppressed, leading to fluorescence. Understanding the electronic states relevant to photoisomerization is a prerequisite to understanding how the protein suppresses it, and preserves the emitting state of the chromophore. We present a solution to the stateaveraged complete active space problem, which is spanned at convergence by three fragmentlocalized orbitals. We generate the diabaticstate representation by block diagonalization transformation of the Hamiltonian calculated for the anionic chromophore model HBDI with multireference, multistate perturbation theory. The diabatic states are charge localized and admit a natural valencebond interpretation. At planar geometries, the diabatic picture of the optical excitation reduces to the canonical twostate chargetransfer resonance of the anion. Extension to a threestate model is necessary to describe decay via two possible pathways associated with photoisomerization of the (methine) bridge. Parametric Hamiltonians based on the threestate ansatz can be fit directly to data generated using the underlying active space. We provide an illustrative example of such a parametric Hamiltonian.

Cumulative reaction probabilities and transition state properties: A study of the and proton exchange reactions
View Description Hide DescriptionCumulative reaction probabilities (CRPs) have been calculated by accurate (converged, close coupling) quantum mechanical (QM), quasiclassical trajectory(QCT), and statistical QCT (SQCT) methods for the and reactions at collision energies up to and total angular momentum. A marked resonance structure is found in the QM CRP, most especially for the system and . When the CRPs are resolved in their ortho and para contributions, a clear steplike structure is found associated with the opening of internal states of reactants and products. The comparison of the QCT results with those of the other methods evinces the occurrence of two transition states, one at the entrance and one at the exit. At low values, except for the quantal resonance structure and the lack of quantization in the product channel, the agreement between QM and QCT is very good. The SQCT model, that reflects the steplike structure associated with the opening of initial and final states accurately, clearly tends to overestimate the value of the CRP as the collision energy increases. This effect seems more marked for the isotopic variant. For sufficiently high values, the growth of the centrifugal barrier leads to an increase in the threshold of the CRP. At these high values the discrepancy between SQCT and QCT becomes larger and is magnified with growing collision energy. The total CRPs calculated with the QCT and SQCT methods allowed the determination of the rate constant for the reaction. It was found that the rate, in agreement with experiment, decreases with temperature as expected for an endothermic reaction. In the range of temperatures between 200 and the differences between SQCT and QCT rate results are relatively minor. Although exact QM calculations are formidable for an exact determination of the , it can be reliably expected that their value will lie between those given by the dynamical and statistical trajectory methods.

Ab initio study of the van der Waals complex
View Description Hide DescriptionThis study reports an ab initio characterization of a prereactive van der Waals complex between an openshell atom and a closed shell molecule HBr. The three adiabatic potential surfaces, , and , which result from the splitting of degenerate state of Br are obtained from coupled cluster calculations. The coupling between samesymmetry states is calculated by multireference configurationinteraction method. A transformation to a diabatic representation and inclusion of the spinorbit couplingeffects on the interactions are also discussed. Bound states are calculated using an adiabatic bender model. The global minimum on the lowest adiabatic potential surface corresponds to a Tshaped geometry and has a well depth of at . A secondary minimum occurs for a hydrogenbonded geometry with at . Upon inclusion of spinorbit coupling the hydrogenbonded minimum remains at the same depth, but the Tshaped minimum washes out to less than half of its spinfree value. The lowest bound state is localized in the linear minimum. The spinorbit coupling plays a very important role in shaping of the potential energy surfaces of Br–HBr.

Symmetry breaking in the ground state of BNB: A high level multireference study
View Description Hide DescriptionA series of multireference approaches based on the SACASSCF wave function, i.e., CASPT2, MRCI, , and MRAQCC with single or multireference states, have been employed to investigate the symmetry breaking effect in the ground state of the triatomic BNB radical. We found that the mixing of the reference states contributes significantly to the dynamical correlation energy, which strongly affects the geometry of the ground state. Our results show that BNB in its ground state has a linear noncentrosymmetric structure with two equivalent global minima of the adiabatic potential energy surface and, respectively, two oppositely directed dipole moments of about 2 D. The barrier between the minima is about . The origin of the doubleminimum potential in the ground state of BNB is explained as due to the pseudoJahn–Teller effect involving vibronic interaction with the first excited state via the asymmetric stretching vibrations.

The line shape problem in the nearinfrared spectrum of selfcolliding molecules: Experimental investigation and test of semiclassical models
View Description Hide DescriptionAn intensitystabilized diode laser absorption spectrometer was developed and used to perform a highly accurate study of the line shape of absorption lines, in the spectral region around , belonging to the combination band, at a temperature of 296.00 K. Standard and complex semiclassical models, including Dicke narrowing and speeddependent broadening effects, were applied, tested, and compared in the pressure range between 0.7 and 4 kPa, in order to single out the model best reproducing the absorption profile and, hence, the physical situation of selfcolliding molecules. Line intensity factors and selfbroadening coefficients were determined. The overall accuracy of our determinations is at a level of 0.1%, which is, to our knowledge, the highest ever reached.