Volume 134, Issue 17, 07 May 2011

Using density functional theory and generalized gradient approximation for exchange and correlation, we present theoretical analysis of the electronic structure of recently synthesized graphyne and its boron nitride analog (labeled as BNyne). The former is composed of hexagonal carbon rings joined by Cchains, while the latter is composed of hexagonal BN rings joined by Cchains. We have explored the nature of bonding and energy band structure of these unique systems characterized by sp and sp ^{2} bonding. Both graphyne and BNyne are found to be direct bandgap semiconductors. The bandgap can be modulated by changing the size of hexagonal ring and the length of carbon chain, providing more flexibilities of energy band engineering for device applications. The present study sheds theoretical insight on better understanding of the properties of the novel carbonbased 2D structures beyond the graphene sheet.
 COMMUNICATIONS


Communication: The electrostatic polarization is essential to differentiate the helical propensity in polyalanine mutants
View Description Hide DescriptionThe folding processes of three polyalanine peptides with composition of Ac(AAXAA)_{2}GYNH_{2} (where X is chosen to be Q, K, and D) are studied by molecular dynamics simulation in solvent of 40% trifluoroethanol using both polarized and unpolarized force fields. The simulations reveal the critical role of polarization effect for quantitative description of helix formation. When polarized force field is used, peptides with distinctive helical propensity are correctly differentiated and the calculated helical contents are in close agreement with experimental measurement, indicating that consideration of polarization effect can correctly predict the effect of sequence variation on helix formation.

Communication: Bubbles, crystals, and laserinduced nucleation
View Description Hide DescriptionShort intense laser pulses of visible and infrared light can dramatically accelerate crystal nucleation from transparent solutions; previous studies invoke mechanisms that are only applicable for nucleation of ordered phases or high dielectric phases. However, we show that similar laser pulses induce CO_{2}bubblenucleation in carbonated water. Additionally, in water that is cosupersaturated with argon and glycine, argon bubbles escaping from the water can induce crystal nucleation without a laser. Our findings suggest a possible link between laserinduced nucleation of bubbles and crystals.

Communication: Avoiding unbound anions in density functional calculations
View Description Hide DescriptionConverged approximate density functional calculations usually do not bind anions due to large selfinteraction error. But HartreeFock (HF) calculations have no such problem, producing negative HOMO energies. Thus, electron affinities can be calculated from density functional total energy differences using approximations such as PBE and B3LYP, evaluated on HF densities (for both anion and neutral). This recently proposed scheme is shown to work very well for molecules, better than the common practice of restricting the basis set except for cases such as CN, where the HF density is too inaccurate due to spin contamination.

Communication: A simple method for simulation of freezing transitions
View Description Hide DescriptionDespite recent advances, precise simulation of freezing transitions continues to be a challenging task. In this work, a simulation method for fluidsolid transitions is developed. The method is based on a modification of the constrained cell model which was proposed by Hoover and Ree [J. Chem. Phys.47, 4873 (1967)]10.1063/1.1701730. In the constrained cell model, each particle is confined in a single WignerSeitz cell. Hoover and Ree pointed out that the fluid and solid phases can be linked together by adding an external field of variable strength. High values of the external field favor single occupancy configurations and thus stabilize the solid phase. In the present work, the modified cell model is simulated in the constantpressure ensemble using tempering and histogram reweighting techniques. Simulation results on a system of hard spheres indicate that as the strength of the external field is reduced, the transition from solid to fluid is continuous at low and intermediate pressures and discontinuous at high pressures. Fluidsolid coexistence for the hardsphere model is established by analyzing the phase transition of the modified model in the limit in which the external field vanishes. The coexistence pressure and densities are in excellent agreement with current stateoftheart techniques.

Communication: Stable carbon nanoarches in the initial stages of epitaxial growth of graphene on Cu(111)
View Description Hide DescriptionTo fully exploit the device potential of graphene, reliable production of largearea, highquality samples is required. Epitaxialgrowth on metal substrates have shown promise in this regard, but further improvement would be facilitated by a more complete understanding of the atomistic processes involved in the early growth stages. Using firstprinciples calculations within density functional theory, we have investigated the energetics and kinetics of graphenenucleation and growth on a Cu(111) surface. Our calculations have revealed an energetic preference for the formation of stable onedimensional carbon nanoarches consisting of 3–13 atoms when compared to twodimensional compact islands of equal sizes. We also estimate the critical cluster size that marks the transition from nanoarch dominance to island dominance in the growth sequence. Our findings may provide the structural link between nucleated carbon dimers and larger carbon nanodomes, and are expected to stimulate future experimental efforts.

Communication: New insight into the barrier governing CO_{2} formation from OH + CO
View Description Hide DescriptionDespite its relative simplicity, the role of tunneling in the reaction OH + CO → H + CO_{2} has eluded the quantitative predictive powers of theoreticalreactiondynamics. In this study a onedimensional effective barrier to the formation of H + CO_{2} from the HOCO intermediate is directly extracted from dissociativephotodetachment experiments on HOCO and DOCO. Comparison of this barrier to a computed minimumenergy barrier shows that tunneling deviates significantly from the calculated minimumenergy pathway, predicting product internal energy distributions that match those found in the experiment and tunneling lifetimes short enough to contribute significantly to the overall reaction. This barrier can be of direct use in kinetic and statistical models and aid in the further refinement of the potential energy surface and reactiondynamics calculations for this system.
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 ARTICLES

 Theoretical Methods and Algorithms

Correlation effects in molecular conductors
View Description Hide DescriptionThe sourcesink potential (SSP) model introduced previously [F. Goyer, M. Ernzerhof, and M. Zhuang, J. Chem. Phys.126, 144104 (2007)10.1063/1.2715932] enables one to eliminate the semiinfinite contacts in molecular electronic devices (MEDs) in favor of complex potentials. SSP has originally been derived for independent electrons and extended to interacting twoelectron systems subsequently [A. Goker, F. Goyer, and M. Ernzerhof, J. Chem. Phys.129, 194901 (2008)10.1063/1.3013815]. Here we generalize SSP to Nelectron systems and consider the impact of electroncorrelation on the transmission probability. In our correlated method for molecular conductors, the molecular part of the Hückel Hamiltonian of the original SSP is replaced by the Hubbard Hamiltonian. For the contacts, however, the singleelectron picture is retained and they are assumed to be spin polarized. Using our method, we study electron transmission in molecular wires, crossconjugated chains, as well as aromatic systems. We find that, for realistic values of the electron–electron repulsion parameter, correlation effects modify the transmission probability quantitatively, the qualitative features remain. However, we find subtle new effects in correlated MEDs, such as Coulomb drag, that are absent in uncorrelated systems.

Testing the parametric twoelectron reduceddensitymatrix method with improved functionals: Application to the conversion of hydrogen peroxide to oxywater
View Description Hide DescriptionParametrization of the twoelectron reduced density matrix (2RDM) has recently enabled the direct calculation of electronic energies and 2RDMs at the computational cost of configuration interaction with single and double excitations. While the original Kollmar energy functional yields energies slightly better than those from coupled cluster with singledouble excitations, a general family of energy functionals has recently been developed whose energies approach those from coupled cluster with triple excitations [D. A. Mazziotti, Phys. Rev. Lett.101, 253002 (2008)]. In this paper we test the parametric 2RDM method with one of these improved functionals through its application to the conversion of hydrogen peroxide to oxywater. Previous work has predicted the barrier from oxywater to hydrogen peroxide with zeropoint energy correction to be 3.3to3.9 kcal/mol from coupled cluster with perturbative triple excitations [CCSD(T)] and 2.3 kcal/mol from complete activespace secondorder perturbation theory (CASPT2) in augmented polarized triplezeta basis sets. Using a larger basis set than previously employed for this reaction—an augmented polarized quadruplezeta basis set (augccpVQZ)—with extrapolation to the complete basisset limit, we examined the barrier with two parametric 2RDM methods and three coupled cluster methods. In the basisset limit the M parametric 2RDM method predicts an activation energy of 2.1 kcal/mol while the CCSD(T) barrier becomes 4.2 kcal/mol. The dissociation energy of hydrogen peroxide to hydroxyl radicals is also compared to the activation energy for oxywater formation. We report energies, optimal geometries, dipole moments, and natural occupation numbers. Computed 2RDMs nearly satisfy necessary Nrepresentability conditions.

Reactivity indicators for degenerate states in the densityfunctional theoretic chemical reactivity theory
View Description Hide DescriptionDensityfunctionaltheorybased chemical reactivity indicators are formulated for degenerate and neardegenerate ground states. For degenerate states, the functional derivatives of the energy with respect to the external potential do not exist, and must be replaced by the weaker concept of functional variation. The resultant reactivity indicators depend on the specific perturbation. Because it is sometimes impractical to compute reactivity indicators for a specific perturbation, we consider two special cases: pointcharge perturbations and Dirac delta function perturbations. The Dirac delta function perturbations provide upper bounds on the chemical reactivity. Reactivity indicators using the common used “average of degenerate states approximation” for degenerate states provide a lower bound on the chemical reactivity. Unfortunately, this lower bound is often extremely weak. Approximate formulas for the reactivity indicators within the frontiermolecularorbital approximation and special cases (two or three degenerate spatial orbitals) are presented in the supplementary material. One remarkable feature that arises in the frontier molecular orbital approximation, and presumably also in the exact theory, is that removing electrons sometimes causes the electron density to increase at the location of a negative (attractive) Dirac delta function perturbation. That is, the energetic response to a reduction in the external potential can increase even when the number of electronsdecreases.

Determining partial differential cross sections for lowenergy electron photodetachment involving conical intersections using the solution of a LippmannSchwinger equation constructed with standard electronic structure techniques
View Description Hide DescriptionA method for obtaining partial differential cross sections for low energy electron photodetachment in which the electronic states of the residual molecule are strongly coupled by conical intersections is reported. The method is based on the iterative solution to a LippmannSchwinger equation, using a zeroth order Hamiltonian consisting of the bound nonadiabatically coupled residual molecule and a free electron. The solution to the LippmannSchwinger equation involves only standard electronic structure techniques and a standard threedimensional free particle Green's function quadrature for which fast techniques exist. The transitiondipole moment for electron photodetachment, is a sum of matrix elements each involving one nonorthogonal orbital obtained from the solution to the LippmannSchwinger equation. An expression for the electron photodetachmenttransition dipole matrix element in terms of Dyson orbitals, which does not make the usual orthogonality assumptions, is derived.

Markov models of molecular kinetics: Generation and validation
View Description Hide DescriptionMarkov state models of molecular kinetics (MSMs), in which the longtime statistical dynamics of a molecule is approximated by a Markov chain on a discrete partition of configuration space, have seen widespread use in recent years. This approach has many appealing characteristics compared to straightforward molecular dynamics simulation and analysis, including the potential to mitigate the sampling problem by extracting longtime kinetic information from short trajectories and the ability to straightforwardly calculate expectation values and statistical uncertainties of various stationary and dynamical molecular observables. In this paper, we summarize the current state of the art in generation and validation of MSMs and give some important new results. We describe an upper bound for the approximation error made by modelingmolecular dynamics with a MSM and we show that this error can be made arbitrarily small with surprisingly little effort. In contrast to previous practice, it becomes clear that the best MSM is not obtained by the most metastable discretization, but the MSM can be much improved if nonmetastable states are introduced near the transition states. Moreover, we show that it is not necessary to resolve all slow processes by the state space partitioning, but individual dynamical processes of interest can be resolved separately. We also present an efficient estimator for reversible transition matrices and a robust test to validate that a MSM reproduces the kinetics of the molecular dynamics data.

Intrinsic stability and hydrogen affinity of pure and bimetallic nanowires
View Description Hide DescriptionA density functional theory study of the intrinsic stability of pure and bimetallic wires is presented. Several bimetallic combinations forming oneatom thick wires are studied. An explanation for the experimental instability of Cu wires in contrast to the stability of Au and Ag wires is given, which relies on the higher surface energy of the former. All the possible intercalations between Ni, Pd, Pt, Cu, Ag, and Au are studied. The bimetallic wires AuCu and AuAg were found to be the most stable ones. The reactivity of the latter two systems is also examined using hydrogen adsorption as a microscopic probe. It was found that at the intermetal interface, up to second neighbors, Cu and Ag become more reactive and Au becomes more inert than the corresponding pure wires. These results are explained within the dband model.

Accelerating chemical reactions: Exploring reactive freeenergy surfaces using accelerated ab initio molecular dynamics
View Description Hide DescriptionA biased potential molecular dynamics simulation approach, accelerated molecular dynamics (AMD), has been implemented in the framework of ab initiomolecular dynamics for the study of chemical reactions. Using two examples, the double proton transferreaction in formic acid dimer and the hypothetical adiabatic ring opening and subsequent rearrangement reactions in methylenecyclopropane, it is demonstrated that ab initio AMD can be readily employed to efficiently explore the reactive potential energy surface, allowing the prediction of chemical reactions and the identification of metastable states. An adaptive variant of the AMD method is developed, which additionally affords an accurate representation of both the freeenergy surface and the mechanism associated with the chemical reaction of interest and can also provide an estimate of the reaction rate.

Theoretical study of the photodissociation of Li_{2} ^{+} in onecolor intense laser fields
View Description Hide DescriptionA theoretical treatment of the photodissociation of the molecular ion Li_{2} ^{+} in onecolor intense laser fields, using the timedependent wave packet approach in a Floquet Born–Oppenheimer representation, is presented. Six electronic states 1,2 ^{2}Σ_{g} ^{+}, 1,2 ^{2}Σ_{u} ^{+}, 1 ^{2}Π_{g}, and 1 ^{2}Π_{u} are of relevance in this simulation and have been included. The dependences of the fragmental dissociation probabilities and kinetic energy release (KER) spectra on pulse width, peak intensity, polarization angle, wavelength, and initial vibrational level are analyzed to interpret the influence of control parameters of the external field. Three main dissociation channels, 1 ^{2}Σ_{g} ^{+} (m = −1), 2 ^{2}Σ_{g} ^{+} (m = −2), and 2 ^{2}Σ_{u} ^{+} (m = −3), are seen to dominate the dissociation processes under a wide variety of laser conditions and give rise to well separated groups of KER features. Different dissociation mechanisms for the involved Floquet channels are discussed.

Thermal Gaussian molecular dynamics for quantum dynamics simulations of manybody systems: Application to liquid parahydrogen
View Description Hide DescriptionA new method, here called thermal Gaussian molecular dynamics (TGMD), for simulating the dynamics of quantum manybody systems has recently been introduced [I. Georgescu and V. A. Mandelshtam, Phys. Rev. B82, 094305 (2010)]. As in the centroid molecular dynamics (CMD), in TGMD the Nbody quantum system is mapped to an Nbody classical system. The associated both effective Hamiltonian and effective force are computed within the variational Gaussian wavepacket approximation. The TGMD is exact for the hightemperature limit, accurate for short times, and preserves the quantum canonical distribution. For a harmonic potential and any form of operator , it provides exact time correlation functionsC _{ AB }(t) at least for the case of , a linear combination of the position, , and momentum, , operators. While conceptually similar to CMD and other quantum molecular dynamics approaches, the great advantage of TGMD is its computational efficiency. We introduce the manybody implementation and demonstrate it on the benchmark problem of calculating the velocity time autocorrelation function for liquid parahydrogen, using a system of up to N = 2592 particles.

Balancing single and multireference correlation in the chemiluminescent reaction of dioxetanone using the antiHermitian contracted Schrödinger equation
View Description Hide DescriptionDirect computation of energies and twoelectron reduced density matrices (2RDMs) from the antiHermitian contracted Schrödinger equation (ACSE) [D. A. Mazziotti, Phys. Rev. Lett.97, 143002 (2006)], it is shown, recovers both single and multireference electron correlation in the chemiluminescent reaction of dioxetanone especially in the vicinity of the conical intersection where strong correlation is important. Dioxetanone, the lightproducing moiety of firefly luciferin, efficiently converts chemical energy into light by accessing its excitedstate surface via a conical intersection. Our previous activespace 2RDM study of dioxetanone [L. Greenman and D. A. Mazziotti, J. Chem. Phys.133, 164110 (2010)] concluded that correlating 16 electrons in 13 (active) orbitals is required for realistic surfaces without correlating the remaining (inactive) orbitals. In this paper we pursue two complementary goals: (i) to correlate the inactive orbitals in 2RDMs along dioxetanone's reaction coordinate and compare these results with those from multireference secondorder perturbation theory (MRPT2) and (ii) to assess the size of the active space—the number of correlated electrons and orbitals—required by both MRPT2 and ACSE for accurate energies and surfaces. While MRPT2 recovers very different amounts of correlation with (4,4) and (16,13) active spaces, the ACSE obtains a similar amount of correlation energy with either active space. Nevertheless, subtle differences in excitation energies near the conical intersection suggest that the (16,13) active space is necessary to determine both energetic details and properties. Strong electron correlation is further assessed through several RDMbased metrics including (i) total and relative energies, (ii) the von Neumann entropy based on the 1electron RDM, as well as the (iii) infinity and (iv) squared Frobenius norms based on the cumulant 2RDM.

Laser control of molecular excitations in stochastic dissipative media
View Description Hide DescriptionIn the present work, ideas for controlling photochemical reactions in dissipative environments using shaped laser pulses are presented. New timelocal control algorithms for the stochastic Schrödinger equation are introduced and compared to their reduced density matrix analog. The numerical schemes rely on timedependent targets for guiding the reaction along a preferred path. The methods are tested on the vibrational control of adsorbates at metallic surfaces and on the ultrafast electron dynamics in a strong dissipative medium. The selective excitation of the specific states is achieved with improved yield when using the new algorithms. Both methods exhibit similar convergence behavior and results compare well with those obtained using local optimal control for the reduced density matrix. The favorable scaling of the methods allows to tackle larger systems and to control photochemical reactions in dissipative media of molecules with many more degrees of freedom.

Cutoff radius effect of the isotropic periodic sum and Wolf method in liquid–vapor interfaces of water
View Description Hide DescriptionAs a more economical but similarly accurate computation method than the Ewald sum, the isotropic periodic sum (IPS) method for nonpolar molecules (IPSn) and polar molecules (IPSp), along with the Wolf method are of interest, but the cutoff radius dependence is an important issue. To evaluate the cutoff radius effect of the three methods, a watervapor interfacial system has been studied by molecular dynamics. The Wolf method can produce adequate results for surface tension compared to that of the Ewald sum (within 2.9%) at a long enough cutoff radius, r _{c}. However, the estimation of the electrostatic potential profile and dipole orientational function is poor. The Wolf method cannot estimate electrostatic configuration at r _{c} ⩽ L _{ z }/2 (L _{ z } is the longest lattice of the system). We have found that the convergence of the surface tension and the electrostatic configuration of the IPSn method is faster than that of the IPSp method. Moreover, the IPSn method is most accurate among the three methods for the same cutoff radius. Furthermore, the behavior of the surface tension against the cutoff radius shows a greater difference for the IPSn and IPSp method. The surface tension of the IPSp method fluctuates and presents a similar result to that of the Ewald sum, but the surface tension for the IPSn method greatly deviates near r _{c} = L _{ z }/3. The cause of this deviation is the difference between the interfacial configuration of the water surface and the cutoff treatment of the IPS method. The deviation becomes insignificant far from r _{c} = L _{ z }/3. In spite of this shortcoming, the IPSn method gives the most accurate result in estimating the surface tension at r _{c} = L _{ z }/2. From all the results in this work, the IPSn and IPSp method have been found to be more accurate than the Wolf method. In conclusion, the surface tension and structure of watervapor interface can be calculated by the IPSn method when r _{c} is greater than or equal to the longest lattice of the system. The IPSp method and the Wolf method require a longer cutoff radius than the longest lattice of the system to estimate interfacial properties.

Sensitivity analysis of statespecific multireference perturbation theory
View Description Hide DescriptionStatespecific multireference perturbation theory (SSMRPT) developed by Mukherjee et al.[Int. J. Mol. Sci.3, 733 (2002)] is examined focusing on the dependence of the perturbed energy on the initial model space coefficients. It has been observed earlier, that nonphysical kinks may appear on the potential energy surface obtained by SSMRPT while related coupledcluster methods may face convergence difficulties. Though exclusion or damping of the division by small coefficients may alleviate the problem, it is demonstrated here that the effect does not originate in an illdefined division. It is shown that nonnegligible model space coefficients may also be linked with the problem. Sensitivity analysis is suggested as a tool for detecting the coefficient responsible. By monitoring the singular values of sensitivity matrices, orders of magnitude increase is found in the largest value, in the vicinity of the problematic geometry point on the potential energy surface. The drastic increase of coefficient sensitivities is found to be linked with a degeneracy of the target root of the effective Hamiltonian. The nature of the oneelectron orbitals has a profound influence on the picture: a rotation among active orbitals may screen or worsen the effect.

Generating transition paths by Langevin bridges
View Description Hide DescriptionWe propose a novel stochastic method to generate paths conditioned to start in an initial state and end in a given final state during a certain time t _{ f }. These paths are weighted with a probability given by the overdamped Langevin dynamics. We show that these paths can be exactly generated by a nonlocal stochastic differential equation. In the limit of short times, we show that this complicated nonsolvable equation can be simplified into an approximate local stochastic differential equation. For longer times, the paths generated by this approximate equation do not satisfy the correct statistics, but this can be corrected by an adequate reweighting of the trajectories. In all cases, the paths are statistically independent and provide a representative sample of transition paths. The method is illustrated on the onedimensional quartic oscillator.