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Volume 124, Issue 4, 28 January 2006
 COMMUNICATIONS


Coaxial carbon nanotubes as shielded nanowires
View Description Hide DescriptionWe report transverse polarizabilities of coaxial carbon nanotubes using first principles density functional theory. These results demonstrate a shielding of the inner nanotube from electric fields by the outer nanotube. This study has implications for nanoelectronics, specifically for the possibility of using coaxial nanotubes as nanoelectrical wires. Shielding is predicted to be on the order of 95% by highlevel polarizability calculations. This shielding occurs regardless of whether the outer nanotube is metallic or semiconducting. In addition, a series of calculations on coaxial nanotubes where the inner nanotube is not centered show that the shielding still occurs with approximately the same magnitude. These calculations therefore indicate that it would be possible to use a coaxial carbon nanotube as a shielded nanowire.

 ARTICLES

 Theoretical Methods and Algorithms

Relativistic quasidegenerate perturbation theory with fourcomponent general multiconfiguration reference functions
View Description Hide DescriptionRelativistic quasidegenerate perturbation theory (QDPT) using general multiconfiguration (GMC) reference functions is developed and implemented. It is the relativistic counterpart of the nonrelativistic QDPT with GMC reference and thus retains all the advantages of the nonrelativistic GMC reference QDPT, such as applicability to any configuration space and small computational cost compared to the complete configurationspace case. The method is applied to the potentialenergy curves of the ground states of and molecules, the excitation energies of , and the energies of the lowest terms of C, Si, and Ge atoms, and is shown to provide a balanced description of potentialenergy curves and accurate transition energies for systems containing heavy elements and to provide much better results compared to the reference function (i.e., active space configuration interaction) level.

Equilibrium thermodynamics from basinsampling
View Description Hide DescriptionWe present a “basinsampling” approach for calculation of the potential energy density of states for classical statistical models. It combines a WangLandautype uniform sampling of local minima and a novel approach for approximating the relative contributions from local minima in terms of the volumes of basins of attraction. We have employed basinsampling to study phase changes in atomic clusters modeled by the LennardJones potential and for ionic clusters. The approach proves to be efficient for systems involving broken ergodicity and has allowed us to calculate converged heat capacity curves for systems that could previously only be treated using the harmonic superposition approximation. Benchmarks are also provided by comparison with parallel tempering and WangLandau simulations, where these proved feasible.

The performance of semilocal and hybrid density functionals in transitionmetal chemistry
View Description Hide DescriptionWe investigate the performance of contemporary semilocal and hybrid density functionals for bond energetics, structures, dipole moments, and harmonic frequencies of transitionmetal (TM) compounds by comparison with gasphase experiments. Special attention is given to the nonempirical metageneralized gradient approximation (metaGGA) of Tao, Perdew, Staroverov, and Scuseria (TPSS) [Phys. Rev. Lett.91, 146401 (2003)], which has been implemented in TURBOMOLE for the present work. Trends and error patterns for classes of homologous compounds are analyzed, including dimers, monohydrides, mononitrides, monoxides, monofluorides, polyatomic oxides and halogenides, carbonyls, and complexes with organic ligands such as benzene and cyclopentadienyl. Weakly bound systems such as , , and are discussed. We propose a reference set of reactionenergies for benchmark purposes. Our allelectron results with quadruple zeta valence basis sets validate semilocal densityfunctional theory as the workhorse of computational TM chemistry. Typical errors in bondenergies are substantially larger than in (organic) main group chemistry, however. The BeckePerdew’86 [Phys. Rev. A38, 3098 (1988); Phys. Rev. B33, 8822 (1986)] GGA and the TPSS metaGGA have the best price/performance ratio, while the TPSS hybrid functional achieves a slightly lower mean absolute error in bondenergies. The popular Becke threeparameter hybrid B3LYP underbinds significantly and tends to overestimate bond distances; we give a possible explanation for this. We further show that hybrid mixing does not reduce the width of the error distribution on our reference set. The error of a functional for the transfer energy of a TM atom does not predict its error for TM bondenergies and bond lengths. For semilocal functionals, selfinteraction error in one and threeelectron bonds appears to be a major source of error in TM reactionenergies. Nevertheless, TPSS predicts the correct groundstate symmetry in the vast majority of cases and rarely fails qualitatively. This further confirms TPSS as a general purpose functional that works throughout the periodic table. We also give workstation timing comparisons for the 645atom protein crambin.

The finite state projection algorithm for the solution of the chemical master equation
View Description Hide DescriptionThis article introduces the finite state projection (FSP) method for use in the stochastic analysis of chemically reacting systems. One can describe the chemical populations of such systems with probability density vectors that evolve according to a set of linear ordinary differential equations known as the chemical master equation (CME). Unlike Monte Carlo methods such as the stochastic simulation algorithm (SSA) or leaping, the FSP directly solves or approximates the solution of the CME. If the CME describes a system that has a finite number of distinct population vectors, the FSP method provides an exact analytical solution. When an infinite or extremely large number of population variations is possible, the state space can be truncated, and the FSP method provides a certificate of accuracy for how closely the truncated space approximation matches the true solution. The proposed FSP algorithm systematically increases the projection space in order to meet prespecified tolerance in the total probability density error. For any system in which a sufficiently accurate FSP exists, the FSP algorithm is shown to converge in a finite number of steps. The FSP is utilized to solve two examples taken from the field of systems biology, and comparisons are made between the FSP, the SSA, and leaping algorithms. In both examples, the FSP outperforms the SSA in terms of accuracy as well as computational efficiency. Furthermore, due to very small molecular counts in these particular examples, the FSP also performs far more effectively than leaping methods.

Philicity indices within the spinpolarized densityfunctional theory framework
View Description Hide DescriptionThe electrophilicity index is analyzed within the framework of spinpolarized densityfunctional theory. In this context, constrained philicities, , are introduced in order to define the capability of a system to acquire or donate electrons in a process at constant spin number. The spinphilicity/spindonicity indices, , are examined and rationalized here as the philicity of a given system to change its spinpolarization state, as being defined through the spin potential and spin hardness for a process at constant number of electrons. The local extension of these indices has been also outlined and numerical results have been discussed on the analysis of the electrophilic nature of some simple carbene systems both in the singlet and triplet states.

Nonequilibrium superoperator GW equations
View Description Hide DescriptionHedin’s equations [Phys. Rev.139, 796 (1965)] for the oneparticle equilibrium Green’s function of a manyelectron system are generalized to nonequilibrium open systems using two fields that separately control the evolution of the bra and the ket of the density matrix. A closed hierarchy is derived for the Green’s function, the selfenergy, the screened potential, the polarization, and the vertex function, all expressed as Keldysh matrices in Liouville space.

The limitations of Slater’s elementdependent exchange functional from analytic densityfunctional theory
View Description Hide DescriptionOur recent formulation of the analytic and variational SlaterRoothaan (SR) method, which uses Gaussian basis sets to variationally express the molecular orbitals, electron density, and the onebody effective potential of densityfunctional theory, is reviewed. Variational fitting can be extended to the resolution of identity method, where variationality then refers to the error in each twoelectron integral and not to the total energy. However, a Taylorseries analysis shows that all analytic ab initioenergies calculated with variational fits to twoelectron integrals are stationary. It is proposed that the appropriate fitting functions be charge neutral and that all ab initioenergies be evaluated using twocenter fits of the twoelectron integrals. The SR method has its root in Slater’s method and permits an arbitrary scaling of the SlaterGàspàrKohnSham exchangecorrelation potential around each atom in the system. The scaling factors are Slater’s exchange parameters . Of several ways of choosing these parameters, two most obvious are the HartreeFock (HF) values and the exact atomic values. The former are obtained by equating the selfconsistent energy and the HF energies, while the latter set reproduces exact atomic energies. In this work, we examine the performance of the SR method for predicting atomization energies,bond distances, and ionization potentials using the two sets of parameters. The atomization energies are calculated for the extended G2 set of 148 molecules for different basisset combinations. The mean error (ME) and mean absolute error (MAE) in atomization energies are about 25 and , respectively, for the exact atomic values. The HF values of exchange parameters give somewhat better performance for the atomization energies with ME and MAE being about 15 and , respectively. While both sets give performance better than the localdensity approximation or the HF theory, the errors in atomization energy are larger than the target chemical accuracy. To further improve the performance of the SR method for atomization energies, a new set of values is determined by minimizing the MAE in atomization energies of 148 molecules. This new set gives atomization energies half as large (MAE ) and that are slightly better than those obtained by one of the most widely used generalizedgradient approximations. Further improvements in atomization energies require going beyond Slater’s functional form for exchange employed in this work to allow exchangecorrelation interactions between electrons of different spins. The MAE in ionization potentials of 49 atoms and molecules is about 0.5 eV and that in bond distances of 27 molecules is about 0.02 Å. The overall good performance of the computationally efficient SR method using any reasonable set of values makes it a promising method for study of large systems.

Effects of anharmonicity on nonadiabatic electron transfer: A model
View Description Hide DescriptionThe effect of anharmonicity in the intramolecular modes of a model system for exothermic intramolecular nonadiabaticelectron transfer is probed by examining the dependence of the transition probability on the exoergicity. The FranckCondon factor for the Morse potential is written in terms of the Gauss hypergeometric function both for a ground initial state and for the general case, and comparisons are made between the firstorder perturbation theory results for transition probability for harmonic and Morse oscillators. These results are verified with quantum dynamical simulations using wavepacket propagations on a numerical grid. The transitionprobability expression incorporating a highfrequency quantum mode and lowfrequency medium mode is compared for Morse and harmonic oscillators in different temperature ranges and with various coarsegraining treatments of the delta function from the Fermi golden rule expression. We find that significant deviations from the harmonic approximation are expected for even moderately anharmonic quantum modes at large values of exoergicity. The addition of a second quantum mode of opposite displacement negates the anharmonic effect at small energy change, but in the inverted regime a significantly flatter dependence on exoergicity is predicted for anharmonic modes.

Efficient step size selection for the tauleaping simulation method
View Description Hide DescriptionThe tauleaping method of simulating the stochastic time evolution of a wellstirred chemically reacting system uses a Poisson approximation to take time steps that leap over many reaction events. Theory implies that tau leaping should be accurate so long as no propensity function changes its value “significantly” during any time step . Presented here is an improved procedure for estimating the largest value for that is consistent with this condition. This new selection procedure is more accurate, easier to code, and faster to execute than the currently used procedure. The speedup in execution will be especially pronounced in systems that have many reaction channels.

Grand canonical Markov model: A stochastic theory for open nonequilibrium biochemical networks
View Description Hide DescriptionIn this paper we present the results of a stochastic model of reversible biochemical reaction networks that are being driven through an open boundary, such that the system is interacting with its surrounding environment with explicit material exchange. The stochastic model is based on the master equation approach and is intimately related to the grand canonical ensemble of statistical mechanics. We show that it is possible to analytically calculate the joint probability function of the random variables describing the number of molecules in each state of the system for general linear networks. Definitions of reactionchemical potentials and conductances follow from inherent properties of this model, providing a description of energy dissipation in the system. We are also able to suggest novel methods for experimentally determining reaction fluxes and biochemical affinities at nonequilibrium steady state as well as the overall network connectivity.

On the theory underlying the CarParrinello method and the role of the fictitious mass parameter
View Description Hide DescriptionThe theory underlying the CarParrinello extendedLagrangian approach to ab initiomolecular dynamics (CPMD) is reviewed and reexamined using “heavy” ice as a test system. It is emphasized that the adiabatic decoupling in CPMD is not a decoupling of electronic orbitals from the ions but only a decoupling of a subset of the orbital vibrational modes from the rest of the necessarily coupled system of orbitals and ions. Recent work [J. Chem. Phys.116, 14 (2002)] has pointed out that, due to the orbitalion coupling that remains once adiabatic decoupling has been achieved, a large value of the fictitious mass can lead to systematic errors in the computed forces in CPMD. These errors are further investigated in the present work with a focus on those parts of these errors that are not corrected simply by rescaling the masses of the ions. It is suggested that any comparison of the efficiencies of BornOppenheimer molecular dynamics (BOMD) and CPMD should be performed at a similar level of accuracy. If accuracy is judged according to the average magnitude of the systematic errors in the computed forces, the efficiency of BOMD compares more favorably to that of CPMD than previous comparisons have suggested.

Coupledcluster response theory with linear corrections: The CC2R12 model for excitation energies
View Description Hide DescriptionCoupledcluster response theory for vertical excitation energies within the secondorder approximate coupledcluster singlesanddoubles model CC2, including linear corrections, is derived and implemented for Ansätze 1 and 2 of R12 theory. An orthonormal auxiliary basis set is used for the resolutionoftheidentity approximation in order to calculate the three and fourelectron integrals needed in R12 theory. The basis set convergence is investigated for a selected set of atoms and small molecules and it is found that in many cases the convergence is not improved. An analysis of the different contributions to excitation energies shows that the present scheme for the construction of the R12 pair functions leads in response theory to an unbalanced description of ground and excitedstatewave functions and needs to be generalized to carry the high accuracy of R12 methods over to response theory.

Equilibrium free energies from fastswitching trajectories with large time steps
View Description Hide DescriptionJarzynski’s [Phys. Rev. Lett.78, 2690 (1997)] identity for the freeenergy difference between two equilibrium states can be viewed as a special case of a more general procedure based on phasespace mappings. Solving a system’s equation of motion by approximate means generates a mapping that is perfectly valid for this purpose, regardless of how closely the solution mimics true time evolution. We exploit this fact, using crudely dynamical trajectories to compute freeenergy differences that are in principle exact. Numerical simulations show that Newton’s equation can be discretized to low order over very large time steps (limited only by the computer’s ability to represent resulting values of dynamical variables) without sacrificing thermodynamic accuracy. For computing the reversible work required to move a particle through a dense liquid, these calculations are more efficient than conventional fastswitching simulations by more than an order of magnitude. We also explore consequences of the phasespace mapping perspective for systems at equilibrium, deriving an exact expression for the statistics of energy fluctuations in simulated conservative systems.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Ab initio study of optical properties of rhodamine 6G molecular dimers
View Description Hide DescriptionEquilibrium atomic geometries of rhodamine 6G (R6G) dye molecule dimers are studied using densityfunctional theory. Electronenergy structure and optical properties of R6G and dimers are calculated using the generalized gradient approximation method with ab initio pseudopotentials. Our theory predicts substantial redshifts or blueshifts of the optical absorptionspectra of R6G dye molecules after aggregation in or dimers, respectively. Predicted optical properties of R6G dimers are interpreted in terms of interatomic and intermolecular interactions. Results of the calculations are discussed in comparison with experimental data.

A classical trajectory study of the photodissociation of acetaldehyde: The transition from impulsive to statistical dynamics
View Description Hide DescriptionPrevious experimental and theoretical studies of the radical dissociation channel of acetaldehyde show conflicting behavior in the HCO and product distributions. To resolve these conflicts, a fulldimensional potentialenergy surface for the dissociation of into HCO and fragments over the barrier on the surface is developed based on ROCCSD(T)/ccpVTZ(DZ) ab initio calculations. 20 000 classical trajectories are calculated on this surface at each of five initial excess energies, spanning the excitation energies used in previous experimental studies, and translational, vibrational, and rotational distributions of the radical products are determined. For excess energies near the dissociation threshold, both the HCO and products are vibrationally cold; there is a small amount of HCO rotational excitation and little rotational excitation, and the reactionenergy is partitioned dominantly ( at threshold) into relative translational motion. Close to threshold the HCO and rotational distributions are symmetrically shaped, resembling a Gaussian function, in agreement with observed experimental HCO rotational distributions. As the excess energy increases the calculated HCO and rotational distributions are observed to change from a Gaussian shape at threshold to one more resembling a Boltzmann distribution, a behavior also seen by various experimental groups. Thus the distribution of energy in these rotational degrees of freedom is observed to change from nonstatistical to apparently statistical, as excess energy increases. As the energy above threshold increases all the internal and external degrees of freedom are observed to gain population at a similar rate, broadly consistent with equipartitioning of the available energy at the transition state. These observations generally support the practice of separating the reactiondynamics into two reservoirs: an impulsive reservoir, fed by the exit channel dynamics, and a statistical reservoir, supported by the random distribution of excess energy above the barrier. The HCO rotation, however, is favored by approximately a factor of 3 over the statistical prediction. Thus, at sufficiently high excess energies, although the HCO rotational distribution may be considered statistical, the partitioning of energy into HCO rotation is not.

The small planarization barriers for the amino group in the nucleic acid bases
View Description Hide DescriptionThe amino group in the nucleic acid bases frequently interacts with other bases or with other molecular systems. Thus any nonplanarity of the amino group may affect the molecular recognition of nucleic acids.Ab initio HartreeFock (HF) and secondorder MøllerPlesset perturbation (MP2) levels of theory have been used to obtain the equilibrium geometries of the and structures for five common nucleic acid bases. The energy barriers between the and structures have also been predicted. A series of correlation consistent basis sets up to ccpCVQZ and augccpVQZ has been used to systematically study the dependence of the amino group nonplanarity. The equilibrium geometries of the nucleic acid bases with an amino group, including adenine, guanine, and cytosine, are examined carefully. At the MP2 level of theory, larger basis sets decrease the extent of nonplanarity of the amino group, but the decrease slows down when the QZ basis sets are used, demonstrating the intrinsic property of nonplanarity for guanine. For adenine and cytosine the situation is less clear; as the HF limit is approached, these two structures become planar. Addition of core correlation effects or diffuse functions further decreases the degree of nucleic acid base nonplanarity, in comparison to the original (, T, and Q) basis sets. The basis shows smaller degrees of nonplanarity than the sets. The basis is less size dependent than the and sets in the prediction of the aminogrouprelated bond angles and dihedral angles and energy barriers for adenine, guanine, and cytosine. The ccpCVQZ and augccpVQZ MP2 results may be regarded as benchmark predictions for the five common bases. The predicted classical barriers to planarization are 0.02 (adenine), 0.74 (guanine), and .

The frequencydependent dipole polarizability of the mercury dimer from fourcomponent relativistic densityfunctional theory
View Description Hide DescriptionThe frequencydependent dipole polarizability of is calculated using response theory within fourcomponent relativistic densityfunctional theory [using the localdensity approximation (LDA) and the hybrid functional B3LYP] including corrections for the basisset superposition error. The anisotropic component of the polarizabilitytensor agrees well with the values obtained from collisioninduced Raman spectroscopy carried out at a wavelength of . The values obtained from the two density functionals agree closely with the experimentally derived anisotropy component of the dipole polarizability, despite their rather large differences in the dimer potentialenergy curves (LDA is strongly overbinding while B3LYP is purely repulsive). The first two refractivity virial coefficients for the generalized ClausiusMossotti function are derived.

Stretching of hydrogenbonded OH in the lowest singlet excited electronic state of water dimer
View Description Hide DescriptionThe lowest singlet excited electronic state of water monomer in the gas phase is strictly dissociative along a OH stretch coordinate but changes its nature when the stretched OH moiety is hydrogen bonded to a neighboring water molecule. This work extends previous exploration of the water dimer excited singlet potentialenergysurface, using computational methods that are reliable even at geometries well removed from the groundstate equilibrium. First, the hydrogenbonded OH moiety is stretched far enough to establish the existence of a barrier that is sufficient to support a quasibound vibrational state of the OH oscillator near the FranckCondon region. Second, the constraint of an icelike structure is relaxed, and it is found that a substantial fraction of liquidlike structures also supports a quasibound vibrational state. These potentialenergy explorations on stretching of the hydrogenbonded OH moiety in a water dimer are discussed as a model for understanding the initial dynamics upon excitation into the lowest excited singlet state of condensed water. The possibility is raised that the excitedstate lifetime may be long enough to allow for exciton migration, which would provide a mechanism for energy transport in condensed water phases.

Control of wave packet dynamics by modification of the quantum mechanical amplitude of a single state
View Description Hide DescriptionSequences of pulses with different spectra are used to control rotational wave packet dynamics in by exploiting quantum interference phenomena. Wave packet superpositions are excited in a twostep resonant Raman process by two different pulses. Interferences between individual states shared by both wave packets can be used to enhance or destroy specific components of a superposition by varying the time delay between the pulses and/or the relative phase within the pulses. Elimination of selected quantum beats is achieved by greater than 94% for each case. A simple, yet effective, method for generating different color phaselocked pairs of laser pulses in a liquidcrystal pulse shaper setup without the need for interferometric stabilization schemes is described. The ability to manipulate single states of a superposition is an important advancement for intuitive control schemes and provides a potential new approach for initialization schemes in the field of quantum information.