Volume 124, Issue 6, 14 February 2006
 COMMUNICATIONS


Exploring the chemical enhancement for surfaceenhanced Raman scattering with Au bowtie nanoantennas
View Description Hide DescriptionSingle metallic bowtie nanoantennas provide a controllable environment for surfaceenhanced Raman scattering(SERS) of adsorbed molecules. Bowties have experimentally measured electromagnetic enhancements, enabling estimation of chemical enhancement for both the bulk and the fewmolecule regime. Strong fluctuations of selected Raman lines imply that a small number of mercaptoaniline molecules on a single bowtie show chemical enhancement , much larger than previously believed, likely due to charge transfer between the Au surface and the molecule. This chemical sensitivity of SERS has significant implications for ultrasensitive detection of single molecules.
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 ARTICLES

 Theoretical Methods and Algorithms

Multistate multimode vibronic dynamics: Entanglement of electronic and vibrational degrees of freedom in the benzene radical cation
View Description Hide DescriptionAn earlier theoretical treatment of multimode and multistate vibronic coupling in the benzene radical cation [Köppel et al. , J. Chem. Phys.117, 2657 (2002)] is extended to investigate also the behavior of the nuclear degrees of freedom and to include additional electronic states. The five lowest doublet electronic states are considered which have been shown earlier to be all interconnected through a series of conical intersections of their potentialenergy surfaces. In the most extensive calculations, they are all included simultaneously in the quantum dynamical calculations performed, which represent a system of unprecedented complexity treated in this way. The results are compared with various reduceddimensionality treatments (i.e., employing reduced vibrational and electronic function spaces). The different temporal behavior of the various electronic populations is emphasized and traced to the different locations of the various seams of conical intersections: due to the coherent oscillations of the timedependent wave packet this leads to an oscillatory behavior in some cases and to monotonous behavior in others. A seemingly irreversible behavior of the system dynamics in this strictly microscopic treatment is confirmed. The importance of this benchmark system to highlight complex, entangled multimode, and multistate vibronic dynamics is pointed out.

Exact decoupling of the Dirac Hamiltonian. III. Molecular properties
View Description Hide DescriptionRecent advances in the theory of the infiniteorder DouglasKrollHess (DKH) transformation of the Dirac Hamiltonian require a fresh and unified view on the calculation of atomic and molecular properties. It is carefully investigated how the fourcomponent Dirac Hamiltonian in the presence of arbitrary electric and magnetic potentials is decoupled to twocomponent form. In order to cover the whole range of electromagnetic properties on the same footing, a consistent description within the DKH theory is presented. Subtle distinctions are needed between errors arising from any finiteorder DKH scheme and effects due to oversimplified and thus approximate decoupling strategies for the Dirac operator, which will, though being numerically negligible in most cases, still be visible in the infiniteorder limit of the twocomponent treatment. Special focus is given to the issue, whether the unitary DKH transformations to be applied to the Dirac Hamiltonian should depend on the property under investigation or not. It is explicitly shown that up to third order in the external potential the transformedproperty operator is independent of the chosen parametrization of the unitary transformations of the generalized DKH scheme. Since the standard DKH protocol covers the transformation of oneelectron integrals only, the presentation is developed for oneelectron properties for the sake of brevity. Nevertheless, all findings for the calculation of oneelectron properties within a twocomponent framework presented here also hold for twoelectron properties as well.

Exact decoupling of the Dirac Hamiltonian. IV. Automated evaluation of molecular properties within the DouglasKrollHess theory up to arbitrary order
View Description Hide DescriptionIn Part III [J. Chem. Phys. 124, 064102 (2005)] of this series of papers on exact decoupling of the Dirac Hamiltonian within transformation theory, we developed the most general account on how to treat magnetic and electric properties in a unitary transformation theory on the same footing. In this paper we present an implementation of a general algorithm for the calculation of magnetic as well as electric properties within the framework of DouglasKrollHess theory. The formal and practical principles of this algorithm are described. We present the first highorder DouglasKrollHess results for property operators. As for modelproperties we propose to use the welldefined radial moments, i.e., expectation values of , which can be understood as terms of the Taylorseries expansion of any property operator. Such moments facilitate a rigorous comparison of methods free of uncertainties which may arise in a direct comparison with experiment. This is important in view of the fact that various approaches to twocomponent molecular properties may yield numerically very small terms whose approximate or inaccurate treatment would not be visible in a direct comparison to experimental data or to another approximate computational reference. Results are presented for various degrees of decoupling of the modelproperties within the DouglasKrollHess scheme.

Pressure derivatives in the classical moleculardynamics ensemble
View Description Hide DescriptionThe calculation of thermodynamic state variables, particularly derivatives of the pressure with respect to density and temperature, in conventional moleculardynamics simulations is considered in the frame of the comprehensive treatment of the moleculardynamics ensemble by Lustig [J. Chem. Phys.100, 3048 (1994)]. This paper improves the work of Lustig in two aspects. In the first place, a general expression for the basic phasespace functions in the moleculardynamics ensemble is derived, which takes into account that a mechanical quantity is, in addition to the number of particles, the volume, the energy, and the total momentum of the system, a constant of motion. is related to the initial position of the center of mass of the system. Secondly, the correct general expression for volume derivatives of the potential energy is derived. This latter result solves a problem reported by Lustig [J. Chem. Phys.109, 8816 (1998)] and Meier [Computer Simulation and Interpretation of the Transport Coefficients of the LennardJones Model Fluid (Shaker, Aachen, 2002)] and enables the correct calculation of the isentropic and isothermal compressibilities, the speed of sound, and, in principle, all higher pressure derivatives. The derived equations are verified by calculations of several state variables and pressure derivatives up to second order by moleculardynamics simulations with 256 particles at two state points of the LennardJones fluid in the gas and liquid regions. It is also found that it is impossible for systems of this size to calculate third and higherorder pressure derivatives due to the limited accuracy of the algorithm employed to integrate the equations of motion.

Accurate and efficient method for the treatment of exchange in a planewave basis
View Description Hide DescriptionWe describe an accurate and efficient extension of Chawla and Voth’s [J. Chem. Phys.108, 4697 (1998)] planewave based algorithm for calculating exchange energies, exchange energy densities, and exchange energy gradients with respect to wavefunction parameters in systems of electrons subject to periodic boundary conditions. The theory and numerical results show that the computational effort scales almost linearly with the number of plane waves and quadratically with the number of vectors. To obtain high accuracy with relatively few vectors, we use an adaptation of Gygi and Baldereschi’s [Phys. Rev. B34, 4405 (1986)] method for reducing Brillouinzone integration errors.

Calculating potentials of mean force and diffusion coefficients from nonequilibrium processes without Jarzynski’s equality
View Description Hide DescriptionIn general, the direct application of the Jarzynski equality (JE) to reconstruct potentials of mean force (PMFs) from a small number of nonequilibrium unidirectional steered moleculardynamics (SMD) paths is hindered by the lack of sampling of extremely rare paths with negative dissipative work. Such trajectories that transiently violate the second law of thermodynamics are crucial for the validity of JE. As a solution to this daunting problem, we propose a simple and efficient method, referred to as the method, for calculating simultaneously both the PMF and the corresponding diffusion coefficient along a reaction coordinate for a classical manyparticle system by employing a small number of fast SMD pullings in both forward and time reverse directions, without invoking JE. By employing Crooks [Phys. Rev. E61, 2361 (2000)] transient fluctuation theorem (that is more general than JE) and the stiffspring approximation, we show that (i) the mean dissipative work in the and pullings is the same, (ii) both and can be expressed in terms of the easily calculable mean work of the and processes, and (iii) can be expressed in terms of the slope of . To test its viability, the method is applied to determine and of singlefile water molecules in singlewalled carbon nanotubes(SWNTs). The obtained is found to be in very good agreement with the results from other PMF calculation methods, e.g., umbrella sampling. Finally, and are used as input in a stochastic model, based on the FokkerPlanck equation, for describing water transport through SWNTs on a mesoscopic time scale that in general is inaccessible to MD simulations.

Pathintegral centroid dynamics for general initial conditions: A nonequilibrium projection operator formulation
View Description Hide DescriptionThe formulation of pathintegral centroid dynamics is extended to the quantum dynamics of density operators evolving from general initial states by means of the nonequilibrium projection operator technique. It is shown that the new formulation provides a basis for applying the method of centroid dynamics to nonequilibrium situations and that it allows the derivation of new formal relations, which can be useful in improving current equilibrium centroid dynamics methods. A simple approximation of uniform relaxation for the unprojected portion of the Liouville space propagator leads to a class of practically solvable equations of motion for the centroid variables, but with an undetermined parameter of relaxation. This new class of equations encompasses the centroid moleculardynamics (CMD) method as a limiting case, and can be applied to both equilibrium and nonequilibrium situations. Tests for the equilibrium dynamics of onedimensional model systems demonstrate that the new equations with appropriate choice of the relaxation parameter are comparable to the CMD method.

On the calculation of absolute free energies from moleculardynamics or Monte Carlo data
View Description Hide DescriptionWe propose a method for calculating absolute free energies from Monte Carlo or moleculardynamics data. The method is based on the identity that expresses the partition function as a Boltzmann average: , where is an arbitrary weight function such that its integral over the phase space is equal to 1. In practice, to minimize statistical errors the weight function is chosen such that the regions of the phase space where sampling statistics are poor are excluded from the average. The “ideal” weight function would be the equilibrium phasespace density itself. We consider two methods for constructing the weight function based on different estimates of the equilibrium phasespace density from simulation data. In the first method, it is chosen to be a Gaussian function, whose parameters are obtained from the covariance matrix of the atomic coordinates. In the second, a clustering algorithm is used to attempt partitioning the data into clusters corresponding to different basins of attraction visited by the system. The weight function is then constructed as a superposition of Gaussians calculated for each cluster separately. We show that these strategies can be used to improve upon previous methods of estimating absolute entropies from covariance matrices.

Acceleration of Markov chain Monte Carlo simulations through sequential updating
View Description Hide DescriptionStrict detailed balance is not necessary for Markov chain Monte Carlo simulations to converge to the correct equilibrium distribution. In this work, we propose a new algorithm which only satisfies the weaker balance condition, and it is shown analytically to have better mobility over the phase space than the Metropolis algorithm satisfying strict detailed balance. The new algorithm employs sequential updating and yields better sampling statistics than the Metropolis algorithm with random updating. We illustrate the efficiency of the new algorithm on the twodimensional Ising model. The algorithm is shown to identify the correct equilibrium distribution and to converge faster than the Metropolis algorithm with strict detailed balance. The main advantages of the new algorithm are its simplicity and the feasibility of parallel implementation through domain decomposition.

Multiscale spatial Monte Carlo simulations: Multigriding, computational singular perturbation, and hierarchical stochastic closures
View Description Hide DescriptionMonte Carlo(MC) simulation of most spatially distributed systems is plagued by several problems, namely, execution of one process at a time, large separation of time scales of various processes, and large length scales. Recently, a coarsegrained Monte Carlo (CGMC) method was introduced that can capture large length scales at reasonable computational times. An inherent assumption in this CGMC method revolves around a meanfield closure invoked in each coarse cell that is inaccurate for shortranged interactions. Two new approaches are explored to improve upon this closure. The first employs the local quasichemical approximation, which is applicable to first nearestneighbor interactions. The second, termed multiscale CGMC method, employs singular perturbation ideas on multiple grids to capture the entire cluster probability distribution function via short microscopic MC simulations on small, finegrid lattices by taking advantage of the time scale separation of multiple processes. Computational strategies for coupling the fast process at small length scales (fine grid) with the slow processes at large length scales (coarse grid) are discussed. Finally, the binomial leap method is combined with the multiscale CGMC method to execute multiple processes over the entire lattice and provide additional computational acceleration. Numerical simulations demonstrate that in the presence of fast diffusion and slow adsorption and desorption processes the two new approaches provide more accurate solutions in comparison to the previously introduced CGMC method.

NonBornOppenheimer path in antiHermitian dynamics for nonadiabatic transitions
View Description Hide DescriptionA serious difficulty in the semiclassical Ehrenfest theory for nonadiabatic transitions is that a path passing across the avoided crossing is forced to run on a potential averaged over comprising adiabatic potential surfaces that commit the avoided crossing. Therefore once a path passes through the crossing region, it immediately becomes incompatible with the standard view of “classical trajectory” running on an adiabatic surface. This casts a fundamntal question to the theoretical structure of chemical dynamics. In this paper, we propose a nonBornOppenheimer path that is generated by an antiHermitian Hamiltonian, whose complexvalued eigenenergies can cross in their real parts and avoid crossing in the imaginary parts in the vicinity of the nonadiabatic transition region. We discuss the properties of this nonBornOppenheimer path and thereby show its compatibility with the BornOppenheimer classical trajectories. This theory not only allows the geometrical branching of the paths but gives the nonadiabatic transition amplitudes and quantum phases along the generated paths.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Infrared spectroscopy of HCNsalt complexes formed in liquidhelium nanodroplets
View Description Hide DescriptionRotationally resolved infrared spectra are reported for the binary complexes of HCN and LiF, LiCl, NaF, and NaCl, formed in heliumnanodroplets. Stark spectroscopy is used to determine the dipole moments for these complexes. Ab initio calculations are also reported for these complexes, revealing the existence of several different isomers of these binary systems. In the frequency region examined in this experimental study we only observe one of these, corresponding to the salt binding to the nitrogen end of the HCN molecule. The experimental rotational constants,dipole moments, and vibrational frequency shifts are all compared with the results from ab initio calculations for this isomer.

The nuclearspinrotation constants of HCY, HSiY, and (, Cl): An ab initio study
View Description Hide DescriptionThe nuclearspinrotation constants of fluoro (HCF) and chloro (HCCl) carbene, of the corresponding silylenes (HSiF and HSiCl), and of difluoro and dichlorosilylene ( and ) are quantumchemically investigated employing the coupledcluster singles and doubles model augmented by a perturbative treatment of triple excitations together with various sequences of correlationconsistent basis sets.Theoretical best estimates are obtained through consideration of corrections for core correlation and of zeropoint vibrational contributions. In addition, nuclear quadrupole coupling constants for the chlorine containing species are determined. A thorough comparison with experiment is made.

Spectroscopic characterization of the ground and lowlying electronic states of via anion photoelectron spectroscopy
View Description Hide DescriptionAnion photoelectron spectra of were measured at photodetachment wavelengths of , , and . Both fieldfree timeofflight and velocitymap imaging methods were used to collect the data. The fieldfree timeofflight data provided better resolution of the features, while the velocitymapimaging data provided more accurate anisotropy parameters for the peaks. Transitions from the ground electronic state of the anion to two electronic states of the neutral were observed and analyzed with the aid of electronic structure calculations and FranckCondon simulations. The groundstate band was assigned to a transition between linear ground states of and , yielding the electron affinity of , . Vibrationally resolved features in the groundstate band were assigned to symmetric and antisymmetric stretch modes of , with the latter allowed by vibronic coupling to an excited electronic state. The energy of the observed excited neutral state agrees with that calculated for the state, but the congested nature of this band in the photoelectron spectrum is more consistent with a transition to a bent neutral state.

Development of modulated rf sequences for decoupling and recoupling of nuclearspin interactions in samplespinning solidstate NMR: Application to chemicalshift anisotropy determination
View Description Hide DescriptionAn approach to design modulated rf sequences under sample spinning which decouple/recouple a specific nuclearspin interaction in solidstate NMR is presented. The Euler angles of the spin rotation caused by a general rf field are forced to fulfill the symmetry principle theory for selecting an interaction of interest. Then, modulated rf sequences are directly obtained from the Euler angles with a large degree of freedom. rf sequences with high performance can be selected from them by numerically optimizing rf sequence parameters. As an example of this approach, an amplitude and phasemodulated rf sequence to recouple chemicalshift anisotropy (CSA) is developed, which is robust with respect to rf inhomogeneity. Twodimensional (2D) experiments with this rf sequence under on and off magicangle spinning (MAS) provide onedimensional and 2D powder patterns, respectively. The latter enables us to determine the CSA principal values more accurately even for overlapped signals in MAS spectra. The effectiveness of this modulated rf sequence is experimentally demonstrated on acetylD,Lalanine for determination of the and CSA principal values.

Twocomponent relativistic densityfunctional calculations of the dimers of the halogens from bromine through element 117 using effective core potential and allelectron methods
View Description Hide DescriptionA twocomponent quasirelativistic Hamiltonian based on spindependent effective core potentials is used to calculate ionization energies and electron affinities of the heavy halogen atom bromine through the superheavy element 117 (ekaastatine) as well as spectroscopic constants of the homonuclear dimers of these atoms. We describe a twocomponent HartreeFock and densityfunctional program that treats spinorbit coupling selfconsistently within the orbital optimization procedure. A comparison with results from highorder DouglasKroll calculations—for the superheavy systems also with zerothorder regular approximation and fourcomponent Dirac results—demonstrates the validity of the pseudopotential approximation. The densityfunctional (but not the HartreeFock) results show very satisfactory agreement with theoreticalcoupled cluster as well as experimental data where available, such that the theoretical results can serve as an estimate for the hitherto unknown properties of astatine, element 117, and their dimers.

Quantum optimal control of molecular isomerization in the presence of a competing dissociation channel
View Description Hide DescriptionThe quantum optimal control of isomerization in the presence of a competing dissociation channel is simulated on a twodimensional model. The control of isomerization of a hydrogen atom is achieved through vibrational transitions on the groundstatesurface as well as with the aid of an excitedstatesurface. The effects of different competing dissociation channel configurations on the isomerization control are explored. Suppression of the competing dissociationdynamics during the isomerization control on the groundstatesurface becomes easier with an increase in the spatial separation between the isomerization and dissociation regions and with a decrease in the dissociation channel width. Isomerization control first involving transfer of amplitude to an excitedstatesurface is less influenced by the dissociation channel configuration on the groundstatesurface, even in cases where the excitedstatesurface allows for a moderate spreading of the excited wave packet.

Auger decay calculations with corehole excitedstate moleculardynamics simulations of water
View Description Hide DescriptionWe report a new theoretical procedure for calculating Auger decay transition rates including effects of corehole excitedstatedynamics. Our procedure was applied to the normal and first resonant Auger processes of gasphase water and compared to highresolution experiments. In the normal Auger decay, calculated Auger spectra were found to be insensitive to the dynamics, while the repulsive character of the first resonant coreexcited state makes the first resonantly excited Auger decay spectra depend strongly on the dynamics. The ultrafast dissociation of water upon excitation was analyzed and found to be very sensitive to initial vibrational distortions in the ground state which furthermore affect the excitation energy. Our calculated spectra reproduce the experimental Auger spectra except for the FranckCondon vibrational structure which is not included in the procedure. We found that the Auger decay of OH and O fragments contributes to the total intensity, and that the contribution from these fragments increases with increasing excitation energy.

Radiative correction to the helium dimer interaction energy
View Description Hide DescriptionThe leadingorder radiative correction to the heliumhelium interaction energy at the equilibrium internuclear distance has been calculated for the first time. The result is . The calculations were performed using a new technique of evaluating expectation values of singular operators in connection with the most accurate wave functions of available today—the exponentially correlated Gaussian functions.