Volume 111, Issue 22, 08 December 1999
 COMMUNICATIONS


Electroninduced “localized atomic reaction” (LAR): Chlorobenzene adsorbed on
View Description Hide DescriptionElectroninduced reaction of chlorobenzene (ClPh) adsorbed on silicon is shown by scanning tunneling microscopy(STM) to result in “localized atomic reaction” (LAR), imprinting Cl as chemicallybound on the surface. Voltage pulses of −4 V from the STM tip give LAR restricted to the site of electron impact. Delocalized electron impact imprints the selfassembledpattern of ClPh(ad) on the surface as The imprint is found to be on the same area of the unit cell as ClPh(ad), but at adjacent atomic sites. The occurrence of LAR is ascribed to a concerted reaction; this can only occur if the new bond is directly adjacent to the old one
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 THEORETICAL METHODS AND ALGORITHMS


General relationship between complex impedance and linear stability in electrochemical systems
View Description Hide DescriptionThe impedance of the electrochemicalsystem is derived in an explicit analytical form in relation to the stability of the system under various driving conditions. It is shown that the complex impedance is represented as the ratio of characteristic polynomials of the Jacobian matrices of linearized system under potentiostatic control and under galvanostatic control. Thus it is definitely shown that the zeros of the impedance are the eigenvalues of the Jacobian of the system under potentiostatic control, and that the poles are the eigenvalues of the Jacobian under galvanostatic control. The obtained impedance formulas are used to derive or prove several electrochemical characteristics. A direct analytical relationship between the hidden negative impedance and the galvanostatic Hopf bifurcation is also derived.

Spin–spin model for twolevel system/bath problems: A numerical study
View Description Hide DescriptionWe study a new model for treating quantum dissipative systems, in which the bath is modeled as a collection of spins coupled to the system of interest. We develop a quasiclassical method to study this model, approximating the quantum Heisenberg equations by the classical ones, supplemented with stochastic initial conditions carefully chosen so that the results obtained from the classical equations are as close as possible to the quantum results. Using this method we compare the dynamics of such a spin–spin system with that of a spin–boson system, in which the bath is modeled as a collection of harmonic oscillators. We verify numerically that when the systembath coupling is spread over many bath spins (the Brownian motion limit), the spin–spin model can be mapped on the spin–boson model (although with a temperature dependent spectral density). We also demonstrate that the two dissipative models are qualitatively very different in a nonBrownian motion regime.

Application of interpolated potential energy surfaces to quantum reactive scattering
View Description Hide DescriptionThe accuracy of an interpolation approach to molecular potential energy surfaces for quantum reactive scattering is demonstrated by comparison of the quantum reaction probability for a model surface and its interpolated approximation. Effective convergence of an ab initiosurface with the size of the interpolation data set is demonstrated for the reaction

A diffusion equation for Brownian motion with arbitrary frictional coefficient: Application to the turnover problem
View Description Hide DescriptionAfter a brief reexposition of the procedure devised by the author in order to reobtain a diffusionequation from the equations of the motion of a mechanical system driven by a random force, this method is applied to derive a thirdorder diffusionequation for an anharmonic oscillator undergoing Brownian motion. This equation is exact to firstorder in the parameter of anharmonicity, and is valid for arbitrary values of the frictional coefficient. The confrontation of this equation with a similar equation obtained previously by asymptotic expansion in inverse powers of the frictional coefficient, shows that although the two equations are different, nevertheless they reduce to the same equation (within the limits of validity of each approximation scheme) when they are both reduced to second order. An asymptotic formula for the mean firstpassage time (MFPT) for escaping over a barrier is then proved in the lowtemperature limit, which is related to an eigenvalue of the diffusion operator, and to the solution of an integral equation with Smoluchowski boundary conditions. This equation yields the correct behavior of the eigenvalue in both limits of high and extremely low friction, with interpolation between the two limits, while in the oscillatory regime yields a complex eigenvalue, whose imaginary part can be interpreted as a stochastic resonance frequency between the anharmonic well and its mirror image beyond the barrier. It is shown how the Kramers’ result for moderate or strong friction fits in with the present theory, and what is the origin of the discrepancies.

A single Lanczos propagation method for calculating transition amplitudes
View Description Hide DescriptionA method using only a single Lanczos propagation to determine multiple transition amplitudes without the explicit calculation of the eigenstates is proposed. Comparing with methods requiring multiple propagations, this method is very attractive for large dimensional problems since the propagation is usually the most computationally intensive step. When overlaps between eigenstates and prespecified quantum states are of interest, it is shown that the “spurious” Lanczos eigenvalues cannot be simply deleted as done in the Cullum–Willoughby procedure. Practical procedures for calculating the overlaps are provided, which take into consideration numerical behaviors of the Lanczos algorithm in finite precision arithmetic, such as the loss of global orthogonality and emergence of “spurious” eigenvalues. Numerical tests in a realistic triatomic system confirm the accuracy of the present method.

Reaction dynamics on a thermally fluctuating potential
View Description Hide DescriptionThis paper analyzes the kinetics of escape of a particle over a barrier fluctuating between two states, the fluctuations being produced by thermal noise. By this we mean that the jump rates for transitions between the two states are positiondependent, satisfying detailed balance at any point along the reaction coordinate. The fastfluctuation limit can be analyzed in terms of the potential of mean force, and for high barriers the survival probability is found to be a single exponential. In the slowfluctuation regime the survival probability is a linear combination of two exponentials. In the case of a linear potential the slowfluctuation solution describes the kinetics, as obtained from simulations, quite well over the entire range of the jump rates between the two states. Our analysis suggests that this is true for more general forms of the potential. Further, for a thermally fluctuating potential the mean lifetime is shown to decrease monotonically as the jump rate increases. This is in contrast to the turnover behavior, or resonant activation, which can occur when fluctuations are produced by nonthermal noise. An extension of our approach to systems with thermal fluctuations between more than two states is discussed.

On the direct evaluation of the equilibrium distribution of clusters by simulation
View Description Hide DescriptionAn expression is derived that relates the average population of a particular type of cluster in a metastable vapor phase of volume to the probability, estimated by simulation, of finding this cluster in a system of volume taken inside where Correct treatment of the translational free energy of the cluster is crucial for this purpose. We show that the problem reduces to one of devising the proper boundary condition for the simulation. We then verify the result obtained previously for a low vapor density limit [J. Chem. Phys. 108, 3416 (1998)]. The difficulty implicit in our recent calculation [J. Chem. Phys. 110, 5249 (1999)], in which the approach in the former was generalized to higher vapor densities, is shown to be resolved by a method already suggested in that paper.

Comparison between two methods for mapping fluctuations in a simulation cell onto a macrovolume
View Description Hide DescriptionThis paper compares two methods for extending the results of simulations of physical clusters (of interest to nucleation theory) to the macrosystem in which the simulation cell is supposed to be immersed. A particular cluster model is studied in which one of the defining parameters is the volume of a “container” to which the cluster molecules are confined. The two mapping processes are conveniently and respectively referred to as the “tiling method” and the “macromethod.” Although the tiling method has been the method of choice in simulations, it is shown to be only approximate, because of a redundant counting of molecular configurations, and it is also shown that the tiling method can be derived if redundancy is ignored. On the other hand, the macromethod is derived when redundancy is properly accounted for. In certain limit situations, the tiling method converges on the macromethod but it still represents an approximation. The issue dealing with redundancy is subtle. We emphasize the fact that, short of a full, direct molecular dynamics simulation, all theories of nucleation require the use of a model. We also present a simple cluster center of mass argument that verifies the “macromethod.” The mapping problem could arise in connection with localized fluctuations beyond those that represent physical clusters.

Histogram filtering: A technique to optimize wave functions for use in Monte Carlo simulations
View Description Hide DescriptionWave functions are optimized using a histogrambased technique that deals with the statistical error plaguing traditional Monte Carlooptimizations. Following a sensitivity study on we variance and energyoptimize explicitly correlated wave functions for He (up to 18 variational parameters), (up to 10 parameters), and LiH (up to 32 parameters). To gauge the convergence of the variational energy as the quality of the wave functions improves, we adopt some simple ones from the literature in addition to more sophisticated ones unique to this paper. One for LiH has the lowest variational energy for a compact, explicitly correlated wave function to date. For the molecules we determine the optimal bond distance at the same time as we optimize either the variational energy or the variance of the local energy, but agreement with experiment is reasonable only for the energy optimizations. The energy of varianceoptimized molecular wave functions appears to converge slowly to the energy optimization results as the wave function quality improves. Variance optimizations done keeping the bond distance fixed equal to the exact value improves the energy somewhat.

A consistent thirdorder propagator method for electronic excitation
View Description Hide DescriptionA propagator method referred to as thirdorder algebraic–diagrammatic construction [ADC(3)] for the direct computation of electronic excitation energies and transition moments is presented. This approach is based on a specific reformulation of the diagrammatic perturbation expansion for the polarization propagator, and extends the existing secondorder [ADC(2)] scheme to the next level of perturbation theory. The computational scheme combines diagonalization of a Hermitian secular matrix and perturbation theory for the matrix elements. The characteristic properties of the method are compact configuration spaces, regularperturbation expansions, and sizeconsistent results. The configuration space is spanned by singly and doubly excited states, while the perturbation expansions in the secular matrix extend through third order in the block, second order in the coupling block, and first order in the block. While the simpler ADC(2) method, representing a counterpart to the MP2 (secondorder Mo/ller–Plesset) groundstate method, recommends itself for application to larger molecules, the ADC(3) scheme is aimed at a more accurate description of molecular excitation spectra. The relationship of the ADC(3) scheme with coupled cluster methods is discussed, focusing here in particular on the treatment of transition moments.

Interfacing relativistic and nonrelativistic methods. III. Atomic 4spinor expansions and integral approximations
View Description Hide DescriptionTwo approximations to the normalized elimination of the small component are presented which enable the work of a relativistic calculation to be substantially reduced. The first involves fixing the ratio of the large and small components in atomic calculations, which corresponds to a basis set expansion in terms of positive energy atomic 4spinors. The second involves the definition of a local, i.e., centerdependent, fine structure constant, which has the effect of making atoms with α=0 nonrelativistic. A series of test calculations on a variety of molecules and properties indicates that the errors incurred in the first approximation are negligible. In the second approximation, the errors are dependent on the property, the chemical environment and the atomic number. For the second period elements the errors in the approximation are for chemical purposes negligible. In the third period this is true for many properties, but for some, such as ligandmetal binding energies, there are discrepancies which may be a cause for concern in more accurate calculations. Beyond the third period it is usually necessary to treat atoms relativistically.
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 GAS PHASE DYNAMICS AND STRUCTURE: SPECTROSCOPY, MOLECULAR INTERACTIONS, SCATTERING, AND PHOTOCHEMISTRY


Resonant degenerate fourwave mixing spectroscopy of transitions with degenerate energy levels: Saturation and polarization effects
View Description Hide DescriptionThe physics of the degenerate fourwave mixing process for resonant transitions between two degenerate energy levels is investigated by direct numerical integration of the timedependent density matrix equations. The Zeemanstructure of the upper and lower energy levels is included in a multistate formulation of the density matrix equations. The inclusion of the Zeemanstructure enables the investigation of the degenerate fourwave mixing process for different polarization configurations of the forward pump, backward pump, and probe beams. Saturation curves and lineshapes are calculated for different polarization configurations and for numerous lowJ transitions. At low laser intensity, the results of our calculations are in excellent agreement with perturbation theory in terms of the relative intensities of the degenerate fourwave mixing signal for linear polarization configurations. As the laser intensity increases and the resonance starts to saturate, we find in general that the relative degenerate fourwave mixingreflectivity increases for the crossed polarization configurations compared to the parallel polarization configuration because the saturation intensity is higher. However, for some resonance transitions, some of the crossed polarization configurations saturate at lower laser intensities than the parallel polarization configuration, even though the reflectivity for these crossed polarization configurations is much lower than for the parallel polarization configuration in the perturbative intensity limit. This result is explained in terms of the coupling of the various Zeeman states during the degenerate fourwave mixing interaction for specific polarization configurations. The effect of saturation on the resonance line shapes for the different polarization configurations is also investigated. Finally, a limited number of calculations are performed for resonances that are Doppler broadened as well as collision broadened. The effect of saturation on the reflectivity of the crossed polarization configurations compared to the parallel polarization configuration is even more significant for resonances with comparable Doppler and collisional broadening.

Joint local and normalmode studies of the overtone spectra of the methyl halides: and
View Description Hide DescriptionThe infrared spectra of and have been investigated in the range and that of in the range New experimental data are reported for and and these data together with existing literature data for and have been analyzed in terms of a hybrid localmode/normalmode model. Localmode basis functions have been used for the C–H(D) stretching vibrations and normalmode basis functions to describe the C–H(D) bending vibrations. This joint approach, which also takes account of Fermi resonances, enabled the determination of stretch/bend anharmonicity and Fermiresonance parameter sets which reproduce the observed data over wide energy ranges and compare much more favorably with literature ab initio results than previous parameter sets. The analyses have lead to a new vibrational assignment in and two corrected band centers in and and predictions of unassigned bands raise several challenges to experiment.

Theory and ab initio calculations of photoabsorption spectra: The lowest Rydberg resonances in HCl
View Description Hide DescriptionWe present a theory for core excitation spectra of linear molecules that explicitly includes the spinorbit splitting of the core orbitals as well as all nonrelativistic effects. This is applied to the absorptionspectrum of HCl at the , and resonance energies. All input data for the spectrum are obtained from ab initio calculations. These are (i) the nonrelativistic energies and transition probabilities of the contributing states, (ii) the spinorbit coupling parameter, and (iii) the total Auger transition rates of the core excited states. The prior theoretical finding that the total Auger decay rate depends substantially on the core hole orientation is supported by a comparison of the theoretical and experimental absorption spectra. Furthermore, the preferred orientation of the core excited HCl molecule with respect to the molecular bond axis is discussed. General considerations about intensity ratios between corresponding states with and holes are given on the basis of the theoretical framework.

Energetic and structural features of the abstraction reaction: Does perturbation theory from a multiconfiguration reference state (finally) provide a balanced treatment of transition states?
View Description Hide DescriptionThe stationary points of the abstraction reaction have been identified at the fully optimized reaction space (FORS) level. For three sets of geometries (FORS plus unrestricted and restrictedopenshell Møller–Plesset second order perturbation theory), singlepoint calculations by unrestricted Møller–Plesset fourth order perturbation theory (UMP4), by unrestricted coupled clustertheory with single and double excitations and a quasiperturbative treatment of fourth and fifthorder tripleexcitation terms (CCDS(T)), and by multireference Møller–Plesset second order perturbation theory (MRMP2) were also performed for the classical barrier height and energy of the reaction. Calculations carried out at the MRMP2/ccpVTZ//FORS/ccpVTZ level predict values for the forward vibrationally adiabatic barrier height and for the energy of the reaction at 0 K equal to 10.3 and 2.0 kcal/mol, respectively. This is in excellent agreement with experiments that show values of the activation energies in the range of 9–12 kcal/mol (at temperatures below 1500 K) and an energy of reaction equal to 1.8 kcal/mol. Expectation values of where is total electron spin, and also the values the coefficients of the configuration state functions show that the reactants and the products of this reaction are well described by singleconfiguration reference states but that the transition structure has a much higher multiconfigurational character. We conclude that MRMP2 may provide some light at the end of the tunnel in the longstanding quest for method that includes nondynamical and dynamical correlation in a balanced way in the electronic wave function of openshell transition states.

An empirical potential energy surface for the Ne–OH/D complexes
View Description Hide DescriptionAn empirical potential energy surface has been developed for the Ne–OH/D complexes from the experimentally observed vibrational and rotational energy levels with the results of ab initio calculations being used to provide initial estimates of the values of the parameters in the empirical potential. To determine the final surface a reassignment of the bend–stretch combination bands, to fundamentals of the bend, was made, and the experimental data for both the Ne–OH and Ne–OD complexes were fit simultaneously due to the small number of available values. The vibrational energies and rotational constants resulting from the fit surface are within 0.2 and 0.0013 cm^{−1}, respectively, of the experimental values. The details of the potential energy surface are discussed in relationship to those of other inert gas complexes containing OH and SH, as well as HCl and HF.

Moleculardynamics study of rotational alignment of drifting in helium—velocity and angular momentum distribution functions
View Description Hide DescriptionCollisioninduced rotational alignment of ions drifting in a helium buffer gas is studied with molecular dynamics using the ab initiopotential surface of S. K. Pogrebnya et al. [Int. J. Mass Spectrom. Ion Proc. 149/150, 207 (1995)], obtained via a coupledcluster singles–doubles approximation. We examine average translational and rotational temperatures, velocity and angular momentum distributions, and the dependence of these quantities on the applied electric field. The distributions show that angular momentum is preferentially aligned perpendicular to the electric field vector. We investigate the mechanism of this alignment through a multipolar moment expansion, and propose and demonstrate the accuracy of a biMaxwellian analytic form for describing the angular momentum distribution.

Vibrational excitation in collisions: Quantum calculations and experiment
View Description Hide DescriptionHelium atoms are scattered from a beam of water clusters with mean size in an angular and velocity resolved collision experiment. The measured peaks are identified as elasticscattering, rotationally inelastic scattering of monomers, and vibrational excitation of the clusters. To interpret the latter processes quantum calculations are performed for collisions using the TDSCF approximation which includes the anharmonic force field of the water clusters and energy transfer between the modes. By comparison of the calculated and experimental results, the most probable excitations correspond to energy transfer for around 7 meV and, with smaller intensities, up to 20 meV. The excitations correspond to shearing modes of the outer rings and the middle ring of the highly nonrigid cluster against each other.

Water dimer to pentamer with an excess electron: Ab initio study
View Description Hide DescriptionWe have studied the electronic structures, energetics, electron vertical detachment energies (VDEs), and O–H vibrational spectra of various conformers of water clusters with an excess electron or anionic water clusters using comprehensive ab initio calculations. As noted in our preliminary work [J. Kim et al., Phys. Rev. A 59, 930 (1999)], the structure of the water dimer anion is characterized to be linearlike (slightly towards the cis conformer) but very floppy with large wideranging zero point vibration motion at 0 K. The lowest energy structures of the water trimer to pentamer anion are all cyclic with very small VDEs 0.05 eV). However, these cyclic structures which are metastable are prone to become the neutral species by releasing an excess electron because the transition barriers seem to be very small. Thus, observation of such cyclic structures would not be feasible. On the other hand, a linear water trimer structure which is 0.8 kcal/mol higher in energy than the cyclic form gives the VDE (0.14 eV) close to the experimentally observed value. A large VDE observed in the pentamer also corresponds to a slightly high energy conformer. This suggests that formation of anionic water clusters in experiments seems to be dynamically and kinetically driven.
