Volume 111, Issue 18, 08 November 1999
 COMMUNICATIONS


Kinetics of the condensation of Cs from its supersaturated vapor: Comments on the entropy of a small Cs cluster
View Description Hide DescriptionThe recently published measurements of temperaturedependent critical supersaturation levels for avalanchecondensations of Cs vapor are interpreted via the recently revised kinetic molecular model that incorporates accretions with dimers as well as monomers. The kinetic parameters required to reproduce the reported condensation rate of, approximately, unit cluster per cm^{3} s permits estimations of the entropies of clusters. Therefrom the mean intermolecular (bulk) frequency derived for (466 K) fits well with a model proposed by Hoare for

Highresolution pulsed field ionization photoelectron–photoion coincidence study of Accurate 0 K dissociation threshold for
View Description Hide DescriptionThe formation of methyl cation from methane has been investigated in high resolution using the newly perfected pulsed field ionization photoelectron–photoion coincidence (PFIPEPICO) scheme. The PFIPEPICO data reveal that fragmentation of in highnRydberg states occurs at energies above the dissociation threshold prior to pulsed field ionization. The crossover point of the breakdown curves is found to depend strongly on the Stark field in the ion source and thus traditional simulation procedures based on such a feature for ion dissociation energy determination are not appropriate in PFIPEPICO studies. We show that for a prompt dissociation process, the disappearance energy of the parent molecule provides an accurate measure of the 0 K ion dissociation threshold, as that for from is 14.323±0.001 eV.

Rationalizing the effects of modified electrostatic interactions in computer simulations: The dielectric selfconsistent field method
View Description Hide DescriptionThe dielectricselfconsistent field method, a novel tool to study solvated systems based on continuum electrostatics, is introduced. It permits the qualitative and even semiquantitative calculation of orientational correlation functions, i.e., it gives insights into the orientational structure of a solute–solvent system. Further, modified Coulomb potentials and periodic boundary conditions can easily be integrated. One possible application is rapid, yet detailed methodological studies of the effects resulting from the various modified electrostatic interactions that are used regularly in computer simulations with explicit solvent molecules. As an example, we report the distance dependent Kirkwood gfactor and ion–dipole correlation functions of a solvated glycine zwitterion obtained with a simple cutoff, a shifted potential, two reaction field techniques, and Ewald summation. For the reaction fields and Ewald summation, conducting and adjusted dielectricboundary conditions are compared.
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 THEORETICAL METHODS AND ALGORITHMS


Application of an equationofmotion coupled cluster method including higherorder corrections to potential energy surfaces of radicals
View Description Hide DescriptionA method proposed some time ago to correct for residual correlation effects within the framework of equationofmotion coupledcluster theory for ionized states in the singles and doubles approximation (EOMIPCCSD) is discussed, and a minor modification is suggested that provides a more balanced theoretical treatment. The resulting approach is used to calculate properties of diatomic radicals, where comparison with experiment and other highlevel calculations is straightforward. In addition, two electronic states of and the ground state of the cyclic molecule are studied, cases in which symmetrybreaking phenomena play an important role. Results indicate that EOMIPCCSD^{*} generally provides a systematic improvement relative to the uncorrected EOMIPCCSD approach for predicting properties of radicals.

A test of the accuracy of the partiallyseparable timedependent selfconsistentfield approach
View Description Hide DescriptionThe accuracy of the timedependent selfconsistentfield (TDSCF) approach assuming partial factorization of the total wave packet is tested against an exact treatment, when applied to calculate asymptotic properties. The test is carried out in the framework of a threedimensional simulation of the Ar–HCl UVphotodissociation dynamics. All the partiallyseparable TDSCF ansatzs possible for this problem are investigated. The quality of the TDSCF results is found to be strongly dependent on the specific partiallyseparable ansatzs applied. In general, the TDSCF predictions are in very good (even quantitative) agreement with the exact ones for magnitudes associated with direct photodissociation dynamics, and are qualitative in the case of indirect photodissociation. The deviation of the TDSCF results from the exact dynamics is interpreted in terms of an error operator defined as the difference between the exact and the TDSCF Hamiltonians. The analysis of this operator also explains the different accuracy of the partiallyseparable ansatzs investigated. Based on this analysis, a simple procedure is suggested to estimate the relative average quality of the different TDSCF ansatzs.

Correlation length and amplitude scaling in critical polymer solutions
View Description Hide DescriptionWe present a light scatteringmeasurement of the correlation length for a series of critical solutions of polystyrene in methylcyclohexane with different molecular weights. Our results show that the correlation length where N is the polymerization index and is the reduced temperature. The N exponent is found to be which is contrary to most earlier direct experimental results but in excellent agreement with theoretical predictions by de Gennes and Stepanow.

Semiclassical theory of multidimensional tunneling and the hopping method
View Description Hide DescriptionThe paper presents a new semiclassical theory of multidimensional tunneling and its application to the decay problem. A simple semiclassical expression for the decay rate constant is derived in terms of complex valued family of classical trajectories in the decay valley while the algebraic form of the family in the tunneling region is found by means of classical canonical perturbation theory. This provides a tool to analytically continue the classical trajectories into the decay valley, with a numerical illustration of such a continuation being done for a model 2D decay rate problem. The calculated results for the rate constant are found to be in good agreement with the exact ones for the high levels where the suggested perturbative treatment is applicable. It is also shown that the formulated theory can be directly compared with a previously proposed hopping method which gives a way to examine the accuracy of the latter without exact quantum calculations.

Master equation analysis of intermolecular energy transfer in multiplewell, multiplechannel unimolecular reactions. II. Numerical methods and application to the mechanism of the reaction
View Description Hide DescriptionHaving elucidated a full theoreticalanalysis of the master equation for intermolecular and intramolecular energy transfer in multiplewell, multiplechannel chemically or thermally activated reactions [J. Chem. Phys. 107, 8904 (1997)], we now present efficient methods of numerical analysis for the computational examination of the dynamics of the master equation. We suggest the use of a Krylovsubspace method to determine the uppermost portions of the internal spectrum of the master equation kernel. Such a computation is pivotal in determining whether there exists a state of secular equilibrium for the population of the moieties and whether there exists within the possible state of secular equilibrium, a state wherein the dynamics are represented by an isolated dominating mode; for only in the state of secular equilibrium can one write rate equations for the dissociating processes that are local in time. And, if such a state is possible, we suggest the use of a Hermite–Laguerre orthogonal collocation method for obtaining highly accurate solutions to the population of the moieties. The theory and numerical analysis is then applied to study the dynamics of the chemicallyactivated reaction Comparison of the master equation treatment with modified strongcollision theory is also given for this system of multiplewell, multiplechannel reactions.

Linear scaling coupled cluster and perturbation theories in the atomic orbital basis
View Description Hide DescriptionWe present a reformulation of the coupled cluster equations in the atomic orbital (AO) basis that leads to a linear scaling algorithm for large molecules. Neglecting excitation amplitudes in a screening process designed to achieve a target energy accuracy, we obtain an AO coupled cluster method which is competitive in terms of number of amplitudes with the traditional molecular orbital (MO) solution, even for small molecules. For large molecules, the decay properties of integrals and excitation amplitudes becomes evident and our AO method yields a linear scaling algorithm with respect to molecular size. We present benchmark calculations to demonstrate that our AO reformulation of the manybody electron correlation problem defeats the “exponential scaling wall” that has characterized highlevel MO quantum chemistry calculations for many years.

Finitesize effects and the stabilized spinpolarized jellium model for metal clusters
View Description Hide DescriptionIn the framework of spherical geometry for jellium and local spin density approximation, we have obtained the equilibrium values, of neutral and singly ionized “generic” Nelectron clusters for their various spin polarizations, Our results reveal that as a function of behaves differently depending on whether N corresponds to a closedshell or an openshell cluster. That is, for a closedshell one, is an increasing function of over the whole range and for an openshell one, it has a decreasing part corresponding to the range where is a polarization that the cluster assumes in a configuration consistent with Hund’s first rule. In the context of the stabilized spinpolarized jellium model, our calculations based on these equilibrium values, show that instead of the maximum spin compensation (MSC) rule, Hund’s first rule governs the minimumenergy configuration. We therefore conclude that the increasing behavior of the equilibrium values over the whole range of is a necessary condition for obtaining the MSC rule for the minimumenergy configuration; and the only way to end up with an increasing behavior over the whole range of is to break the spherical geometry of the jellium background. This is the reason why the results based on simple jellium with spheroidal or ellipsoidal geometries show up MSC rule.

Mean first passage times of Brownian rotators from differential recurrence relations
View Description Hide DescriptionAn exact method of calculation of mean first passage times (analogous to that previously used [W. T. Coffey, Yu. P. Kalmykov, E. S. Massawe, and J. T. Waldron, J. Chem. Phys. 99, 4011 (1993)] for the correlation time) is developed in terms of continued fractions from the zero frequency limit of the Laplace transform of the set of differential recurrence relations generated by the Fokker–Planck or Langevin equations. The method because it is based on a Floquet representation avoids the use of quadratures and so may be easily generalized to multidegree of freedom systems by the use of matrix continued fractions. The procedure is illustrated by considering the mean first passage time of a fixed axis rotator with two equivalent sites.

Possibilities for a density matrix theory
View Description Hide DescriptionTwo possible routes are considered to arrive at a oneparticle reduced density matrix formulation of electronic structuretheory. In the first scheme, an extended Fock matrix H is defined that has twice the dimension of the oneparticle basis set. The corresponding Green’s function, defined as the upper left block of yields the exact oneparticle density matrix and energy. The poles of the Green’s function are precisely the ionization potentials and electron affinities of the extended Koopmans theorem. In the second scheme, a generalized Fock equation is derived that is satisfied by the exact nonidempotent oneparticle density matrix. The antisymmetric matrix X on the righthand side is obtained from the irreducible part of the twoparticle reduced density matrix, while F is the usual Fock matrix defined using the correlated onematrix. The generalized Fock equation is a necessary condition but does not determine ρ uniquely. Alternatively, the onematrix can be obtained from the irreducible part of the twomatrix directly, using a sum rule. The analysis leads to some additional desiderata and separability properties that may be imposed on traditional wave function based approaches. Possibilities for practical computational schemes are addressed briefly.

Mean field approximation for the stochastic Schrödinger equation
View Description Hide DescriptionA stochastic meanfield(SMF) approach to nonadiabatic molecular simulations is introduced. Based on the quantumclassical meanfield approximation, SMF extents the classical model of the environment to incorporate its quantum properties. SMF differs from the ordinary meanfield method by the presence of additional terms in the Schrödinger equation that are due to the systemenvironment interaction. SMF resolves the two major drawbacks of mixed quantumclassical models. First, decoherence effects in the quantum subsystem are rigorously included. Present in all open systems, decoherence is crucial for nonadiabatic transitions taking place in condensed media. Second, the correct branching of the quantumclassical trajectories is achieved. In earlier approaches, the correct branching of the trajectories was attained via ad hoc surface hopping procedures, which experienced the hop rejection problem and could produce unfavorable classical trajectories in regions of nonadiabatic transitions depending on the quantum basis. It is shown that the correct branching of the trajectories is a direct consequence of decoherence. It is argued that the hop rejection problem disappears in SMF. The decoherence operator is discussed in detail, and the properties of the SMF method are illustrated with model simulations.
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 GAS PHASE DYNAMICS AND STRUCTURE: SPECTROSCOPY, MOLECULAR INTERACTIONS, SCATTERING, AND PHOTOCHEMISTRY


Nonadditive intermolecular forces in –HF van der Waals clusters: Effects on the HF vibrational frequency shift
View Description Hide DescriptionThe effects of nonadditive forces on –HF van der Waals clusters are investigated for 3, 4, and 12. The pair potentials operating in these systems are accurately known. Earlier models of nonadditive forces in –HF, including nonadditive dispersion, induction, and overlap distortion, are generalized to handle clusters of arbitrary size. Calculations of vibrational frequency shifts (redshifts) are then performed and compared with experiment. The geometries of the clusters are first optimized by simulated annealing; the cage is then held fixed, and the resulting fivedimensional Schrödinger equation is solved for the hindered rotational and translational motion of the HF molecule in the field of the Ar atoms. The nonadditive potentials are found to account remarkably well for the observed frequency shifts.

A CASSCF–MRCI study on the lowlying excited states of
View Description Hide DescriptionA theoretical study on the excited states of methylhypochlorite has been carried out using high level ab initio molecular orbital methods. The vertical excitation energies for the lowest two states, three states, three states, and three states are calculated using the multireference configuration interaction (MRCI) method with ccpVTZ and basis sets. In addition, the potential energy curves for the lowest eight states are examined along both the ClO and CO coordinates at the complete active space SCF (CASSCF) level of theory with ccpVTZ basis set. Except for the ground state, all seven excited states are strongly repulsive along the ClO coordinate, which is in good agreement with recent experimental work. Two absorption bands with maximums at 235 nm and 308 nm in the experimental UV spectra of can be assigned to the transitions and

Electronic structure and chemical bonding between the first row transition metals and A photoelectron spectroscopy study of (M=Sc, V, Cr, Mn, Fe, and Co)
View Description Hide DescriptionVibrationally resolved photoelectron spectra of (M=Sc, V, Cr, Mn, Fe, and Co) are reported at two detachment photon energies, 532 and 355 nm. All the spectra showed a well resolved vibrational progression in the ground state detachment features. Electron affinities, vibrational frequencies, and information about the lowlying electronic states were obtained for the first row transition metal dicarbide molecules. The measured electron affinities for the species show strong metaldependence with a minimum at and a maximum at The ground state vibrational frequencies were observed to decrease from to a minimum in and then increases slightly in and The trends of the electron affinities and vibrational frequencies for the species were found to correlate well with the corresponding monoxides, suggesting that the chemical bonding in is analogous to that in M–O. The bonding was thus interpreted to be quite ionic, and can be qualitatively viewed as analogous to

The hyperfine interactions in CsF
View Description Hide DescriptionThe molecular beam electric resonance technique has been used to examine the hyperfinespectrum of CsF to determine the nuclear quadrupole interaction of the cesium nucleus. A total of 95 transitions in vibrational states and rotational states have been included in a fit to determine the cesium nuclear quadrupole and spin–rotation interactions, the fluorine spin–rotation interaction, and the tensor and scalar parts of the spin–spin interaction. Vibration and rotation dependencies of these constants have been determined, allowing correction for zero point vibration effects. This experimental Cs nuclear quadrupole coupling constant when combined with the electric field gradient calculated using a relativistic coupled cluster method yields a nuclear quadrupole moment of the Cs nucleus equal to The vibrational dependence of the coupling constant is smaller than the theoretical estimate. The coupling constants we have determined are the following: All values are in kHz units, with one standard deviation uncertainty estimates in the last two digits shown in

Spectroscopic and theoretical characterization of linear centrosymmetric
View Description Hide DescriptionThe first high resolution infrared spectrum of the ionic complex and its deuterated derivative is reported. The spectra were obtained in direct absorption in a supersonic slit nozzle plasma. The observed rovibrational transitions were assigned to the antisymmetric NN stretching vibration and the spectrum is consistent with a linear centrosymmetric equilibrium structure. The band origin is found at 2352.2364(6) and the ground staterotational constant is determined as The assignment is supported by ab initio calculations including electron correlation effects. The best estimate for the equilibrium structure is (NN)=1.095 Å and =1.277 Å. The transition moment of the band of is predicted to be 0.21 D, an order of magnitude larger than for the NN stretching vibration of The equilibrium dissociation energy for fragmentation into and is calculated to be

Energydependent cross sections and nonadiabatic reaction dynamics in
View Description Hide DescriptionHighsensitivity direct IR laser absorption methods are exploited to investigate quantum stateresolved reactive scattering dynamics of in lowdensity crossed supersonic jets under single collision conditions. Nascent rotational state distributions and relative cross sections for reactive scattering into the energetically highest HF vibrational manifold are obtained as a function of centerofmass collision energies from down to 0.3 kcal/mole. This energy range extends substantially below the theoretically predicted transition state barrier [ K. Stark and H. Werner, J. Chem. Phys. 104, 6515 (1996)] for the lowest adiabatic potential energy surface, therefore preferentially enhancing nonadiabatic channels due to spin–orbit excited in the discharge source. The HF cross sections decrease gradually from 2.4 kcal/mole down to the lowest energies investigated in contrast with exact adiabatic quantum calculations that predict a rapid decrease below and vanishing reaction probability by Further evidence for a nonadiabaticreaction channel is provided by nascent rotational state distributions in HF which are >2–3fold hotter than predicted by purely adiabatic calculations. Most dramatically, the nascent product distributions reveal multiple HF rovibrational states that would be energetically inaccessible from ground state atom reactions. These quantum state resolved reactive scattering studies provide the first evidence for finite nonadiabatic dynamics involving multiple potential energy surfaces in this wellstudied “benchmark” reaction system.

Evolution of the potential energy surface with size for LennardJones clusters
View Description Hide DescriptionDisconnectivity graphs are used to characterize the potential energy surfaces of LennardJones clusters containing 13, 19, 31, 38, 55, and 75 atoms. This set includes members which exhibit either one or two “funnels” whose lowenergy regions may be dominated by a single deep minimum or contain a number of competing structures. The graphs evolve in size due to these specific size effects and an exponential increase in the number of local minima with the number of atoms. To combat the vast number of minima we investigate the use of monotonic sequence basins as the fundamental topographical unit. Finally, we examine disconnectivity graphs for a transformed energy landscape to explain why the transformation provides a useful approach to the global optimization problem.
