Volume 114, Issue 20, 22 May 2001
 COMMUNICATIONS


Branching ratio in the HD+OH reaction: A fulldimensional quantum dynamics study on a new ab initio potential energy surface
View Description Hide DescriptionA fulldimensional quantum dynamical study is reported for the title reaction on the YZCL2 potential energy surface. The influence of reagent rotation on the dynamics is examined in detail. It is found that the rotational excitation of the HD reagent substantially enhances the rate coefficient for forming the product, and plays an important role in determining the branching ratio at low temperatures. The theoretical results are compared with available experimental data for an integral cross section, thermal rate coefficients, and their corresponding branching ratios. Excellent agreement between theory and experiment is revealed for available thermal rate coefficients and its branching ratio. The agreement between theory and experiment for the integral cross section is also satisfactory. The study clearly shows that the YZCL2 potential energy surface is capable of producing “quantitatively” accurate results for the title reaction.

Nonequilibrium tube length fluctuations of entangled polymers
View Description Hide DescriptionWe investigate the nonequilibrium tube length fluctuations during the relaxation of an initially stretched, entangled polymer chain. The timedependent variance of the tube length follows in the earlytime regime a simple universal power law originating in the diffusive motion of the polymer segments. The amplitude is calculated analytically both from standard reptation theory and from an exactly solvable lattice gas model for reptation and its dependence on the initial and equilibrium tube length, respectively, is discussed. The nonuniversality suggests the measurement of the fluctuations (e.g., using flourescence microscopy) as a test for reptationmodels.
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 ARTICLES

 Theoretical Methods and Algorithms

Wave packet methods for charge exchange processes in ionatom collisions
View Description Hide DescriptionThe efficiency of different timeindependent and timedependent wave packet methods to calculate chargeexchange cross sections is discussed. The timeindependent spectral projection method is based on the Chebyshev expansion of the resolvent function and represents an interesting alternative to the usual Fourier method which involves a time propagation. On the other hand, the flux operator method still requires propagation in time but uses the properties of absorbing potentials in order to calculate the flux operator matrix elements. We show the necessity of introducing the appropriate Hankel–Riccati functions when the full Hamiltonian contains a centrifugal term in in order to reduce the computational time. The collisional system is studied as a test case.

A generalpurpose biasing scheme for Monte Carlo simulation of associating fluids
View Description Hide DescriptionWe present a method for accelerating convergence of Monte Carlo simulations of associating fluids. Such fluids exhibit strong, shortranged, orientationspecific intermolecular attractions which are difficult to sample via conventional molecular simulation. We propose a bias scheme that preferentially attempts Monte Carlo trials that lead to “unbonding” or “bonding” (UB) transitions of the associating molecules. The proposed method is most like the recently introduced aggregation volume bias Monte Carlo (AVBMC) algorithm of Chen and Siepmann. Both algorithms are much simpler, more efficient, and more generally applicable than previously proposed associationbias schemes. We study the UB algorithm via application to the simple idealassociation model of van Roij. Although unrealistic, the model contains the basic features of association that cause problems for simulation, and its simple nature facilitates analysis of the performance of the simulation algorithm. We find, at least in application to this model, that the UB algorithm exhibits better convergence properties when compared to AVBMC, and through analysis of the acceptance probability distributions we can develop an explanation for this difference. We also demonstrate the UB algorithm in the context of the Gibbs ensemble, reproducing the phase coexistence behavior of a dimerization model originally proposed by Tsangaris and de Pablo.

Extending the vibrational selfconsistent method: Using a partially separable wave function for calculating anharmonic vibrational states of polyatomic molecules
View Description Hide DescriptionA new method for the treatment of correlation effects between modes in vibrational selfconsistentfield (VSCF) calculations is introduced. It is based upon using a partially separable form for the wave function. As a result, some of the modes are treated as mutually fully correlated, while the rest are separable. The modes which are explicitly coupled together in the calculation are chosen on physical grounds. Trial calculations are performed upon and and indicate that the method performs well. The agreement with experiment for the explicitly coupled modes is improved when compared to both the vibrational selfconsistentfield method and its correlationcorrected extension. When interfaced with an electronic structure code this method opens the way for the accurate firstprinciples prediction of vibrational frequencies of strongly coupled modes. If only a few modes are mutually strongly coupled, the method has a very favorable scaling with system size, as does VSCF itself.

Fluctuations and thermodynamics properties of the constant shear strain ensemble
View Description Hide DescriptionWe develop the statistical mechanics of a pair of new ensembles called the constant shear strain ensembles that include the uniform dilation ensemble used frequently in computer simulations. We present a direct calculation of fluctuation formulas for the elastic constants, the specific heat, and the thermal expansiontensor in these new ensembles.

Intermolecular exchangeinduction and charge transfer: Derivation of approximate formulas using nonorthogonal localized molecular orbitals
View Description Hide DescriptionPrevious work on the efficient evaluation of the secondorder exchange repulsion energy [Mol. Phys. 89, 1313 (1996)] is extended to exchange induction and charge transferenergies. The approximations outlined in the previous work are shown to be sufficient to simplify all new terms in the exchange induction and charge transferenergy terms. Both variational and couple perturbed Hatree–Fock approaches are discussed as is the use of these new energy terms in conjunction with hybrid “quantum mechanical/molecular mechanics” methods [specifically the effective fragment potential method, J. Chem. Phys. 105, 1968 (1996)].

Atomic shell structure in Hartree theory
View Description Hide DescriptionIn this paper we show that atomic shell structure is exhibited throughout the periodic table, and accurate core–valence separations thereby obtained, via the radial probability density determined from the uncorrelated wave functions of Hartree theory. Further, essentially equivalent results are obtained via Hartreetheorylevel quantal density functional theory in an approximation in which the correlation contributions to the kinetic energy are also neglected. Thus, accurate atomic shell structure can be obtained solely via electrostatic fields determined from charge distributions that are derived from wave functions which neither obey the Pauli exclusion principle nor incorporate Coulomb correlations.

Molecular excitation energies computed with Kohn–Sham orbitals and exact exchange potentials
View Description Hide DescriptionExact local exchange potentials are computed for the diatomic molecules and CO, based on expansions in terms of molecular orbitals. Kohn–Sham orbitals and orbital energies are obtained for the exact exchange potentials, with correlation effects neglected. The ionization potential is in all cases found to be accurately predicted by the orbital energy of the highest occupied orbital. Limited configuration interaction calculations are performed based on the Kohn–Sham orbitals, and are found to yield accurate excitation energies for a series of singly excited states, in particular for and CO. Clearly inferior results are obtained from similar calculations by use of Hartree–Fock orbitals. Thus Kohn–Sham orbitals obtained with exact exchange potentials tend to have an interesting potential as basis for sophisticated manybody methods.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Quantum reactive scattering calculations for the reaction
View Description Hide DescriptionThe results of accurate 3D quantum scattering calculations in symmetrized hyperspherical coordinates are reported for the reaction at 64 values of total energy in the range 0.5–1.9 eV. Integral and differential cross sections are computed using the Boothroyd–Keogh–Martin–Peterson potential energy surface for all values of total angular momentum Several transition state resonances survive the sum over J and are observed in many of the fully converged statetostate integral and differential cross sections. In some cases a series of resonances is observed. The energy spacings between many of the resonances are consistent with the energy spacings between the even or odd bending modes of the quantized transition states of

Transferring vibrational population between electronic states of diatomic molecules via lightinducedpotential shaping
View Description Hide DescriptionWe investigate twophoton, selective excitation of diatomic molecules with intense, ultrafast laser pulses. The method involves transfer of a vibrational population between two electronic states by shaping of lightinduced potentials (LIPs). Creation and control of the LIPs is accomplished by choosing pairs of transformlimited pulses with proper frequency detunings and time delays. Depending on the sequence of pulses (intuitive or counterintuitive) and on the sign of the detuning (below or above the first transition) four schemes are possible for population transfer by LIP shaping. We develop a simple analytic model to predict the optimal laser pulses, and to model the adiabatic dynamics in the different schemes. Based on a harmonic, threestate model of the sodium dimer we demonstrate numerically that all four schemes can lead to efficient, selective population transfer. A careful analysis of the underlying physical mechanisms reveals the varying roles played by the adiabatic and diabatic crossings of the LIPs. The detailed mechanisms influence the robustness and experimental applicability of the schemes.

Measurement of the autodetachment lifetime of as a function of electron energy in a free jet expansion
View Description Hide DescriptionA pure free jet expansion has been used for the measurement of the autodetachment lifetime of the resonant excited anion as a function of electron energy in the range 0–100 meV. In this low temperature environment, the lifetime was found to be 19.1±2.7 μs and independent of electron energy. This result is consistent with earlier statistical modeling of this process in terms of a coupling to the bath of states which is only a smoothly varying function across the energy range spanned by the electron affinity plus the small variation in electron kinetic energy. The temperature dependence of the autodetachment lifetime also suggests a strong coupling of vibrational motion in with the autodetachment process consistent with the picture of nuclear excited Feshbach resonances. In addition, the rate coefficient for the very inefficient secondary stabilization rate of the states on collision with neutrals below 10 K is determined to be

Intermolecular potential for the interaction of helium with ammonia
View Description Hide DescriptionWe develop an intermolecular potential for the interaction between helium and ammonia including flexibility in the ammonia inversion tunneling coordinate. The potential energy surface is generated by fitting to scaled perturbation theory calculations and is shown to be comparable with highquality ab initiosupermolecule calculations. We have characterized the potential energy surface for a number of ammonia geometries from planar to a highly distorted geometry. For all but the most distorted ammonia geometry, the global minimum has the helium atom in an equatorial location, equidistant from the two closest hydrogen atoms. As the ammonia molecule moves away from the planar configuration, the equatorial minima become less strongly bound while the binding energy increases in the axial regions of the potential energy surface. At the most distorted ammonia geometry, the equatorial minimum is a local minimum, and the global minimum has the helium atom on the symmetry axis of the molecule at the hydrogen end.

The and 6, local mode states of Fourier transform infrared and laser photoacoustic spectra and ab initio calculations of spectroscopic parameters
View Description Hide DescriptionThe rotational structure of the local mode Si–H stretching vibrational bands 4, and 6, of have been studied by highresolution Fourier transform infrared and by photoacoustic laser spectroscopy. The recorded bands have been rotationally analyzed with a Hamiltonian model which makes use of simple arithmetic relations between some of the rovibrational parameters. While the states were found to be unperturbed, severe perturbations by unknown dark states affect the and states for J values exceeding 8. Ab initio calculations have been performed to form the quadratic and the cubic potential energy surfaces which have been used to calculate spectroscopic parameters for the Si–H stretching fundamentals. These results, together with the local mode relations, have been successfully used to model the vibrational dependence of effective rovibrational parameters in the excited local mode states.

Spectroscopy and MRCI calculations on CrF and CrCl
View Description Hide DescriptionThe band system of the CrCl radical has been recorded in thermal emission with FTS techniques in the region 6900–11 700 cm^{−1}, using a resolution of 0.025 cm^{−1}. An analysis of the (0,0) band of this system has been carried out. A rotational constant of and a spin–orbit parameter of have been estimated for the state. Improved values for the γ and λ parameters of the ground state have been obtained. MRCI calculations have been performed on CrF and CrCl and comparisons have been made with both experiments and DFT calculations [Bencheikh et al., J. Chem. Phys. 106, 6231 (1997)]. The calculations on CrF have provided valuable aids in the interpretations of the fluorescence excitation and dispersed fluorescence spectra of a state observed at 31 700 cm^{−1}. This state has now been assigned as A number of transitions in the dispersed fluorescence spectra are believed to involve the hitherto unknown state. Spin–orbitconfigurationinteraction (SOCI) calculations have been carried out on both CrF and CrCl. It is shown that the secondorder spin–orbit parameters of the ground states are due mainly to interactions with the states.

Quantum optimal control of multiple targets: Development of a monotonically convergent algorithm and application to intramolecular vibrational energy redistribution control
View Description Hide DescriptionAn optimal control procedure is presented to design a field that transfers a molecule into an objective state that is specified by the expectation values of multiple target operators. This procedure explicitly includes constraints on the time behavior of specified operators during the control period. To calculate the optimal control field, we develop a new monotonically and quadratically convergent algorithm by introducing a quadruple space that consists of a direct product of the double (Liouville) space. In the absence of the timedependent constraints, the algorithm represented in the quadruplespace notation reduces to that of the doublespace notation. This simplified formulation is applied to a two dimensional system which models intramolecular vibrational energy redistribution (IVR) processes in polyatomic molecules. An optimal pulse is calculated that exploits IVR to transfer a specific amount of population to an optically inactive state, while the other portion of the population remains in the initial state at a control time. Using trajectory plots in quantumnumber space, we numerically analyze how the control pathway changes depending on the amount of the excited population.

Gas phase dihydrogen bonded phenol–borane–trimethylamine complex
View Description Hide DescriptionSpectroscopic investigation of a dihydrogen bonded complex between phenol and borane–trimethylamine is reported here. Laserinduced fluorescence excitation, fluorescence detected infrared, and infrared–ultraviolet holeburning spectroscopic studies were carried out in supersonic jets to investigate the complex formation between phenol and boranetrimethylamine. The redshift in the electronic transition and the lowfrequency shift of the O–H stretching vibration established the proton donating ability of phenol in the complex. The experimental results together with the ab initio quantum mechanical calculations affirmed the formation of the dihydrogen bond in the complex.

Quasiclassical treatment of the Stereodynamics of chemical reactions: vector correlation for the reaction
View Description Hide DescriptionWe present a classical treatment of the vector correlation for atom–diatom reactions, involving the directions of the initial and final relative velocities and the internuclear axis of the diatom. The formalism is based on the expansion of the joint probability distributions in multipolar moments, and it is analogous to that developed for the vector correlations implying the initial or final rotational angular momentum. Within the framework of classical mechanics, the present treatment allows the determination of the differential cross section for any preparation of the internuclear axis and for any initial rotational angular momentum of the reactants. This methodology has been applied to the study of the steric effect in the reaction and the theoretical results have been compared via simulation with the recent experimental determination by Loesch and coworkers of laboratory angular distributions (LAB ADs) for several distributions of the internuclear axis of HF. Very good agreement has been found between experimental and simulated LAB AD, allowing an interpretation of the experimental results. Although the integral steric effect is very small, the differential and/or state resolved steric effects are more pronounced. Moreover, it has been found that by varying the preparation of the internuclear axis of the HF molecule, the population of final states of the LiF changes noticeably, which represents a clear case of control of the outcome of a chemical reaction.

Glyoxal photodissociation. An ab initio direct classical trajectory study of
View Description Hide DescriptionUnimolecular dissociation of glyoxal via a threebody fragmentation channel has been studied by direct classical trajectory calculations using Hartree–Fock (HF) and hybrid density functional methods (BH&HLYP, B3LYP) with split valence and polarized basis sets [HF/321G, and The transition state for has a dihedral angle of 90–110° between the carbonyl groups and a calculated barrier of ∼59 kcal/mol above the trans conformer. To simulate the experimental conditions, trajectories were started from a microcanonical ensemble at the transition state with 4, 8, and 16 kcal/mol excess energy distributed among the vibrational modes and the transition vector. In agreement with experiment, the CO rotational distribution is very broad with a high 〈J〉. However, the calculations yielded more CO vibrational excitation for the triple dissociation channel than observed for all channels combined. Hydrogen is produced with low J but significant vibrational excitation, in accord with experiment. Similar to trajectory studies on there is a good correlation between the energy released along the part of the reaction path where most of the bond length change occurs and the average vibrational excitation of the products.

Band strengths for C–H stretching polyads of calculated by use of a twodimensional electric dipole moment surface from density functional theory
View Description Hide DescriptionBand strengths of the Fermi resonance polyads involving C–H stretching and bending vibrations for the molecule are calculated with a onedimensional dipole function and a twodimensional dipole surface. These are obtained by the ab initiodensity functional method. Both treatments reproduce the interpolyad band strengths quite well, while the twodimensional dipole momentsurface is superior to the onedimensional one in modeling the intrapolyad band strength pattern, indicating the importance of the bending vibrations in dipole momentsurface and intensities calculations. The different behavior of interpolyad band strengths of compared to with an intensity anomaly occurring in the latter case, is illustrated by “dipole–weighted” overlap integrals.