ALBERT

Notes: The diffusion of hydrogen atoms on a reconstructed Si(111)-(7×7) surface has been investigated using variational phase-space theory methods. The dimer–adatom-stacking (DAS) fault model of the reconstructed Si(111)-(7×7) surface proposed by Takayanagi et al. is employed to describe a four-layer lattice structure containing 292 atoms. The lattice potential is that developed by Bolding and Andersen; the gas–lattice interaction potential is described by a sum of Morse functions and bending terms between the hydrogen adatom and the Si atoms in the first and second layers. Canonical Markov walks with importance sampling are used to evaluate the flux across a set of dividing surfaces separating different adsorption sites. The minimum jump frequencies are then used as input to a set of coupled phenomenological kinetics equations that describe the diffusion rates of adatoms between adjacent adsorption sites. The diffusion coefficients D at different temperatures are computed from the slope of plots of the time variation of the root-mean-square displacements obtained from the solution of the rate equations. The results at 300, 500, and 800 K yield D=0.023 exp(−1.54 eV/kT) cm2/s. The calculated activation energy of 1.54 eV is in excellent agreement with the experimental results obtained by Reider et al. using an optical second-harmonic diffraction technique. The coordinates corresponding to the minimum energy diffusion path suggest that hydrogen-atom diffusion between atop sites occurs along paths that involve lattice penetration. Calculated upper limits for the tunneling rates at 300, 500, and 800 K show that tunneling processes make only a small contribution to the total diffusion rate.

Notes: The deazetization reaction of 2,3-diazabicyclo(2.2.1)hept-2-ene-exo, exo-5,6-d2 is investigated using Monte Carlo classical variational transition-state theory, implemented by the efficient microcanonical sampling procedure. Comparison is made with the results of trajectory calculations performed on the same global potential-energy surface. The microcanonical reaction rates have been determined for both reaction channels, i.e., the stepwise and concerted cleavage of the two C–N bonds of the reactant. The results demonstrate that the thermal decomposition of 2,3-diazabicyclo (2.2.1)hept-2-ene-exo,exo-5,6-d2 is well described by statistical theories that assume equal weighting for all energetically accessible phase-space points. It is found that the rate coefficients of the statistical calculations are close upper bounds of the rates determined in trajectory calculations. Previously reported classical trajectory simulations have shown that the distribution of internal energy in the reactant configuration, at the transition state and beyond is very nearly microcanonical for the range of excitation energies analyzed (60–175 kcal/mol). Under such conditions, the agreement obtained between the present statistically computed rate coefficients and those extracted from the trajectory results is not surprising. It is suggested that nonstatistical post-transition-state events account for the nonunity ratio of the exo/endo reaction products observed experimentally. These events are not considered in the present statistical theories of the reaction rates. © 1995 American Institute of Physics.

Notes: A semiempirical potential-energy surface for bicyclo(2.1.0) pentane which includes bond stretching, bending, and torsional terms is reported. The bond dissociation energies have been estimated using the available thermochemical data and results of ab initio molecular orbital calculations performed at the fourth order Møller–Plesset (MP4) perturbation theory level using a 6-31G** basis set. The predicted equilibrium geometry of bicyclo(2.1.0) pentane and of the 1,3-cyclopentanediyl radical, the barrier for the ring inversion, and the fundamental frequencies of bicyclo(2.1.0) pentane are in fair-to-good agreement with the measured and ab initio calculated values. Using a projection method of the instantaneous Cartesian velocities onto the normal mode vectors and classical trajectory calculations, the skeletal inversion and the intramolecular energy flow in bicyclo(2.1.0) pentane are studied for different types of excitation. For random energization of the vibrational modes, the results of trajectory calculations agree with the predictions of statistical unimolecular theory. The same statistical behavior is supported by the results of power spectra calculated at different energization levels. The significant broadening and overlapping of the spectral bands, together with the disappearance of characteristic spectral features in the power spectra of the flap angle, indicate high intramolecular vibrational redistribution rates and global statistical behavior. The total intramolecular vibrational relaxation rates for the energy flow from the flap mode have been extracted from the time dependence of the average total normal-mode energy in this mode. For initial excitation of the flap mode in the range 30–60 kcal/mol, the calculated total intramolecular vibrational relaxation rates are found to be significantly larger than the microcanonical ring inversion rates. This result further supports the statistical character of the ring inversion in bicyclo(2.1.0) pentane.

Notes: The power spectrum line shapes for oscillators undergoing a continuous modulation of the vibrational frequency are investigated. It is shown that the single, sharp line normally characteristic of such systems broadens and exhibits a wealth of fine structure components. The characteristic fine structure pattern is one of decreasing amplitude and spacing. This continuous frequency modulation (CFM) effect has been examined for a series of model oscillators that includes harmonic systems with linear and exponential variation of the frequency without amplitude damping, a harmonic system with exponential damping of both the resonant frequency and the amplitude, and a Morse oscillator whose kinetic energy is being exponentially damped. An analytic expression for the power spectrum of a harmonic oscillator whose frequency is varying linearly with time is derived. This result demonstrates that the position of the fine structure extrema depends linearly upon the initial oscillator frequency and the square root of the absolute value of the modulation rate. The peak-to-peak spacing is shown to be proportional to the square root of the absolute value of the modulation rate. It is suggested that the CFM effect is the fundamental explanation of many previous empirical observations concerning power spectra. The CFM effect for a harmonic system with an exponentially modulated frequency is very similar to that observed for linear modulation. When amplitude depression is included, there is a significant intensity decrease of many of the spectral lines. Investigation of a Morse oscillator shows that energy transfer in an anharmonic system produces a CFM effect. By assuming that the analytic result for a harmonic oscillator with a linear modulation is transferable to the anharmonic case, an expression is obtained that relates the peak-to-peak fine structure spacing to the Morse potential parameters, the initial oscillator energy and the IVR rate coefficient. An experimental example of a CFM effect is presented by taking an NMR spectrum of H2O and HCCl3 in DCCl3 while the main B0 field is varying with time. The CFM effect is used to extract energy transfer rate coefficients for a diatomic molecule isolated in an argon matrix at 12 K and for total IVR rate coefficients for relaxation of the N=O and O–H local modes in cis-HONO. It is also shown that instantaneous energy transfer rates in small molecules can be determined by using local frequency analysis to compute the temporal variation of the CFM band spacings. It is concluded that line shape analysis can be effectively used as a probe of energy transfer rates. © 1996 American Institute of Physics.

Notes: We have developed a semiclassical method, based on the models proposed by Miller and co-workers, for calculating tunneling effects in asymmetric double-well systems. The procedure can be easily implemented within standard classical trajectory simulations and thus allows for explicit treatment of the full-dimensional dynamics. We have applied the method to HSiOH cis–trans isomerization. © 1996 American Institute of Physics.

Notes: The reaction dynamics of the thermal gas-phase decomposition of 2,3-diazabicyclo (2.2.1)hept-2-ene-exo, exo-5,6-d2 have been investigated using classical trajectory methods on a semiempirical potential-energy surface. The global potential is written as a superposition of different reaction channel potentials containing bond stretching, bending and torsional terms, connected by parametrized switching functions. Reaction channels for stepwise and concerted cleavage of the two C–N bonds of the reactant have both been considered in construction of the potential. The geometries of 2,3-diazabicyclo(2.2.1)hept-2-ene, the diazenyl biradical and of the transition state corresponding to breaking of the remaining C–N bond of diazenyl biradical have been determined at the second order Möller–Plesset perturbation theory (MP2/6-31G*) and at Hartree–Fock (HF/6-31G*) levels, respectively. The bond dissociation energies have been estimated using the available thermochemical data and previously reported results for bicyclo(2.1.0)pentane [J. Chem. Phys. 101, 3729 (1994)]. The equilibrium geometries predicted by the semiempirical potential for reactants and products, the barrier height for thermal nitrogen extrusion from 2,3-diazabicyclo(2.2.1)hept-2-ene and the fundamental vibrational frequencies are in good to excellent agreement with the measured or ab initio calculated values. Using a projection method of the instantaneous Cartesian velocities onto the normal mode vectors and classical trajectory calculations, the dissociation dynamics of 2,3-diazabicyclo(2.2.1)hept-2-ene-exo, exo-5,6-d2 are investigated at several excitation energies in the range 60–175 kcal/mol.The results show the following: (1) The thermal reaction takes place with a preference for inversion of configuration in the reaction products, the exo-labeled bicyclo(2.1.0) pentane being the major product. The exo/endo ratio of bicyclo(2.1.0) pentane isomers is found to vary between 1.8–2.2 for the energy range considered. (2) For random energization of the vibrational modes, the energy dependence of the rate coefficients can be described by a RRK expression. (3) The significant broadening and overlapping of the power spectral bands, together with the disappearance of characteristic features in the power spectra of the internal coordinates calculated at different energies, indicate high intramolecular vibrational redistribution rates and global statistical behavior. (4) The energy partitioning among products shows that the internal energy is preferentially distributed into the vibrational degrees of freedom in BCP, while N2 is formed with small amounts of rotational and vibrational energies. Overall, the distribution of energy among the product degrees of freedom follows statistical predictions in the internal energy range investigated. (5) Stepwise dissociation of the C–N bonds is the predominant mechanism which characterizes the N2 elimination from the parent molecule. (6) Although statistical theories of reaction rates, such as Rice–Ramsperger–Kassel–Marcus (RRKM) theory, are unable to predict the product exo/endo ratio, this is not a result of the breakdown of the statistical assumption inherent in these theories, but rather to the fact that statistical theory does not address mechanistic questions related to post transition-state events. Although the results show that there is a near microcanonical distribution of energy in the 1,3-cyclopentanediyl radical, the system does not have sufficient time to explore all of the energetically accessible configuration space prior to the closure of the 1–3 bridgehead bond. The result is a nonstatistical exo/endo product ratio that deviates from the statistically expected result of unity. © 1995 American Institute of Physics.