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Volume 102, Issue 20, 22 May 1995

Measuring internal electric fields with atomic resolution
View Description Hide DescriptionThis paper describes a scheme for analyzing the effects of external electric field on the excitation energy of a conjugated probe molecule that is faithful to the actual microscopic situation and treats all aspects of the problem consistently. Structure is obtained from a molecular mechanics simulation, internal and local fields are calculated by classical electrostatics, and shifts in excitation energy are calculated by incorporating site energies into a simple π‐electron model. An example calculation demonstrates the ability of this procedure to determine microscopic electric fields and molecular charge distributions.

Theoretical analysis of the emission spectra of the NaCd excimer
View Description Hide DescriptionWe present simulations of bound–bound and bound–free emissions of the NaCd* excimer, along with new experimental results concerning the red band system. The simulations, based on ab initio potential energy curves, confirm that the initial states are 2 ^{2}Σ^{+} for the red emission and 2 ^{2}Π for the blue emission of NaCd*. The two main peaks in the blue band system are due to spin–orbit splitting. The band shape obtained in the simulations is extremely variable, depending on the population distribution of the vibrational states of NaCd*. The comparison of simulated and measured spectra leads us to conclude that, in the experimental conditions adopted here and in previous work, the thermal equilibration of the excimer is far from complete.

Jet‐cooled fluorescence excitation spectrum, carbonyl wagging, and ring‐puckering potential energy functions of 3‐cyclopenten‐1‐one in its S _{1}(n,π*) electronic excited state
View Description Hide DescriptionThe jet‐cooled fluorescence excitation spectrum of 3‐cyclopenten‐1‐one has been recorded in the 308–330 nm region, and the electronic origin for the S _{1}(n,π*) state of A _{2} symmetry was observed at 30 229 cm^{−1}. The observed spectrum consists of more than 80 bands involving primarily ν_{3} (carbonyl stretch), ν_{29} (carbonyl out‐of‐plane wagging), and ν_{30} (ring puckering). Bands were also assigned to combinations with seven other vibrational modes. The energies for the v=0 to 11 quantum states of ν_{29} were measured and used to determine a one‐dimensional potential energy function. This function has energy minima at wagging angles of ±24° and a barrier to inversion of 939 cm^{−1}. Four bands associated with ν_{30} were observed and were used to determine an asymmetric single‐minimum one‐dimensional ring‐puckering potential energy function for the S _{1}(n,π*) state. The ring‐puckering energy levels in the ν_{29} vibrational excited states are little changed from the v=0 state indicating that there is little interaction between the carbonyl wagging and the ring‐puckering motions.

Infrared spectroscopy, infrared photoconversion, and ultraviolet photodissociation of NO dimers in neon and nitrogen matrices
View Description Hide DescriptionThe nitric oxide dimers isolated in neon or nitrogen matrices have been irradiated in the infrared by selected lines of a cw CO laser and in the UV at 193 nm by an ArF excimer laser. IR excitation of the antisymmetric mode of the cis dimer in neon induces a conversion to a special van der Waals dimer. At T<6 K UVirradiation dissociates the dimers mainly to NO monomers and, in smaller proportion, to NO_{2} in the neon matrix or to N_{2}O in the nitrogen matrix. NO_{2} is formed exclusively from the cis dimer and N_{2}O from the trans dimer. At higher temperature in nitrogen, the oxygen atoms produced in the N_{2}O formation migrate and react with NO to form NO_{2}. The vibrational spectroscopy in nitrogen reveals several new features. The symmetrical vibrational mode of planar trans‐(NO)_{2}, normally IR inactive, becomes observable at 5.8 K owing to the matrix strain. cis‐(NO)_{2} is trapped in two sites and the energy difference between them changes abruptly around 14 K, suggesting a structural transformation in the neighborhood of the sites. Cooling at 5.8 K induces a reversible decrease of the cis dimer bands, correlated with the appearance of vdW dimer bands. In both matrices, the antisymmetric band of the cis dimer is broadened by a predissociation effect as in the gas phase.

The structure and internal dynamics of CO–CO–H_{2}O determined by microwave spectroscopy
View Description Hide DescriptionThe rotational spectra of CO–CO–H_{2}O, CO–CO–HDO, ^{13}CO–CO–H_{2}O, and ^{13}CO–^{13}CO–H_{2}O have been measured using a pulsed‐molecular‐beam Fabry–Perot Fourier‐transform microwave spectrometer. The complex exhibits internal motion involving an exchange of the CO subunits as well as an hydrogen exchange. In the normal species this is indicated in the spectrum by transition doublets separated by a few hundred kHz and an effective shift of alternating transitions which prevents a good semirigid rotor fit. The other isotopically substituted complexes have spectra in which the transitions are either singlet, doublet or quartets depending on the appropriate spin weights or because of dampening of the internal motion. All the spectra are mutually consistent with a tunneling path with four isoenergetic states. By treating the tunneling frequency of the CO interchange as a vibrational frequency, the rotational constants of two internal rotor states and a tunneling frequency could be determined. The tunneling frequency in CO–CO–H_{2}O is 372 kHz and the ground state rotational constants are A=4294.683(70) MHz, B=1685.399(35) MHz, C=1205.532(35) MHz. The tunneling frequency corresponding to the hydrogen exchange is not determined but the observed transition splittings are comparable to those found for other van der Waals complexes containing a water subunit. The dipole moments determined for CO–CO–HDO are μ_{ a }=4.790(87)×10^{−30} C m [1.436(26) D], μ_{ b }=1.79(12)×10^{−30} C m [0.533(35) D], and μ_{ c }=1.10(37)×10^{−30} C m [0.33(11) D]. The general structure of the complex is found to be cyclic. The CO–CO configuration is approximately T‐shaped with the carbon atom of one subunit directed toward the molecular axis of the other subunit. The H_{2}O subunit has a hydrogen atom directed toward the CO subunits but not in the expected linear hydrogen bonded configuration. The uncertainties given in parentheses are one standard deviation.

Calculations of the tunneling splittings in water dimer and trimer using diffusion Monte Carlo
View Description Hide DescriptionThe diffusionMonte Carlo (DMC) method is used to calculate rovibrational bound states of the water dimer and trimer. The rigid body form of DMC is employed, together with correlated sampling of energy differences between states of different symmetry. This allows calculation of the tunneling splittings in (H_{2}O)_{2} and (H_{2}O)_{3}. The results for (H_{2}O)_{2} are in quite good agreement with those obtained using a basis set method, and also agree well with experiment. In addition, we have made predictions for similar splittings in (D_{2}O)_{3} and several water dimer isotopomers. In all the calculations, we have used the potential energy surface due to Millot and Stone which is known to give quite good agreement with experiment for the tunneling splittings in (H_{2}O)_{2}.

Three dimensional quantum calculation of the visible absorption spectrum of Ar^{+} _{3}
View Description Hide DescriptionWe present a theoretical visible absorptionspectrum of Ar^{+} _{3}. It relies on DIM potential energy surfaces and transitiondipole moments and the dynamical calculations have been performed using a full quantum treatment for each degree of freedom of the molecule. We used hyperspherical coordinates in order to describe the full symmetry of the molecule and the wave packet was developed on a grid. We computed the spectrum with the RRG method, for three different excited electronic states and found a very good agreement with experimental data and previous calculations of restricted dimensionality.

Quantum tunneling in an anharmonic classical bath. Enhanced kinetic isotope effects in an Arrhenius region
View Description Hide DescriptionQuantum tunnelingreactions in a general classical bath are studied. By invoking the semiclassical approximation, a general theoretical framework for an arbitrary quantum double‐well reactive system, coupled to the anharmonic classical modes is developed in a strong tunneling regime. For illustration, a simple two‐dimensional model proton transfer system in solution at room temperature is considered. It is found that the bath anharmonicity strongly modulates the overall rate constant and kinetic isotope effect. For the positive anharmonicity, the reaction rate decreases compared to the harmonic case, while the associated kinetic isotope effect increases. By contrast, the negative anharmonicity reduces the kinetic isotope effect, while it enhances the overall rate. The temperature dependence of the rate constant and kinetic isotope effect is also analyzed. Despite tunneling (k ^{(H)}/k ^{(D)}=10–40), the Arrhenius behavior for the rate constant is found, regardless of the bath anharmonicity. This clearly indicates a strong interplay between the quantum and classical modes of the system.

State‐selected ion‐molecule reactions: Statistical calculations with constraints
View Description Hide DescriptionFor the two reactive systems, NH_{3} ^{+}(E _{int})+N H_{3}→NH_{4} ^{+}+NH_{2} and H_{2} ^{+}(E _{int})+H_{2}→H_{3} ^{+}+H, for which the relative cross sections were measured earlier in our group for E _{c.m.}≊40 meV we calculated the relative cross section as a function of internal energy using the statistical Rice–Ramsperger–Kassel–Marcus (RRKM) theory that implicitly conserves total energy and total angular momentum. We found satisfactory agreement between theory and experiment by imposing rather mild constraints upon the loose transition state configuration. These constraints involve inactive vibrations and steric hindrance. The steric hindrance imposed in case of the (NH_{3}–NH_{3})^{+} system is interpreted as being due to the anisotropic interaction of the ionic charge with the permanent electric dipole of the respective neutral collision partner in the two dissociation channels. We cannot be absolutely sure that the specific combination of modifications we propose for each of the two systems is the only one that agrees well with experiment. However, we find it striking that an agreement can be obtained by such weak and physically meaningful modifications, and we take this as a strong indication that the two studied systems do behave statistical.

Laser initiated half reaction study of H+O_{2}→OH+O
View Description Hide DescriptionThe H+O_{2}reaction system was studied under geometry limited half reaction conditions. The weakly bonded complex O_{2}–H_{2}S was formed by supersonic expansion, and reaction was initiated by 193 nm photoirradiation of the complex. Rotational, spin‐orbit, and lambda doublet state distributions of product OH were determined by a laser‐induced fluorescence(LIF) technique. The populations of the two spin‐orbit states were observed to be statistical. The population of the Π(A’) level was almost twice that of the Π(A‘) level, and the planar geometry was suggested for reaction path. These populations of the fine structures of OH were similar to those of OH formed under bimolecular reaction conditions. On the other hand, the rotational state distribution of OH from the half reaction has two components and the dominant one shows a very cold rotational distribution, in sharp contrast with that of the bimolecular reaction where rotation is highly excited. This cold rotational distribution could be partially explained by the absorption of a part of available energy by the internal motion of SH. However, the distribution with a peak at the lowest rotational level could not be explained by this effect, but ascribed to the exit interaction between SH and OH and/or the entrance channel specificity, i.e., the reaction occurs in limited impact parameters.

VB resonance theory in solution. I. Multistate formulation
View Description Hide DescriptionA theory for the description of electronic structure in solution for solution phase chemical reactions is formulated in the framework of a dielectric continuum solvent model which takes solute boundary effects into account. This latter feature represents a generalization of the Kim–Hynes theory, in which the solute boundary was treated in the dielectric image approximation. The electronic structure of the molecular solute, embedded in a cavity of the dielectric, is described by a manifold of orthogonalized diabatic—e.g., valence bond (VB)—states. The polarization of the dielectricsolvent is partitioned into an electronic (fast) and an orientational (slow) component. The formulation encompasses both nonequilibrium and equilibrium regimes of the orientational polarization with respect to the solute charge distribution. The analysis is carried out in the general case of quantized solvent electronic polarization, but with reference to two limits in terms of which the general results can be most readily comprehended: with the electronic polarization much slower than the solute electronic motions and equilibrated to a delocalized solute charge distribution—the self‐consistent limit; with the electronic polarization fast enough to equilibrate to components of the solute electronic distribution rather than to the average distribution—the Born–Oppenheimer limit. The general results depend on the relative time scales of the resonant interconversion between the VB states and the solvent electronic polarization. With the ansatz that the nonequilibrium orientational polarization is a linear combination of equilibrium terms with nonequilibrium coefficients, the solute–solvent system free energy is obtained together with a nonlinear Schrödinger equation for the soluteelectronic structure. A procedure is given for the natural definition of the set of solvent coordinates which describe the nonequilibrium regime necessary for the treatment of chemical reactions, and convenient matrix forms for the free energy and the Hamiltonian matrix elements are provided.

VB resonance theory in solution. II. I_{2} ^{−}■I+I^{−} in acetonitrile
View Description Hide DescriptionThe electronic structure in solution theory developed in the preceding article is applied to the molecular ion I_{2} ^{−}■I+I^{−}reaction system in the dipolar, aprotic solvent acetonitrile, which illustrates in detail the implementation of the general theory. A two‐dimensional, nonequilibrium free energy surface in the nuclear separation and a difference solvent coordinate is constructed via solution of a nonequilibrium solvation, nonlinear Schrödinger equation. The reduction to a single important solvent coordinate—from a manifold of three solvent coordinates—is motivated by an examination of the equilibrium solvation path and an analysis of the harmonic nonequilibrium fluctuations around this path. The evolving solute electronic structure over the basis of two orthogonal valence bond diabatic states—approximately corresponding to ^{−}II and II^{−}—is discussed. Comparisons with the limiting Born–Oppenheimer and self‐consistent approximations for the solvent electronic polarization are made, with the former proving to be more accurate, and the latter giving a qualitatively inaccurate picture of the electronic structure near the equilibrium geometry. The validity of the dielectric image approximation is also examined. The polarization force associated with the charge shift in the reaction system and important for the system vibrational relaxation is also calculated.

The mechanism of the unimolecular dissociation of trichloroethylene CHCl=CCl_{2} in the ground electronic state
View Description Hide DescriptionThe unimolecular dissociation of trichloroethylene in its electronic ground state has been investigated using an infrared multiphotondissociation combined with photofragmentation translational spectroscopy to measure product translational energies. The main reaction channel was found to be HCl elimination on the basis of observed product time‐of‐flight (TOF) spectra. A center‐of‐mass translational energy distribution for this channel provides direct evidence for competition between two channels, three‐ and four‐centered HCl eliminations. Cl elimination was found to be a minor but significant channel from observed Cl^{+} and C_{2}HCl^{+}TOF spectra. The branching ratios were determined as 0.28, 0.55, and 0.17 for the three‐ and four‐centered HCl eliminations and the Cl elimination, respectively. The three‐centered channel exhibits a ‘‘statistical’’ translational energy distribution which is typical for a reaction with no potential energy barrier in the reverse reaction, that is to say, no exit barrier reaction. In contrast, the four‐centered channel exhibits a ‘‘nonstatistical’’ translational energy distribution having a peak at around 2 kcal/mol in energy, indicating that a significant exit barrier exists in the channel. The fraction of potential energy converted to translational energy was estimated to be around 10%. Ab initio calculations at the QCISD(T)/6‐311+G**//MP2(FC)/6‐31G* level were employed to confirm the reaction mechanism. The agreement in the energetics is quite good.

Molecular dynamics studies of the thermal decomposition of 2,3‐diazabicyclo(2.2.1)hept‐2‐ene
View Description Hide DescriptionThe reactiondynamics of the thermal gas‐phase decomposition of 2,3‐diazabicyclo (2.2.1)hept‐2‐ene‐exo, exo‐5,6‐d _{2} 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 dissociationdynamics of 2,3‐diazabicyclo(2.2.1)hept‐2‐ene‐exo, exo‐5,6‐d _{2} 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 N_{2} 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 N_{2} 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.

Kinetic energy analysis of (HI)_{ n } cluster photofragments
View Description Hide DescriptionWe have employed a time‐of‐flight analysis to determine the velocity and spatial distribution of photofragments resulting from excitation of (HI)_{ n } cluster species at approximately 240 nm. The formation of clusters in the supersonic expansion broadens the I^{+} flight‐time distribution and destroys the spatialanisotropycharacteristic of HI monomerphotodissociation, indicating that these fragments experience strong solvent cage effects when exiting the cluster environment. In addition, a high velocity component with an anisotropic distribution appears and is due to the photodissociation of I_{2}, a product of cluster chemistry. Even with extensive clustering, the main features of the H^{+} flight‐time spectrum do not change and cage effects are not as pervasive as for the I atom fragments. However, there is also a broad H^{+} component peaked near zero velocity and exhibiting an isotropic spatial distribution. Inelastic H atom collisions involving excitation of internal modes in HI cage species likely play a role in dissipating the excess photolysis energy and producing the low velocity distribution. Other pathways involving the reactive nature of H+HI collisions may be more important. Wavelength resolved spectra of the I^{+} flight‐time features provide further insight into the origins of the observed behavior.

Effects of solvent polarization relaxation on nonadiabatic outersphere electron transfer reactions in ultrafast dipolar solvents
View Description Hide DescriptionSince the important work of Efrima and Bixon [J. Chem. Phys. 70, 3531 (1979)], it is believed that solventpolarization relaxation is usually too slow (compared to the rate of electron transfer) or the amplitude of energy fluctuation too large to have any noticeable effect on the dynamics of the nonadiabatic(NA)electron transferreactions. On the other hand, recent studies have demonstrated that solventpolarization relaxation in several common dipolar liquids can proceed at a rate much faster than that anticipated in the earlier studies. This calls for a re‐examination of the role of solvent dynamics on NAelectron transferreactions in these ultrafast solvents. In this paper, the results of such studies are presented for NAreactions in water and acetonitrile. It is found that because of ultrafast solvation, many NAreactions may lie in the dynamic region where the solvent effects are just beginning to be important. The present study further reveals the following new results. (i) In the case of high barrier reactions in solvents such as acetonitrile, the polarization relaxation in the reactant well can contribute significantly to the total rate of the nonadiabaticelectron transferreaction. (ii) In water, on the other hand, the reactive friction is still sufficiently high to make energydiffusion in the reactant well efficient and so, the solvent effects are predicted to be negligible. This is in accord with the earlier theoretical suggestions and is demonstrated here clearly for real systems. (iii) We find an interesting limiting situation where the long time rate can be significantly larger than the rate given by the Marcus expression.

Dynamical angular momentum models for rotational transfer in polyatomic molecules
View Description Hide DescriptionWe propose a model for collision‐induced rotational transfer (RT) in polyatomic molecules based on the angular momentum (AM) sphere, a classical representation of the dynamical motion of the rotational AM vector in the molecular frame. The model develops further that proposed by us [AlWahabi et al., J. Chem. Soc., Faraday Trans. 85, 1003 (1989)] in which RT probabilities are related to the AM gap linking initial and final N _{ k } _{ ak } _{ c } states. The AM sphere representation embodies the full internal motion of the molecule via its effect on the inertial axes and the trajectory of the individual rotational state vectors. In this representation there is no unique AM gap for a particular transition between states of nominally well‐defined N _{ kak } _{ c } and here we propose and test several models for obtaining the distance in AM space between initial and final trajectories. Models are evaluated from their ability to fit data on NH_{2}–H collisions. We find that even the simplest approximations, such as shortest distance in AM space, give good fits to data sets but the best fits are obtained when both AM trajectory and molecular geometry are averaged over.

The energy‐dependent transmission coefficient and the energy distribution of classical particles escaping from a metastable well
View Description Hide DescriptionWe investigate the distribution of energies of thermally activated particles escaping from a metastable well. This energy distribution is connected by detailed balance to the energy‐dependent transmission coefficient, the probability that a particle injected into a well will stick. Theoretical expressions for the energy‐dependent transmission coefficient show good agreement with simulation results for a one‐dimensional reaction coordinate coupled to a frictional bath. Slight deviations from theoretical predictions based on turnover theory [E. Pollak, H. Grabert, and P. Hänggi, J. Chem. Phys. 91, 4073 (1989)] are understood in light of the assumptions of turnover theory. Furthermore, the theoretical expressions for energy distributions also provide good fits for fully three‐dimensional simulations of sticking and desorption of Ar and Xe on Pt(111) [J. C. Tully, Surf. Sci. 111, 461 (1981)]. Finally, we compare the theoretical efficiencies of several reactive flux sampling schemes, including a scheme designed to be optimal.

The initial vibrational state distribution of HCN X̃ ^{1}Σ^{+}(v _{1},0,v _{3}) from the reaction CN(^{2}Σ^{+})+C_{2}H_{6}→HCN+C_{2}H_{5}
View Description Hide DescriptionThe reaction of the cyano radical (CN) with ethane was studied using time‐resolved infrared absorption spectroscopy to monitor individual rovibrational states of the HCN product. A method is described that can be used to determine the initial vibrational state distribution at pressures of several Torr. This technique was applied to the title reaction to determine that the vibrational states of HCN(v _{1},0,v _{3}), where v _{1}, v _{3}=0, 1, and 2, were not directly populated in the title reaction to any significant extent. The initial vibrational energy content of the CN radical was also varied but did not influence the initial population in the HCN vibrational levels probed in this experiment. The time dependence of HCN(v _{1},0,v _{3}) was followed and interpreted in terms of bimolecular rate constants for vibrational relaxation with ethane. The title reaction is mode specific in its energy disposal in that at least every HCN product appears to have at least one quantum of bending excitation, likely in combination with stretching vibrations.

One‐dimensional chemical master equations: Uniqueness and analytical form of certain solutions
View Description Hide DescriptionThe eikonal (WKB) approximation is applied to a stationary one‐dimensional master equation describing an arbitrary reaction mechanism. The uniqueness of a nontrivial (fluctuational) eikonal solution is proven. Consistent eikonal and exact analytical solutions are obtained for systems with an arbitrary, but unique step size of stochastic transitions. An analytical eikonal solution for the stationary probability density for systems with mixed step sizes of 1 and 2 is also obtained and found to differ significantly from the systems with a uniform step size, particularly in the case of multiple stationary states.