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Volume 103, Issue 12, 22 September 1995

A stochastic theory of inhomogeneously broadened linewidths in solids
View Description Hide DescriptionWe investigate spectral diffusion decay using a model for solids that consists of two‐level‐systems (TLSs) interacting via strain fields. For the case when the rate of TLS flips vanishes, we find algebraic decay of correlation functions of the local field. We show that properties of equilibrium fluctuations are in agreement with the hierarchical picture proposed by Basché and Moerner: TLSs far away produce fast fluctuations that are small in magnitude, and close TLSs produce large fluctuations that are less frequent.

Structure of chemically synthesized nanophase GaAs studied by nuclear magnetic resonance and x‐ray diffraction
View Description Hide DescriptionNanophase GaAs produced by organometallic synthesis was studied by ^{71}Ga, ^{69}Ga, and ^{75}As nuclear magnetic resonance(NMR) as well as x‐ray diffraction. The structure of the samples synthesized below 250 °C is predominantly amorphous. Raising the temperature of synthesis (or post‐synthesis annealing) above 280 °C improves significantly the crystallinity as evidenced by the appearance of a sharp bulklike ^{71}Ga (and ^{69}Ga) peak. In addition, a sharp peak shifted up‐field also appears. Other NMR features of this up‐field shifted peak are very similar to the bulklike peak including quadrupole interactions and spin–lattice and spin–spin relaxations. These results are consistent with the presence of stacking faults in nanocrystallineGaAs.

Ab initio model potential study of the optical absorption spectrum of Mn^{2+}‐doped CaF_{2}
View Description Hide DescriptionAn ab initio calculation of the optical absorptionspectrum of Mn^{2+}‐doped CaF_{2} is performed in which electrostatic and quantum embedding effects originated by a relaxed and polarized CaF_{2} lattice on the ligand field ground and excited states of a MnF_{8} ^{6−} cluster have been considered. The theoreticalspectrum is calculated by means of the complete active space self‐consistent‐field (CASSCF) and average coupled pair funtional (ACPF) methods, correlating up to 23 electrons. An excellent overall agreement with the experiments is found and a detailed analysis of the results is presented. The initial assignment of the ^{4} A _{1g }(^{4} G) and ^{4} E _{ g }(^{4} G) states, lately reversed, is supported. The wrong assignment of the ^{4} T _{1g }(^{4} P) state is shown to be responsible for a recently proposed change of the value of the crystal field splitting paramenter initially accepted, 10Dq=4250 cm^{−1}, which is in turn supported here. Also, new assignments for the absorptions to the ^{4} T _{1g }(^{4} F) and ^{4} T _{2g }(^{4} F) excited states are suggested.

A two‐color (1+1′)+1 multiphoton ionization study of CS_{2} in the 61 000–65 600 cm^{−1} energy region
View Description Hide DescriptionThe (1+1′)+1 resonance enhanced multiphoton ionization (REMPI) spectrum of jet‐cooled CS_{2} has been recorded in the 61 000–65 600 cm^{−1}excitation energy range. Four prominent band groups are observed that can be assigned to Δν_{2}=−1 and Δν_{2}=1 sequences of the two‐photon electronically forbidden 4p ^{1,3}Δ_{ u }←X̃ ^{1}Σ^{+} _{ g } transitions. Weak bands to higher energy appear to be associated with the 3^{1} _{0}, 2^{3} _{0} and 1^{1} _{0}2^{1} _{0} bands and corresponding sequence bands. The results show that the upper states are not 3dRydberg states as has been previously supposed, and are consistent with a recent reinvestigation of the corresponding (3+1) REMPI spectrum. Further experimental information is obtained on the anomalous vibrational band structure of transitions to the ^{3}Δ_{ u } state. The 2^{0} _{1} and 2^{1} _{2} bands of the 4p ^{1}Π_{ u }←X̃ ^{1}Σ^{+} _{ g } transition are also observed, but are much weaker, suggesting that vibronic interactions are less important in this state compared to the 4p ^{1,3}Δ_{ u } states.

van der Waals vibrations and isomers of 2,3‐dimethylnaphthalene⋅Ne: Experiment and quantum three‐dimensional calculations
View Description Hide DescriptionWe report a combined experimental and theoretical study of the van der Waals isomers and intermolecular vibrations of the 2,3‐dimethylnaphthalene⋅Ne complex in the S _{1} electronic state. The two‐color resonant two‐photon ionization spectrum exhibits eight bands within ≊40 cm^{−1} of the electronic origin. Theoretical considerations in combination with hole‐burning spectroscopic measurements show that the transition closest to the electronic origin (at 0^{0} _{0}+5 cm^{−1}) arises from an isomer which is different from that responsible for the other seven bands in the spectrum. The latter involve excitations of the intermolecular vibrations of the main isomer of 2,3‐dimethylnaphthalene⋅Ne. Accurate three‐dimensional quantum calculations of the van der Waals vibrational levels of the complex were performed using a discrete variable representation method. Combination of theory and experiment led to a complete assignment as well as to a quantitative theoretical reproduction of the experimental intermolecular vibrational level structure, and a parametrization of the intermolecular potential energy surface, modeled as sum of atom–atom Lennard‐Jones pair potentials. This potential surface exhibits a global minimum above (and below) the aromatic ring plane of 2,3‐dimethylnaphthalene and a shallower local minimum at C _{2v } geometry, on the C _{2} axis of the molecule, adjacent to the two methyl groups. The main and minor isomers identified experimentally are associated with the global and the local minimum, respectively. The quantum calculations were extended to ≊1000 van der Waals vibrational states, i.e., to energies up to 78% of D _{0}. These include levels localized either in the global or local minima, as well as highly excited vibrational states delocalized over all three potential minima, providing comprehensive insight into the quantum dynamics of the high‐lying van der Waals states of an atom–large aromatic molecule complex.

Effects of magnetic field on the 15V 31 344.9 band of CS_{2} studied by sub‐Doppler high‐resolution spectroscopy
View Description Hide DescriptionEffects of an external magnetic field on the excitation spectrum of the 15V 31 344.9 band of the CS_{2} molecule are measured with sub‐Doppler resolution. New lines are observed to appear near the R(2) and P(4) lines when a magnetic field is applied. These lines are observed to be composed of five components both for the π pump and for the σ pump. From a theoretical analysis, we identify the new lines as transitions to the ^{3} A _{2}(A _{1}−B _{1})(v ^{−};12M) levels, which become allowed by Zeemaninteraction with the V ^{1} B _{2}(v′;03M) level that is mixed with the ^{3} A _{2}(B _{2})(v;03M) level by spin–orbit interaction. Variations of energy shifts and intensities with the magnetic field strength are explained quantitatively by this analysis. M‐dependent perturbation and the quenching of fluorescence are observed. The reason why large Zeeman splittings are observed at many lines in the V system of CS_{2} can be attributed to the spin–orbit interaction between the V ^{1} B _{2}(v′;KJM) level and the ^{3} A _{2}(B _{2})(v;KJM) level combined with the rotational and/or the Zeemaninteractions between ^{3} A _{2}(B _{2})(v;KJM) level and either ^{3} A _{2}(A _{1}+B _{1})(v ^{0};K±1JM) or ^{3} A _{2}(A _{1}−B _{1})(v ^{±}; K±1J±1M) levels which are accidentally close in energy.

Photodissociation of HNO_{3} at 193 nm: Near‐infrared emission of NO detected by time‐resolved Fourier transform spectroscopy
View Description Hide DescriptionRotationally resolved emission of NO, produced from photolysis of HNO_{3} at 193 nm, in the near infrared region (8900–9300 cm^{−1}) was recorded with a step‐scan Fourier‐transform interferometer at a resolution of 0.1 cm^{−1}. The emission is assigned as NO D ^{2}Σ^{+}−A ^{2}Σ^{+} (v′,v″)=(0,0) band with rotational states N′=17–42. Emission from selective rotational states of NO D ^{2}Σ^{+} was observed when HNO_{3} was photolyzed with an ArF excimer laser having a narrow bandwidth ≊0.01 nm. The experimental results indicate that the D ^{2}Σ^{+} state of NO is formed via absorption of another 193 nm photon by NO (v″=1) in the ground electronic state. The measured distribution of intensity implies that NO is produced highly rotationally excited; the most likely mechanism for formation of NO is from the unstable NO_{2} fragment undergoing secondary dissociation.

Subpicosecond transient infrared spectroscopy of water: A theoretical description
View Description Hide DescriptionThe pump–probe response of water in infrared is examined theoretically at time scales of the order of 100 fs; these times scales are characteristic of spectraldiffusion. The theory is a statistical theory using correlation function description of the nonlinear optical processes involved. An analytical expression for the transient infrared signal is presented, and the corresponding time‐ and frequency‐resolved spectra are discussed. Real time shifts of spectral bands, preceded by a redistribution of their intensities, are predicted. Physical interpretation of these findings is proposed, corroborated by the help of simple models. The intrinsic interest of this time domain is emphasized.

Vibronic coupling and energy transfer in bichromophoric molecules: The effect of symmetry
View Description Hide DescriptionThe fluorescence spectra of a series of bichromophoric molecules consisting of covalently linked fluorene units were investigated in a supersonic jet. In three of the systems (spirobifluorene, d _{8} h _{8}‐spirobifluorene and 1‐methyl spirobifluorene) no electronic coupling and no corresponding exciton splitting were detected in the zero‐point level of the S _{1} state. Only 9,9′‐bifluorene exhibited an exciton splitting in the v=0 state. The lack of coupling was attributed to symmetry; in the spirobifluorenes the planes of the fluorene moieties and the S _{1}←S _{0}transition moments are perpendicular. When low vibrational levels were excited, state mixing, and energy transfer between the chromophores was observed. This behavior is characteristic of the ‘‘small molecule’’ regime of radiationless transition theory. When higher vibrational levels were excited, the systems exhibited typical ‘‘large molecule’’ behavior. In this limit, both electronic energy transfer, as well as intramolecular vibrational relaxation contribute to the decay of the initially excited state. Intramolecular dispersive interactions were also investigated by comparing the bifluorenes with a series of reference compounds.

On the low‐lying Rydberg states of azabenzenes
View Description Hide DescriptionMass resolved excitation spectra of supersonic expansion cooled mono‐ and diazabenzenes are reported for the low lying Rydberg states. Transitions are located for pyridine, pyrazine, and pyridazine, but not pyrimidine. The Rydberg state lifetimes of these molecules are estimated, based on a Lorentzian line shape analysis, to be ca. 500 fs. Ab initio calculations for pyrazine at the complete active space self‐consistent‐field (CASSCF) and CASSCF many‐body second‐order perturbation theory (CASSCF/MBPT2) levels show that extensive configuration interaction and dynamic electron correlation are necessary to account for the excited states of these systems.

The quasi‐minimal residual algorithm applied to complex symmetric linear systems in quantum reactive scattering
View Description Hide DescriptionThe solution of systems of linear equationsA x = b with complex symmetric coefficient matrix A of size N, typically appearing in quantum‐reactive scattering problems, is discussed. The quasiminimal residual (QMR) method is introduced to solve the complex symmetric linear system and is compared to the generalized minimal residual (GMRES) method. The methods are applied to two different chemical problems: the initial state‐selected reaction probability for the H_{2}+OH→H +H_{2}O reaction, and the cumulative reaction probability for the isomerization of ketene, both with N≳10^{4}. It is shown that the QMR method behaves more favorably, i.e., converges faster, than the GMRES for large N, especially when high accuracy is needed.

Critical scaling behavior in the activated barrier crossing problem. II. Power‐law potential
View Description Hide DescriptionUsing the Pollak–Grabert–Hänggi (PGH) weak‐coupling approximation, the activated barrier crossing (ABC) problem is studied with a general memory friction kernel and for a general power‐law potential added to a parabolic barrier. We focus on the recently discovered critical behavior of the rate for large memory frictioncorrelation times. All the relevant critical exponents in different regimes of the strength of the friction are determined, and explicit expressions for the scaling function are obtained. We verify that the universality of exponents and amplitudes is applicable for this model within the PGH approximation. The results are compared with the results for canonical variational transition state theory (CVTST) recently obtained by us.

Characterization of the minimum energy path for the reaction of singlet methylene with N_{2}: The role of singlet methylene in prompt NO
View Description Hide DescriptionWe report calculations of the minimum energy pathways connecting ^{1}CH_{2}+N_{2} to diazomethane and diazirine, for the rearrangement of diazirine to diazomethane, for the dissociation of diazirine to HCN_{2}+H, and of diazomethane to CH_{2}N+N. The calculations use complete active space self‐consistent field (CASSCF) derivative methods to characterize the stationary points and internally contracted configuration interaction (ICCI) to determine the energetics. The calculations suggest a potential new source of prompt NO from the reaction of ^{1}CH_{2} with N_{2} to give diazirine, and subsequent reaction of diazirine with hydrogen abstracters to form doublet HCN_{2}, which leads to HCN+N(^{4}S) on the previously studied CH+N_{2} surface. The calculations also predict accurate 0 K heats of formation of 77.7 kcal/mol and 68.0 kcal/mol for diazirine and diazomethane, respectively.

Bridge‐assisted electron transfer driven by dichotomically fluctuating tunneling coupling
View Description Hide DescriptionThe influence of dichotomically fluctuating tunneling coupling on long‐range electron transfer is studied theoretically. Within an approach similar to the noninteracting blip approximation known from the spin‐boson model a set of coupled integrodifferential kinetic equations is derived. These equations describe the time development of the electronic populations difference between the donor and acceptor states averaged with respect to the stochastic process and the quantum fluctuations of the bath. Furthermore, they contain the correlator between the level population difference and the fluctuating tunneling matrix element. A detailed analysis is carried out for the case of a strong coupling of the transferred electron to a single soft reaction coordinate. Within a Markovian approximation and an adiabatic removing of the correlator, the balance type kinetic equations can be derived which contain effective transfer rates. These rates depend strongly on the correlation time of fluctuations and can exhibit a resonancelike behavior.

Orbital alignment during cage‐exit of open‐shell photofragments: F in solid Ar and Kr
View Description Hide DescriptionThe statistical theory for sudden cage‐exit [J. Zoval and V. A. Apkarian, J. Phys. Chem. 98, 7945 (1994)] is extended to orbitally degenerate photofragments, specifically treating the case of F atoms in solid Ar and Kr. It is shown that the experimental energy‐dependent quantum yields of photodissociation of F_{2} are only compatible with the p hole on the F atom being completely aligned parallel to the cage wall during the sudden exit. Although relative quantum yields and energy thresholds are well predicted, the calculated absolute quantum yields are a factor of ∼2 smaller than the experimental values.

Vibrational energy transfer in shock‐heated norbornene
View Description Hide DescriptionRecently, Kiefer et al. [J. H. Kiefer, S. S. Kumaran, and S. Sundaram, J. Chem. Phys. 99, 3531 (1993)] studied shock‐heated norbornene (NB) in krypton bath gas using the laser‐schlieren technique and observed vibrational relaxation, unimolecular dissociation (to 1,3‐cyclopentadiene and ethylene), and dissociation incubation times. Other workers have obtained an extensive body of high‐pressure limit unimolecular reaction rate data at lower temperatures using conventional static and flow reactors. In the present work, we have developed a vibrational energy transfer‐unimolecular reactionmodel based on steady‐state RRKM calculations and time‐dependent master equation calculations to satisfactorily describe all of the NB data (incubation times, vibrational relaxation times, and unimolecular rate coefficients). The results cover the temperature range from ∼300 to 1500 K and the excitation energy range from ∼1 000 to 18 000 cm^{−1}. Three different models (based on the exponential step‐size distribution) for the average downward energy transferred per collision, 〈ΔE〉_{down} were investigated. The experimental data are too limited to enable the identification of a preferred model and it was not possible to determine whether the average 〈ΔE〉_{down} is temperature dependent. However, all three 〈ΔE〉_{down}models depend linearly on vibrational energy and it is concluded that standard unimolecular reaction rate codes must be revised to include energy‐dependent microcanonical energy transfer parameters. The choice of energy transfermodel affects the deduced reaction critical energy by more than 2 kcal mol^{−1}, however, which shows the importance of energy transfer in determining thermochemistry from unimolecular reaction fall‐off data. It is shown that a single set of Arrhenius parameters gives a good fit of all the low temperature data and the shock‐tube data extrapolated to the high pressure limit, obviating the need to invoke a change in reaction mechanism from concerted to diradical for high temperature conditions. Some possible future experiments are suggested.

Effects of solvation on chemical bonding: An electron‐flow analysis
View Description Hide DescriptionEffects of nonspecific solvation on chemical bonding, described with a simple self‐consistent reaction field model, are rigorously analyzed in terms of electron flow and electronegativity equalization between two molecular fragments A and B. In most (but not all) systems AB, the energy‐lowering rise in the dipole moment that accompanies solvation is the result of an enhanced charge transfer between A and B, the enhancement stemming from both the increased electronegativity difference Δχ_{ AB } and the decreased bondhardness κ_{ AB }. In systems, such as H⋅Cl, H⋅CN, and CH_{3}⋅CN, that ensue from interactions between charged closed‐shell fragments (H^{+}+Cl^{−}, H^{+}+CN^{−}, CH^{+} _{3}+CN^{−}, etc.) the energy‐stabilizing effect of solvation is a trade‐off between the energy lowering due to the enhanced charge‐transfer component of bonding and destabilization due to diminished covalent bonding. On the other hand, interactions between electrically neutral fragments (NH_{3}+SO_{3}, etc.) produce systems, such as the zwitterion of sulfamic acid (^{+}H_{3}N⋅SO^{−} _{3}), in which charge‐transfer and covalent components of bonding are strengthened in tandem by solvation. The aforementioned phenomena account for the experimentally observed solvation‐induced changes in the A–Bbonds, namely their lengthening (or even a complete dissociation) in the former systems and shortening in the latter ones.

Characterization of the minimum energy paths and energetics for the reaction of vinylidene with acetylene
View Description Hide DescriptionThe reaction of vinylidene (CH_{2}C) with acetylene may be an initiating reaction in soot formation. We report minimum energy paths and accurate energetics for a pathway leading to vinylacetylene and for a number of isomers of C_{4}H_{4}. The calculations use complete active space self‐consistent field (CASSCF) derivative methods to characterize the stationary points and internally contacted configuration interaction (ICCI) and/or coupled cluster singles and doubles with a perturbational estimate of triple excitations [CCSD(T)] to determine the energetics. We find an entrance channel barrier of about 5 kcal/mol for the addition of vinylidene to acetylene, but no barriers above reactants for the reaction pathway leading to vinylacetylene.

Theoretical investigation of the Kerr effect for CH_{4}
View Description Hide DescriptionThe vibrational contributions to the Kerr effect and to electric‐field‐induced second‐harmonic generation (ESHG) are calculated for methane for a number of optical frequencies. The latter results, together with the experimental ESHG values of the total mean second hyperpolarizability, allow for the determination of the ω^{2} _{ L }‐dispersion curve for the mean electronic hyperpolarizability. Since this curve is identical, to fourth order, for both processes, we are able to combine it with the calculated Kerr vibrational hyperpolarizabilities and predict the totalKerr hyperpolarizabilities for CH_{4} for several laser frequencies.

Novel adiabatic invariant for the three‐body Coulomb problem
View Description Hide DescriptionThe two‐(fixed) center Coulomb problem possesses in nonrelativistic mechanics, besides the ‘‘classical’’ constants of motion, an additional constant of motion associated with dynamical symmetry and separability of the problem. When the motion of the nuclei is taken into account the constant of motion is destroyed but reappears as an adiabatic invariant. We have identified this novel adiabatic invariant for the unrestricted three‐body problem in the limit of two heavy particles and one light particle. Unlike all other known adiabatic invariants, it is globally conserved to order δ=m/M in the light‐ to heavy‐mass ratio. The significance of this invariant for the semiclassical description of the chemical bond and for diatomic molecules beyond the Born–Oppenheimer approximation is discussed.