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Volume 104, Issue 19, 15 May 1996

Dynamical structure of water in dioxane aqueous solution by low‐frequency Raman scattering
View Description Hide DescriptionThe low‐frequency Raman spectra of dioxane aqueous solutions have been analyzed from a dynamical aspect of water structure. The reduced Raman spectra χ″(ν̄) of the dioxane aqueous solutions are well explained by a superposition of three characteristic modes of water and one Gaussian mode (∼60 cm^{−1}) of dioxane. The concentration dependence of χ″(ν̄) spectra shows that the 190 cm^{−1} mode of water disappears below about 0.8 molar fraction of water. This molar fraction corresponds to the ratio of four water molecules to one dioxane molecule. This means that the tetrahedral‐like structure of water which is formed by five water molecules is almost destroyed below about 0.8 molar fraction. Thus the basic idea of the five water molecules model of liquid water has been confirmed from Raman spectroscopic point of view.

The influence of solvent dynamics on the lifetime of solute–solvent hydrogen bonds
View Description Hide DescriptionThe lifetimes of the hydrogen bonds formed between resorufin and the solventsethanol, ethylene glycol, and 1,3‐butanediol are measured as a function of temperature. The results show that the hydrogen‐bond breaking reaction is strongly influenced by the dynamics of the solvent, in violation of traditional transition‐state theory. The relevant solvent dynamics are not well described by the viscosity of the solvent, but do correlate with the dielectric relaxation time. We propose a model in which the hydrogen bond initially breaks to form a poorly solvated, ‘‘dangling’’ hydrogen bond, which has a high probability of geminate recombination. The product is not stabilized until the solvent hydrogen‐bond structure can reorganize to incorporate the ‘‘dangling’’ bond. The same reorganization determines the dielectric relaxation time.

Vibration–torsion–rotation dipole moment operator for a molecule with an internal rotor
View Description Hide DescriptionThe sequential contact transformation technique is applied to the vibrational–torsional–rotational dipole moment operator for a molecule containing a threefold symmetric internal rotor in order to be consistent with the transformed Hamiltonian to be used in the analysis of the spectra of the molecule. The detailed discussion is presented of various types of dipole moments and corresponding vibration–torsion–rotation transitions. The transition matrix elements of the transformed dipole moment operator are given for CH_{3}OH‐like molecule.

Observation of the ν_{1} OH(OD) stretch of HOI and DOI by Fourier transform infrared emission spectroscopy
View Description Hide DescriptionThe spectra of vibrationally hot HOI formed in the reaction of alkyl iodides with oxygen atoms are observed by Fourier transform infrared emission spectroscopy. The v=1–3 levels of the OH stretch are observed via the Δv=−1 and Δv=−2 sequence bands. The spectrum of DOI is observed by using 2,2,2‐d _{3}‐iodoethane as the precursor in the oxygen atom reaction. The v=1–4 levels of the OD stretch are observed in the Δv=−1 sequence band, and the v=1–5 levels of the OD stretch are observed in Δv=−2. Medium resolution spectra (0.031 cm^{−1} apodized) are recorded and rotationally analyzed for the ν_{1} fundamental and 2ν_{1}−ν_{1} hot band of HOI. An estimate of the HOI ground state structure is made by constraining the OH bond length to its value for HOCl and HOBr and calculating the HOI bond angle and the OI bond length by least squares fit to the ground state rotational constants.

The high resolution absorption spectrum of jet‐cooled CS_{2} between 50 500 and 65 500 cm^{−1}
View Description Hide DescriptionThe absorptionspectrum of jet‐cooled CS_{2} has been photographed between 50 500 and 65 500 cm^{−1} at a resolution limit of 0.008 Å. Ab initio calculations are carried out to estimate the energy of the lower Rydberg states of ionic cores ...2π^{3} _{ g }, ...2π^{3} _{ u }, and ...5σ_{ u }, as well as those belonging to the doubly excited configuration ...2π^{2} _{ g }3π^{2} _{ u }. Assigned electronic states include the ...2π^{3} _{ g }4s ^{1}Π_{ g } (with vibronic bands 2^{0} _{1} and 2^{ n } _{0}, n=1,3,5,7, observed thanks to a concurrent of Herzberg–Teller intensity borrowing and Renner–Teller intensity redistribution) and ...2π^{3} _{ g }4p ^{1,3}Π_{ u }, and ^{3}Σ_{ u } ^{−} (observed bands being the electronic origin, 1^{1} _{0} and 2^{2} _{0} bands). Model calculations of Renner–Teller interaction in the ^{1}Π states are performed leading to ε and ω_{2} parameter values. In the case of the 4p ^{1}Π_{ u } state, Fermi resonance between the v _{1} ^{′}=1 level and the v _{2} ^{′}=2 RT‐split levels of Π_{ u } vibronic symmetry, is also taken into account. The rotational band contours of the origin bands of the whole set of the ...2π^{3} _{ g }4pRydberg transitions excited by one or three photons are calculated using a model based on Hund’s case (e) representation. The calculated band contours, wave numbers, and relative intensities are in excellent agreement with the observations of the present vuvabsorptionspectrum, and the multiphoton (3+1) ionizationspectrum of Baker et al. [J. Chem. Phys. 103, 2436 (1995)] provided that in the latter, the ^{1}Σ^{+} _{ u } state is reassigned as ^{3}Σ_{ u } ^{−}. Fitted values of the 4p quantum defects and of the 4pπ(^{1}Σ^{+} _{ u })/4pσ(^{1}Π_{ u }) transition moment ratio are found to be perfectly consistent with the ab initio calculation results. Possible assignments of 3d transitions in the present and previous vuvabsorption spectra as well as in recent multiphoton ((1+1′)+1) ionizationspectra of CS_{2} below 65 500 cm^{−1} are also discussed in the light of the present calculation results.

Isotope selective overtone spectroscopy of CHCl_{3} by vibrationally assisted dissociation and photofragment ionization
View Description Hide DescriptionOvertone spectroscopy in the gas phase by vibrationally assisted dissociation and photofragment ionization (OSVADPI) has been coupled with mass spectrometric detection of fragments enabling us to separate congested spectra into components arising from several naturally occurring isotopomers. The new technique of isotope selective overtone spectroscopy (ISOS) has been applied to the 4_{1} component of the CH chromophore absorption near 11 385 cm^{−1} in CHCl_{3} at room temperature and in supersonic jet expansions. These spectra allow us to assign a close local resonance with a CCl_{3} frame mode indicating vibrational energy redistribution within some ps. This is to be compared with the ultrafast (ca. 50 fs) redistribution between the CH stretching and bending modes established previously.

Millimeter‐wave spectra of CaSH and CaSD
View Description Hide DescriptionThe pure rotational spectra of CaSH and CaSD were observed using millimeter‐wave absorption spectroscopy. The gas phase free radicals were produced in a high‐temperature cell by the reaction of Ca vapor with H_{2}S or D_{2}S in the presence of an electrical discharge. The spectra were analyzed using an S‐reduced Hamiltonian. The molecular constants including the rotational constants, centrifugal distortion constants, and spin‐rotation constants were extracted from the spectra. The off‐diagonal spin‐rotation term, ‖ε_{ ab }+ε_{ ba }‖/2, is 3.38(12) MHz and 4.59(4) MHz for CaSH and CaSD, respectively. The moment of inertia data of CaSH and CaSD yielded the r _{0} structure. The three structural parameters are Ca–S=2.564(2) Å, S–H=1.357(17) Å, and ∠Ca–S–H=91.0(18)°.

Microwave spectrum of the FS_{2} radical in the ground electronic X̃ ^{2} A″ state
View Description Hide DescriptionThe FS_{2} radical has been detected in the glow discharge of the SF_{6} gas by microwave spectroscopy. Both a‐type and b‐type rotational transitions with the fine and hyperfine structure were observed in the millimeter‐wave range of 120–185 GHz. The least‐squares analysis for the 440 line frequencies led to the determination of the rotational constants, the centrifugal distortion constants, the spin‐rotation interaction constants with the centrifugal distortion corrections, and the hyperfine interaction constants. Especially, the off‐diagonal constants (ε_{ ab }+ε_{ ba })/2 and T _{ ab } were determined in good precision because some nearly degenerate energy levels were mixed strongly by the off‐diagonal spin‐rotation interaction, which separated the energy levels up to 3 GHz and even induced the forbidden transitions to be observed strongly. The spin density on the fluorine atom and the chemical bond moments were derived for FS_{2}, and the possible signs of T _{ ab } and (ε_{ ab }+ε_{ ba })/2 were discussed. The behaviors of the FS_{2} radical and other related transient species in the SF_{6}‐discharge system were compared by using the corresponding rotational transitions observed in the microwave spectra.

Vibrational energy transfer from four levels below 410 cm^{−1} in S _{1} p‐difluorobenzene. I. A strong collision partner dependence in state‐to‐state transfer by monatomics
View Description Hide DescriptionCollision‐induced vibrational energy transfer has been studied from four levels [30^{2} (E _{vib}=240 cm^{−1}), 8^{2} (E _{vib}=361 cm^{−1}), 27^{1} (E _{vib}=403 cm^{−1}) and 6^{1} (E _{vib}=410 cm^{−1})] in S _{1} p‐difluorobenzene in supersonic free jet expansions of He, Ne, Ar, and Kr at ∼30–40 K. In broad terms the trends are similar to those observed previously in studies of aromatics: the transfer is highly selective, and one quantum changes in the low frequency modes are preferred. However, a significant collision partner dependence is observed, whereby changing from He through to Kr causes a substantial increase in multiple quanta (‖Δυ‖≳1) transfer. SSH‐T calculations fail to capture this trend. The preference for ‖Δυ‖≳1 transfer appears to be enhanced as the interaction time and attractive force on the collision partner increase. Consequently, it is predicted that (i) differences in the state‐to‐state branching ratios between collision partners will increase as the temperature is lowered; (ii) for a particular collision partner there will be an increase in ‖Δυ‖≳1 transfer with decreasing temperature; and (iii) ‖Δυ‖≳1 transfers will be most important for collision partners with small velocities (i.e., large masses), large intermolecular potential well depths (ε) and size (σ). The nearly isoenergetic 27^{1} and 6^{1} levels have virtually identical state‐to‐state branching ratios for Ar and small differences are observed for He. This suggests that the branching ratios are not particularly sensitive to the initial vibrational motion. Relaxation of 6^{1} and 27^{1} is inefficient compared with relaxation from 30^{2} and 8^{2}.

The correlated product state distribution of ketene photodissociation at 308 nm
View Description Hide DescriptionThe correlated product state distribution for ketene photodissociation (CH_{2}CO→CH_{2}+CO) at 308 nm has been measured by using quantum‐state‐specific metastable time‐of‐flight (TOF) spectroscopy. This distribution is a matrix whose elements are the probability that if CO is produced in the dissociation with quantum‐state ‖n _{CO}〉, CH_{2} will be produced with quantum‐state ‖n _{CH2}〉. It was found that ketene photodissociation yields CH_{2} in three resolved states; the ^{1} A _{1}(000), and ^{1} A _{1}(010) states of CH_{2} are the major channels, while the ^{3} B _{1} state is a minor channel. In addition to this scalar distribution, the vector correlations between the recoil velocity and the angular momentum of the CO fragment (v⋅jcorrelation), expressed by the β^{0} _{0}(22) bipolar moment, have also been obtained as a function of the kinetic energy release of the photoreaction. The correlated product state distribution was found not to follow the predictions of phase space theory, suggesting that dynamic hindrances exist in the photoreaction that have not been previously observed. A phase space theory calculation with restricted impact parameter values was also performed and compared to experiment. The impact parameter restricted phase space theory more accurately reproduced all of the correlated product state information obtained in this work as well as previous uncorrelated product state distributions for CH_{2} and CO. Both the ranges and the values of the allowed impact parameters obtained from these restricted calculations increase as the rotational energy of CO increases. Also, the values of the allowed impact parameters for ^{1} A _{1}(010) CH_{2} are larger than for ^{1} A _{1}(000) CH_{2}. This strongly suggests that C–C–O bending modes are hindered at the transition state and therefore play an important role in the photodissociation.

Geometric phase effects in H+O_{2} scattering. I. Surface function solutions in the presence of a conical intersection
View Description Hide DescriptionThe general vector potential (gauge theory) approach for including geometric phaseeffects in accurate 3D quantum scattering calculations in hyperspherical coordinates is presented. A hybrid numerical technique utilizing both the DVR (discrete variable representation) and the FBR (finite basis representation) is developed. This method overcomes the singular behavior of the vector potential terms giving accurate surface function solutions to the complex Hermitian nuclear Schrödinger equation. The hybrid DVR/FBR technique is applied explicitly to HO_{2} for zero total angular momentum. The resulting complex surface functions include the geometric phaseeffects due to the C _{2v } conical intersection. The O_{2} permutation symmetry is implemented to give real double‐valued surface functions which exhibit both even and odd symmetry. The surface functioneigenvalues are compared to calculations without the geometric phase. The results indicate that geometric phaseeffects should be significant for H+O_{2}scattering even at low energies.

Geometric phase effects in H+O_{2} scattering. II. Recombination resonances and state‐to‐state transition probabilities at thermal energies
View Description Hide DescriptionThe general vector potential (gauge theory) approach for including geometric phaseeffects in accurate 3D quantum scattering calculations in hyperspherical coordinates is applied to low‐energy (thermal) H+O_{2} collisions. The hybrid DVR/FBR (discrete variable representation/finite basis representation) numerical technique is used to obtain accurate surface function solutions which include geometric phaseeffects due to the C _{2v } conical intersection in HO_{2}. The relevant potential coupling and overlap matrices are constructed and a log‐derivative matrix of solutions to the coupled‐channel radial equations is propagated and transformed to obtain the scattering matrix S. The results for zero total angular momentum (J=0) show significant shifts in the resonance energies and lifetimes. Significant changes in the state‐to‐state transition probabilities are also observed. The results indicate that geometric phaseeffects must be included for H+O_{2} scattering even at low energies.

Kinetic study of the reaction of Mn(a ^{6} S _{5/2}) with N_{2}O from 448 to 620 K
View Description Hide DescriptionThe gas phase reactivity of Mn(a ^{6} S _{5/2}) with N_{2}O in the temperature range 448–620 K is reported. Manganese atoms were produced by the photodissociation of 2‐methylcyclopentadienyl manganese tricarbonyl and detected by laser‐induced fluorescence. The reaction rate of the a ^{6} S _{5/2} state is very slow and temperature dependent. The rate constants are independent of total pressure indicating a bimolecular reaction. The rate constants are described in Arrhenius form by (2.05±0.45)×10^{−10} exp(−44.7±1.0 kJ/mol/RT) cm^{3} s^{−1}.

Photodissociation spectroscopy of Ca^{+}–rare gas complexes
View Description Hide DescriptionWeakly bound complexes of the form Ca^{+}–RG (RG=Ar, Kr, Xe) are prepared in a pulsed nozzle/laser vaporization cluster source and studied with mass‐selected resonance enhanced photodissociationspectroscopy. The Ca^{+} (^{2} P←^{2} S) atomic resonance line is the chromophore giving rise to the molecular spectra in these complexes. Vibrationally resolved spectra are measured for these complexes in the corresponding ^{2}Π←X ^{2}Σ^{+} molecular electronic transition. These spectra are red shifted from the atomic resonance line, indicating that each complex is more strongly bound in its excited ^{2}Π state than it is in the ground state. Vibronic progressions allow determination of the excited state vibrational constants: Ca^{+}–Ar, ω_{ e } ^{′}=165 cm^{−1}; Ca^{+}–Kr, ω_{ e } ^{′}=149 cm^{−1}; Ca^{+}–Xe, ω_{ e } ^{′}=142 cm^{−1}. Extrapolation of the excited state vibrational progressions, and combination with the known atomic asymptotes and spectral shifts, leads to determination of the ground state dissociation energies Ca^{+}–Ar, D _{0} ^{″}=700±100 cm^{−1} (0.09 eV); Ca^{+}–Kr, D _{0} ^{″}=1400±150 cm^{−1} (0.17 eV); Ca^{+}–Xe, D _{0} ^{″}=2300±150 cm^{−1} (0.29 eV). The spin–orbit splitting in the ^{2}Π_{1/2,3/2} state for these complexes is larger than expected by comparison to the Ca^{+} atomic value.

Exact and semiclassical density matrix of a particle moving in a barrier potential with bound states
View Description Hide DescriptionWe present a barrier potential with bound states that is exactly solvable and determine the eigenfunctions and eigenvalues of the Hamiltonian. The equilibrium density matrix of a particle moving at temperature T in this nonlinear barrier potential field is determined. The exact density matrix is compared with the result of the path integral approach in the semiclassical approximation. For opaque barriers the simple semiclassical approximation is found to be sufficient at high temperatures while at low temperatures the fluctuation paths may have a caustic depending on temperature and endpoints. Near the caustics the divergence of the simple semiclassical approximation of the density matrix is removed by a nonlinear fluctuation potential. For opaque barriers the improved semiclassical approximation is again in agreement with the exact result. In particular, bound states and the form of resonance states are described accurately by the semiclassical approach.

A mixed momentum‐position space representation to study quantum vibrational energy transfer
View Description Hide DescriptionIn this paper we describe a new technique that enables us to study vibrational energy transfer in linear hydrocarbon chains significantly more efficiently than by earlier approaches. The principal feature of our method is that the conjugate momentum operators that appear in the coupling terms in the Hamiltonian for the system are projected in the complete set of momentum states of the bonds. This allows us to express the expectation values of the time evolution operator in various energy eigenstates as one‐dimensional momentum integrals which can be performed very rapidly and stored. All survival probabilities can then be expressed in terms of these stored integrals. We have evaluated the survival probability for HC_{2} and HC_{6} for up to eight time steps. Finally, we indicate how our approach may be extended to more general coupling terms.

Resonances in the cumulative reaction probability for a model electronically nonadiabatic reaction
View Description Hide DescriptionThe cumulative reaction probability, flux–flux correlation function, and rate constant are calculated for a model, two‐state, electronically nonadiabaticreaction, given by Shin and Light [S. Shin and J. C. Light, J. Chem. Phys. 101, 2836 (1994)]. We apply straightforward generalizations of the flux matrix/absorbing boundary condition approach of Miller and co‐workers to obtain these quantities. The upper adiabatic electronic potential supports bound states, and these manifest themselves as ‘‘recrossing’’ resonances in the cumulative reaction probability, at total energies above the barrier to reaction on the lower adiabatic potential. At energies below the barrier, the cumulative reaction probability for the coupled system is shifted to higher energies relative to the one obtained for the ground state potential. This is due to the effect of an additional effective barrier caused by the nuclear kinetic operator acting on the ground state, adiabatic electronic wave function, as discussed earlier by Shin and Light. Calculations are reported for five sets of electronically nonadiabatic coupling parameters.

A three‐dimensional wave packet study of Ar⋅ ⋅ ⋅I_{2}(B )→Ar + I + I electronic predissociation
View Description Hide DescriptionA three‐dimensional wave packet study of Ar...I_{2}(B)→ Ar + I(^{2} P _{3/2})+ I(^{2} P _{3/2}) electronic predissociation, arising from the argon‐induced electrostatic coupling between the B(^{3}Π_{0+ u }) and the repulsive a(^{3}Π_{1g }) state of I_{2}, is presented. A time‐dependent golden rule approach is used. The initial wave packet corresponds to a bound vibrational wave function of the Ar...I_{2}(B) complex (with zero total angular momentum) multiplied by the electronic coupling. A 3‐D propagation in the final dissociative surface is then performed and the predissociation rates are obtained by Fourier transform of the wave packet autocorrelation function. The potential energy surfaces are described by sums of atom–atom interactions. For the B(^{3}Π_{0+ u }) state potential, empirically determined van der Waals parameters available from the literature are used. For the final dissociative a(^{3}Π_{1g }) electronic state, the van der Waals parameters are adjusted to reproduce the experimentally observed oscillations of the electronic predissociation rate as a function of the initial vibrational quantum number v ^{′} of I_{2}. It is shown that good agreement between calculated and measured values can be obtained with a van der Waals well of 100 cm^{−1} and an interstate coupling of the order of 14 cm^{−1}.

Solvent free energy curves for electron transfer reactions: A nonlinear solvent response model
View Description Hide DescriptionMarcus theory for electron transfer assumes a linear response of the solvent so that both the reactant and product free energy curves are parabolic functions of the solventpolarization, each with the same solvent force constant k characterizing the curvature. Simulation data by other workers indicate that the assumption of parabolic free energy curves is good for the Fe^{2+}–Fe^{3+} self‐exchange reaction but that the k of the reactant and product free energy curves are different for the reactionD ^{0}+A ^{0}→D ^{1−}+A ^{1+}. However, the fluctuations sampled in these simulations were not large enough to reach the activation barrier region, which was thus treated either by umbrella sampling or by parabolic extrapolation. Here, we present free energy curves calculated from a simple model of ionic solvation developed in an earlier paper by Hyun, Babu, and Ichiye, which we refer to here as the HBI model. The HBI model describes the nonlinearity of the solvent response due to the orientation of polar solvent molecules. Since it is a continuum model, it may be considered the first‐order nonlinear correction to the linear response Born model. Moreover, in the limit of zero charge or infinite radius, the Born model and the Marcus relations are recovered. Here, the full free energy curves are calculated using analytic expressions from the HBI model. The HBI reactant and product curves have different k for D ^{0}+A ^{0}→D ^{1−}+A ^{1+} as in the simulations, but examining the full curves shows they are nonparabolic due to the nonlinear response of the solvent. On the other hand, the HBI curves are close to parabolic for the Fe^{2+}–Fe^{3+}reaction, also in agreement with simulations, while those for another self‐exchange reactionD ^{0}−A ^{1+} show greater deviations from parabolic behavior than the Fe^{2+}–Fe^{3+}reaction. This indicates that transitions from neutral to charged species will have the largest deviations. Thus, the second moment of the polarization is shown to be a measure of the deviation from Marcus theory. Finally, since the HBI expressions for the free energy curves are not simple, the HBI curves are compared with various approximate parabolic descriptions of the curves, including Marcus parabolas.

Quantum calculations for rotational energy transfer in nitrogen molecule collisions
View Description Hide DescriptionRotational energy transfer in collisions of nitrogen molecules has been studied theoretically, using the N_{2}–N_{2} rigid‐rotor potential of van der Avoird et al. [J. Chem. Phys. 84, 1629 (1986)]. For benchmarking purposes, converged close coupling (CC) calculations have been carried out to a total energy of about 200 cm^{−1}. Coupled states (CS) approximation calculations have been carried out to a total energy of 680 cm^{−1}, and infinite order sudden (IOS) approximation calculations have also been carried out. The CC and CS cross sections have been obtained both with and without identical molecule exchange symmetry, whereas exchange was neglected in the IOS calculations. The CS results track the CC cross sections rather well: between 113–219 cm^{−1} the average deviation is 14%, with accuracy improving at higher energy. Comparison between the CS and IOS cross sections at the high energy end of the CS calculations, 500–680 cm^{−1}, shows that IOS is sensitive to the amount of inelasticity and the results for large ΔJ transitions are subject to larger errors. State‐to‐state cross sections with even and odd exchange symmetry agree to better than 2% and are well represented as a sum of direct and exchange cross sections for distinguishable molecules, an indication of the applicability of a classical treatment for this system. This result, however, does not apply to partial cross sections for given total J, but arises from a near cancellation of the interference terms between even and odd exchange symmetries on summing over partial waves. In order to compare with experimental data for rotational excitation rates of N_{2} in the n=1 excited vibrational level colliding with ground vibrational level (n=0) bath N_{2} molecules, it is assumed that exchange scattering between molecules in different vibrational levels is negligible and direct scattering is independent of n so that distinguishable molecule rigid rotor rates may be used. With these assumptions good agreement is obtained. Although the IOS approximation itself is found to provide only moderately accurate values for rate constants, IOS/ECS scaling methods, especially if based on fundamental rates obtained from coupled channel results, are found to provide generally good accuracy.