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Volume 99, Issue 10, 15 November 1993

Fast responses from ‘‘slowly relaxing’’ liquids: A comparative study of the femtosecond dynamics of triacetin, ethylene glycol, and water
View Description Hide DescriptionWe have measured the ultrafast solvent relaxation of liquid ethylene glycol, triacetin, and water by means of femtosecondpolarizationspectroscopy, using optical‐heterodyne‐detected Raman‐induced Kerr‐effect spectroscopy. In the viscous liquids triacetin and ethylene glycol, femtosecond relaxation processes were resolved. Not surprisingly, the femtosecond nonlinear optical response of ethylene glycol is quite similar to that of water. Using the theory of Maroncelli, Kumar, and Papazyan, we transform the pure‐nuclear solvent response into a dipolar‐solvation correlation function for comparison with ultrafast electron‐transfer reaction rates.

Phase transitions and chemical transformations of benzene up to 550 °C and 30 GPa
View Description Hide DescriptionThe phase diagram of benzene has been investigated up to 550 °C and 30 GPa in a diamond anvil cell by Raman scattering. A new triple point at 400 °C and 5 GPa and a new phase of solid benzene, called phase IV, have been located at high temperature. The boundaries have been determined between the following solid phases: (i) benzene II and benzene III; (ii) benzene III and benzene III’. The irreversible chemical transformation line of benzene has been determined and can be divided in three parts leading to three different recovered compounds. The P–T diagram obtained by our experimental results is discussed in comparison with published works.

Microwave measurements and ab initio dynamics of the large amplitude ring puckering motion in 2‐sulpholene
View Description Hide DescriptionMicrowave measurements were made on the rotational spectrum of 2‐sulpholene using a modified Flygare–Balle pulsed beam Fourier transformspectrometer.Analysis and calculations provided information on the large amplitude ring puckering vibration of this system. Twelve and six rotational transitions were measured for the v=0 and v=1 states of the ring puckering vibration, respectively. The transitions for each vibrational state were fitted to a Watson’s A reduced Hamiltonian including terms for quartic distortion yielding for v=0 the values B=2125.96(6), C=1983.28(8), Δ_{ JK }=0.664(4), Δ_{ K }=−0.34(4) MHz, and for v=1 the values A=3995(26), B=2128.3(1), C=1984.6(1), Δ_{ JK }=−0.8(1), Δ_{ K }=−32(6) MHz. Subsequently, ab initio calculations were performed at the self‐consistent‐field (SCF)/3‐21G*, MP2/6‐31G*, and MP4/6‐31G* levels of theory to determine the barrier to inversion. The MP4/6‐31G* barrier was ΔE=116 cm^{−1}, and can be considered to be the most accurate barrier value calculated in this study. An ab initio potential energy curve was calculated at the SCF/3‐21G* level in terms of a single parameter (ω) describing the large amplitude motion of the ring puckering. Vibration‐coordinate dependence of the effective reduced mass associated with this large amplitude motion and the resultant kinetic energy expression was determined. The solutions of a one‐dimensional Schrödinger equation solved within this double well potential yield a separation between the v=0 and v=1 large amplitude motion vibrational states of 8 cm^{−1} when the effective reduced mass was assumed constant, and a separation of 9 cm^{−1} when the effective reduced mass was expressed as a function of the ω coordinate. The v=0 and v=1 eigenfunctions for the SCF ring puckering potential were found to give vibrationally averaged rotational constants in good agreement with those obtained from the microwave spectrum.

Auger electron spectroscopy of molecules: Theory for angular and spin correlations with photoelectrons
View Description Hide DescriptionThis paper introduces a theory to interpret future experiments to simultaneously observe angular distribution of spin‐resolved Auger and photoelectrons from a molecule belonging to one of the 32 point groups. The Auger electrons are emitted in the decay of the vacancy created by photoionization. We show that the desired correlation can be completely characterized by 12 parameters which are coefficients of trigonometric functions of the spherical angles of spin quantization directions of two outgoing electrons. The expressions for the parameters themselves, although reduced to the simplest possible forms by using the symmetry properties of the molecular point group to maximum advantage, depend upon bipolar harmonics involving the propagation directions of the Auger and photoelectrons. The angular and spin correlation function thus obtained is completely general and can be readily specialized to any experimental geometry used to observe the ejected electrons. In particular, it is found that for a linear experimental arrangement with spins oriented longitudinally to the respective propagation vectors of the two electrons moving out in opposite directions, the parameters become geometry independent with their number reducing to three, which are now coefficients of the first three Legendre polynomials. Correlation between the spin‐quantization directions of Auger and photoelectrons is, on the other hand, described by six parameters which do not depend upon the experimental arrangement. Directional correlation between the two outgoing electrons has also been studied without observing their spins. These angular and/or spin correlation functions are shown to take particularly simpler forms for Auger and photoelectrons emitted from linear molecules. We have applied the procedures developed in this paper to study directional correlation between photoelectrons from 2a _{1} orbital in a T _{ d } molecule and the Auger electrons emitted in the decay of the consequent vacancy.

On the use of divergent series in vibrational spectroscopy. Two‐ and three‐dimensional oscillators
View Description Hide DescriptionProspects for higher order perturbation theory in evaluating accurate eigenvalues and eigenvectors of the vibrational Hamiltonian are investigated by performing calculations on a series of two‐ and three‐dimensional quartic anharmonic oscillators imitating vibrational motions in the H_{2}O, H_{2}S, NO_{2}, SO_{2}, and HOF triatomic molecules. Despite the fact that most of the corresponding perturbation expansion series diverge strongly they can be summed efficiently using the same methods as in previous studies on one‐dimensional oscillators. Hence, higher order perturbation theory appears as a reasonable alternative to accurate variational methods in the case of small molecular systems and as a very promising tool for a proper treatment of larger systems.

Vibrational spectroscopy and intramolecular relaxation of benzene
View Description Hide DescriptionBy making use of Lie algebraic methods, we construct the complete vibrational spectrum of benzene. We use this construction to study the process of intramolecular vibrational energy relaxation in the first and second overtone of the CH stretching mode.

Intramolecular vibrational redistribution of energy in the stimulated emission pumping spectrum of acetylene
View Description Hide DescriptionUsing a combination of low resolution dispersed Ã→X̃ fluorescence spectra and high resolution stimulated emission pumping, we have spectroscopically identified the first stages of vibrational energy flow in the highly vibrationally excited acetylene prepared by Ã→X̃ emission over the energy range 5 000–18 000 cm^{−1}. A detailed study of the stimulated emission pumping (SEP) spectrum of acetylene in the E _{VIB}=7000 cm^{−1} region, in which we report spectroscopic constants and rovibrational term values for 12 vibrational levels, has conclusively shown that Darling–Dennison resonance between the cis and trans degenerate bending vibrations is the first step in the redistribution of vibrational energy from the initially excited Franck–Condon bright CC stretch and trans‐bend vibrational combination levels. This allows an extension of our prior dispersed fluorescence (DF) assignments which suggested the crucial role of Darling–Dennison coupling between the cis and trans bends in IVR [J. Chem. Phys. 95, 6336 (1991)].
We prove that the symmetric CH stretch vibration, previously thought to play a crucial role in the redistribution of vibrational energy, is Franck–Condon inactive. We have also shown that vibrational‐l‐resonance among the states with excitation of both degenerate bending modes, when combined with a Fermi resonance which couples CC stretch/trans/cis‐bend excited states to the antisymmetric CH stretch, determines the subsequent flow of vibrational energy after the Darling–Dennison bending resonance. These resonances all scale with vibrational excitation in nearly the simple manner expected for the lowest order anharmonic terms in the Hamiltonian, which allows the prediction of the fastest processes at high energy from a detailed study of the high resolution spectrum at lower energy. We find some interesting rules for vibrational energy flow in the short time dynamics: (i) CC stretch excitation is necessary for stretch–bend coupling; (ii) if V _{2} ^{‘} and V _{4} ^{‘} are the quantum numbers of the initially excited bright state, and v _{ b } ^{‘} = v _{4} ^{‘} + v _{5} ^{‘} is the total bending quantum number of a state coupled to that bright state, then V _{4} ^{‘} ≥ v _{ b } ^{‘} ≥ (V _{4} ^{‘}–2V _{2} ^{‘}); (iii) the total stretch quantum number n _{ s } ^{‘} = (v _{1} ^{‘} + v _{2} ^{‘} + v _{3} ^{‘}) is also conserved by the short time dynamics.
These are severe and well characterized restrictions on the range of quantum numbers accessible to the initial bright state during the first stages of intramolecular vibrational redistribution of energy.

The ν_{1}+ν_{3} combination mode of C_{3} in Ar and Kr matrices: Evidence for a bent structure
View Description Hide DescriptionThe ν_{1}+ν_{3} combination mode of laser‐ablated C_{3} has been observed in Ar and Kr matrices for all six possible ^{12}C/^{13}C isotopomers. The ν_{1} totally symmetric mode frequencies have been determined by difference with the known ν_{3} asymmetric stretching frequencies, corrected for anharmonicity effects. A comparison of certain isotopomer pairs reveals that C_{3} is bent in these matrices. A normal coordinate analysis using four force constants resulted in an excellent fit of the 12 observed frequencies (ν_{1} and ν_{3} for six isotopomers). From the fit, a value for the ν_{2} bending mode frequency of 82 cm^{−1} was obtained. This is shown to be in good agreement with the value obtained from the C_{3}phosphorescence spectrum. Finally, the molecular bending angle which was determined to be 160.0° (in Ar and Kr) is shown to match very well with the predicted value from ab initio theory (161.6°) and from a fitting of a Morse oscillator–rigid bender potential to gas phase vibrational frequencies (162.5°). The influence of the matrix environment on the vibrational force constants and frequencies of C_{3} is discussed.

Electron spin resonance investigation of Sc^{+} _{2} in neon matrices and assignment of its ground electronic state as X ^{4}Σ^{−}. Comparison with theoretical calculations
View Description Hide DescriptionThe discandium radical cation, Sc^{+} _{2}, has been isolated in neon matrices at 4 K and studied by electron spin resonance(ESR)spectroscopy and theoretical methods. It was produced by the x‐irradiation of neon matrix samples containing neutral Sc_{2} which was formed by trapping the products generated from the pulsed laservaporization of scandiummetal. The experimental and theoretical findings indicate that Sc^{+} _{2} has a ^{4}Σ^{−} _{ g } electronic ground state compared to an X ^{5}Σ^{−} _{ u } state for the neutral discandium radical. The large decrease in the ^{45}Sc hyperfineinteraction (Atensor) going from Sc_{2} to Sc^{+} _{2} provides direct experimental information concerning the types of valence molecular orbitals that are involved in these diatomic radicals. The neon matrix magnetic parameters for ^{45}Sc^{+} _{2} are g _{∥}≊2.00, g _{⊥}=1.960(1), ‖A _{∥}‖=28(6), and ‖A _{⊥}‖=26.1(3) MHz; the D value (zero field splitting) was 15 381(3) MHz. Ab initio configuration interaction (CI) calculations of the nuclear hyperfineinteractions yielded results in reasonable agreement with the experimental observations.

Electron spin resonance studies of P_{2}H^{+} _{6} and PH^{+} _{3} radical cations in rare gas matrices at 4 K. Comparison with theoretical calculations
View Description Hide DescriptionDetailed experimental and theoreticalelectron spin resonance(ESR) studies of the cation radicals, PH^{+} _{3} and P_{2}H^{+} _{6}, isolated in neon and argon matrices are reported. These cations were generated by photoionization (17 eV) and x‐irradiation (80 keV) methods. The observed nuclear hyperfine interactions (Atensors) showed reasonable agreement with A _{iso} and A _{dipolar} values calculated at the ab initioconfiguration interaction (CI) level. These ESR results for PH^{+} _{3} clearly indicate its nonplanarity; for P_{2}H^{+} _{6}, an earlier theoretical prediction of a C _{2h } distortion from C _{3v } was confirmed by these new experimental results which reveal two different H atom environments. The neon magnetic parameters for PH^{+} _{3} are g _{∥}=2.002(1), g _{⊥}=2.007(1), A _{⊥}=920(3), and A _{∥}=1638(15) MHz for ^{31}P and A(H)≤6 MHz. The neon parameters for P_{2}H^{+} _{6} are g _{∥}=2.001(1), g _{⊥}=2.003(1), A _{⊥}=1527(2), and A _{∥}=1909(4) MHz for ^{31}P and A(2H)=182(2) and A(4H)=±22(2) MHz.

The vibrational spectra of molecular ions isolated in solid neon. XI. NO^{+} _{2}, NO^{−} _{2}, and NO^{−} _{3}
View Description Hide DescriptionWhen a Ne:NO_{2} or a Ne:NO:O_{2} sample is codeposited at approximately 5 K with a beam of neon atoms that have been excited in a microwavedischarge, infrared absorptions of NO^{+} _{2}, NO^{−} _{2}, and NO^{−} _{3} appear. Detailed isotopic substitution studies support the assignment of prominent absorptions to ν_{3} of NO^{+} _{2} and NO^{−} _{2} and of weak to moderately intense absorptions to the ν_{1}+ν_{3} combination band of each of these species. When the contribution of anharmonicity is considered, the positions of the NO^{+} _{2} absorptions are in satisfactory agreement with the values for the stretching fundamentals obtained in a recent gas‐phase study of that species. When the sample is exposed to 240–420 nm mercury‐arc radiation, the initially present absorptions of NO^{−} _{3} trapped in sites with a small residual cation interaction diminish in intensity, and the unsplit ν_{3}(e’) absorption of isolated NO^{−} _{3} grows. The mechanism responsible for this growth in the absorption of isolated NO^{−} _{3} is considered.

Triplet exciton formation due to interaction between singlet excitons in polydiacetylene
View Description Hide DescriptionThe time‐resolved spectroscopy in polydiacetylene single crystals (PDA‐MADF {poly‐1‐[3‐(methylamino)phenyl]‐4‐[3,5‐bis(trifluoromethyl)phenyl]‐1, 3‐butadiyne}) on femtosecond and picosecond time scales was performed. The time dependence of the photoinduced reflectance change in PDA‐MADF exhibits three components with lifetimes ∼200 fs, 1–2 ps, and ≫200 ps. These components are assigned to the free ^{1} B _{ u }excitons, self‐trapped excitons, and triplet excitons. From the excitation intensity dependence of the reflectance change, a significant role of bimolecular interactions between singlet excitons for the formation of triplet excitons is clarified. A model of the mechanism of triplet exciton formation after the creation of singlet excitons is proposed.

First observation of the quasibound levels and tunneling line broadening in the 3 ^{1}Π_{ g } state of Na_{2} using an ultrasensitive ionization detector
View Description Hide DescriptionAll quasibound vibrational energy levels v=27 and 28 of the Na_{2} 3 ^{1}Π_{ g } state were accessed by using optical–optical double resonance and detected with a shielded ionizationdetector. The line broadening due to the tunneling effect was observed to be larger than 1 cm^{−1} at the rovibrational level v=28, J=31. The potential curve has been determined by the Rydberg–Klein–Rees method and modified using Jeung’s calculation for the large distance barrier and comparison of the calculated and the measured line widths. The barrier height was found to be ∼126 cm^{−1} above its asymptotic limit (3s+4p) at 5.98 Å. There also exists an unobserved shallow outer well with depth ∼35 cm^{−1} at 9.5 Å according to our modification of Jeung’s calculated potential. One way to possibly probe this outer well is also discussed.

Fourier transform microwave spectrum of the propane–water complex: A prototypical water‐hydrophobe system.
View Description Hide DescriptionThe Fourier transformmicrowave spectrum of the propane–water complex (C_{3}H_{8}–H_{2}O) has been observed and analyzed. This spectrum includes transitions assigned to propane complexed with both the ortho and paranuclear spin confirmations of water. The rotational constants indicate that the vibrationally averaged structure has all four heavy atoms coplanar, with the water center of mass lying on or near the C _{2} axis of propane, inside the CCC angle, 3.76(±0.02) Å from the propane center‐of‐mass, and 4.35(±0.02) Å from the methylene carbon. The projection of the electric dipole onto the a inertial axis of the complex (0.732 D for the ortho state and 0.819 D for the para state) indicates that one of the protons of the water subunit lies on the C _{2} axis of the propanemonomer, which is also the axis connecting the subunit centers of mass. The small projection of the dipole along the b axis (0.14 D for the ortho state and 0.38 D for the para state) is most consistent with an equilibrium structure in which all three atoms of the water lie in the CCC plane of propane, with torsional tunneling about the hydrogen bond occurring on the same time scale as the overall rotation. The small internal rotation tunneling splittings that occur in the rotational spectrum of the propanemonomer are not observed in the spectrum of the complex.

Far‐infrared laser vibration–rotation–tunneling spectroscopy of the propane–water complex: Torsional dynamics of the hydrogen bond.
View Description Hide DescriptionThe far‐infrared laser vibration–rotation–tunneling (FIR‐VRT) spectrum of the propane–water complex has been measured in the range 18–22 cm^{−1}. A C‐type VRT band has been assigned with a band origin of 19.6 cm^{−1}. The data support the ‘‘kite‐shaped’’ structure determined from microwave spectroscopy in the accompanying paper, and indicate that the observed VRT band corresponds to torsional motion of the free water proton about the hydrogen bond. This motion is impeded by a barrier that is less than 5 cm^{−1}. We describe our modification of the supersonic slit‐jet source designed to permit Stark effects to be measured, and have used second‐order Stark shifts to help assign the perpendicular transition observed.

Nonlinear dynamics of large‐amplitude molecular excitation by shaped optical pulse sequences
View Description Hide DescriptionThe effects of nonlinear dynamical phenomena on strategies for creating large amplitude excitations in molecular systems are studied. A simple area‐preserving mapping modeling a Morse oscillator coupled to a second intramolecular degree of freedom is considered. The optical field is approximated by a finite sequence of impulsive interactions with arbitrary amplitudes and time increments. The goal of exciting the system to 75% of its dissociation energy is established. For the uncoupled Morse oscillator, an analytic solution for the optimal spacing between pulses of minimal equal intensity is given. When intramolecular coupling is present, the existence of a nonlinear resonance zone is shown to strongly interfere with the efficacy of this strategy. Dramatic improvements in efficiency can be obtained by employing pulse sequences that explicitly take into account the presence of strong perturbations of the zeroth order phase portrait.

Orientational order in liquid crystal solutions of polyhexylisocyanate. II. Deuterium nuclear magnetic resonance
View Description Hide DescriptionThe concentration dependence of the order parameter was measured for liquid crystal solutions of deuterated samples of polyhexylisocyanate of two molecular weights in two solvents, chloroform and toluene. Trends in and values of order parameters determined from deuterium nuclear magnetic resonance(DNMR)spectroscopy for this semiflexible polymer were analyzed in terms of a recent modification [DuPré and Yang, J. Chem. Phys. 94, 7466 (1991)] of the Onsager theory that takes into account macromolecular flexibility and the higher solute densities characteristic of these polymer liquid crystals. Computer simulation of DNMR spectra with the consideration of internal flexibility of the polymer main chain was performed also to interpret unusual line shape features observed in liquid crystal solutions of this polymer.

Line shapes of strongly radiation‐damped nuclear magnetic resonance signals
View Description Hide DescriptionLine shapes of strongly radiation‐damped nuclear magnetic resonance(NMR) signals are theoretically analyzed. Analytical expressions for the radiation‐damped signals in the frequency domain are reported for the first time. It is shown that the line shapes are generally dependent on the flip angle θ_{0} of the excitation pulse. In the range of 0≤θ_{0}<π, the peak height increases linearly, but the linewidth decreases monotonically with the flip angle. An oscillating feature is predicted for the line shape when θ_{0}≳π/2. The theoretical predictions are confirmed by the experimental results.

Isotropic Raman line widths in binary mixtures of van der Waals liquids: A comparison between isotopically and chemically diluted states of liquid methyl iodide
View Description Hide DescriptionTo analyze vibrational depopulation and dephasing mechanisms of polyatomic liquids, the presently most comprehensive study on the dilution behavior of isotropic Raman line widths has been made. By way of example, and following early proposals of Evans and Yarwood [Adv. Mol. Relaxation Int. Processes 21, 1 (1981)], liquid methyl iodide (MeI) was chosen. The low temperature study (T=207 K) covers the detailed concentration dependencies (x) of the isotropic half‐widths (FWHH) in total 17 (of 18 possible) polarized fundamentals of CH_{3}I and in the isotopically modified molecules CH_{2}DI, CHD_{2}I, and CD_{3}I (^{12}CD_{3}I) (i) in chemical mixtures with xenon and (partially) CF_{3}I and (ii) in all the six binary isotopic mixtures of the isotopic species above. Furthermore, isotopic and chemical dilutions are combined in ternary mixtures of type (CX_{3}I)_{0.014}−(CY_{3}I)_{ x−0.014}−Z_{1−x } with X, Y=H, D and Z=Xe, CF_{3}I, where the trace CX_{3}I has been investigated to study the modulations of the vibrational transition frequency by changes of the intermolecular potential in an isotopically diluted state free of vibrational resonance coupling. The manifold of curves FWHH_{iso}(x) are discussed in terms of a recent Raman line shape theory of Bratos and Tarjus [Phys. Rev. 32A, 2431 (1985)] which explicitly considers the time‐dependent cross correlation between the environmentally induced frequency shifts Δω_{ ei }(t) and those induced by (intermolecular) resonance coupling (RC) Δω_{RC}(t). Overall, strong indications have been found that intermolecular coupling Δω_{ ij }=ω_{ i }−ω_{ j } play a very significant role in line broadening. This holds true not only for the bending modes (as known beforehand), but also for the C–H (C–D) and C–I stretching modes. However, to be effective, these coupling has to be of a strictly resonant nature, i.e., near‐resonant transitions with 0.05≤ℏ‖Δω_{ ij }‖/k _{ BT }≪1 are ineffective in line broadening in the same way as strictly off‐resonant transitions with ℏ‖Δω_{ ij }‖/k _{ BT }≳1.

Potential energy surfaces for Ar–OH (X ^{2}Π) obtained by fitting to high‐resolution spectroscopy
View Description Hide DescriptionEmpirical potential energy surfaces for Ar interacting with OH (X ^{2}Π) are obtained by fitting to experimental results from microwave and stimulated‐emission pumping (SEP) spectra of the Ar–OH complex. The sum V _{Π} and difference V _{2} of the potentials for A’ and A‘ symmetry are determined. The sum potential is 126 cm^{−1} deep, which is about 24 cm^{−1} deeper than the ab initio CEPA potential of Degli Esposti and Werner [J. Chem. Phys. 93, 3351 (1990)]. The equilibrium geometry is near‐linear, Ar—H–O, with a barrier to internal rotation of 44 cm^{−1}. The potential satisfactorily reproduces all the parameters obtained from the SEP experiments, but not the parity doubling obtained from the microwave spectrum.