Volume 91, Issue 4, 15 August 1989
Index of content:

Diode laser spectroscopy of C_{3}: The ν_{2}+ν_{3}−ν_{2}, 2ν_{2}+ν_{3}− 2ν_{2}, and 2ν_{2}+ν_{3} bands
View Description Hide DescriptionThe ν_{3} hot bands (011)–(010), (021)–(020), and the combination band (021)–(000) of C_{3} were observed by a diode laserspectroscopic method. The C_{3} molecule was produced by the photolysis of allene or by the discharge in cyclopropane or furan. Analysis gave molecular constants in each vibrational state and also the energy difference between (020) and (000). The derived vibrational frequencies were compared with the result of a Morse oscillator‐rigid bender internal dynamics (MORBID) calculation by Jensen.

Matrix induced frequency shifts of transition metal atoms in Ar, Kr, and Xe matrices at 10 K
View Description Hide DescriptionA linear correlation was found for rare gas polarizabilities and matrix induced frequency shifts of Ru, Os, and Ir atoms. Nickel,Mo,Ag, and Au atoms also showed the same trend. A modified Lennard‐Jones (6‐12) function where many‐body interactions are considered between an isolated atom (guest) and matrix atoms (host) was used to investigate the relationship between the matrix induced frequency shifts and the rare gas polarizability. It is concluded that van der Waals interaction is the major source of the frequency shift for Ru, Os, Ir as well as Ni,Mo,Ag, and Au atoms. However, Y atoms did not show such a linear correlation, and additional interaction modes are indicated.

The Baldet–Johnson (B ^{2}Σ^{+}–A ^{2}Π_{ i }) system of ^{1} ^{3}C^{1} ^{8}O^{+}
View Description Hide DescriptionThe rotational structure of the 1–0, 0–0, and 0–1 bands of the Baldet–Johnson (B ^{2}Σ^{+}–A ^{2}Π_{ i }) system of the molecular ion ^{1} ^{3}C^{1} ^{8}O^{+}, excited in the cathodeglow of a hollow‐cathode discharge tube, was recorded in the spectral region 3700–4225 Å and analyzed. An effective Hamiltonian proposed by Brown e t a l. [J. M. Brown, E. A. Colbourn, J. K. G. Watson, and F. D. Wayne, J. Mol. Spectrosc. 7 4, 294 (1979)] was used to obtain the molecular constants from the wave number data of these three bands. These molecular constants were first ‘‘merged’’ together and the resulting constants were then ‘‘merged’’ with those of the comet‐tail (A ^{2}Π_{ i }–X ^{2}Σ^{+}) system of ^{1} ^{3}C^{1} ^{8}O^{+} recently reported by us [C. V. V. Prasad and S. P. Reddy, J. Chem. Phys. 9 0, 3010 (1989)] to obtain a unique set of constants for the X ^{2}Σ^{+}, A ^{2}Π_{ i }, and B ^{2}Σ^{+} states. Some of the derived constants of ^{1} ^{3}C^{1} ^{8}O^{+} (in cm^{−} ^{1}) are for X ^{2}Σ^{+}: B _{ e }=1.794 28(4), α_{ e }=0.016 61(3), ω_{ e } =2110.2_{7}(2), and ω_{ e } x _{ e } =13.8_{1}(6); for A ^{2}Π_{ i } : B _{ e }=1.441 92(4), α_{ e }=0.016 76(1), ω_{ e } =1488.9_{9}(2), ω_{ e } x _{ e } =12.45_{4}(7), and ω_{ e } y _{ e } =0.027_{9}(8); for B ^{2}Σ^{+}: B _{ e }=1.632 62(4), α_{ e }=0.025 49(2), ω_{ e }=1657.5_{6}, and ω_{ e } x _{ e } =27.4_{2}.

Coupling of hindered internal rotation with van der Waals vibration in aniline–H_{2}(D_{2} ) complexes
View Description Hide DescriptionThe laser‐induced fluorescence excitation spectra from the van der Waals complexes of aniline with hydrogen and deuterium, formed in a free jet expansion, have been recorded in the spectral region associated to the electronic band origin S _{0} –S _{1} (0^{0} _{0}) of the free aniline molecule. For each complex the spectrum exhibits a vibrational progression involving a van der Waals vibration in the excited state. Each vibrational band of this progression is made of a doublet, the components of which are assigned to the ‘‘j=0’’ (para‐H_{2} , ortho‐D_{2} ) and ‘‘j=1’’ ortho‐H_{2} , para‐D_{2} ) Δj=0 transitions, as confirmed by nuclear spin statistics. The internal rotation of the hydrogen molecule in the complex is hindered by a barrier, the height of which is different in the ground X̃ ^{1} A _{1} state and the excited Ã ^{1} B _{2} state. The doublet splitting (going from 3.1 to 6.2 cm^{−1} ) shows a systematic variation with the van der Waals vibrational quantum number, which is monotonic for D_{2} and presents a minimum for H_{2} , indicative of a strong coupling between internal rotation and the involved van der Waals motion. A quantum‐mechanical treatment using the ‘‘nearly free rotor’’ picture has been done, which is able to reproduce the two spectra with very good accuracy, both for the positions and the intensities of the various bands. A detailed description of the full potential energy surfaceV(R, θ), including the coupling terms between the van der Waals bond length R and the hydrogen rotation angle θ in the excited state, is derived.

Electronic quenching, fluorescence lifetime, and spectroscopy of the A ^{3}Π_{ u } state of NCN
View Description Hide DescriptionLaser‐induced fluorescence of the NCN radical was observed downstream of a microwave discharge of N_{2} and CF_{4} in He via the A ^{3}Π_{ u }–X ^{3}Σ^{−} _{ g } transition near 329 nm. The zero‐pressure fluorescence lifetime of the 000 vibrational level of the A state was measured from the time‐resolved laser‐induced fluorescence to be 183±6 ns. Other spectral features were observed both to the blue and red of the 000–000 band. The blue‐shifted features are tentatively assigned to the 020–000, 100–000, 030–010, and 110–010 vibrational bands. Quenching cross sections were determined for NCN (A ^{3}Π_{ u }, 000) at 300 K for Ar, Kr, Xe, O_{2}, CO, CO_{2}, N_{2}O, SF_{6}, NO, and NO_{2}. The molecules He, N_{2}, and CF_{4} are inefficient quenchers and upper limits only were obtained. The large variation in cross section among the colliders does not correlate with predictions of simple electronic quenching models.

(e,2e) momentum spectroscopic study of the C=C π orbitals of the vinyl halides
View Description Hide DescriptionThe distribution of electron momentum density has been measured for the outermost occupied orbitals of the vinyl halides and ethylene using the (e,2e) technique. In contrast to the ionization potentials for these π orbitals which decrease monotonically from vinyl fluoride to vinyl iodide, the values of the momenta where the distributions are a maximum, p _{max}, increase from the fluoride through the bromide and then shift back to a lower value for the iodide. This observation can be analyzed in terms of B(r), the Fourier transform of the observed momentum distribution, and ΔB(r), the difference between B(r) functions. The shape of ΔB(r) for the fluoride, chloride, and bromide in comparison to ethylene reflects the effect of the carbon–halogen antibonding interaction in these vinyl halides. On the other hand, in vinyl iodide the antibonding interaction is compensated for by the diffuse iodine 5p character of the molecular orbital. The relation of these observations to chemical properties of the vinyl halides is discussed along with differences between experiment and calculations at low momentum.

Photoacoustic measurement of differential broadening of the Λ doublets in NO(X ^{2}Π_{1} _{/} _{2},v=2–0) by Ar
View Description Hide DescriptionA differential broadening of the Λ doublets in the v=2–0 overtone band of the ^{2}Π_{1} _{/} _{2}ground electronic state of NO in an Ar buffer gas has been observed by photoacoustic spectroscopy using a tunable color‐center laser. The broadening coefficients for the f symmetry components are larger than for the e symmetry components by up to ∼6% for J∼16.5. This differential depends on J and vanishes at low J, implicating the anisotropy of the unpaired electron Π orbital in the plane of rotation. The ^{2}Π_{3} _{/} _{2} transitions are slightly broader than the ^{2}Π_{1} _{/} _{2} as a result of spin‐flipping collisional relaxation. The observed line shapes also exhibit collisional or Dicke narrowing due to velocity‐changing collisions.

On the 1593 Å transition of CS_{2}
View Description Hide DescriptionThe optical absorptionspectrum of the 1593 Å transition of static (room temperature) and jet‐cooled CS_{2} has been remeasured to determine the temperature dependence of the spectrum and to better characterize the experimental band shapes and intensities. Based on these results and others, current assignment controversies are resolved and the separation between the singlet and triplet components of the excited state, the excited state vibrational frequencies, and electronic and vibronic properties of the excited state are determined.

Diffuse vibrational structures in photoabsorption spectra: A comparison of CH_{3}ONO and CH_{3}SNO using two‐dimensional a b i n i t i o potential energy surfaces
View Description Hide DescriptionWe investigated the photodissociation of methyl nitrite (CH_{3} ONO) and methyl thionitrite (CH_{3} SNO) within the first absorption band (S _{1} ←S _{0} ). The calculations were based on a two‐dimensional model including the O–NO/S–NO and N=O bond distances as active coordinates. The S _{1} ‐potential energy surfaces were calculated with quantum chemical methods and the dynamical calculations were performed exactly within the time‐independent approach. The main emphasis is on the origin of diffuse vibrational structure in the photoabsorptionspectrum of both molecules. A low potential barrier of 0.086 eV along the O–NO dissociation coordinate in CH_{3} ONO prevents immediate dissociation and leads to an initial state dependent lifetime for the excited complex of 100–250 fs corresponding to 3–8 NO vibrational periods. CH_{3} ONO decays nonadiabatically via vibrational predissociation. The absorptionspectrum of CH_{3} ONO is dominated by narrow Feshbach‐like scattering resonances which can be characterized by two quantum numbers, m and n*: m=0 and 1 specifies the quanta of excitation in the O–NO bond and n*=0,1,2,... specifies the excited vibrational level of the N=O bond. The potential barrier is absent in CH_{3} SNO and the dissociation is direct on the time scale of about 10 fs corresponding to only one third of a NO vibrational period. Nevertheless, the absorptionspectrum exhibits diffuse vibrational structures. The shape of the individual absorption peaks is determined by the classical Franck–Condon reflection principle. The dissociation of CH_{3} SNO is primarily adiabatic which leads to a pronounced energy dependence of the final NO vibrational state distribution. The diffuse structures originate in both cases from excitation of the NO stretching vibration. In order to make contact with time‐dependent theory we calculated the autocorrelation function of the time‐dependent wave function by inverse Fourier transformation of the energy‐dependent spectra. The agreement with available experimental data for both molecules is quite satisfactory. This includes the energy spacing of the vibrational structure, the overall shape of the absorptionspectrum, and the
lifetime of the excited complex.

Line‐shape analysis of extra resonance signal in coherent Stokes Raman scattering of acridine in the T _{1} state
View Description Hide DescriptionThe coherent anti‐Stokes Raman scattering(CARS) and coherent Stokes Raman scattering (CSRS) line shapes near the 1350 cm^{−} ^{1} region of acridine in the T _{1} state were recorded in the various resonance (ω_{1} frequency) conditions over the T _{ n }←T _{1} absorption band in the n‐heptane solution at room temperature. The ω_{1} frequency dependencies of CARS and CSRS line shapes of the T _{1} signal at 1368 cm^{−} ^{1} were simulated well on the basis of the theoretical χ^{(} ^{3} ^{)} expression. On the other hand, the ω_{1} frequency dependence of the line shape of the extra resonance (ER) signal observed at 1335 cm^{−} ^{1} in CSRS, showing no obvious change of the line shape by changing the ω_{1} frequencies, could not be simulated at all on the basis of the similar expression. The discrepancy of the ER line‐shape simulation was discussed.

Fluorescence from photoexcitation of BCl_{3} at 45–106 nm
View Description Hide DescriptionThe photoabsorption,fluorescence cross sections, and the fluorescence yield of BCl_{3} are measured in the 45–106 nm region. Fluorescence spectra are dispersed to identify the emitting species. The emission observed at excitation wavelengths longer than 96 nm is attributed to the excited BCl^{*} _{2}. The BCl (A–X) emission appears at excitation wavelengths shorter than 97.5 nm. Emissions observed at the thresholds of 88 and 81 nm are attributed to the excited BCl^{+*} _{3} (C̄ ^{2} A ^{‘} _{2} and D̄ ^{2} E’) states, respectively. Emissions from excited B* atoms appear in the 48–64 nm region. In the 88–96 nm region the maxima and minima of the fluorescence cross section are complimentary with those of the BC1^{+} _{3}ionization yield, indicating where superexcited state(s) exist that decay through competitive channels of fluorescence and autoionization.

Multiphoton excitation spectroscopy of the B ^{1}Σ^{+} and C ^{1}Σ^{+} Rydberg states of CO
View Description Hide DescriptionTwo‐photon absorption spectra of the CO 3s B ^{1}∑^{+}←←X ^{1}∑^{+} (v’,v‘)=(0,0), (1,1), (2,2), (1,0), and 3pσ C ^{1}∑^{+}←←X ^{1}∑^{+} (0,0) transitions have been observed in a room temperature cell and in an atmospheric pressure hydrocarbon flame using fluorescence (B ^{1}∑^{+}→A ^{1}Π) and ionization detection. The ratio of the transition strengths for the B ^{1}∑^{+}←←X ^{1}∑^{+} (0,0) Q‐branch head is found to exceed 200:1 for excitation with two identical linearly polarized photons compared with two circularly polarized photons. Weak O and S branches are observed for the first time for the B ^{1}∑^{+}←←X ^{1}∑^{+} (0,0) transition and show the expected 2:3 polarization ratio. These measured polarization ratios are well described by two‐photon absorption theory for ∑←←∑ transitions. In contrast, an earlier study by another group obtained a value of 0.7:1 for the Q‐branch polarization ratio which did not fit the predictions of two‐photon absorption theory.

The permanent electric dipole moment of chromium monoxide
View Description Hide DescriptionThe permanent electric dipole moments for the X ^{5}Π and B ^{5}Π states of gas‐phase chromium monoxide, CrO, have been experimentally determined using the sub‐Doppler optical technique of intermodulated fluorescence spectroscopy in conjunction with the Stark effect. The measured values are 3.88±0.13 and 4.1±1.8 D for the X ^{5}Π and B ^{5}Π states, respectively. The theoretical values determined for the X ^{5}Π state, using multireference configuration interaction iterative‐natural‐orbital and finite‐field calculations, are in excellent agreement with the experimental value.

Confirmation of anomalous pressure dependence of linewidths of the electron paramagnetic resonance spectrum of molecular oxygen
View Description Hide DescriptionIntrinsic linewidths of the M _{ J }=−1 to M _{ J }=0 electron paramagnetic resonance(EPR) transitions of O_{2} for total rotational quantum numbers N=3, 5, and 7 were redetermined by the second harmonic zero crossing method using direct calibration of modulation depth and analytic accounting for the effect of harmonic distortion of the magnetic field modulation waveform. The collisional linewidths were found to be 4.38±0.05, 4.26±0.07, and 4.22±0.10 MHz/Torr, respectively, for N=3, 5, and 7, corresponding to relaxation/reorientation cross sections of 0.679, 0.661, and 0.655 nm^{2}. Anomalous negative zero‐pressure linewidths detected in an earlier study were also given by linear regressionanalysis of the present data at pressures over 0.5 Torr. Extending the pressure range down to 0.05 Torr using a voltage controlled oscillator (VCO) to mimic tracking gaussmeter signals showed that the linewidth does appear to extrapolate finally to a physically meaningful positive value at zero pressure. No satisfying interpretation of the measured intrinsic widths being approximately 200 kHz too small to yield physically meaningful linearly extrapolated zero‐pressure widths was found.

Two‐dimensional experiments with collision‐induced transfer of populations in microwave Fourier transform spectroscopy
View Description Hide DescriptionThe two‐dimensional (2D) technique in microwaveFourier transform (MWFT) spectroscopy has been extended to four‐level double resonance. By applying a three‐pulse sequence with a particularly selected phase cycle, it was possible to correlate the spectra excited by pump and signal radiation in two dimensions. Cross peaks in such 2D spectra appeared only when collision‐induced transitions took place between the levels of the irradiated transitions. Also the dynamics of such collision processes could be investigated. The power of the method is greatly enhanced by the high sensitivity of the MWFT technique. Experiments were performed on HC^{1} ^{5}N in order to investigate the collision‐induced transitions between different pairs of l‐type doublets. The one‐dimensional analog of this 2D method was tested on acetaldehyde.

The benzene ground state potential surface. IV. Discrimination between multiple E _{1u } force field solutions through infrared intensities
View Description Hide DescriptionAccurate values for integrated intensities of the infrared active ^{1} ^{3}C_{6}H_{6} fundamentals, ν_{1} _{8}, ν_{1} _{9}, ν_{2} _{0}, and ν_{1} _{1} (Wilson notation) have been measured and redetermined for ν_{1} _{8} and ν_{1} _{9} in C_{6}H_{6} and C_{6}D_{6}. The ^{1} ^{3}C_{6}H_{6} intensities are I _{1} _{8}=6.52±0.15, I _{1} _{9}=12.60±0.20, I _{2} _{0}=55.6±1, and I _{1} _{1}=74.6±3 km/mol. Unlike C_{6}H_{6} and C_{6}D_{6}, interfering transitions in ^{1} ^{3}C_{6}H_{6} are minor and these intensities can be used as a critical test for theoretical predictions of atomic polar tensors. The ν_{1} _{8} intensities in C_{6}H_{6} and C_{6}D_{6} (7.48±0.15 and 7.09±0.14 km/mol, respectively) and the ν_{1} _{9} intensity in C_{6}D_{6} (2.51±0.12 km/mol) are measured to be substantially lower than the literature values. The qualitative intensity pattern of benzene in‐plane fundamentals uniquely discriminate among the eight possible real E _{1u } force field solutions obtained from frequency information alone. Isotopically invariant dipole moment derivatives, ∂μ/∂S _{18a }, ∂μ/∂S _{19a }, and ∂μ/∂S _{20a } are 0.494±0.005, 0.395±0.016, and 0.770±0.008 D/Å, respectively, obtained from the ^{1} ^{3}C_{6}H_{6} experimental intensities and the complete experimental force field of Part II. Using these quantities and the L ^{−} ^{1} matrix (Table III), dipole moment gradients for C_{6}H_{6} become ∂μ/∂Q ^{0} _{18a } =+0.298, ∂μ/∂Q ^{0} _{19a } =+0.371, and ∂μ/∂Q ^{0} _{20a } =+0.814 D/Å. Mode decomposition matrices expressing normal modes of benzene in terms of isotopically labeled molecule modes have been used to definitively determine the C_{6}H_{6} dipole gradient signs. The signs are in agreement with theoretical calculations. The D _{6} isotopic labeling effect on C_{6}H_{6} ν_{1} _{8} intensity provides a sensitive test of E _{1u } force field quality and reveals the inadequacy of present theoretical force field approaches. A b i n i t i o atomic polar tensors have been obtained both at the HF level, using several basis sets up to the 6‐311+G(d,p) and at the
MP2 level up to the 6‐31+G(d) basis set. The dipole derivative for the CC stretch is highly sensitive to both basis set (particularly diffuse functions) and correlationeffects. Qualitative CH and CC stretching dipole derivative and intensity predictions by the MP2/6‐31+G(d) calculation are encouraging (i.e., within 15% of the experimental values). However, the same calculation yields 20% and 45% errors for the CH bending dipole derivative and fundamental intensity, respectively.

Field dependence of the nuclear magnetic resonance static powder line shape: Studies of the mutual orientation of interaction tensors from the field dependence of the critical frequencies
View Description Hide DescriptionA procedure for determining the interaction tensor orientations and the interaction parameters for mutually oriented electric field gradient (efg) or dipolar and shielding tensors has been developed based upon the magnetic field dependence of the critical frequencies from the polycrystalline nuclear magnetic response (NMR) spectrum. The central transition line shape of half‐integer quadrupolar nuclei in the presence of mutually oriented shift anisotropy and second order quadrupolar interaction is discussed for the first time. Analytical expressions for the field dependent critical frequencies have been determined for special orientations when the shift principal Z axis lies on the X Z, Y Z, or X Y plane of the efg (or dipolar) tensor for the first order as well as the second order interactions. The plots resulting from the analytical expressions provide a convenient graphical approach in determining approximate tensorial orientations and interaction parameters through pattern recognition. For general orientations, a numerical procedure has been developed to determine these parameters by iteratively minimizing the squares of the differences of the calculated and the experimental critical frequencies. Higher order perturbation terms can be incorporated in the present treatment. The method is demonstrated by variable field static proton spectra of trichloro–acetic acid at three different fields (1.3, 2.3, 5.2 T). The near‐orthogonal orientation between the dipolar and shielding tensors and the interaction parameters obtained from this approach are consistent with those obtained previously from single crystal studies.

Microwave spectroscopic detection of dichlorosilylene SiCl_{2} in the ground state
View Description Hide DescriptionThe microwave spectrum of dichlorosilylene SiCl_{2} has been observed to characterize this molecule of chemical interest. The molecule was generated by the thermal reaction between siliconpowder and tetrachlorosilane at about 1000 °C. The rotational constants and the centrifugal distortion constants were determined for the three isotopic species Si^{3} ^{5}Cl_{2}, Si^{3} ^{5}Cl^{3} ^{7}Cl, and Si^{3} ^{7}Cl_{2}. The nuclear quadrupole coupling constants were determined from triplet hyperfine splittings observed for several transitions. The asymmetry of the Cl nuclear quadrupole coupling tensor was found to be very large and was accounted for by π electron backdonation from Cl to Si.

The Wei–Norman Lie‐algebraic technique applied to field modulation in nuclear magnetic resonance
View Description Hide DescriptionBy implementing the Wei–Norman Lie algebra approach, this paper focuses on the development of a new method of solution to the quantum Liouville equation for NMR field modulation. First, the general method is reviewed and discussed for systems of any finite dimensional Lie algebra. The theory is then applied to arbitrary time‐dependent Zeeman interactions [or S U(2) Hamiltonians] in which the complete arbitrary spin I≥1/2 density operator problem reduces to a Riccati equation. Novel exact analytical solutions of the complete spin density operator for a class of temporal field modulations are obtained. In particular, a spherical tensor operator basis is used to expand the density operator, and the solutions retain the physically appealing form of Wigner rotations with time‐modulated rotation angles which are special functions with well known analytical properties. The exact solutions include the frequency swept hyperbolic secant pulse shapes, as well as any exponentially modulated amplitude pulse. In contrast to all other existing formulations, the present treatment provides the first known examples of exactly soluble nonrectangular pulse shapes for all resonance off‐set, all field amplitudes, all time and valid for all spin I≥1/2. In addition, from the underlying Riccati equation, a new series solution for the complete spin density matrix is given which is valid for any well‐behaved field modulations. Spin inversion profiles are also calculated for exponentially decaying pulses. These show applications to selective excitation.

Raman line shape analysis in isotopic mixtures of liquid hydrogen and deuterium chloride
View Description Hide DescriptionRaman scattering in liquid (and in some cases in solid) isotopic mixtures of HC1 and DC1 is analyzed to prove recent theories by Bratos and Tarjus [Phys. Rev. A 3 2, 2431 (1985)], Logan [Mol. Phys. 5 8, 97 (1986)], and Knapp [J. Chem. Phys. 8 1, 643 (1984)] on vibrational line broadening in liquids. The concentration and temperature dependencies of isotropic [J _{ i }(ω)] and anisotropic [J _{ a }(ω)] line shapes have been studied between triple point (T _{ t }) and critical temperature (T _{ c }). It has been found that in accordance with the Bratos–Tarjus theory,J _{ i } (ω) is much more sensitive of isotopic composition of the liquid than J _{ a }(ω). An analysis of the concentration dependence of the broadening parameters near T _{ t } illustrates the importance of cross correlations between the environmental broadening and the resonant intermolecular coupling. The spectral activity of three‐particle resonant transfer also becomes significant. From the change of the maximum of J _{ i }(ω) with isotopic dilution, which is a linear function of mole fraction, the dipole moment derivative δμ/δq is estimated to be more than twice that of its gas phase value. The asymmetry of the isotropic bands of both HC1 and DC1 changes with concentration at constant temperature. With increasing temperature, J _{ i }(ω) of pure and diluted samples narrows as T ^{−0.5} and T ^{−0.3}, respectively. J _{ i }(ω) has been found to be intermediate between the slow and the fast modulation limit. From the high frequency wing of J _{ i } (ω) the time constant of the zeroth order memory function was obtained. Its activation energy increases with increasing T. This is in qualitative agreement with the temperature dependence of the Enskog collision time and the spin–rotational correlation time. Taking into account the results of the Bratos–Tarjus theory, orientational correlation times τ^{(} ^{2} ^{)} are determined from J _{ a } (ω). The Raman method yields τ^{(} ^{2} ^{)} values which are twice as long as those determined from NMR relaxation.