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Volume 85, Issue 2, 15 July 1986

Theory of continuum surface Raman scattering from electrons in metals
View Description Hide DescriptionA theory for continuum Raman scattering from a bounded free electron gas is developed. The theory is able to account for the observed magnitude of the effect. By suitably generalizing the theory we are also able to account for the observed spectral features. Our theory implies that it is possible to measuredensities of states to photonspectroscopic accuracy.

Circular dichroism in photoelectron angular distributions as a probe of atomic and molecular alignment
View Description Hide DescriptionIn this paper we show that circular dichroism in photoelectron angular distributions (CDAD) can be used to probe atomic and molecular alignment in the gas phase. Careful choice of photon (left or right circularly polarized) propagation and photoelectron collection directions breaks the cylindrical symmetry of the target, giving rise to dichroic effects. CDAD exists in the electric dipole approximation. We illustrate the sensitivity of CDAD to alignment by considering photoionization of the A ^{2}Σ^{+} state of NO. Most of the cases of alignment we consider are created by multiphoton absorption while the others, more general, might be created in fragmentation, desorption, etc. The alignment created by n‐photon absorption quickly reaches a classical limit which is reflected in the CDAD spectrum. Finally, we show that CDAD is also a sensitive probe of gas phase atomic state alignment by considering photoionization of the 7P _{3} _{/} _{2} state of cesium created by single photon absorption from the ground state.

Observation and analysis of the ν_{2} and ν_{3} fundamental bands of the D_{2}H^{+} ion
View Description Hide DescriptionThe high‐resolution absorptionspectrum of the D_{2}H^{+} molecular ion in the 1800–2300 cm^{−} ^{1} region has been measured in a discharge through a mixture of H_{2} and D_{2} using a tunable infrared diode lasersource and a cooled hollow‐cathode absorption cell. A total of 72 new lines of D_{2}H^{+} have been observed, as well as five previously measured in ion‐beam experiments by Wing and Shy, and these have been assigned to specific rotational transitions of the ν_{2} and ν_{3} fundamental bands. Two different and complementary theoretical models are used to fit these data: one is an A‐reduced asymmetric rotor effective Hamiltonian including the Coriolis and higher‐order rotational interactions between ν_{2} and ν_{3}; and the other is a supermatrix model in which the matrix of the untransformed Hamiltonian is set up and diagonalized directly, using a large vibration–rotation basis that diagonalizes the vibrational energy. The former approach is less expensive and provides a better fit, but because of the large number of parameters varied may be more tolerant of incorrect assignments, whereas the latter is more expensive but may be more reliable because a smaller number of parameters is varied, most of the vibrationally off‐diagonal parameters being constrained at values from a b i n i t i o calculations. These analyses have made it possible to assign 11 other lines observed by Wing and Shy, giving a total of 88 assignments. The observed band origins, ν_{2}=1968.17 cm^{−} ^{1} and ν_{3}=2078.42 cm^{−} ^{1}, and rotational constants are in good agreement with recent a b i n i t i o calculations.

Tunneling flip flops and spin‐lattice relaxation in solid CH_{4}
View Description Hide DescriptionMeasurements of T _{1} in solid CH_{4} at T=4.2 K as a function of frequency up to 200 MHz and at lower temperatures as a function of the spin isomer populations are reported. A model is proposed, based on simultaneous tunneling transitions of nearest neighbors. These tunneling flip flops are able to account quantitatively for the whole set of observed relaxation times. The contributions of the different pairs of tunneling levels could be separated.

The rotational spectrum and geometry of the heterodimer oxirane ⋅ ⋅ ⋅ hydrogen cyanide in the vibrational ground state and the v _{β(0)}=1 state
View Description Hide DescriptionThe rotational spectrum of the heterodimer formed by oxirane and hydrogen cyanide has been observed by pulsed‐nozzle, Fourier‐transform microwave spectroscopy. Two sets of rotational transitions of similar intensity have been identified for each of the isotopic species (CH_{2})_{2}O ⋅⋅⋅ HC^{1} ^{4}N, (CH_{2})_{2}O ⋅⋅⋅ HC^{1} ^{5}N, and (CH_{2})_{2}O ⋅⋅⋅ DC^{1} ^{4}N. Each set of rotational transitions was fitted to give rotational constantsB and C, centrifugal distortion constants Δ_{ J }, Δ_{ J K }, δ_{ J }, and H _{ J K }, and, where appropriate, ^{1} ^{4}N–nuclear quadrupole coupling constants χ_{ a a } and χ_{ b b }. The rotational constants for each of the two states (labeled A and B) were interpreted in terms of a molecule of C _{ s } symmetry, with a hydrogen bond O ⋅⋅⋅ HCN and a pyramidal geometry at the oxygen atom. For the species (CH_{2})_{2}O ⋅⋅⋅ HC^{1} ^{4}N, the angle φ between the bisector of the COC angle and the HCN axis increases from 52.2(3)° in state A to 61.3(3)° in state B, while the distance r(O ⋅⋅⋅C) correspondingly increases from 3.035(4) to 3.130(4)Å. Similar changes are observed in (CH_{2})_{2}O ⋅⋅⋅ HC^{1} ^{5}N and (CH_{2})_{2}O ⋅⋅⋅ DC^{1} ^{4}N between states A and B. It is concluded that the potential energy barrier to inversion of the configuration at O by means of the low frequency hydrogen bond bending mode ν_{β(0)} is relatively low and that states A and B correspond to the ground state and the state having v _{β(0)}=1, respectively.

Rotational spectrum and structure of a linear B_{2}H_{6}–H/DF dimer
View Description Hide DescriptionRotational spectra have been observed at 4–18 GHz for several isotopic species of a diborane–hydrogen fluoride complex, using a Flygare, Fourier transformmicrowave spectrometer with a pulsed supersonic nozzle as the molecular source. The dimer is a near symmetric prolate top (κ=−0.9995); it has a linear BB–H/DF equilibrium structure with the H/D end of the H/DF attracted axially to one of the diborane’s terminal BH_{2} groups. The B, C, D _{ J }, and D _{ J K }rotational constants are: for ^{1} ^{1}B_{2}H_{6}–HF, 2111.601(1) and 2091.308(1) MHz, and 5.83(3) and 46.1(5) kHz; for ^{1} ^{1}B_{2}H_{6}–DF, 2092.991(2) and 2072.772(2) MHz, and 5.34(13) and 56.6(11) kHz; and for ^{1} ^{0}B^{1} ^{1}BH_{6}–HF, 2176.086(1) and 2154.566(1) MHz, and 6.28(3) and 56.1(5) kHz, respectively. The spectra are insensitive to the value of A, which is assumed to be that of diborane itself (79.6 GHz). The hyperfine structure of the J=0→1 transitions for ^{1} ^{1}B_{2}H_{6}–HF and ^{1} ^{0}B^{1} ^{1}BH_{6}–HF shows that the outer boron nucleus in the dimer has a very small quadrupole coupling constant (‖χ_{ a a }‖ ≲15 kHz for ^{1} ^{1}B) while that for the inner boron is appreciable (χ_{ a a } ∼−220 kHz for ^{1} ^{1}B). The implications of these results are considered. The hyperfine structure also gives an average torsional amplitude for the HF of 27° with respect to the a axis. In‐plane torsional amplitudes of 13.5° were determined for the ^{1} ^{1}B_{2}H_{6} and ^{1} ^{0}B^{1} ^{1}BH_{6} from the rotational constants for the HF dimers. With allowance for the torsional oscillations, the B⋅⋅⋅H distance is 2.5032 and 2.5038 Å in the dimers. A somewhat smaller B⋅⋅⋅D distance of 2.4955 Å is estimated for ^{1} ^{1}B_{2}H_{6}–DF. The attractive potential between B_{2}H_{6} and HF is estimated from D _{ J } to have a well depth ε of ∼530 cm^{−} ^{1}, which is comparable with that reported for the N_{2}–HF dimer. The novel structure of the B_{2}H_{6}–H/DF complex is discussed.

Intensities in the ν_{7}, ν_{8}, and ν_{9} bands of CH_{2}NH and the harmonic force field of methyleneimine
View Description Hide DescriptionA high resolution Fourier transforminfrared spectrum of methyleneimine, HN=CH_{2}, has been obtained in the gas phase in the region 700 to 1300 cm^{−} ^{1}. The rovibrational line intensities of the three lowest fundamentals ν_{7} (A’), ν_{8} (A‘), and ν_{9} (A‘) have been simulated including all Coriolis interactions between the three bands, and by fitting the observed spectrum the relative signs and magnitudes of the vibrational transition moments have been determined. All of the available spectroscopic data have been used to determine the harmonic force field of methyleneimine.

Nuclear spin relaxation studies of the spin‐rotation interaction of ^{1} ^{3}C in CO in various buffer gases
View Description Hide DescriptionNuclear spin‐lattice relaxation timesT _{1} have been measured for ^{1} ^{3}C in ^{1} ^{3}C^{1} ^{6}O in pure CO gas and in CO in Ar, Kr, Xe, N_{2}, O_{2}, CO_{2}, HCl, CH_{4}, and SF_{6} gases as a function of temperature. The relaxation is completely dominated by the spin‐rotation mechanism so that empirical values of the cross sections for rotational angular momentum transfer σ_{ J } are obtained as a function of temperature.

Stimulated Raman amplification spectra in a four‐level atomic system interacting with a strong bichromatic field
View Description Hide DescriptionWe have considered the stimulated Raman spectra arising from interaction of a four‐level atom with a strong bichromatic field and a weak signal field simultaneously. The atomic system consists of two upper excited states ‖3〉 and ‖4〉 and two lower states ‖1〉 and ‖2〉, where the metastable state ‖2〉 is depleted through the action of two strong laser fields operating between the states ‖2〉↔‖4〉 and ‖2〉↔‖3〉, respectively. Using a model Hamiltonian, where all the free and interacting fields are quantized, and the Green function method in the limit of high photon densities of both laser fields, we have studied stimulated two‐photon processes near the frequencies ±ω≊ω_{2} _{1}≊ω_{4} _{1} −ω_{ a }≊ω_{3} _{1} −ω_{ b } for the ‖1〉→‖2〉 electric dipole forbidden transition describing physical processes, where one photon of the signal field with frequency ω_{4} _{1}(ω_{3} _{1}) is absorbed while a photon of the laser field with frequency ω_{ a }(ω_{ b }) is emitted and vice versa; ω_{ i j } refers to an atomic transition frequency between the states ‖i〉 and ‖j〉. The spectral function for the stimulated two‐photon processes consists of a central peak at the frequency ω=ω_{2} _{1}, which has a delta function distribution indicating the stability of the mode in question, and three pairs of sidebands, where one pair of sidebands is induced by each laser field, respectively, while the third pair of sidebands is induced by both laser fields simultaneously. The intensities of the sidebands are always negative indicating that strong amplification (stimulated emission) takes place at the corresponding frequencies. The computed resonance and off‐resonance spectra are graphically presented and discussed. When a classical description for both laser fields is used, the spectral function is found to describe one pair of sidebands, which is induced by both laser fields simultaneously; this classical result is graphically presented and compared with those obtained when the fields are quantized. It is shown that the results obtained when the fields are quantized and in the limit of high photon densities describe the classical
as well as the quantum nature of the photon fields which is lost in the classical picture. The effect of the quantum nature or, equivalently, the boson character of the photon is to split the ‘‘classical’’ spectrum described by one pair of sidebands into three pairs, whose sum of relative intensities is equal to that of the original pair derived classically.

Diatomic–diatomic molecular collision integrals for pressure broadening and Dicke narrowing: A generalization of Hess’s theory
View Description Hide DescriptionThe line shape theory of Hess draws its attractiveness from the fact that it approaches the correct asymptotic theories at low and high pressures. In this paper, Hess’s theory is generalized slightly to describe overlapping lines of diatomic molecules immersed in a bath of diatomic molecules. A ‘‘spherical’’ approximation is introduced in which the collision integrals are averaged over the propagation direction. In terms of a reduced S matrix evaluated in three commonly used coupling schemes, the pressure broadening cross sections agree with well‐known results, and the isotropic Dicke line narrowing cross section is expressed in a form suitable for numerical computation. Both cross sections can be expressed as linear sums of generalized cross sections having the same formal structure.

Quantitative photoabsorption and fluorescence study of HCl in vacuum ultraviolet
View Description Hide DescriptionThe photoabsorption and fluorescence cross sections of HCl were measured in the 106–185 nm region. Sharp absortion bands appear at wavelengths shorter than 135 nm, and fluorescence occurs at several excited states. The fluorescence cross sections are generally quite small, indicating that the excited states are strongly predissociative. The molecular processes for producing the VUV and UV fluorescences are investigated, and the Rydberg characteristics of the strong absorption bands are discussed.

Water–hydrocarbon interactions: Structure and internal rotation of the water–ethylene complex
View Description Hide DescriptionThe rotational spectra of C_{2}H_{4}–H_{2}O and C_{2}H_{4}–D_{2}O were measured using the molecular beam electric resonance technique. The rotational and centrifugal distortion constants obtained for C_{2}H_{4}–H_{2}O are: B+C=7274.747 (24), B−C=371.103 (8), A=25 858.4 (36), Δ_{ J }=0.0279 (17), Δ_{ J K }=1.7352 (66), and δ_{ J }=0.002 99 (22) MHz. The dipole moment for both isotopic species is 1.094 (1) D. The structure derived from an analysis of the rotational constants and dipole moment is nonplanar with C _{ s } symmetry. The water molecule is singly hydrogen bonded perpendicular to the plane of the ethylene; i.e., into the π system. The plane of the water bisects the C–C bond. The hydrogen bond length is 2.48 Å. Splittings are observed in the rotational transitions of C_{2}H_{4}–H_{2}O but not in C_{2}H_{4}–D_{2}O. These are assigned to excited torsional levels of the hindered internal rotation of the water with respect to the ethylene. The barrier height is estimated to be V _{2}=1.0±0.2 kcal/mol which is surprisingly high for this weakly bound complex.

Measurement of the radii of low axial ratio ellipsoids using cross correlation spectroscopy
View Description Hide DescriptionThe intensity cross correlation from a system of Brownian rotating ellipsoids is calculated using the Rayleigh–Gans–Debye (RGD) approximation. In principle, estimates of the rotational diffusion coefficient, radii, and axial ratio can be made from one measurement. Close to the Rayleigh–Gans–Debye minimum the technique appears sensitive to very low axial ratios (∼1.025). The theory is tested well below the RGD minimum using cross‐linked and swollen polystyrene latex particle approximating an ellipsoid of revolution of low axial ratio (∼1.5). Measurements of the initial decay of the field autocorrelation function at various angles are used to confirm the estimated radii and axial ratio and illustrate some advantages of the cross‐correlation technique.

^{1}H and ^{2}H NMR study of pyridinium iodide. Disorder and molecular motion between inequivalent sites
View Description Hide Description^{1}H NMR spin‐lattice relaxation times and ^{2}H NMR line shapes were measured in the low temperature phase of pyridinium iodide. The results are consistent with reorientation of pyridinium ions by 60° to populate secondary potential minima, 5.43 kJ/m above the favored orientation. This process, which constitutes the creation of orientational defects in the ordered phase, takes place by reorientation over a potential barrier of 14.6 kJ/m.

Sub‐Doppler Zeeman spectroscopy of the CeO molecule
View Description Hide DescriptionSub‐Doppler Zeemanspectra of several low‐J rotational lines in 0–0 bands of CeO[16.5]2–X _{1}2, [16.5]4–X _{2}3, [18.4]4–X _{3}4, and [19.3]3–X _{4}3 systems have been recorded by intermodulated fluorescence spectroscopy. Electronic g values for the four lower states [the Ω=J _{ a } states of the Ce^{+2}(4 f 6s)O^{−} ^{2}] superconfiguration obtained from Zeeman splittings of low‐J lines at magnetic fields up to 1100 G, are found to agree with g values calculated from the eigenvectors of a ligand field effective Hamiltonian. The present results demonstrate the capability of the ligand field model to predict electronic properties in addition to energies and illustrate the value of the Zeeman effect for uncovering the atomic–ion quantum numbers which are not normally specified for molecules in the strong spin‐orbit [Hund’s case (c)] limit.

Polarizabilities for light scattering from chiral particles
View Description Hide DescriptionThe coupled dipole method is used to calculate the circular intensity differential scattering (CIDS) from chiral particles. The particles are described by a collection of spherical or ellipsoidal dipoles. In the case of ellipsoidal dipoles, it is shown that triaxial polarizabilities have to be used to quantitatively describe the scattering matrix of the particle. For certain collections of ellipsoidal dipoles, the dipolar interactions may be neglected in calculating CIDS from the structure. The coupled dipole approximation also provides a convenient method for calculating CIDS from a one dimensional helical crystal.

Raman spectrum and structure of thermally treated silica aerogel
View Description Hide DescriptionRaman spectra have been obtained from untreated SiO_{2} aerogel at 25 °C, and after vacuum heating between 350 and 620 °C. The untreated aerogel displays a strong Raman peak near 478 cm^{−} ^{1} due to eight‐membered (4‐SiO) s u r f a c e rings, but no measurable intensity at 600 cm^{−} ^{1} from six‐membered (3‐SiO) rings. However, an intense 600 cm^{−} ^{1} peak develops upon heating between 350 and 620 °C as the 478 cm^{−} ^{1} peak is replaced by a 490 cm^{−} ^{1} peak characteristic, in fused silica, of eight‐membered i n t e r n a l rings. Vibrations involving surface CH_{3}O groups disappear along with the fluorescence at 350 °C, well before the 478 cm^{−} ^{1} Raman intensity is gone. The untreated aerogel is protected from water absorption by the hydrophobic surface methoxy groups, but the thermally treated aerogel reacts readily to form Si–OH groups as shown by the 970–980 cm^{−} ^{1} Si vs OH and 3750 cm^{−} ^{1} surface OH stretches. Raman contour shapes near 800 cm^{−} ^{1} and between 900–1300 cm^{−} ^{1} are sensitive to the conditions of thermal treatment. The Hokmabadi–Walrafen vibrational correlation relating d e c r e a s e of the mean Si–O–Si bridging angle to i n c r e a s e of the mean Si–O bond length is obeyed for both treated and untreated aerogels.

Supersonic molecular jet studies of the pyrazine and pyrimidine dimers
View Description Hide DescriptionMass selected optical spectra for the first excited singlet nπ* states of the pyrazine and pyrimidine dimers are presented. The species are created in a pulsed supersonic jet expansion. The spectra are analyzed based on ionizationenergy, vibronic structure, and relative energy with respect to the isolated monomer (cluster spectroscopic shift). Calculations of binding energy and geometry for these dimers are carried out employing a Lennard‐Jones (6‐12‐1) and hydrogen bonding (10‐12‐1) potential. In the case of pyrazine, calculations and experiments agree that both parallel planar hydrogen bonded and perpendicular dimers are present in the expansion. The calculations also predict a parallel stacked and 90° rotated pyrazine dimer which is not observed. This latter species most likely forms an excimer in the excited state with a short lifetime and a highly red shifted broad spectrum. In the case of pyrimidine, calculations yield four planar hydrogen bonded species and a parallel stacked and displaced species. The spectra for the pyrimidine dimer are consistent with these configurations, in agreement with the calculations. No perpendicular configuration is calculated for the pyrimidine dimer and no spectroscopic features require postulating the existence of such a configuration. To explore further the agreement between calculated and experimental results for aromatic dimers, calculations are also presented for the tetrazine dimer. Three calculated geometries are obtained for the tetrazine dimer: a parallel stacked and 90° rotated species, a planar hydrogen bonded species, and a perpendicular species. Experimental spectra and calculations are in basic agreement for all dimers studied and, in general, support one another.

Spectral hole burning in semicrystalline polymers between 0.3 and 4.2 K
View Description Hide DescriptionOptical dephasing in the S _{1}←S _{0} 0–0 transitions of organic guest molecules in semicrystalline polyethylene hosts has been studied via hole burning from 0.3 to 4.2 K and compared to amorphous systems. In contrast to the latter, a temperature dependence of the homogeneous linewidth much steeper than T ^{1.3} was found, which approaches that of crystalline materials and varies with the degree of crystallinity of the polymer. Parameters which fit the equations of specific theoretical models to the experimental data are calculated.

Studies of depolarized and polarized Rayleigh–Brillouin spectra of a supercooled liquid: Salol
View Description Hide DescriptionAn extensive interferometric study of polarized and depolarized Rayleigh–Brillouin spectra of neat salol was carried out as a function of temperature and scattering angles. Considerable dispersion is observed in the isotropic spectrum, as manifested by the nonlinear temperature dependence in the longitudinal hypersonic frequency and a maximum in the linewidth. The relaxation behavior of the longitudinal hypersonic frequency is shown to be due to the bulk viscosity. Upon decreasing the sample temperature, the shear wave spectrum changes from diffusive to oscillatory behavior. In the oscillatory region, the shear wave frequency decreases linearly with increasing temperature and extrapolates to a vanishingly small value at the temperature at which the longitudinal acoustic wavelinewidth is maximum. Curve fitting the VH spectrum to theory shows that the shear frequency is proportional to q; the shear wavelinewidth and the rotation–translation coupling parameter to q ^{2}. These results are consistent with a linear viscoelastic theory, or the microscopic displacement density theory (taking in the small q limit) previously developed.