Index of content:
Volume 86, Issue 2, 15 January 1987

Theoretical investigation of fluorescence concentration quenching in two‐dimensional disordered systems. Application to chlorophyll a in monolayers of dioleylphosphatidylcholine
View Description Hide DescriptionA master equation approach is used for investigating energy transfer and trapping in two‐dimensional disordered systems, where the traps are statistical pairs of pigment molecules closer than a critical distance R _{ c }. Fluorescence decay curves are calculated over a range of concentrations as a function of R _{ c } and the Förster transfer radius R̄_{0}. The concentration dependence of the lifetimes is compared to the fluorescence self‐quenching data that Chauvet e t a l. obtained from real‐time measurements in monolayers of chlorophyll a and dioleylphosphatidylcholine (DOL). This dependence is found to be close to second order and for a choice of R _{ c } =10 Å the experimental data are fit if R̄_{0}=78±2 Å. This value is in close agreement with those found in the literature from depolarization measurements.

Spin‐forbidden radiative decay of the a ^{4}Π_{ u } state of O^{+} _{2}
View Description Hide DescriptionThe spin‐forbidden radiative decay of a ^{4}Π_{ u } O^{+} _{2} has been measured in a radio frequency octopole ion trap.Photodissociation is used to probe the a ^{2}Π_{ u } population as a function of trapping time. We have found that the a ^{4}Π_{ u } state exhibits a multiple exponential decay, ranging from a few milliseconds to hundreds of milliseconds. The state dependence of the decay is seen in the photodissociation spectrum (b ^{4}Σ^{−} _{ g }←a ^{4}Π_{ u }), which changes dramatically from 0.1 to 100 ms. The major changes in the spectrum are simulated by assuming that the F _{2} and F _{3} spin components of the a ^{4}Π_{ u } state decay faster than the F _{1} and F _{4} components. We can account for this dependence on spin sublevel by assuming that the primary mechanism for radiative decay arises from spin‐orbit coupling of the a ^{4}Π_{ u } and A ^{2}Π_{ u } states. Our results suggest that the a ^{4}Π_{ u } radiative lifetime of 0.22 s measured by O’Keefe and McDonald reflects the decay of only the longest living a ^{4}Π_{ u } sublevels.

Resonant multiphoton ionization spectrum and electronic structure of CH radical. New states and assignments above 50 000 cm^{−} ^{1}
View Description Hide DescriptionResonantmultiphoton ionizationspectra, with mass and photoelectron analysis, of photolytically produced CH radical yields previously unobserved bands arising from two‐photon transitions to Rydberg and highly excited valence states. Rotational analysis of the spectrum for m/e=13, coupled with vibrational labeling of the resonant state by photoelectron kinetic energy analysis, identifies a new state, designated E’ ^{2}Σ^{+}. Breaking off of rotational structure near N’=11 in the v=2 level of the D ^{2}Π_{ i } state is attributed to predissociation by a doubly excited potential curve calculated to lie in this energy region. Comparison is made with earlier absorption spectra taken following flash photolysis.

Site‐selective spectroscopy of hydrogenic sites in CaF_{2}:Er^{3} ^{+} crystals
View Description Hide DescriptionLaser selective excitation and optical absorption studies of hydrogenated CaF_{2}:0.05% Er^{3} ^{+} crystals have revealed 16 Er^{3} ^{+} ion sites involving H^{−} or D^{−} ion charge compensation. The relative occurrence of these sites can be controlled over a wide range by varying the duration of the hydrogenation treatment. The hydrogenic nature of these sites is established by the observation of local mode absorption lines in the infrared, Er^{3} ^{+} ion electronic line isotope shifts and associated local mode vibronic lines involving the H^{−} and D^{−} ions. Local mode infrared absorption frequencies of four sites are reported for most rare‐earth ions. Five new Er^{3} ^{+}−F^{−} sites were identified in the laser selective excitation study. For 〈100〉 and 〈111〉 oriented crystals the fluorescence spectra of several of the sites exhibit well‐defined polarization which determines their Er^{3} ^{+} ion site symmetries. Symmetry confirmations are also established for the two previously reported single Er^{3} ^{+} ion sites involving fluoride ion compensation. Eleven of the hydrogenic sites reported here are classified into two families, each derived from a single Er^{3} ^{+} ion site of the parent crystal, while three others are attributed to sites of nearly cubic Er^{3} ^{+} ion symmetry. Detailed spectroscopic results for these sites are presented, together with a crystal‐field analysis for the C_{4} _{ v } symmetry sites and some model assignments.

Spectra and structure of small ring compounds. XLVIII. Conformational stability of methylcyclobutane from low frequency Raman data of the gas
View Description Hide DescriptionThe low frequency (500–80 cm^{−} ^{1}) Raman spectra of gaseous methylcyclobutane, c‐C_{4}H_{7}CH_{3}, and methyl‐d _{3}‐cyclobutane have been recorded. A series of Q branches beginning at 161 cm^{−} ^{1} for the light molecule and 154 cm^{−} ^{1} for the d _{3} compound with successive transitions falling to lower frequencies have been assigned to the ring puckering vibrations of both the low energy equatorial and high energy axial conformers. These data have been fitted to an asymmetric potential function of the form: V(cm^{−} ^{1})=(4.78±0.10)×10^{5} X ^{4}−(3.08±0.04)×10^{4} X ^{2} +(2.18±0.1)×10^{4} X ^{3} with an assumed reduced mass of 160 amu for the light compound. Utilizing this potential the difference between the puckering angles for the two conformers was calculated to be 4.3° with the equatorial conformer having the larger value of 20.7°. A similar potential was obtained for the d _{3} molecule. The energy difference between the equatorial and axial forms was found to be 247±20 cm^{−} ^{1} (706 cal/mol) and a barrier of 641±20 cm^{−} ^{1} (1.83 kcal/mol) was found for the interconversion. Experimental values for the ΔH of both the liquid (354±179 cm^{−} ^{1}) and gas (295±75 cm^{−} ^{1}) from relative intensities of different Raman band pairs over 85 and 37 °C temperature ranges, respectively, were found to be consistent with the value obtained from the potential function. These results are compared to the corresponding quantities for similar molecules.

Excited state dynamics of guaiazulene using laser‐saturated fluorescence
View Description Hide DescriptionWe report the results of a laser‐saturated fluorescence study of the S _{2}←S _{0} 0^{0} _{0} vibronic bands of two conformers of guaiazulene in a supersonic jet. Photophysical parameters were derived from the saturation study using a three‐state kinetic model which explicitly accounted for heterogeneous broadening. Since heterogeneous broadening (rotational and Doppler) is significant in heavy polyatomics, this method could become important in extending the utility of saturation studies beyond the atomic and diatomic systems to which the technique has usually been applied. To assess the utility of our kinetic model, we compared the results to those obtained with another commonly used kinetic model which ignores all frequency dependence in a spectroscopic resonance. We also collected direct absorption and unsaturated fluorescence excitation spectra in the jet, and extensive laser beam diagnostics, to parametrize the kinetic model and to provide an independent determination of the absorption cross section. The kinetic fit yielded cross sections around 3 Å^{2} for the transitions, in good agreement with the direct absorption measurement, and excited‐state lifetimes of 760±230 ps, in reasonable agreement with literature values from condensed‐phase experiments.

Amorphous solid carbon dioxide
View Description Hide DescriptionCarbon dioxide gas condensed at 10 K was found to form amorphous solid films whose infrared spectra differ substantially from those of crystalline CO_{2}. With the help of a sample of ^{1} ^{3}C‐enriched CO_{2}, the fundamental absorption bands of different isotopic species of CO_{2} in the spectra of the amorphous solid,crystalline solid, and of CO_{2} dispersed in solid nitrogen matrix were analyzed. Some conclusions regarding the structure of the amorphous solid are derived from the spectra.

Analysis of torsional spectra of molecules with two internal C _{3v } rotors. XXIV. High resolution far infrared spectra of acetone‐d _{0}, ‐d _{3}, and ‐d _{6}
View Description Hide DescriptionThe high resolution (0.10 cm^{−} ^{1}) far infrared spectra of gaseous acetone‐d _{0}, ‐d _{3}, and ‐d _{6} were measured between 370 and 40 cm^{−} ^{1}. The region of the methyl torsional transitions below 130 cm^{−} ^{1} was analyzed in terms of the semirigid rotor model for molecules with two internal C _{3v } rotors and the two‐dimensional torsional potential functions were determined. Effective barriers of 291 cm^{−} ^{1} (832 cal/mol) and sine–sine interaction terms of −l08 cm^{−} ^{1} (−309 cal/mol) were found for all three isotopic species. The results are compared with those from a b i n i t i o calculations and from the analysis of splittings in the microwave spectrum.

Rotational spectra and structures of the Ar_{2}–H/DF trimers
View Description Hide DescriptionThe feasibility of studying weakly bound, neutral van der Waals clusters through their microwave rotational spectra has been shown by identifying and characterizing Ar_{2}–H/DF. Detection of the trimeric complexes was accomplished with the Flygare Mark II Fourier transformspectrometer, modified to better utilize its inherent sensitivity. Twenty‐six b‐dipole transitions (all ee↔oo) were observed in the 3–18 GHz region for Ar_{2}–HF, and 19 for Ar_{2}–DF, and their hyperfine structure analyzed. Fitting of the line centers with Kirchhoff’s NBS program gave values (all in MHz) for Watson’s determinable parameters of 3576.508(1), 1739.139(1), and 1161.054(1) for the rotational constantsA‘, B‘, and C‘ in Ar_{2}–HF, and of 3506.791(1), 1744.056(1), and 1155.636(1) in Ar_{2}–DF. The centrifugal distortion constants τ_{1}, τ_{2}, τ_{ a a a a }, τ_{ b b b b }, and τ_{ c c c c } were found to be −0.2039(3), −0.0522(1), −0.5353(5), −0.1159(1), and −0.02021(1) in Ar_{2}–HF, and −0.2116(7), −0.0528(2), −0.4941(7), −0.1123(1), and −0.0191(1) in Ar_{2}–DF. Three small sixth order terms were necessary to fit the data within experimental error. The trimer is found to be a planar T‐shaped, highly asymmetric top (κ=−0.521) with the equilibrium position of the H/DF on the C _{2v } figure axis (the b axis), the H/D end pointing toward the two argon atoms. The structure can be viewed as a composite of three dimers, the Ar_{2} dimer and two Ar–H/DF’s. In the trimer the Ar–Ar and the two Ar–H/DF distances are a bit longer (0.04 and 0.01 Å) than in the dimers, suggesting the presence of second‐order effects. This picture is supported by an approximate, pseudotriatomic analysis of the force field, based on the four independent planar centrifugal distortion constants. The cluster is quite ‘‘floppy.’’ The hyperfine structure shows that torsional oscillations of the H/DF are comparable with those in the Ar–H/DF dimers, but anisotropic, being 3° larger in‐plane than out‐of‐plane. The in‐plane torsional oscillation of the Ar_{2} is considered.

Absolute photoionization cross sections for Kr(5s) and Kr_{2} 5s ^{3}Σ^{+} _{ u } (1_{ u }, 0^{−} _{ u }) excited states at 248 nm
View Description Hide DescriptionAbsolute cross sections for the photoionization of Kr (5s) and Kr_{2} 5s ^{3}Σ^{+} _{ u } (1_{ u }, 0^{−} _{ u } ) at 248 nm have been measured to be (5.7±1.1)×10^{−} ^{1} ^{9} and (1.4±0.3)×10^{−} ^{1} ^{8} cm^{2}, respectively. In these experiments, absolute photoelectron densities were measured in real time with a microwave absorption apparatus, and the excited atomic and molecular species were produced and subsequently photoionized by excimer lasers. The measured Kr (5s) cross section is consistent with the upper limit experimentally determined by Dunning and Stebbings [Phys. Rev. A 9, 2378 (1974)] and is close to the theoretical value calculated by Hartquist [J. Phys. B 1 1, 2101 (1978)]. For Kr_{2} 5s ^{3}Σ^{+} _{ u } (1_{ u }, 0^{−} _{ u }) , the cross section reported here is intermediate to those measured previously for the lowest ^{3}Σ^{+} _{ u } states of Ar_{2} and Xe_{2}.

Rotational energy level structure of stretching vibrational states in some small symmetrical molecules
View Description Hide DescriptionThe vibrational dependence of various vibration–rotation parameters in XY_{2}, XY_{3}, and XY_{4} molecules with C _{2v }, C _{3v }, and T _{ d } point groups has been investigated between normal mode and local mode limits. The results at these two limiting cases differ drastically from each other. The rotational constants of the two lowest vibrational states in each overtone manifold (v=v _{1}+v _{3}=constant) are equal for v≥2 in the local mode limit. The effective Coriolis constants between these vibrational pairs disappear but the vibrationally off‐diagonal H _{2} _{2}resonance terms remain important as the local mode limit is approached. The vibrational dependence of the rotational constants of the stretching vibrational states in the symmetrically substituted acetylenes and in normal silane has been analyzed. It is shown that it is necessary to couple levels by quartic anharmonic resonance terms in the normal coordinate space in order to explain the vibrational behavior of the rotational constants.

Sideband intensities in two‐dimensional NMR spectra of rotating solids
View Description Hide DescriptionIn the presence of magic angle sample spinning (MASS), two‐dimensional solid‐state NMRspectra of magnetically dilute I=1/2 nuclei split into rotational sidebands spaced at the spinning frequency in both dimensions. The intensities of these sidebands contain information on the sizes and relative orientations of the interactions present in the two experimental time domains. Here we extend an earlier analysis of sideband intensities in one‐dimensional MASS spectra to two‐dimensional MASS spectra. The resulting equations are applicable to heteronuclear and homonuclear correlationspectra, dipolar/chemical shift spectra, and slow chemical exchange spectra. We use the equations to deduce the orientation of the ^{1} ^{5}N chemical shifttensor in the amide group of L‐asparagine⋅H_{2}O from the sideband intensities in the ^{1} ^{5}N–^{1}H dipolar/chemical shift spectrum. This application to an AX_{2} system enlarges on previous work with AX systems and may be generalized to AX_{ n } systems.

Matrix and temperature effects on the relaxation of large molecules: A simultaneous time and spectral study
View Description Hide DescriptionWe present data of picosecond time‐resolved unrelaxed and relaxed emission spectra of naphthazarin (H_{2}NP) in low‐temperature matrices. Risetime and decay rates of the fluorescence originating from individual excited state vibronic levels suggest that the relaxation does not follow the predicted statistical behavior, but rather proceeds via a specific pathway. The kinetic data also suggests that the proton translocation between the two oxygens may be described by a quantum mechanical mechanism. Variations with temperature and size of the host matrix molecules have been studied and their influence on the relaxation mechanism is discussed.

The effect of vibrational excitation on the 225 nm absorption spectrum of OCS: A non‐Condon analysis
View Description Hide DescriptionA model for the calculation of the electronic spectrum of a triatomic molecule for the case of a forbidden transition that becomes allowed due to vibronic coupling is presented. The model represents the upper electronic state potential in terms of a small number of variables that can be determined from experimental measurements, and takes into account the dependence of the transition moment on the geometry of the molecule. The model is used to analysis the 225 nm system of OCS. In general, there is good agreement between available experimental information on the absorptionspectrum and the results obtained from the model. There are however some limitations in the model, particularly in the way in which it treats higher order and coupling terms in the upper state stretching modes of OCS. The model is useful for predicting the effect of vibrational excitation on a molecular electronic spectrum. The model can be used to analyze the spectra of a number of other molecules besides OCS, and provides a starting point for more sophisticated photodissociationmodels.

Measurements of the Rayleigh ratio of some pure liquids at several laser light wavelengths
View Description Hide DescriptionThe Rayleigh ratios R _{ v,v } for vertically polarized incident and scattered radiation of benzene, toluene, carbon tetrachloride, and cyclohexane have been measured at a scattering angle of 90° and at 25 °C using argon–ion and krypton–ion lasers at wavelengths 488, 514.5, and 647.1 nm. The problem of the change of the scattering geometry with the refractive index of the investigated liquid was solved by a suitable experimental procedure. Errors are estimated to be in the range of 1%–2%.

Pure rotational spectrum of boron trifluoride–^{1} ^{1}B observed by microwave Fourier transform spectroscopy
View Description Hide DescriptionPure rotational transitions of ^{1} ^{1}BF_{3} in the ground vibrational state with Δk=±3 selection rule have been measured between 14 and 17 GHz. The extremely weak transitions have been observed with a pulsed microwaveFourier transformspectrometer. The Q subbranch between k=±1 and ∓2 has been assigned for transitions with J=11 to 50. In addition, an R and a P subbranch have been identified for transitions with J between 17 and 45 and k between 10 and 32. A total of 60 measured transition frequencies has been combined in a least squares fit of the molecular constants B, C−B, D _{ J }, D _{ J K }, D _{ K }, H _{ J }, H _{ J K }, H _{ K J }, and H _{ K }.

EPR of VO^{2} ^{+} in Zn(antipyrine)_{2}(NO_{3})_{2}: On the orientation of vanadyl doped in a low symmetry crystal field
View Description Hide DescriptionSingle crystalEPR of VO^{2} ^{+}doped in Zn(antipyrine)_{2}(NO_{3})_{2} is reported. The orientation of substitutionally incorporated vanadyl in relation to the geometry of the ligand field in the host lattice is examined. The preferential orientation of vanadyl is analyzed in terms of factors that are known to effect the energy of the complex such as steric hindrance and molecular in plane bonding. Our results indicate that, for VO^{2} ^{+} in Zn(antipyrine)_{2}(NO_{3})_{2}, while the V–O bond is not oriented along any metal–ligand bond, it is close to the principal z direction of g for Cu^{2} ^{+} (with a formal d _{ x 2–y 2 }ground state) in the same host lattice. Based on this it is concluded that molecular in‐plane bonding is probably the determining factor for the orientation of vanadyl in the present case.

Tridiagonal Fermi resonance structure in the vibrational spectrum of the CH chromophore in CHF_{3}. II. Visible spectra
View Description Hide DescriptionThe near IR and visible vibrational absorption spectra of CHF_{3} were recorded up to wave numbers of 17 500 cm^{−} ^{1} providing complete frequency coverage, together with paper I, from the low frequency fundamentals to the N=6 CH stretching–bending overtone multiplet. All strong bands in the high overtone spectra could be predicted and assigned by means of the tridiagonal Fermi resonance Hamiltonian, including a few combinations with intense CF_{3} stretching vibrations already observed for the low overtones. Improved vibrational Fermi resonance constants are presented on the basis of a fit to 35 assigned bands. An analysis of the rotational fine structure of the 2ν_{4} (E) overtone component and several Fermi resonance component bands result in values for α_{ b } and α_{ s }, which allow us to determine B _{ e }. In the high overtone bands no rotational fine structure is observed. The bands can be understood by introducing additional homogeneous rovibrational structures of phenomenological widths Γ≊1 to 10 cm^{−} ^{1}. The results are discussed in relation to the separation of time scales for mode selective vibrational redistribution and further evolution. The overtone band strengths are reported and analyzed approximately with the empirical local Mecke dipole function.

Calculation of ESR spectra and related Fokker–Planck forms by the use of the Lanczos algorithm. II. Criteria for truncation of basis sets and recursive steps utilizing conjugate gradients
View Description Hide DescriptionThe complex symmetric Lanczos algorithm (LA) has proven to be a very efficient means of calculating magnetic resonanceline shapes and spectral densities associated with Fokker–Planck forms. However, the relative importance of the various components of the basis set in an accurate representation of the spectrum and the proper number of recursive steps are not easily assessed in practice using the Lanczos algorithm. A systematic and objective procedure for the determination of optimal basis sets and number of recursive steps is developed using a generalization of the conjugate gradient method (CGM) appropriate for the type of complex symmetric matrices occuring in these problems. The relative importance of the individual basis vectors is determined by using the CGM to obtain the ‘‘solution vector’’ from the set of algebraic equations defining the spectrum. This is done at several values of the sweep variable (e.g., the frequency or the magnetic field). The maximum (over these values of sweep variable) for each component of the solution vector is taken to be a measure of the overall importance of the corresponding basis
vector in the complete spectrum. Using this method signficant basis set truncation is conveniently possible. The number of recursive steps needed for an accurate representation of the spectrum is easily obtained by monitoring the residual in the approximate solution vector at the center of the spectrum and by recognizing the close relationship between the LA and the CGM. It is this relationship that enables construction of the Lanczos tridiagonal matrix with the CGM which can either be used to calculate the cw ESR spectrum directly or else the eigenvalues. The information obtained from the CGM can be used to ‘‘turbocharge’’ the LA by taking advantage of the nearly optimal basis set and number of recursive steps. Significant savings in computation time are possible, and relative savings are greatest for the most difficult problems. This is illustrated with a variety of examples of slow‐motional cw ESR spectra and of the new two‐dimensional electron‐spin‐echo technique. In keeping with the greater sensitivity of the latter technique to motional dynamics, it is consistently found to require significantly larger optimal basis sets and number of recursive steps for an accurate representation. One of the most challenging problems for both types of spectroscopy is the case of macroscopically oriented samples where the macroscopic director is tilted at an angle relative to the applied static magnetic field, since this removes much of the symmetry in the problem. This case is found to yield to very significant truncation of basis sets, and a new symmetry‐based decoupling of certain basis vectors was found in this study for the particular example of a 90° tilt angle.

Brillouin scattering studies of isotopic effects in solid ammonia
View Description Hide DescriptionThe technique of high resolution Brillouinspectroscopy has been used to determine the adiabatic elastic constants and the elasto‐optic coupling (Pockels) coefficient ratios of oriented single crystals of (solid I) ND_{3} at temperatures near the gas–liquid–solid triple point. The values of the elastic constants at 196.0 K are C _{1} _{1}=83.3, C _{1} _{2}=44.0, and C _{4} _{4}=49.6 (in units of kbar) with an estimated absolute uncertainty of ±2%. The values of the elasto‐optic coefficient ratios are P _{1} _{2}/P _{1} _{1}=0.90 and P _{4} _{4}/P _{1} _{1}=0.16 for ND_{3} and 0.89 and 0.16 for NH_{3}, respectively. Other than that expected from the mass ratio, no significant isotopic differences are evident.