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Volume 77, Issue 9, 01 November 1982

Linear response theory of polypeptide circular dichroism: Bogoliubov exciton theory
View Description Hide DescriptionA linear response theory of polypeptide circular dichroism is presented. The Bogoliubov collective excitation theory is derived without the use of second quantization techniques and therefore direct insight to the approximations is obtained. The static field at each chromophore is approximated as an external field unaffected by the polarization it induces. Susceptibilities that contain the static field effect are obtained via a Green operator method. These susceptibilities are then used in the geometric expansion of time dependent Hartree theory to obtain the result. Also, a partitioning technique is presented for handling the resulting normal mode problem.

Mode amplitudes in dynamic light scattering by concentrated liquid suspensions of polydisperse hard spheres
View Description Hide DescriptionThis paper concerns the dynamic light scattering by suspensions of polydisperse hard spherical particles. It is concluded that for relatively high volume fractions and fairly narrow distributions, the light scatteringcorrelation function should, to a good degree of approximation, be composed of two independent modes with well‐separated decay times. The faster decaying mode describes collective stochastic compression–dilation motions and is present even for a monodisperse system. The slower decaying mode describes the exchange of different species. The relative mode amplitudes are calculated in the Percus–Yevick approximation for hard spheres. The two decay times of fast and slow mode are associated with diffusion coefficients D _{+} and D _{−}, respectively. In the case of scattering power polydispersity D _{+} and D _{−} are rigorously identified with collective and self‐diffusion, respectively. In the case of size polydispersity D _{+} and D _{−} can be associated with ‘‘average’’ collective and self‐diffusion coefficients. The considerations are limited to zero scattering wave vector and volume fractions above 0.15. Comparison with experimental results from other papers are in favor of the theory.

The relative Raman intensities of ν(M–L) A _{1} _{ g } and E _{ g } modes for some d ^{0}ML_{6} anions of O _{ h } symmetry
View Description Hide DescriptionThe observation that unusual relative ν(M–L) Raman intensities are associated with a t ^{6} _{2} _{ g } configuration has prompted calculations on d ^{0} systems based on the hypothesis that charge transfer transitions to the t _{2} _{ g } shell make a dominant contribution to the corresponding Raman intensities of these systems. A combination of Albrecht and Wolkenstein–Eliashevich models leads to the prediction of relative Raman intensities in good qualitative agreement with those observed experimentally.

Short time behavior of the dipole autocorrelation function and molecular gases absorption spectrum
View Description Hide DescriptionA quasistatic theory of the dipole autocorrelation function for isolated molecular spectral lines has been developed and applied to linear molecules perturbed by atoms and molecules. The matrix elements of the evolution operator associated with the molecular dipole moment are treated to all orders in the interaction without any cutoff procedure. An analytical expression of the intensity distribution in terms of the intermolecular potential has been obtained which is easily tractable for involved molecular systems. Numerical tests of this theory have been performed for rotation–vibration lines of HCl–Ar, HCl–Xe, and CO_{2}–Ar gas mixtures by comparing the present results with that of a unified theory of the line shape for molecule–atom couples, valid from resonances to the far wings and including all orders in the interaction. These tests justify the present approach and show a considerable reduction of the computation time required (by more than two orders of magnitude), allowing now the study of the polyatomic preturbers case. Application to infrared absorption lines of HCl self‐perturbed and perturbed by CO_{2} leads to a good agreement with the experimentally determined super‐Lorentzian profile.

Vacuum UV spectrum of C_{3} trapped in argon at 8 K
View Description Hide DescriptionThe vacuum ultraviolet absorptionspectrum to 1200 Å has been obtained for the products from the evaporation of graphite at 2700 °C, trapped in argon at 8 K. Based on correlations with the ^{1}Π_{ u }–X ^{1}Σ^{+} _{ g } transition of C_{3} in the near ultraviolet, the results of ^{1} ^{3}C substitution, and other observational evidence, it is proposed that a band system originating at 1890 Å be assigned to the ^{1}Σ^{+} _{ u }–X ^{1}Σ^{+} _{ g } transition of C_{3}. Vibrational analysis yields ν_{1}′≂1080, ν_{2}′≂300, and ν_{3}′≂780 cm^{−} ^{1} for the ^{1}Σ^{+} _{ u } state.

Coherent Raman scattering in liquid benzene from symmetric ring vibrations in the ^{1} B _{2u } electronic state excited by two‐photon absorption
View Description Hide DescriptionIn the presence of two‐photon absorption in benzene at 5268 Å, we observe coherent anti‐Stokes Raman scattering at 993 and 935 cm^{−} ^{1}. These energies correspond to symmetric ring breathing vibrations (a _{1g } symmetry) in the ^{1} A _{1g } ground, and ^{1} B _{2u }excited state of benzene, respectively. Raman activity in the latter state is demonstrated for the first time. Its observation is made possible by strong two‐photon absorption to the ^{1} B _{2u } level via vibronically assisted transitions, and resonance enhancement of the Raman process by ^{1} B _{2u }–^{1} E _{1u } one‐photon transitions. Simultaneously, we observe a resonance enhanced electronic background at the anti‐Stokes frequency over a broad, featureless spectrum arising from two‐photon transitions to ^{1} B _{2} _{ u }. At wavelengths well below the two‐photon absoprtion band of benezene, neither electronic contributions nor the 925 cm^{−} ^{1} peak are observed and only the ground state vibrations at 993 cm^{−} ^{1} remain.

Deuterium quadrupole coupling in BD_{3}CO
View Description Hide DescriptionThe hyperfine structure of the J=1→0 rotational transitions of ^{10}BH_{3}CO, ^{1} ^{1}BH_{3}CO, and ^{1} ^{1}BD_{3}CO was observed with a molecular beammaser spectrometer. Rotational constants,quadrupole coupling, spin rotation, and spin‐spin interaction constants were determined from the data analysis. The deuterium quadrupole coupling constant in ^{1} ^{1}BD_{3}CO, was determined to be e Q q _{ a } _{ a }(D)=−48.5±2.3 kHz and e Q q _{ z } _{ z }(D)=116.9±5.4 kHz. The procedure for determining the matrix elements of the spin‐spin interaction between the equivalent deuterium nuclei is presented.

Energy transfer between Eu^{3+} ions in LiNbO_{3}, CaWO_{4}, and Eu_{ x }Y_{1−x }P_{5}O_{14} crystals
View Description Hide DescriptionNarrow‐band laser excitation is used to selectively pump Eu^{3+} ions in different types of crystal field sites in four host crystals LiNbO_{3}, CaWO_{4}, EuP_{5}O_{14}, and Eu_{0.01}Y_{0.99}P_{5}O_{14}. Energy transfer between ions in nonequivalent sites is characterized using time‐resolved spectroscopy techniques and phenomenological rate parameter models. In all four cases, the energy transfer is found to occur by a single‐step process through a weak electric dipole–dipole interaction. However, the different spatial distributions of the Eu^{3+} ions in these hosts produce differences in the energy transfercharacteristics.

Detection of the a ^{1}Π_{ g } (v′=0, 1)←X ^{1}Σ^{+} _{ g } (v″=0) transition in N_{2} by laser‐induced fluorescence
View Description Hide DescriptionThe a ^{1}Π_{ g }(v′=0.1)←X ^{1}Σ^{+} _{ g }(v″=0) transitions in N_{2}, part of the Lyman–Birge–Hopfield bands, have been seen by two‐photon absorption detected by VUV fluorescence.Fluorescence was observed over a pressure range from 5 m Torr to 10 Torr. From the lifetime decrease with pressure at low pressure, quenching rate constants were determined, which are equivalent to cross sections in the range of 2.6×10^{−} ^{1} ^{6} cm^{2}. At higher pressures a slow decay was observed that is interpreted as being due to the a′ state which acts as an energy reservoir with a pressure dependent decay constant. We anticipate that laser‐induced fluorescence will be a useful scheme for measuringground state rotational and vibrational populations for the nitrogen molecule.

Correlation between the observed infrared stretching frequency and the bond character of the Si–H bond
View Description Hide DescriptionIt is shown that the empirical correlation between the infrared (IR) stretching frequency of the Si–H bond in substituted silane molecules (SiH_{3}R_{1}, SiH_{2}R_{1}R_{2}, and SiHR_{1}R_{2}R_{3} with R_{ i } the substituted molecular fragment) can be understood on a fundamental basis as the dependence of frequency on the bond order (S component) of the bond.

A determination of hyperfine constants for the RCONHO radical in randomly oriented samples of x‐irradiated hydroxamic acids
View Description Hide DescriptionRCONHO radicals are identified in x‐irradiated acetohydroxamic acid, hydroxyurethane, and propiohydroxamic acid. The hydrogen and nitrogen hyperfine coupling constants for these radicals are evaluated from ESR spectra taken of polycrystalline samples. The characteristic spectrum of randomly oriented RCONHO radicals is described. Equations for the coupling constants in terms of the width of the spectrum are given.

Infrared spectrum and potential constants of silicon tetrafluoride
View Description Hide DescriptionDoppler‐limited tunable diode laserspectra of ν_{4} of ^{2} ^{8}SiF_{4} have been analyzed and the spectroscopic constants determined. In contrast to most earlier low‐resolution studies, the Coriolis constant ζ_{4}, when combined with ζ_{3} as obtained from previous laser spectroscopy, yields a zeta sum that is within 5% of the expected harmonic value of 1/2. The band origins of 12 overtones and combinations have been obtained from Fourier‐transform spectra (0.04 cm^{−} ^{1} resolution), resulting in estimates of the anharmonicity constants and harmonic frequencies. From the Coriolis constants and the isotope shifts in ν_{3} we have redetermined the general quadratic force field of SiF_{4}.

The microwave spectrum and molecular structure of CO_{2}–HCl
View Description Hide DescriptionRadio frequency and microwave molecular beam electric resonance spectra have been obtained for three isotopic species of the hydrogen‐bonded weakly bound complex CO_{2}–HCl. The following spectroscopic constants have been determined: This complex most likely has a linear equilibrium geometry with an O–H bond length of 2.14 Å. A large induced dipole moment is found in this complex. A comparison of structural properties for this and other related weakly bound molecules is made.

Yields and mean free paths of photoelectrons from liquid hexamethyl phosphoric triamide
View Description Hide DescriptionMonochromatic photons between 775 and 500 Å were incident almost normally (15°) on the surface of liquid hexamethyl phosphoric triamide (HMPT). Incident and reflected beam strengths were measured with a double ion chamber filled with argon and the current leaving the cup of liquid was determined. After subtracting a portion of the current due to Ar^{+} drift into the cup, we obtained the photocurrent and, hence, the absolute photoemission yield. The yield falls from 9% at 16 eV to 5% at 25 eV. Such a falloff with increasing photon energy is expected from theory. The values are about double those calculated from theory using a three‐step model for the photoemission and using the Born approximation to calculate electron mean free paths. Conversely, if the experimental yields are used in the three‐step model, the electron mean free paths calculated from the data range from about 935 Å at 16 eV to about 80 Å at 24 eV and are about two to three times the theoretically predicted values.

Raman intensities of overtones and combination bands of C_{2}H_{2}, C_{2}HD, and C_{2}D_{2}
View Description Hide DescriptionMeasurements of absolute gas phase vibrational Raman scattering cross sections of binary overtone and combination bands of C_{2}H_{2},C_{2}HD, and C_{2}D_{2} are reported. Calculated values for these cross sections, which take into account the contribution of the anharmonic force field and the electro‐optical anharmonicity, are also presented. Within limitations due to approximations in the theory and uncertainties in the parameters, the comparison between the experimental cross sections and the calculated ones is quite encouraging.

Variable‐angle sample‐spinning high resolution NMR of solids
View Description Hide DescriptionWe have obtained high‐resolution solid‐state NMRspectra of a variety of nonintegral‐spin quadrupolar nuclei (^{2} ^{3}Na,^{5} ^{1}V, and ^{5} ^{5}Mn) under conditions of ‘‘magic‐angle’’ sample‐spinning (MASS) and ‘‘variable‐angle’’ sample‐spinning (VASS). We show for systems in which the second‐order quadrupole interaction dominates the breadth of the (1/2,−1/2) spin transition, that optimum line narrowing is achieved by rapid sample rotation at angles other than the familiar θ=54.7° ‘‘magic‐angle.’’ The effect originates in the more complex angle dependence of the second‐order quadrupole interaction, rather than the more familiar P_{2} (cos θ) dependence of dipolar and chemical shift interactions, and theoretical VASS line shapes for a variety of spinning angles, and electric field gradient tensor asymmetry parameters (η), are presented. We show that VASS NMR at low fields generates complex spectral line shapes, which at some angles exhibit well‐resolved centerbands and spinning sidebands. We also discuss briefly, with examples, the complexities introduced by the presence of dipolar and/or chemical shiftanisotropy interactions in such experiments and investigate the question of the optimum field‐strengths for NMR of quadrupolar nuclei. Our results indicate that the VASS NMR technique appears to have considerable utility in obtaining high‐resolution NMRspectra of a wide variety of quadrupolar nuclei in inorganic solids, especially those with relatively small (≲5 MHz) quadrupole coupling constants.

Deuterium quadrupole coupling in methanol, salicyclic acid, catechol, resorcinol, and hydroquinone
View Description Hide DescriptionDeuteron NQR spectra of several model systems involving alcoholic of phenolic‐OD groups are discussed. The spectra of alpha hydroquinone and its two isomers resorcinol and catechol show complex structure due to the presence of inequivalent O–D⋅⋅⋅O hydrogen bonds. In the case of hydroquinone, this structure collapses to that characteristic of a single type of hydrogen bond in the beta‐ or clathrate‐forming phase. An attempt is made to place the data in theoretical perspective by calculations of the deuterium field gradient in hydroxide ion, hydroxyl radical, methanol, and methanol dimer and by comparison with precise Hartree–Fock computations from the literature.

Isolated ultracold porphyrins in supersonic expansions. I. Free‐base tetraphenylporphyrin and Zn‐tetraphenylporphyrin
View Description Hide DescriptionIn this paper we report the results of an experimental study of the fluorescence excitation spectra and of the time‐resolved emission of Zn‐tetraphenylporphyrin (ZnTPP) and of free‐base tetraphenylporphyrin (H_{2}TPP) seeded in pulsed supersonic expansions of He. We have studied the S _{0}→S _{1} transition (the Q band) and the S _{0}→S _{2} transition (the Soret, B band) of ZnTPP, as well as the S _{0}→S _{1} ^{ x } transition (the Q _{ x } band), the S _{0}→S _{1} ^{ y } transition (the Q _{ y } band), and the S _{0}→S _{2} ^{ x } transition (the B _{ x } band) of H_{2}TPP. Information was obtained on the electronic energy levels, the vibrational level structure, the details of low‐frequency nuclear motion, and some characteristics of electronic relaxation.

Isolated ultracold porphyrins in supersonic expansions. II. Zn‐tetrabenzoporphyrin
View Description Hide DescriptionLaser‐induced fluorescence excitation spectra of zinc tetrabenzoporphyrin in seeded, pulsed, supersonic expansions of He reveal well‐resolved vibrational excitations for the S _{0}→S _{1} and S _{0}→S _{2} electronic transitions. Electronic relaxation in the S _{1}manifold was interrogated by time‐resolved spectroscopy, exhibiting a practical independence of the lifetimes on the excess vibrational energies in the range E _{ v }=0–10 000 cm^{−} ^{1}. Spectroscopic line broadening data provided semiquantitative information on interstate electronic relaxation from the electronic origin of the S _{2} state, whose lifetime is τ(S _{2})≳4 ps.

Isolated ultracold porphyrins in supersonic expansions. III. Free‐base porphine
View Description Hide DescriptionThe vibrational level structure of the S _{0}→S _{1} ^{ x } transition (the Q _{ x } band) and of the S _{0}→S _{1} ^{ y } transition (the Q _{ y } band) of free‐base porphine in supersonic expansions of He was interrogated by laser‐induced fluorescence excitation spectroscopy. Electronic relaxation in the S _{1} ^{ x }manifold was explored by time‐resolved spectroscopy, revealing a constant value of the decay lifetime τ=9.5±1.0 ns for excess vibrational energies in the range E _{ v }=0–5000 cm^{−} ^{1}. The line broadening (FWHM) Δ=1.0–1.5 cm^{−} ^{1} of the electronic origin and of low‐lying vibrational excitations in the S _{1} ^{ x }manifold originates from inhomogeneous unresolved rotational structure, while the large linewidth Δ=11.9 cm^{−} ^{1} of the electronic origin of the S _{1} ^{ y } state is due to homogeneous electronic relaxation broadening in the statistical limit. The line shape of the electronic origin of S _{1} ^{ y } was found to be Lorentzian, providing a quantitative determination of the lifetime τ=5×10^{−} ^{1} ^{3} s for interstate S _{1} ^{ y }–S _{1} ^{ x } electronic relaxation within a bound level structure of a large isolated molecule.