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Volume 101, Issue 7, 01 October 1994

Analysis of nuclear magnetic resonance spin echoes using simple structure factors
View Description Hide DescriptionThe measured amplitude M(q,t) in a pulsed field gradient spin echo experiment probes the pore structure using two length scales, the gradient length q ^{−1}, and the diffusion length [D(t)t]^{1/2}. M(q,t) can be well represented by a convolution of the structure factor of the connected pore space with an appropriate Gaussian propagator. This ansatz provides a model‐independent way of obtaining the structure factor. In this paper, we consider the forward problem of understanding the amplitude M(q,t) using the simplest possible models for the structure factors which involve only one length scale. The most prominent among the simple models is the Debye model, which provides us with an understanding of the various length scales in the problem. We study several other structure factors, all definable by a single parameter—collections of tubes, collections of sheets, and collections of impenetrable spheres. We discuss periodic geometries for which the ansatz becomes exact in the long time limit. Implications for a ball and stick model for the pore geometry are discussed.

Reassignment of the vibrational structure of the Huggins absorption band of ozone
View Description Hide DescriptionA new assignment of the vibrational structure of the Huggins band of ozone is given. The assignment is consistent with the symmetry requirements on changes in the asymmetric stretching (v _{3}) quantum number and with data on the differences in the location of vibronic bands between ^{16}O_{3} and ^{18}O_{3}. Based on the reassignment of the spectrum, new values for the vibrational constants for ^{16}O_{3} and ^{18}O_{3} in the excited electronic state responsible for the Huggins system are calculated. The reassignment of the Huggins system provides a simple explanation for several otherwise puzzling observations concerning the spectrum, and suggests that the Huggins and Hartley band systems arise from transitions to different electronic states, in accord with previous molecular orbital calculations.

On the choice of inertial axes for interpreting spectroscopic properties of van der Waals complexes
View Description Hide DescriptionProperties such as the dipole moments and nuclear quadrupole coupling constants of van der Waals complexes are important in the determination of intermolecular potential energy surfaces from high‐resolution spectra. The properties are often interpreted in terms of angular expectation values. It is shown that, when calculating such properties, it is important to use an inertial axis system that satisfies the Eckart conditions. Projections onto other axes, such as the intermolecular vector or the instantaneous principal axes, can lead to substantial errors when the individual monomers have large moments of inertia.

Interaction of an aluminum atom with an alkaline earth atom: Spectroscopic and ab initio investigations of AlCa
View Description Hide DescriptionA spectroscopicanalysis of diatomic AlCa generated by laser vaporization of a 2:1 Al:Ca metal alloy followed by supersonic expansion has been completed using resonant two‐photon ionization spectroscopy. Four excited electronic states have been identified and investigated in the energy region from 13 500 to 17 900 cm^{−1}. These are the [13.5] ^{2}Π_{ r }, the [15.8] ^{2}Σ, the [17.0] ^{2}Δ_{3/2}(?), and the [17.6] ^{2}Δ_{3/2} states. From rotational analysisexcited state bond lengths have been measured for three of the four excited states, and the ground state has been unambiguously determined as a ^{2}Π_{ r } state with a weighted least squares value of the ground state bond length of r _{0} ^{‘} = 3.1479± 0.0010 Å. The ionization energy of the molecule has also been directly determined as 5.072±0.028 eV. Ab initio calculations for the potential energy curves of seven low‐lying states of AlCa [X ^{2}Π_{ r }, ^{2}Σ^{+}, ^{4}Σ^{−}, ^{4}Π_{ r }, ^{2}Π_{ r }(2), ^{2}Δ, and ^{2}Σ^{−}] and for the X ^{1}Σ^{+}ground electronic state of AlCa^{+} have been carried out. In agreement with experiment, ^{2}Π_{ r } is calculated to be the ground electronic state of the neutral molecule. The dissociation energies of AlCa (X ^{2}Π_{ r }) into Al(3s ^{2}3p ^{1},^{2} P ^{0})+Ca(4s ^{2},^{1} S) and for AlCa^{+} (X ^{1}Σ^{+}) into Al^{+}(3s ^{2},^{1} S)+Ca(4s ^{2},^{1} S) are calculated to be 0.47 and 1.50 eV, respectively. The excited ^{2}Σ^{+}, ^{4}Σ^{−}, ^{4}Π_{ r }, ^{2}Π_{ r }(2), ^{2}Δ, and ^{2}Σ^{−} states are calculated to lie 0.2, 0.7, 0.7, 1.1, 1.1, and 1.1 eV above X ^{2}Π_{ r }, respectively, and the vertical and adiabatic ionization energies of AlCa have been calculated to be 5.03 and 4.97 eV, respectively.

Interaction of an aluminum atom with a closed subshell metal atom: Spectroscopic analysis of AlZn
View Description Hide DescriptionResonant two‐photon ionization spectroscopy has been employed to investigate diatomic AlZn produced by laser vaporization of a 1:2 Al:Zn alloy target disk in a supersonic expansion of helium. Several discrete transitions are reported in the energy range from 18 400 to 19 100 cm^{−1}. Most of these are assigned as members of the B ^{2}Π←X ^{2}Π system, although an isolated band has been observed and assigned as the 2‐0 band of the A Ω’=0.5←X ^{2}Π_{1/2} system. A pair of strongly mixed levels are identified as resulting from a homogeneous spin–orbit perturbation between the A Ω=0.5, v’=3 and the B ^{2}Π_{1/2}, v’=1 levels, and the perturbation matrix element has been deduced to be 8.11 cm^{−1} for ^{27}Al^{64}Zn, 8.23 cm^{−1} for ^{27}Al^{66}Zn. The ground state has been unambiguously identified as a ^{2}Π_{ r } state with a bond length of 2.6957±0.0004 Å. Comparisons to the results of the preceding article on the spectroscopy of AlCa are also provided, along with a discussion of the chemical bonding in AlZn in relation to AlCa, AlAr, and AlKr.

Field‐induced intensity and Stark shift measurements of the electric dipole moment of ICl in the B ^{3}Π_{0+} state
View Description Hide DescriptionThe laser‐induced fluorescencespectrum in ICl of the (2’–0‘) vibrational band in the B ^{3}Π_{0+}–X ^{1}Σ^{+} electronic system has been measured as a function of the electric field strength up to 32.5 kV/cm. Field‐induced intensity measurements on I^{35}Cl have been used to determine the magnitude and sign of the electric dipole moment μ_{ B } in the B state relative to the magnitude and sign of the moment μ_{ X } in the X state. From the intensity ratio of the field‐induced line Q(0) to the allowed Stark component P(1,0), which has the same upper state, it was found that μ_{ B }/μ_{ X }=+(0.888±0.051). The positive sign indicates that the polarity is the same in the B and the X states. Intensity ratio measurements for Q(0) to R(5) and for Q(1) to R(5) yield similar (but less precise) results. In order to test this first application of the method to excited electronic states, Stark shift measurements were carried out on a number of P‐branch Stark components. It was found for I^{35}Cl that ‖μ_{ B }/μ_{ X }‖=(0.8984±0.0036), in good agreement with the intensity measurements. The corresponding determination for I^{37}Cl is that ‖μ_{ B }/μ_{ X }‖=(0.900±0.014). The present results are in agreement with those obtained earlier from studies of the absorptionspectrum by Watanabe et al. [Jpn. J. Appl. Phys. 31, 901 (1992)].

Extreme‐ultraviolet photodissociation of N_{2}O in superexcited states
View Description Hide DescriptionWe demonstrate the observation of neutral dissociation, which provides the possibility of a spectroscopy of highly lying superexcited states. The yield spectrum of the undispersed fluorescence radiation of wavelength λ_{ f } in the region 113≤λ_{ f }≤180 nm from excited neutral fragments in the photodissociation of N_{2}O is presented in the region of excitation photon wavelength λ_{ex} in the region 30≤λ_{ex}≤111 nm (photonenergy region 41.3–11.2 eV). We show the evidence of selective or preferential neutral dissociation in the decay of superexcited N_{2}O in competition with autoionization; in particular, the evidence for an important role of neutral dissociation of superexcited N_{2}O followed by the production of ionic fragments. We also show the neutral dissociation of superexcited states with the character of double‐holed doubly excited states located for 30≤λ_{ex}≤60 nm. The aspect of superexcitation (bound channel of electron promotion) in the region of inner‐valence excitation is discussed in relation with free (continuum) channels.

Microwave spectrum and molecular structure of the cyclic C_{3}H radical
View Description Hide DescriptionThe rotational spectral lines of the cyclic C_{3}H radical in the ^{2} B _{2}ground electronic state are observed by microwave spectroscopy. The radical is produced in an absorption cell by discharging a mixture of C_{2}H_{2}, CO, and He. The spectral lines of two ^{13}C isotopic species are also observed. The radical is a planar molecule with C _{2v } symmetry, and the r _{ s } structure is determined as follows: r _{ s }(C–H)=1.0760 Å, r _{ s }(C–C)=1.3771 Å, and r _{ s }(C–CH)=1.3739 Å. From the observed inertial defect, the vibrational frequency of the C–C antisymmetric vibration is estimated to be about 500 cm^{−1}, which is fairly low for the frequency of the C–C stretching mode. The low vibrational frequency arises from the vibronic interaction between the ground electronic state and the low‐lying ^{2} A _{1} electronic state. On the basis of the hyperfine coupling constants obtained for the ^{13}C species, the unpaired electron is found to be almost evenly distributed among the three carbon atoms. Such delocalization of the unpaired electron is consistent with the observed geometrical structure.

Infrared absorption of cis–cis peroxynitrous acid (HOONO) in solid argon
View Description Hide DescriptionNitric acid (HONO_{2}) isolated in solid argon at 12 K was irradiated with 193 nm emission from an ArF excimer laser. Recombination of the photofragments led to formation of peroxynitrous acid (HOONO) in various conformers. In addition to previously reported lines due to trans–perp HOONO, lines at 3285.4, 1600.3, 1395.0, 927.2, 794.3, and 629.1 cm^{−1} were observed; they are assigned to cis–cis HOONO having a five‐membered hydrogen‐bonded ring. The observed vibrational frequencies and the corresponding isotopic shifts of both conformers are in agreement with recent theoretical calculations. Cis–cis HOONO was photolyzed much more rapidly than trans–perp HOONO upon irradiation at 308 nm with a XeCl laser. Lines due to a HO_{2}...NO complex were also observed; they disappeared upon irradiation with the globar source of the infrared spectrometer. The mechanism of formation of various conformers of HOONO is discussed.

Fine vibrational structure in core‐to‐bound spectra of polyatomic molecules
View Description Hide DescriptionNear‐edge x‐ray‐absorption fine‐structure (NEXAFS)spectra of 1‐butene (C_{4}H_{8}), acrylonitrile (C_{2}H_{3}CN) and 1,3‐butadiene (C_{4}H_{6}) multilayers were recorded with high resolution (better than 100 meV at the carbon edge) and a theoretical method to interpret the vibrational structure of the observed C _{1s }→π* bands is presented. The method is based on local (quadratic) approximations for the potential energy surfaces of both ground and excited electronic states, with input data obtained by ab initio calculations of normal modes for the ground state and energy gradients for the excited state within the framework of the equivalent core model. The method proved to be useful in qualitative terms, providing information on the nature of the excited modes and on the geometrical changes following the electronic excitation. We have also calculated the C _{1s }→π* spectrum of ethylene (C_{2}H_{4}) and compared it to those obtained for C_{4}H_{8}, C_{2}H_{3}CN, and C_{4}H_{6}. Since the latter can be considered as substituted ethylenes, the validity of the building‐block scheme for the vibrational splittings in inner‐shell absorption spectra could be assessed by this comparison.

Vibronic analysis of overlapping resonances and the third‐harmonic‐generation spectrum of β‐carotene
View Description Hide DescriptionVibronic contributions to third‐harmonic‐generation (THG) are obtained in the Condon approximation for displaced harmonic oscillators in the region of overlapping three‐ and two‐photon resonances, where enhanced THG intensity and explicit dependence on the relative signs of the displacements are found. The THG intensity and phase of β‐carotene are then modeled in terms of four electronic states, including overlapping 2 ^{1} A _{ g } and 1 ^{1} B _{ u } resonances whose displacements are taken from two‐photon and linear spectra, respectively, and a high‐energy A _{ g } state based on a Pariser–Parr–Pople (PPP) sum rule for transition dipoles. Relations between THG and other spectra show the limitations of three‐state models and provide useful constraints on the excited‐state structure of related conjugated systems such as polyenes and β‐carotene.

Predissociation supported high‐resolution vacuum ultraviolet absorption spectroscopy of excited electronic states of NH_{3}
View Description Hide DescriptionUsing monochromatic vacuum ultraviolet radiation generated by two‐photon resonant sum frequency mixing in a Mg–Kr mixture we have investigated the electronic transition of NH_{3} in the 67 000–73 000 cm^{−1} region by detecting the fluorescence from the predissociation fragments of NH_{3}. The spectrum is simplified using a pulsed molecular beam. Vibronic bands of the B ^{1} E‘ (2^{9}, 2^{10}, 2^{11}, 2^{12}, 2^{7}3^{1}, 2^{8}3^{1}) state are clearly identified and relevant molecular constants are deduced. The predissociation in the B̃ ^{1} E‘ state is found to be nearly independent of the rotational quantum numbers (J,K) within one vibrational band. The linewidths of different vibronic components of the B̃ ^{1} E‘ state are measured. In addition, other absorption bands are presented including previously unobserved weak absorption features.

Theory of two‐dimensional Fourier transform electron spin resonance for ordered and viscous fluids
View Description Hide DescriptionA comprehensive theory for interpreting two‐dimensional Fourier transform (2D‐FT) electron spin resonance(ESR) experiments that is based on the stochastic Liouville equation is presented. It encompasses the full range of motional rates from fast through very slow motions, and it also provides for microscopic as well as macroscopic molecular ordering. In these respects it is as sophisticated in its treatment of molecular dynamics as the theory currently employed for analyzing cw ESRspectra. The general properties of the pulse propagator superoperator, which describes the microwave pulses in Liouville space, are analyzed in terms of the coherence transfer pathways appropriate for COSY (correlation spectroscopy), SECSY (spin–echo correlation spectroscopy), and 2D‐ELDOR (electron–electron double resonance) sequences wherein either the free‐induction decay (FID) or echo decay is sampled. Important distinctions are made among the sources of inhomogeneous broadening, which include (a) incomplete spectral averaging in the slow‐motional regime, (b) unresolved superhyperfine structure and related sources, and (c) microscopic molecular ordering but macroscopic disorder (MOMD). The differing effects these sources of inhomogeneous broadening have on the two mirror image coherence pathways observed in the dual quadrature 2D experiments, as well as on the auto vs crosspeaks of 2D‐ELDOR, is described. The theory is applied to simulate experiments of nitroxide spin labels in complex fluids such as membrane vesicles, where the MOMD model applies and these distinctions are particularly relevant, in order to extract dynamic and ordering parameters.
The recovery of homogeneous linewidths from FID‐based COSY experiments on complex fluids with significant inhomogeneous broadening is also described. The theory is applied to the ultraslow motional regime, and a simple method is developed to determine rotational rates from the broadening of the autopeaks of the 2D‐ELDOR spectra as a function of the mixing time, which is due to the development of ‘‘motional crosspeaks.’’ The application of this method to recent experiments with nitroxide probes illustrates that rotational correlation times as slow as milliseconds may be measured. It is shown how 2D‐ELDOR can be useful to distinguish between the cases of very slow motional (SM) rates with little or no ordering and of very high ordering (HO) but substantial motional rates even though the cw ESRspectra are virtually the same. The effects of motion and of microscopic ordering on the nuclear modulation patterns in 2D‐FT‐ESR are compared, and it is suggested that these effects could be utilized to further distinguish between SM and HO cases. Key aspects of the challenging computational problems are discussed, and algorithms are described which lead to significant reductions in computation time as needed to permit nonlinear least‐squares fitting of the theory to experiments.

Separation of quadratic and linear external field effects in high J quantum beats
View Description Hide DescriptionWe discuss quantum beats in electronically excited molecular states with high rotational angular momenta J appearing in time resolved fluorescence in conditions of quadratic and linear energy shift dependence on magnetic quantum number M and external field strength. Density matrix formalism is used to obtain in explicit form the expressions for time dependent fluorescence intensity after δ‐function pulsed excitation. In case of pure quadratic Stark effect, which is typical for ^{1}Σ state diatomics, excited statequantum beats for J≫1 exhibit a regular, or ‘‘grill’’ structure, consisting of narrow equidistant ‘‘principal’’ peaks with equal relative amplitudes on the exponential decay background. At linear polarized excitation the time intervals between the adjacent peaks are 2π/ω_{20}, ω_{20} being the splitting frequency between coherently excited M‐sublevels with M=2 and M’=0. If an admixture of linear contribution is present in field induced level shifts, the grill structure is superimposed by a single frequency harmonic modulation. A special geometry was found in which the quadratic beats are fully absent and the modulated grill pattern is brought into existence only by the influence of linear term. Such a case takes place when the light polarization vector in fluorescence is directed at 45° angle with respect to the exciting light polarization vector and yields the most sensitive way to separate quadratic and linear contribution. We considered the examples when the first order term appears by a combined action of electric and magnetic field, as well as due to the e–f level electric field induced mixing, with the parameters typical for the NaK molecule.

Quantum kinetic equations incorporating the Fano collision operator: The generalized Hess method of describing line shapes
View Description Hide DescriptionA Laplace‐transformed quantum kinetic equation, quadratic in the singlet density matrix, is derived for gas mixtures in which, embedded as the collision term, the Fano relaxation tetradic allows for off‐energy‐shell scattering, i.e., incomplete collisions. A sufficient condition for the derivation is a stosszahl ansatz which is weaker at low frequencies than the one usually employed to derive Botlzmann‐type equations. At high frequencies or, conversely, short times, it seems rather more stringent. The generalized Hess method, which is a quantum version of the Bhatnagar–Gross–Krook approximation, is used to solve it approximately, yielding a solution that describes the main features of collision broadening and Dicke narrowing. The relaxation tetradics that appear in the generalized Hess method, replace the collision term and are expressed in terms of collision integrals that are defined for finite concentration of optically active molecules. This means that self and resonant broadening and quenching are also included to some degree. The scattering operators in these collision integrals are expanded in partial waves—assuming that gas is composed of diatomic molecules—and recombined in the total angular momentum representation. Extensions to other representations seem straightforward. The reduction to the standard ‘‘impact approximation’’ or Shafer–Gordon theory is indicated as well as the symmetry effects of nuclear spin.

Bound‐state wave functions from coupled channel calculations using log‐derivative propagators: Application to spectroscopic intensities in Ar–HF
View Description Hide DescriptionA method for obtaining wave functions from coupled‐channel bound state calculations using log‐derivative propagators is presented. Bound states occur at energies for which the inward and outward log‐derivative solutions match at a central point in the propagation; at such energies, the log‐derivative matching matrix has one eigenvalue which is zero. The wave function at the matching point is the eigenvector corresponding to this zero eigenvalue. The wave function at other points can be obtained by back‐substitution in the log‐derivative propagation equations. The method is tested by calculating infrared intensities for the Ar–HF van der Waals complex, using the H6(4,3,2) potential.

Ab initio calculations on monohalogenophosphanes PH_{2}X (X=F,Cl,Br,I), and experimental detection and characterization of PH_{2}F and PH_{2}Cl by high resolution infrared spectroscopy
View Description Hide DescriptionThe harmonic and anharmonic force fields of the title compounds have been calculated at the ab initio self‐consistent‐field level using effective core potentials and polarized double‐zeta basis sets. Additional calculations for PH_{2}F employ larger basis sets and include electron correlation. Many rovibrational constants are predicted theoretically. The infrared spectra generated from the ab initio data have guided the experimental identification of PH_{2}F and PH_{2}Cl in the gas phase. High resolution Fourier transforminfrared spectra of these unstable molecules have been recorded for the first time. Rotational analyses for several bands are reported which provide accurate ground state constants and a precise characterization of a number of vibrationally excited states. The accuracy of the ab initio predictions for PH_{2}F and PH_{2}Cl is evaluated by comparisons with these experimental data.

Nonresonant two‐photon pulsed field ionization of CH_{3}S formed in photodissociation of CH_{3}SH and CH_{3}SSCH_{3}
View Description Hide DescriptionThreshold photoelectron (PE) spectra for CH_{3}S formed in the photodissociation of CH_{3}SH and CH_{3}SSCH_{3} in the photon energy range of 36 850–38 150 cm^{−1} have been measured using the nonresonant two‐photon pulsed field ionization (N2P‐PFI) technique. Both spin–orbit states CH_{3}S(X̃ ^{2} E _{3/2}) and CH_{3}S(^{2} E _{1/2}) are observed from CH_{3}SH and CH_{3}SSCH_{3} in this photodissociation energy range. However, negligible intensities of vibrationally excited CH_{3}S radicals are produced from CH_{3}SH. In the case of CH_{3}S from CH_{3}SSCH_{3}, the population ratio CH_{3}S(ν_{3}=1)/CH_{3}S(ν_{3}=0) is estimated to be ≊0.18. The simulation of the N2P‐PFI‐PE spectra reveals that the rotational temperature for CH_{3}S(X̃ ^{2} E _{3/2,1/2}) formed by photodissociation of CH_{3}SH is ≊200–250 K and the branching ratio CH_{3}S(^{2} E _{1/2})/CH_{3}S(X̃ ^{2} E _{3/2}) is 0.5±0.1. For CH_{3}S(X̃ ^{2} E _{3/2,1/2}) produced from CH_{3}SSCH_{3}, the rotational temperature for CH_{3}S(X̃ ^{2} E _{3/2,1/2}) is ≊800–900 K and the branching ratio CH_{3}S(^{2} E _{1/2})/CH_{3}S(X̃ ^{2} E _{3/2}) is 1.1±0.2. This experiment demonstrates that the PFI‐PE spectroscopic method can be a sensitive probe for nascent rovibronic state distributions of photoproducts. Furthermore, the simulation also shows that the photoionizationdynamics of CH_{3}S may involve rotational angular momentum changes up to ±4. The ionization energy and C–S stretching frequency for CH_{3}S^{+}(X̃ ^{3} A _{2}) are determined to be 74 726±8 cm^{−1} (9.2649±0.0010 eV) and 733±5 cm^{−1}, respectively. The spin–orbit splitting for CH_{3}S(X̃ ^{2} E _{3/2,1/2}) is 257±5 cm^{−1}, in agreement with the literature values.

A fitting law for rotational transfer rates: An angular momentum model with predictive power
View Description Hide DescriptionWe have formulated a law for state‐to‐state rotational transfer (RT) in diatomic molecules based on the angular momentum (AM) theory proposed by McCaffery et al. [J. Chem. Phys. 98, 4586 (1993)]. In this, the probability of angular momentum change in the rotor is calculated by assuming the dominant process to be the conversion of linear to angular momentum at the repulsive wall of the intermolecular potential. The result is a very simple expression containing three variable parameters, each of which has physical significance in the context of the model. Fits to known RT data are very good and suggest strongly that linear to angular momentum change is indeed the controlling process in RT. The parameters of the fit are sufficiently available to give the model predictive power. Using this formulation, RT probabilities may be calculated for an unknown system with little more than the atomic masses,bond length, and velocity distribution. We feel that this represents an important step in the development of a simple physical picture of the RT process.

On superexchange electron‐transfer reactions involving three paraboloidal potential surfaces in a two‐dimensional reaction coordinate
View Description Hide DescriptionA stochastic Liouville theory is presented for the superexchange electron‐transfer reactions involving three paraboloidal potential surfaces in a two‐dimensional reaction coordinate. Its close relationship with the spin–boson model for photosynthesis is discussed. A triangle representation is used to explain the relationship between the reorganization energy and the degree of correlation for the solvent fluctuations experienced by the donor, the intermediate, and the acceptor. Explanations for a small reorganization energy for an efficient superexchange mechanism in natural photosynthesis are offered.