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Volume 78, Issue 12, 15 June 1983

Visible spectroscopy of matrix isolated HCO: The ^{2} A″(Π)←X ^{2} A′ transition
View Description Hide DescriptionThe absorptionspectrum of the ^{2} A″(Π)←X ^{2} A′ transition of HCO has been measured in Ar, Kr, Xe, CH_{4}, CO, and N_{2} matrices and in the mixtures CO/H_{2}O/NH_{3}/CH_{4} (10:4:3:2) and (3:5:2:1). In the noble gas matrices, the spectrum appears with an alternating intensity pattern opposite that found in the gas phase. In a 10 K matrix, the transition originates from the K″=0 level instead of the K″=1 level and the ΔK=±1 selection rule is still important. Transitions into states normally strongly predissociated in the gas phase are measured indicating the importance of the cage effect. In the molecular matrices, the intensity alternation disappears and a strong underlying broad absorption is observed. This behavior is explained in terms of the complete breakdown of the ΔK=±1 selection rule. This interpretation is supported by calculations, using the Pople–Longuet–Higgins formulation, which show that the Renner effect is significantly greater in the molecular matrices then in the noble gas matrices. Upon warmup from 10 to 15 K the absorbance of HCO increases in Ar, Kr, and CH_{4} matrices indicating the release of H atoms which react with a low activation energy with CO. Simultaneously, the controversial infrared absorptions assigned either to matrix isolated hydrogen atoms or Ar_{ n }H^{+} (Kr_{ n }H^{+}) disappear.

Infrared gas phase intensity measurements, polar tensors, and effective charges of cis‐difluoroethylene and its deuterated modifications
View Description Hide DescriptionAll gas phase fundamental vibrational intensities for cis‐difluoroethylene and its deuterated modifications have been measured. Isotopic invariance, Gsum rule, and quantum chemical information have been used in selecting preferred experimental values for the dipole moment derivatives and polar tensor elements of cis‐C_{2}H_{2}F_{2} and C_{2}D_{2}F_{2}. The Gsum rule has been used to determine individual intensity values for the ν_{1} _{1}, ν_{1} _{2}, overlapped band system of the dihydrogen molecule. Values of the polar tensor elements for cis‐difluoroethylene are compared with those found previously for vinylidene fluorine. The hydrogen effective charge value of 0.17 e of cis‐difluoroethylene is much smaller than the value of 0.29 e for vinylidene fluoride. The polar tensor of cis‐difluoroethylene is shown to provide an excellent estimate of the vibrational intensities of trans‐difluoroethylene.

Effect of anion substitution on the electron spin resonance of Cr^{5+} in calcium phosphate apatite
View Description Hide DescriptionElectron spin resonance studies have been made at 4.2 K of CrO^{3−} _{4} substituted for PO^{3−} _{4} in three calcium phosphate apatites. The hydroxyapatite studied has a hexagonal structure stabilized by Cl^{−} impurities. The fluorapatite is confirmed by the ESR to undergo a phase transition involving small structural changes to a noncentrosymmetric phase. But the ESR shows that the distortion of the PO^{3−} _{4} tetrahedra is remarkably similar to that of the hydroxyapatite. Chlorapatite has a centrosymmetric monoclinic structure and has a considerably more distorted PO^{3−} _{4} tetrahedron. Comparison of the results with previously studied hexagonal barium and strontiumapatites shows that cation substitution has a much stronger effect on the PO^{3−} _{4} structure than does anion substitution.

Electronic reorganization in the photoelectron spectra of transition metal compounds
View Description Hide DescriptionThe validity of Koopmans’ theorem in a series of 16 transition metal compounds with a large variety of 3d centers (Ti, Cr, Mn, Fe, Co, Ni, and Zn) is investigated. The reorganization energies are determined by means of the Green’s function method employed in a semiempirical INDO Hamiltonian. A self‐energy approximation is used that allows a fragmentation of the calculated Koopmans’ defects into relaxation increments as well as into correlation parameters that take into account the loss of pair correlation in the electronic ground state and the modification of the pair correlation in the cationic hole state. The magnitude and the importance of these parameters are studied as a function of the 3d occupation pattern, the oxidation state of the transition metal center, the nature of the orbital wave functions and the one‐particle energies. It is demonstrated that pair relaxation energies in the various hole states are by no means negligible in comparison to the relaxational corrections that lead to the most pronounced deviations from I ^{ K } _{ v,j } (I ^{ K } _{ v,j }=− ε_{ j }). The limitations of purely relaxational models (e.g., ΔSCF approach) are analyzed in detail. The gradual modifications of the calculated Koopman’s defects within the 3d series are rationalized. The most pronounced reorganization energies are encountered in d ^{6}–d ^{8} complexes. The magnitude of relaxation and correlation is reduced with a decreasing and an increasing number of 3d electrons. The physical background leading to the breakdown of Koopman’s theorem in 3d derivatives is compared with the results of recent studies in various molecular species (e.g., small molecules, organic lone‐pair systems).

Deuterium magnetic resonance in the discotic columnar mesophases of hexaalkyloxytriphenylenes: The conformation of the aliphatic side chains
View Description Hide DescriptionDeuterium NMR spectra of chain perdeuterated hexa‐pentyloxy, ‐hexyloxy, ‐heptyloxy, and ‐octyloxy triphenylene (THE5, THE6, THE7, and THE8) were studied as functions of temperature in the mesophase region. The deuterium quadrupole splittings exhibited several characteristic features, in particular a steplike decrease in the splitting along the alkyl chain and an even–odd alteration in the methyl splittings within the homologous series. The results are interpreted in terms of possible conformational distributions of the alkyl chain. It is found that there is bending of the alkyl chains out of the aromatic plane, and a considerable degree of chain disorder.

Radiative lifetimes of trapped molecular ions: HCl^{+} and HBr^{+}
View Description Hide DescriptionExcitation spectra in the A ^{2}Σ^{+}−X ^{2}Π system of HCl^{+}(0,0) and HBr^{+}(1,0) as well as radiative lifetimes of selectively excited rotational levels in the A ^{2}Σ^{+} electronic states have been measured in a RFion trap using laser induced fluorescence and time‐resolved single‐photon counting techniques. Coherent ultraviolet radiation was generated by frequency mixing of a Nd:YAG/dye laser system. For HBr^{+} the lifetimes of four rotational levels adjacent to the v′=1 predissociation limit at J′=25/2 were measured. No statistically significant variation with J was found. The average of these four values (3.89±0.15 μs) is therefore reported as the effective lifetime of the v′=1 level of A ^{2}Σ^{+} HBr^{+}. For HCl^{+} the lifetime measurements likewise indicate no strong variation with J. The average lifetime of the v′=0 level of the A ^{2}Σ^{+} state of HCl^{+} is 3.4±0.4 μs. Measurements of radiative lifetimes of molecular ions by the RFion trap technique eliminates the determinate error that results from drift of ions out of the detection volume in conventional experiments.

Ab initio infrared and Raman spectra
View Description Hide DescriptionWe discuss several ways in which molecular absorption and scatteringspectra can be computed ab initio, from the fundamental constants of nature. These methods can be divided into two general categories. In the first, or sequential, type of approach, one first solves the electronic part of the Schrödinger equation in the Born–Oppenheimer approximation, mapping out the potential energy, dipole moment vector (for infrared absorption) and polarizability tensor (for Raman scattering) as functions of nuclear coordinates. Having completed the electronic part of the calculation, one then solves the nuclear part of the problem either classically or quantum mechanically. As an example of the sequential ab initio approach, the infrared and Raman rotational and vibrational‐rotational spectral band contours for the water molecule are computed in the simplest rigid rotor, normal mode approximation. Quantum techniques are used to calculate the necessary potential energy, dipole moment, and polarizability information at the equilibrium geometry. A new quick, accurate, and easy to program classical technique involving no reference to Euler angles or special functions is developed to compute the infrared and Raman band contours for any rigid rotor, including asymmetric tops. A second, or simultaneous, type of ab initio approach is suggested for large systems, particularly those for which normal mode analysis is inappropriate, such as liquids, clusters, or floppy molecules. Then the curse of dimensionality prevents mapping out in advance the complete potential, dipole moment, and polarizability functions over the whole space of nuclear positions of all atoms, and a solution in which the electronic and nuclear parts of the Born–Oppenheimer approximation are simultaneously solved is needed. A quantum force classical trajectory (QFCT) molecular dynamic method, based on linear response theory, is described, in which the forces, dipole moment, and polarizability are computed quantum mechanically, using gradient techniques step by step along a classical trajectory whose path is determined by these quantum forces. We believe the QFCT method to be a more practical ab initio route to spectral band contours for large molecules, clusters, and solutions, and it can be equally applied to equilibrium and nonequilibrium systems. It is pointed out that a similar ab initio QFCT molecular dynamic approach could be used to compute other types of spectra, e.g., electronic absorption, as well as other parameters such as transport properties and thermodynamic functions and their quantum corrections. For parameters not depending on momenta, a parallel ab initio Monte Carlo approach would use electronic energies and other parameters of interest generated quantum mechanically, and ‘‘classical’’ trial moves of the nuclei.

ESR and ENDOR study of photoexcited triplets of cyanosubstituted porphyrins
View Description Hide DescriptionAn ENDOR study has been made of the photoexcited triplets of some cyanosubstituted zinc tetraphenylporphyrins randomly oriented in a rigid matrix. The results demonstrate that the ENDOR method can be applied in studies of shortlived triplets (triplet lifetime < 1 ms) in amorphous solids. The application is possible because of the fact that the ESR signal intensity is strongly enhanced by electron spin alignment. As a consequence of the spin alignment, ENDORspectra can appear in absorption or emission depending on the field setting employed. Hyperfine data derived from the spectra reflect the effect of CN substitution on the electron spin distribution.

Electron spin‐lattice relaxation in the phosphorescent state of xanthione
View Description Hide DescriptionSpin‐lattice relaxation in the phosphorescent T _{1} state of xanthione has been measured at 1.0 K in a dilute n‐hexane matrix. Direct excitation of the T _{1} _{ z }←S _{0} transition with a laser pulse of 10^{−} ^{8} s width was followed by observation of the phosphorescence decay monitoring either a T _{1} _{ z } or T _{1} _{ y } emission band. These bands are optically resolved in the n‐hexane Shpol’skii matrix because of the large zero‐field splitting, D=−15.5 cm^{−} ^{1}. Depopulation of T _{1} _{ z } by the spin‐lattice relaxation processes, T _{1} _{ z }∼≳T _{1} _{ x }, T _{1} _{ y } was found to be complete within 10^{−} ^{7} s, the time resolution of the measurement. The relaxation process, which at 1.0 K requires the spontaneous creation of a lattice phonon of 15.5 cm^{−} ^{1}, is unusually efficient. Thus, when the T _{1} state is populated by intersystem crossing using either S _{1}←S _{0}, or S _{2}←S _{0}optical pumping, lack of observed T _{1} _{ z }phosphorescence at 1.0 K does not imply that the lower T _{1} _{ x } and T _{1} _{ y } sublevels are selectively populated. Observation of T _{1} _{ z } emission at higher bath temperatures, ∼3.3 K, following a T _{1} _{ z }←S _{0} pulse reveals a peculiar initial rise in intensity followed by an eventual decay. This behavior is explained in terms of lattice heating which accompanies the radiationless T _{1}∼≳S _{0} decay. The initial increase in intensity results from a thermal pumping rate from the lower energy sublevels which exceeds the overall decay rate of the T _{1} state. Nonexponential decay of the T _{1} _{ y } emission is explained by the same model. We find that the T _{1} _{ z } emission intensity vs time cannot be explained quantitatively by a uniform lattice temperature during the decay, but that temperature gradients must be present.

Vibronic coupling theory of infrared vibrational transitions
View Description Hide DescriptionThe theory of vibronic coupling is developed for infrared vibrational transitions. It is shown that the lowest order nonadiabatic Born–Oppenheimer correction terms contain an important adiabatic component which may be used to describe infrared transition intensity for imaginary Hermitian operators, such as the momentum and angular momentum operators. This previously unrecognized source of adiabatic infrared intensity forms a complement to the traditional Herzberg–Teller vibronic coupling expressions, which are active for the position operator, and resolves the paradox of vanishing electronic intensity for momentum operators in the Born–Oppenheimer approximation. Expressions for infrared absorption and vibrational circular dichroism are derived that utilize only ground electronic statewave functions; LCAO wave functions are used in these expressions to provide a more detailed description of these new momentum intensity contributions.

Photoelectron angular distributions of the N_{2}O outer valence orbitals in the 19–31 eV photon energy range
View Description Hide DescriptionPhotoelectron asymmetry parameters, partial cross sections, and branching ratios for the X, A, B, and C states of N_{2}O^{+} were measured using synchrotron radiation in the photon energy range 19–31 eV. Vibrationally averaged data are reported for all four states, as well as vibrationally resolved data for the A and C states. The data are compared with a multiple scattering calculation, (e, 2e) dipole measurements, and similar data on CO_{2}. The N_{2}O and CO_{2} results show remarkable state‐by‐state similarity in their asymmetry parameters.

Multiphoton ionization of nitrogen dioxide: Four photon spectroscopy of the n pσ_{ u } Rydberg series
View Description Hide DescriptionMass resolved multiphoton ionization (MPI) of NO_{2} reveals resonance‐enhanced production of NO^{+} _{2} in the region from 490 to 540 nm. From an analysis of the MPI spectrum, we assign these resonant features to four photon transitions to high‐lying members of the n pσ_{ u }Rydberg series. A high resolution scan of one of these features shows clear rotational structure, the assignment of which yields a rotational constant for the linear upper state (B′=0.440±0.005 cm^{−} ^{1}).

Intermolecular coupling in HOD solutions
View Description Hide DescriptionIntermolecular coupling of OD oscillators from HOD in H_{2}O has been investigated by Raman spectroscopy. The data indicate that at concentrations of HOD greater than 10 mol % the effects of intermolecular coupling of OD ⋅⋅⋅ OD pairs become noticeable. Difference spectra show a characteristic derivativelike feature with an increase of intensity around 2400 cm^{−} ^{1} as intermolecular coupling increases. The peak frequency of the OD stretching vibration in HOD decreases from 2525 cm^{−} ^{1} at infinite dilution to 2500 cm^{−} ^{1} in 50 mol % HOD, while the width of the OD stretching band increases from 150 cm^{−} ^{1} (infinite dilution) to 178 cm^{−} ^{1} (50 mol % HOD). Depolarization measurement indicates that the band at ∼2500 cm^{−} ^{1} is polarized. By comparing these difference spectra with the spectrum of OD oscillators from D_{2}O we suggest that the major features of the D_{2}O spectrum in the liquid state can be obtained by considering intermolecular coupling of OD oscillators.

A self‐consistent eikonal treatment of electronic transitions in molecular collisions
View Description Hide DescriptionWe develop an eikonal treatment of electronic transitions in many‐atom collisions, in which classical nuclear trajectories are self‐consistently coupled to quantal electronic transitions. The treatment starts with a discussion of the electronic representations required to assure that Hamiltonian matrices are Hermitian. The amplitudes of wave functions are found to satisfy coupled equations which are expanded in powers of a local de Broglie wavelength. Time‐dependent equations are transformed to derive a Hamiltonian formalism that couples nuclear positions and momenta with electronic amplitudes. Cross sections are obtained from flux conservation and also from T‐matrix elements.

Fluorescence lifetimes of single vibrational levels in HSO (Ã ^{2} A′)
View Description Hide DescriptionFluorescence lifetimes of single vibrational levels of the first excited state of HSO and DSO have been measured under effusive flow conditions following excitation by a pulsed dye laser. The lifetimes show a systematic decrease with v′_{3} (S–O stretch) from 74 μs (v′_{3}=1) to 26 μs (v′_{3}=8) for HSO. For DSO, the lifetimes are longer than the corresponding ones of HSO. These results are interpreted in terms of a second‐order coupling model (Ã ^{2} A′→X ^{2} A′′→continuum) in which the final states are those of H+SO dissociation continuum. An analytical expression is given to compute the vibrational energy dependence of nonradiative rates assuming an energy dependent linewidth from the dissociation.

Rotational energy transfer in HF
View Description Hide DescriptionA rotational nonequilibrium model has been developed to simulate the infrared double‐resonance experimental technique designed to study rotational relaxation of HF gas in the v=1 and higher vibrational states. State‐to‐state rate coefficients for this rotation‐to‐translation relaxation model have been obtained from a surprisal analysis and are found to scale as an inverse power of the rotational energy transferred. Phenomenological rates for the rotational energy transfer in the v=1 state for J=0 to J=7 with Δ J =+1, +2, +3, and +4 are found to be in excellent agreement with the reported phenomenological rates from available experiments for both the v=1 and v=2 states. It appears, therefore, that the state‐to‐state rate coefficients for rotational relaxation of HF are insensitive to the v state. Angular momentum statistics corresponding to conservation of m _{ j } are found to give better fits to the data than those with m _{ j } assumed to be completely randomized.

Intermolecular multiple scattering of electrons. I. Theory
View Description Hide DescriptionCoherent intramolecular multiple scattering by free molecules has been investigated extensively in the literature. Scant attention has been paid to incoherent intermolecular multiple scattering, however, a potentially serious problem under some circumstances. Therefore, a treatment of this problem has been carried out, taking advantage of simplifications afforded by the predominance of forward scattering. Explicit expressions of elementary form are derived for the differential cross sections corresponding to double, triple, and higher scatterings, and for the fractional contribution of each to the total intensity. Illustrative calculations are presented for electronsdiffracted at various sample pressures encountered in a recent diffraction study of collisionally assisted laser pumping of SF_{6}.

Intermolecular multiple scattering of electrons. II. Observed effects for SF_{6}
View Description Hide DescriptionA theory of intermolecular multiple scattering of electrons by vapor molecules is tested by comparing predicted effects with effects observed over a wide range of sample densities. It is found that the theory, which contains no adjustable constants and is based on small angle approximations, gives a good account of experimental observations. The degree to which experimental structure refinements are degraded by multiple scattering is also examined. It is found that derived internuclear distances are disturbed very little even when the mean number of scatterings per electron is as high as 2 and the interference features are washed out by a factor of 2. Apparent amplitudes of vibration are influenced more significantly but are still correctable with fair precision.

IR multiple photon dissociation of C_{2}HCl_{3}: Molecular elimination vs bond fission and efficient dissociation of the C_{2}Cl_{2} product^{a)}
View Description Hide DescriptionThe primary step in the IR multiple photondissociation (IRMPD) of C_{2}HCl_{3} is molecular elimination of HCl, even with laser fluences as high as 10^{2} J cm^{−} ^{2}. A large amount of atomic chlorine derives from the secondary photolysis of the vibrationally excited C_{2}Cl_{2} produced concomitantly with HCl in the molecular elimination step. This C_{2}Cl_{2} is dissociated very efficiently ([Cl]/[HCl]=0.6±0.2), since it absorbs radiation readily and is born with considerable vibrational excitation. We point out that the ultimate production of C_{2} molecules almost certainly involves the IRMPD of C_{2}Cl, which has a low lying A ^{2} A′′ electronic state that facilitates such optical excitation.

The dynamics of infrared photodissociation of van der Waals molecules containing ethylene: An experimental study
View Description Hide DescriptionInfrared (∼950 cm^{−} ^{1}) predissociation of ethylene clusters has been studied using a crossed laser beam–molecular beam apparatus equipped with a moveable detector. van der Waals molecules undergo dissociation following absorption of a single infrared photon. Angular distributions, obtained for product molecules (C_{2}H_{4})_{ n }, n=1–3, all show nearly exponentially decreasing product flux with increasing scattering angle. A product flux contour map has been generated for the photolysisreaction (C_{2}H_{4})_{2} → C_{2}H_{4}+C_{2}H_{4}. Two isotropic center‐of‐mass distribution functions yield excellent agreement with experimental results. One is a function of reaction kinetic energy E, with P(E)=exp(−E/80 cm^{−} ^{1}); the other is a function of product velocity (momentum) u, with U(u) =u exp(−u/9×10^{3} cm/s). The latter distribution is characteristic of a dissociation pathway with a barrier in the exit channel. Such a barrier could result from centrigufal effects. It is argued that isotropic product scattering can be consistent with a direct dissociationreaction occurring on the subpicosecond time scale. It is not possible to determine, unambiguously, if dissociation is direct or if the reaction proceeds through a long‐lived intermediate. Experimental results indicate that only a small fraction of the energy available to products appears as translation, with the remainder appearing as rotational excitation of C_{2}H_{4}. Results are compared with other experimental studies on infrared predissociation of van der Waals cluster as well as a recent theoretical analysis of (C_{2}H_{4})_{2}dissociation.