Volume 84, Issue 6, 15 March 1986
Index of content:

Spectra, lifetimes, and kinetics of matrix‐isolated NI b ^{1}Σ^{+} and a ^{1}Δ
View Description Hide DescriptionNI in argon and in argon/10% N_{2} matrices has been excited into b ^{1}Σ^{+}, v’=0–4 with a pulsed tunable dye laser. The regular line structure in the fluorescence excitation and emission spectra in pure argon matrices is attributed to a local phonon progression of 15 cm^{−} ^{1}, both in the X ^{3}Σ^{−} and b ^{1}Σ^{+} states. ‘‘Hot’’ local phonon lines, which originate in the thermally populated levels n’=1 and 2 of the local phonon mode at elevated temperatures, have been identified. The matrix lifetime of the vibrationally relaxed b state, which does not relax via the a state in pure argon, extrapolates to a radiative lifetime of 15 μs i n v a c u o, in satisfactory agreement with a recent gas phase determination. The a state of NI, which emits at 1185 and 1173 nm, could be populated via the b state only in mixed matrices of argon and N_{2}. The lifetime in these matrices is 20.5±2 ms, which extrapolates to a gas phase radiative lifetime of approximately 38 ms. The b state of NI is completely quenched in pure nitrogen matrices, but emission from the a state is still detected with a lifetime of 4.6±0.5 ms. On the basis of these results recently reported a‐state lifetimes of NCl and NBr in the ms to sub‐ms range appear unreasonably low.

The ligand dependence of lanthanide 4f → 4f magnetic dipole transition moments
View Description Hide DescriptionThe magnetic‐dipole moments associated with 4f → 4f radiative transitions in lanthanide complexes are usually calculated on the basis of a s t a t i c crystal‐field model in which the ligands’ influence is confined to mixing (and splitting) the 4f ^{ N } eigenstates of the ‘‘free’’ lanthanide ion. In this model the ligand charge distributions are assumed to be passive to the radiation field, with the latter acting only on the ligand‐perturbed 4f ^{ N } states of the lanthanide ion. Here we consider another model in which the ligand charge distributions are assumed to be polarized by the radiation field and then coupled to 4f → 4f electric‐multipolar transition moments to effect a resonant magnetic‐dipole interaction with the radiation field. This model (or mechanism) is exactly analogous to the dynamic‐coupling (or ligand‐polarization) model described previously for lanthanide 4f → 4f electric‐dipole transition moments [see, for example, J. Phys. Chem. 8 8, 3579 (1984)]. It is shown that the dynamic‐coupling (DC) mechanism for 4f → 4f magnetic‐dipole transition moments will be competitive with the static‐coupling (SC) mechanism only for transitions with strong ‖ΔJ‖>1 character, and even for these transitions the DC contributions to total magnetic‐dipole strength are predicted to be small (<10^{−} ^{7} D^{2}). However, it is also shown that the DC contributions to the electric‐ and magnetic‐dipole transition moments of 4f → 4f transitions in c h i r a llanthanide systems may be crucial to explaining (or rationalizing) the rotatory strengths of these transitions. The latter suggestion is especially applicable to transitions whose intensities are known to be h y p e r s e n s i t i v e to the ligand environment.

An ESR‐ENDOR study of the disulfide anion in x‐irradiated L‐cystine dihydrobromide dihydrate
View Description Hide DescriptionThe disulfide anion radical produced by x irradiation in single crystals of L‐cystine dihydrobromide dihydrate was characterized from ESR and ENDOR measurements. The gtensor of the absorption and the hyperfine coupling tensors of four β protons were determined. The hyperfine and quadrupole coupling tensors of a weakly interacting bromine nucleus were also deduced from ENDOR measurements. The distribution of spin density as inferred from anisotropic parts of the proton hyperfine couplings is discussed.

Selection rules for surface Raman spectroscopy: Experimental results
View Description Hide DescriptionWe report the results of an experimental survey determining the contributing factors for Raman spectral activity of molecules adsorbed on metal surfaces. The systems investigated are benzene, pyrazine, and s‐triazine physically adsorbed onto the (111) and (110) faces of single crystalsilver. We consider the relative importance of three factors: symmetry reduction, image dipoles (metal optics), and quadrupole polarizability contributions. The experimental data may be explained satisfactorily by involving both the adsite geometry and image effects in the theoretical selection rules. Quadrupole interactions appear neither necessary nor sufficient to predict the proper surface spectra.

A modification of the image dipole selection rules for surface Raman scattering
View Description Hide DescriptionWe have modified the selection rules for surfaceRaman scattering derived from consideration of the real dipole‐image dipole system for a molecule adsorbed at the surface of a metal, to bring the predictions into accord with the exact electromagnetictheory.

Photoacoustic signal in a cylindrical resonator: Theory and laser experiments for CH_{4} and C_{2}H_{6}
View Description Hide DescriptionThe theory of the photoacoustic signal is developed for acoustic resonances in a cylindrical resonator. Measurements were performed to determine the signal strength in the pressure range between 1 and 760 Torr for CH_{4} and C_{2}H_{6}. For CH_{4} the optical power absorbed in the cavity is nearly constant but vibrational relaxation varies the signal in the investigated pressure region. C_{2}H_{6} shows a strong pressure dependence of the optical power absorbed, however, V–R,T relaxation is so fast that in this case no relaxational variation of the signal is observed in the range of ν/p values studied. As expected, the strength of the acoustic signal is proportional to optical power deposition in this case. For CH_{4}, the influence of V–V and V–R,T exchange processes on the photoacoustic signal is studied in detail. The ratio of heat generated by fast V–V processes to heat generated by slow V–R,T transfer is determined. Using the relaxation time 5.2 ns bar obtained by laser‐induced fluorescence experiments for double quantum V–V exchange between the stretching levels ν_{1},ν_{3} and the bending levels ν_{2},ν_{4} a value of 33 ns bar is derived for single quantum V–V exchange between these manifolds.

Infrared diode laser study of the hydrogen bifluoride anion: FHF^{−} and FDF^{−}
View Description Hide DescriptionThe ν_{3} vibration–rotation transition of the hydrogen bifluoride anion in the X̃ ^{1}Σ^{+} _{ g } state has been detected for the first time by infrared diode laser spectroscopy using the magnetic field modulation technique. The anion was generated by a hollow cathode discharge in a mixture of H_{2} and a fluorine‐contained molecule such as CF_{4}, C_{2}F_{4}, and CHF_{3}. The carboncompound was indispensable to produce the anion. Identification of the species was based on the spectral pattern showing intensity alternation, the magnitude of the rotational constant (B‘=0.334 181 cm^{−} ^{1}), and the ion drift velocity sign determined by the velocity modulation method. The observed ν_{3} frequencies of FHF^{−}(1848.699 cm^{−} ^{1}) and FDF^{−}(1397.236 cm^{−} ^{1}) are much different from the reported values in the solid phase. By contrast, the ν_{1} and ν_{2} frequencies estimated from the centrifugal distortion constant and the perturbation of Coriolis interaction between the ν_{1}+ν_{2} and ν_{3} states are in good agreement with solid state measurements.

Theory of the interaction of light with large inhomogeneous molecular aggregates. I. Absorption
View Description Hide DescriptionA general method to describe the spectroscopy of large, internally inhomogeneous particles is presented. The theory utilizes an approach similar to the one used by DeVoe in the treatment of the optical properties of polymers. The particle is divided into groups and the internal field is calculated by solving a self‐consistent set of linear equations in the field amplitude at each group in the particle. It is found that if the particle is dense the intermediate and radiation coupling mechanisms must be included in addition to the dipole–dipole coupling. Through these coupling mechanisms it is found that the excitation generated at each group in the chromophore can delocalize over regions comparable to the size of the wavelength of light. The response of the particle to the light can then be described in terms of ‘‘collective modes’’ of excitation of the entire particle, the amplitude of each mode being controlled by the geometrical relation between the groups and the efficiency in energy transfer between any two groups in the aggregate. The spatially averaged equations of the absorbance for a collection of large inhomogeneous arbitrarily shaped aggregates are derived.

Theory of the interaction of light with large inhomogeneous molecular aggregates. II. Psi‐type circular dichroism
View Description Hide DescriptionA theory of the polymer and salt induced (psi)‐type circular dichroism observed in DNA aggregates is presented. Using the main formalism developed in the previous paper to treat the interaction of light and large, dense molecular aggregates, it is shown that the anomalously large signals observed in the circular dichroism of certain molecular aggregates result from: (a) the presence of a long‐range chiral structure in the aggregate; (b) delocalization throughout the entire particle of the light‐induced excitations in the chromophores. This delocalization and the resulting ‘‘collective response’’ of the chromophores in the aggregate is favored in particles having a three‐dimensional packing. It is shown that to describe adequately the internal field in these aggregates, intermediate and radiation coupling mechanisms should be taken into account in addition to the regular dipole–dipole interactions. Furthermore, no dipole approximation in the exponentials of the form e ^{ i k⋅x } are made. It is shown that in these circumstances, one of the circular polarizations of the light can exchange energy more efficiently than the opposite polarization. This gives rise to a circular dichroism signal whose magnitude is proportional to the overall size and long‐range chiral nature of the aggregates. The theory is applied to two cases: (1) to the dimer ApA when it is shown (for the case of this small system) to reduce to the classical theories of DeVoe and Tinoco, and (2) for a toroidal aggregate of DNA of 3000 Å diameter with an internal chiral structure, as found by Haynes e t a l. in polylysine–DNA condensates. Good qualitative agreement with the observed spectra is found. The theory represents the first successful attempt to explain the physical origin of the psi‐type CD effect. Useful information regarding the chiral structure of the aggregates can be inferred from the theory.

The psi‐type circular dichroism of large molecular aggregates. III. Calculations
View Description Hide DescriptionComputations have been carried out to determine how the magnitude and shape of the polymer and salt induced (psi)‐type CD spectra depend on the structuralproperties of a collection of randomly oriented large chiral aggregates. Uniaxial polarizable groups located at the cubic lattice points have been used to model the aggregates. The structure of the model is similar to that of a cholesteric liquid crystal. All computations have been carried out for the case of polarizable groups possessing only one electronic transition between 200 and 320 nm. It is found that the radiation and intermediate couplings between the chromophores in the aggregate which are neglected in previous theories play an important role in determining the shape and magnitude of the psi‐type CD spectrum. It is shown that when these couplings are included, only three‐dimensional large chiral aggregates show huge and nonconservative psi‐type CD spectra. It is shown that the magnitude of the psi‐type CD spectrum is controlled by the volume, the chromophore density, and the pitch of the aggregate, while the shape of the psi‐type CD spectrum is determined mostly by the pitch and the handedness of an aggregate. When the pitch is close to the center of the absorption band of the chromophore in the aggregate the most distorted (least conservative) psi‐type CD spectrum is obtained. The CD spectra of aggregates with opposite handedness are mirror images of each other. It is shown that a rotationally disordered collection of chiral aggregates cannot give rise to a selective reflection of one circular polarization over the other as shown by liquid crystals. The results obtained confirm the theoretical predictions of the two previous papers in this series.

Theory of concentration depolarization in the presence of orientational correlations
View Description Hide DescriptionA theory is presented that incorporates the effect of orientational correlations between luminescent molecules on the fluorescence depolarization due to incoherent energy transfer. The luminescent molecules are embedded in a homogeneous two‐ or three‐dimensional medium which is in an axially symmetric phase with the x y plane as a symmetry plane, and consists of axially symmetric molecules. For the general orientational singlet distribution and the general form of orientational correlations consistent with these symmetries, we derive analytical expressions for the anisotropy of fluorescence emission. In a no back transfer model, numerical results are evaluated for a simple choice of correlations that tend to align nearby molecules. In a pure donor system, the anisotropy of fluorescence is found to be strongly dependent on these correlations. By ignoring them, the critical transfer distance, as obtained from depolarization experiments, may be drastically underestimated. In a system where donors are surrounded by a huge majority of traps, the critical transfer distance can be determined from the intensity of trap fluorescence. Its anisotropy also strongly depends on correlations and may thus give an indication of the correlation length scale.

Spin‐coupling in ferric metalloporphyrin radical cation complexes: Mössbauer and susceptibility studies
View Description Hide DescriptionThe ferric metalloporphyrin π‐radical cation complexes Fe(III) (OClO_{3})_{2} (TPP^{ . }) and [Fe(III) Cl (TPP^{ . })] [SbCl_{6}] were examined in microcrystalline form by Mössbauer spectroscopy and magnetic susceptometry over a range of temperatures and applied fields. All measurements on the six‐coordinate Fe(OClO_{3})_{2} (TPP^{ . }) were consistent with isolated molecules having an S=5/2 iron site with zero field splitting (12 cm^{−} ^{1}) S ^{2} _{ z } that is ferromagnetically coupled to the S=1/2 porphyrin radical by an energy term (−110 cm^{−} ^{1}) S⋅s. Thus the ground state is overall spin‐3. In the five‐coordinate [FeCl (TPP^{ . })] [SbCl_{6}] the susceptibility is in reasonable agreement with the results of a calculation based on zero field splitting (12 cm^{−} ^{1}) S ^{2} _{ z } for the S=5/2 iron and antiferromagnetic coupling (200 cm^{−} ^{1}) S⋅s with the radical to give an overall spin‐2 ground state. However, the Mössbauer measurements require a more complicated model having the same large intramolecular iron–radical coupling, a smaller zero field splitting (3 cm^{−} ^{1}) S ^{2} _{ z }, and weak intermolecular antiferromagnetic coupling between heme pairs given by (32 cm^{−} ^{1}) s _{1}⋅s _{2} or, equivalently, (0.65 cm^{−} ^{1}) S _{1}⋅S _{2}. A slightly improved correspondence with the measured susceptibility results. The intermolecular antiferromagnetic coupling probably results from crystallization of the [FeCl (TPP^{ . })]^{+} cations in face‐to‐face dimers as observed in other closely related five‐coordinate iron (III) porphyrins.

Moment analysis in depolarized light scattering: Determination of a single‐parameter empirical pair polarizability anisotropy for Ne, Ar, Kr, Xe, and CH_{4}
View Description Hide DescriptionA method, based on classical physics, to utilize the first four even moments of the depolarized collision induced light scatteringspectrum to derive an empirical model for the pair polarizabilityanisotropy of interacting molecules, with only one adjustable parameter, is described and applied to the spectra of Ne, Ar, Kr, Xe, and CH_{4}. Good agreement with a b i n i t i o results in the literature is obtained and profiles calculated with these models are in excellent agreement with experiment.

Fluorescence excitation spectra of butynal in a supersonic jet. The effect of internal rotation
View Description Hide DescriptionThe fluorescence excitation spectrum of the 0^{0} _{0} and 11^{1} _{0} vibronic bands of the S _{1}(nπ*) electronic state of butynal, CH_{3}–C≡CCHO, and that of the 0^{0} _{0} vibronic band of α‐d‐butynal have been measured in a supersonic expansion. The effects of internal rotation are discussed in comparison with the rigid‐rotator spectrum of the 0^{0} _{0} band of propynal, HC≡CCHO. Rotational constants and barrier heights were determined from contour calculations based on a rigorous semirigid C _{ s } F‐C _{3v } T model. At beam temperatures of 3 K≤T _{rot} ≤8 K, only the Γ^{0} ^{+}ground state and the Γ^{1} first excited state of the internal rotation are populated significantly. Already in the latter state the methyl group behaves as an almost free rotator owing to a very low barrier which is V ^{‘} _{3} =3.7±1 cm^{−} ^{1} in the electronic ground state and V _{3} =10±1 cm^{−} ^{1} in the S _{1} state. By means of quantum‐beat spectroscopy assignments of the rovibronic spectra obtained from simulated spectra are verified. A non‐Boltzmann population observed in the ground state is shown to be consistent with a conservation of nuclear spin symmetry during the supersonic expansion process.

Photoelectron spectroscopy and inferred femtosecond intramolecular dynamics of C_{2}H^{+} _{2} and C_{2}D^{+} _{2}
View Description Hide DescriptionThe 584 Å photoelectron spectra of rotationally cold C_{2}H_{2} and C_{2}D_{2} were obtained with improved resolution, permitting the first three electronic states of the ions to be characterized in greater detail. Temperature‐dependent studies led to a definitive assignment of the low intensity features in the X̃ ^{2}∏_{ u } state, yielding ν_{4}=837±12 cm^{−} ^{1} for C_{2}H^{+} _{2} and ν_{4}=702±12 cm^{−} ^{1} for C_{2}D^{+} _{2}. The ν_{5} origin of the Renner–Teller multiplet was identified. In the case of C_{2}D^{+} _{2}, a Fermi resonance with this multiplet contributed intensity to the ν_{1} mode, facilitating its evaluation at 2572±16 cm^{−} ^{1}. The C _{2h } geometry of the Ã ^{2} A _{ g } state was determined from the two previously unobserved bending progressions, assigned to ν_{4} and ν_{5B }, and evaluated at 492±12 and 605±12 cm^{−} ^{1} for C_{2}H^{+} _{2} and 339±12 and 516±12 cm^{−} ^{1} for C_{2}D^{+} _{2}, respectively. A more extensive vibrational progression than previously evident, comprised of irregular spectral features indicative of nonadiabatic effects, was observed for the B ^{2}∑^{+} _{ u } state. Autocorrelation functions were derived from the spectra for all three electronic states, and the two electronically excited states exhibit an ultrafast decay on a 10^{−} ^{1} ^{4} s time scale. The Ã ^{2} A _{ g } state decays within one period of bending vibration, while the B̃ ^{2}∑^{+} _{ u } state survives only 14 fs, corresponding to a single period of symmetric stretching motion.

Hyperfine structure and lifetime of the C ^{2}Σ^{+}, v=0 state of CH
View Description Hide DescriptionFrom a laser induced fluorescence(LIF) experiment on a molecular beam of CH, we have obtained the b and chyperfine constants, the γ and γ_{ D } spin‐rotation constants as well as accurate values for the rotational constantsB, D, and H for the C ^{2}Σ^{+}, v=0 state. From measurements of the linewidths, that are partially caused by predissociation, and by comparing relative line intensities, we determined different lifetimes for upper (F _{1}) and lower (F _{2}) ρ‐doublet states of the C ^{2}Σ^{+} state. For the F _{1} states we find a constant lifetime of 3.7±1.0 ns, that is independent of N, while for the F _{2} states we observed an increase in lifetime for higher N up to 8.0±1.5 ns for N=11.

The vibrational spectrum of the water dimer: Some model based predictions
View Description Hide DescriptionWe report an analysis of the vibrational spectrum of the water dimer, including Fermi resonance and the adiabatic coupling between intra‐ and intermolecular modes. Three recently proposed pair potentials for water, each of which includes a representation of the intra‐ and intermolecular force fields, are tested by comparing the predicted and observed infrared spectra. Our results show that dynamical effects in the vibrational spectrum are underestimated by these potentials. Despite the considerable uncertainty in the experimental data it is clear that currently available water–water potentials are too inaccurate to be trusted except for predictions of the qualitative properties of the vibrational spectrum.

On the physical origin of propensity rules in collisions involving molecules in ^{2}Σ electronic states
View Description Hide DescriptionA general quantum treatment of the collisiondynamics of ^{2S+1}Σ‐state diatomic molecules is developed, with particular emphasis given to the physical origin of the collisional propensity for conservation of the e / fmolecular symmetry label. State‐resolved integral cross sections are expressed as a weighted sum of tensoropacities which are related to the probability that a collision will reorient the nuclear rotational angular momentum vector. Previous derivations of the propensity rules for collisions of ^{2S+1}Σ‐state diatomic molecules were restricted to the sudden or Born approximations. Here a general derivation is developed that is free of dynamical approximations, and that clearly establishes the direct connection between the observed propensity for the conservation of the e / fmolecular symmetry and the collisional propensity for the conservation of the orientation of the nuclear rotational angular momentum vector. A power‐law model suggested by previous semiempirical fits to cross sections for ^{1}Σ^{+}‐state molecules is extended to open‐shell molecules. This simple model allows us to predict semiquantitatively the degree to which the e / f symmetry index is conserved without performing a full dynamical calculation.

An improvement of the Li+HF PES based on a 3D quasiclassical trajectory test
View Description Hide DescriptionA quasiclassical trajectory test of some potential energy surfaces designed for the Li+HF reaction is reported. A comparison of scattering quantities with experimental data has allowed the selection of a surface sufficiently accurate for reproducing reactive cross sections and detailed experimental data.

The second Born approximation for electron scattering. II. The high energy limit for small angle dipole allowed inelastic scattering from atoms
View Description Hide DescriptionThe exact second Born amplitude for direct electron scattering from atoms in the LS coupling approximation is evaluated by use of an analytic model for the transition charge densities for n s→m p excitations. Coupling to all channels is treated rigorously for intermediate s, p, and d state coupling in the limit as the momentum transfer approaches zero. Exchange is considered approximately by using a high energy exchange approximation. Expressions for the slope of the second order cross section as a function of momentum transfer are developed for the limit as the momentum transfer approaches zero. It is shown that the first Born result is achieved in the limit as K→0 of the effective generalized oscillator strength (Lassettre’s theorem) only if the limit is taken off the energy shell. The on energy shell limit as K→0 yields a second Born correction to the Lassettre’s theorem result. On the two off energy shell paths for taking the limit of the effective GOS as K→0 that were investigated the leading correction term is found to be proportional to K. For the on energy shell path, in addition to the second Born correction to the first Born limiting value the first order correction was found to be proportional to K ^{2}. The expansions in powers of K of the effective GOS investigated here showed no anomalies in contrast to findings in a previously reported investigation. We can only surmise, in view of the extreme sensitivity of the result to the choice of the path in the limit process K→0, that these previous results were due to a different choice of the limit path than those investigated here.