Index of content:
Volume 67, Issue 7, 01 October 1977

Calculation of linear and nonlinear electric susceptibilities of conjugated hydrocarbon chains
View Description Hide DescriptionWe calculated the π electron contributions to the linear and nonlinear static electric susceptibilities of a linear conjugated hydrocarbon chain. We started from the Hückel equations for the π electrons in the presence of an electric field, and we expanded the equation in terms of the electric field by using perturbation theory. We solved the successive perturbation equations analytically, and we derived exact analytical expressions for the energy perturbations up to fourth order. We used these energy perturbations to derive values for χ^{(1)} _{ X X }, χ^{(2)} _{ X X X }, and χ^{(3)} _{ X X Y Y } where the X axis is along the chain. We found that the molar linear susceptibility χ^{(1)} _{ X X } is roughly proportional to the 2.8 power of N and that the nonlinear susceptibility χ^{(3)} _{ X X X X } is roughly proportional to the 5.3 power of N. For larger values of N the π electron contributions to the susceptibilities become much larger than the σ electron contributions.

Exciton–lattice interaction and the line shape of exciton absorption in molecular crystals
View Description Hide DescriptionThe exciton–lattice interaction cannot be treated adiabatically in many molecular crystals where the exciton bandwidth is at most comparable to lattice‐vibration energies. It cannot also be treated perturbationally at about room temperatures where the absorption line width of excitons is comparable to the larger of the exciton bandwidth and lattice‐vibration energies in most molecular crystals. A simple model which describes excitons in molecular crystals from a unified viewpoint is proposed. The model has three characteristic energies: the half‐width B of the exciton band, the average amplitude of the scattering potential for excitons produced by lattice vibrationsD, and the inverse of the correlation time of the potential fluctuation γ on the order of lattice‐vibration energies in units of C=1. It describes singlet excitons when B≳γ and triplet excitons when B≪γ. The dynamical‐coherent‐potential approximation applied to this model bridges reasonably the following two limits: the strong‐scattering limit for D≫B and D≫γ in which the exciton absorption has a Gaussian line shape, and the weak‐scattering limit for D≪B or D≪γ in which the exciton absorption has a motionally narrowed Lorentzian line shape. The exponentially decreasing low‐energy absorption tail, obeying the Urbach–Martienssen rule, grows up as B/γ increases towards the adiabatic limit of B/γ ≫1. The model is consistently applied to observed excitonspectra in various molecular crystals.

Variational constraints on perturbed eigenvalues and their perturbation expansions
View Description Hide DescriptionThe variational principle, in the form of the minimum principle, the Hellmann–Feynman theorem, the curvature theorem, and the virial theorem, is used to derive a number of variational constraints on perturbed exact and variational eigenvalues and on their respective Rayleigh–Schrödinger (RS) and perturbational–variational (PV) perturbation expansions. These constraints are applicable to the lowest state of each symmetry of any system with a Hamiltonian of the form H=H _{0}+H _{1}λ, where H _{1} is positive or negative definite, and λ is a real perturbing parameter; in slightly weakened form the constraints are extended to all states of all atomic isoelectronic sequences. The interaction of the constraints severely limits the behavior of the eigenvalue and its first and second λ derivatives as the radius of convergence is approached from within along the real λ axis, and thus drastically restricts the possible form of the RS and PV perturbation expansions. In one application it is shown that for positive definite H _{1} the only possible geometric series expansion is an alternating one with even‐order coefficients negative and odd‐order coefficients positive; for negative definite H _{1} only the nonalternating geometric series with all coefficients negative is possible. Other summable series can be similarly investigated. In another application the constraints are used to study the determination of the radius of convergence of the expansions, and it is shown that violation of the constraints is a sufficient condition for ‖λ‖ equaling or exceeding the radius of convergence. It is argued that the existence of a finite radius of convergence due to a singularity on the real λ axis may be regarded as a mechanism by which the variational principle separates admissible from inadmissible eigenfunctions. Several examples of both exact and variational eigenfunctions and eigenvalues are presented to support these conclusions.

Decomposition theory of chemical reactions
View Description Hide DescriptionThe coupled channel formulation is utilized to variationally derive approximate closed‐form expressions for reactive transition matrices. In conjunction with this effort it is shown that the effect of differing choices of possible channel coupling arrays becomes important when incomplete channel basis sets are used. Generalized techniques are employed to derive the necessary variational principles. The inherent coupling of the Green’s functions in the resulting expression for the transition matrix makes inclusion of continuum states in the basis sets less crucial. The practical viability of this formulation as a computational scheme for chemical systems is discussed.

Molecular photoionization. II. Photoelectron angular distributions
View Description Hide DescriptionPhotoelectron angular distributions of atomic and molecular systems are discussed. The theory is developed in terms of the single center expansion model, and the photoionization differential cross section is separated into terms corresponding to the various partial wave components of the photoelectron wavefunction. The differential cross section is decomposed into a series of (1) direct (incoherent) terms for each final state partial wave, plus (2) a series of interference (coherent) terms between the various partial waves. The resulting description is particularly useful for emphasizing the contribution of individual partial wave components to the differential cross section. Illustrative results are presented for the photoionization of the hydrogen molecule–ion. These results provide further evidence of the reliability of the noniterative integral equation method for studying photoionization processes.

Vibrational relaxation in seeded supersonic alkali halide beams
View Description Hide DescriptionA seeded supersonic beam source for alkali halides is described which can provide high intensity, a narrow velocity distribution, enhanced or reduced translational energy (by choice of diluent mass), low rotational temperature, and partially relaxed vibrational populations. Alkali halide vapor at ∼1200–1400 °K and ∼0.1 Torr is mixed with a diluent gas at ∼30–100 Torr and expanded through a pinhole nozzle 0.1 mm in diameter. Velocity analysis of a seeded CsF beam with Ar as the diluent indicates the beam properties conform approximately to the theory of isentropic expansions, with deviations attributable to the relatively low source pressure used. The vibrational populations of the v=0, 1, 2, 3 states in seeded beams of LiF with Ar, NH_{3}, ND_{3}, and SF_{6} as diluents were determined by electric resonancespectroscopy. For Ar as diluent, the LiF vibrational energy has a Boltzmann distribution with a temperature only ∼10% lower than the beam source. For the polyatomic diluents, the LiF vibrational distribution is markedly non‐Boltzmann. The nominal vibrational temperature T _{ v }, defined by comparing the population of state v to that of the ground state, drops substantially for the higher v states. The vibrational relaxation becomes more pronounced as the source pressure of alkali halide or diluent gas is increased. For the experimental conditions used here, T _{ v } for the v=3 state drops to ∼2/3 of the source temperature; much stronger relaxation can be expected at higher source pressures.

The linear dichroism in a liquid crystalline matrix of 2,4,6‐trimethyl pyridine N‐oxide. Evidence for out‐of‐plane components of the absorbed intensity in the region 270–350 nm
View Description Hide DescriptionThe linear dichroism of 2,4,6‐trimethyl pyridine N‐oxide has been measured in the range 270–350 nm in a liquid crystal matrix. With respect to the parent molecule pyridine N‐oxide, the trimethyl derivative is closer to the model of a disc shaped molecule and presents a larger energy separation of the two lowest ππ* states. Between the first two absorptions of the molecule, underneath the second intense ππ* absorption, negative contributions to the linear dichroism are observed. A b i n i t i oconfiguration interaction energies and wavefunctions are obtained with a minimal and a more extended orbital basis. The computed energies, transition intensities, and the dipole moments of the ground and excited states of the molecule are in better agreement with the available spectral properties than the theoretical values in the literature obtained by semiempirical procedures. The most likely assignment of the negative contribution to the linear dichroism is the first excited n→π* state (A _{2}), allowed by vibronic interactions. It is suggested that, as in formaldehyde, an excited state of the molecule (A _{1},ππ*) exists with a bent structure at the nitrogen atom.

ClF_{ x }–H_{2} chemical lasers (x=1,3,5): vibration–rotation emission by HF from states with high rotational excitation
View Description Hide DescriptionStimulated vibration–rotation emission by HF has been observed from states with high rotational excitation following flash photolysis of ClF_{ x }–H_{2}–Ar mixtures (ClF, ClF_{3}, ClF_{5}). We report here only those observations connected with the very high rotational states J′?9 (e.g., up to v=1, J=20 and v=2, J=15) which are found to emit under grating‐selective conditions. The patterns of emission indicate that direct population of the high J states by the vibrational pumping reaction(s) can be ruled out. Neither is the behavior consistent with Boltzman equilibration. The late threshold times and extended durations point to an energy transfer mechanism that involves rapid V→R deactivation with large ΔJ coupled with V→V up pumping in HF^{‡}–HF^{‡} collisions to give a cumulative increase in rotational energy. Thus, V→V and V→R processes divert vibrational excitation into rotational excitation where it will tend to ’’pool’’ in high J states for which rotational equilibration is a slow process. These high J, P branch laser emissions reflect the role of rotational degrees of freedom in reactiondynamics and they furnish distinctive clues to energy processes that can influence significantly the efficiency and spectral composition of chemical laser emission.

Parametric energy level analysis of Ho^{3+}: LaCl_{3}
View Description Hide DescriptionA 20‐parameter least‐squares fit to the levels of Ho^{3+}:LaCl_{3} observed by Dieke and Pandey has been obtained. The results are in substantial agreement with their assignments and with the subsequent analysis of Rajnak and Krupke. A considerably more extensive atomic Hamiltonian was used, including operators for two‐ and three‐particle electrostaticinteractions, spin–orbit and spin–other‐orbit magnetic interaction, two‐particle pseudomagnetic configuration‐mixing interactions, and single‐particle crystal‐field interactions. The fit of twenty parameters to 128 observed levels resulted in a mean error of 5.2 cm^{−1}. The results are consistent with similar recent studies of Nd^{3+} and Pm^{3+} in the LaCl_{3} host.

The photoelectron and far‐ultraviolet absorption spectra of simple oximes
View Description Hide DescriptionThe HeI photoelectron and far ultraviolet absorption spectra of formaldoxime (CH_{2}=N–OH) and three other simple nonconjugated oximes are reported and compared to those of simple imines. Contrary to imines the lowest ionization potential seems to be related to the π orbital although this assignment must be considered tentative. In the uv spectrum the π*←n, π*←π and 3s←π bands are readily identified.

Collision‐induced ion‐pair formation of the thallium halides TlF and Tl_{2}F_{2}
View Description Hide DescriptionAbsolute cross sections have been determined for collision‐induced ion‐pair formation (polar dissociation) of TlF and Tl_{2}F_{2} from collisions with Xe and Kr atoms. A crossed‐beam method was used in which the Xe or Kr atoms were aerodynamically accelerated to energies up to 17 eV (in the laboratory frame). Time‐of‐flight mass spectrometry permitted the determination of partial cross sections for each positive and negative ion channel in the collision. The cross sections for both monomer and dimer thallium fluoride were considerably smaller than those previously reported for thallium chloride, the difference most likely resulting from the poor energy transfer into the molecular target due to the light F atom. The cross section for the reaction Xe(Kr)+TlF→Xe(Kr)+Tl^{+}+F^{−} exhibited, near threshold, a power‐law rise with increasing energy σ =const.× (E _{tot}−E _{0})^{ n }/E _{rel}, where E _{tot} is the total collision energy (kinetic plus internal), E _{0} is the threshold energy, E _{ r e l } is the relative kinetic energy and n=1.85(1.95). The cross section for rearrangement ionization Xe +TlF→TlXe^{+}+F^{−} exhibited a step behavior. Collisions of Xe with the dimer Tl_{2}F_{2} resulted in both Tl_{2}F^{+}+F^{−} and Tl^{+}+TlF^{−} _{2} ion products, the cross sections for the latter ion pair being about one third those for the former. With new values of the heats and entropies of formation of Tl_{2}Cl_{2}, Tl_{2}Br_{2}, and Tl_{2}I_{2} the absolute cross sections for the previously reported reactions of the dimers Xe(Kr)+Tl_{2}X_{2}→Xe(Kr)+Tl_{2}X^{+}+X^{−} have been recalculated. The threshold behaviors of these reactions have also been analyzed in terms of the above power law, giving values of the power n in the range 2.1–2.7. Model calculations have been performed to determine bond energies of the (Tl–X–Tl)^{+} and (X–Tl–X)^{−} ions, which were used to determine theoretical thresholds for the formation of these ions. The difference between the experimental and theoretical thresholds then gives the internal excitation of the molecular ions at threshold (assuming the inert gas atom carries away negligible energy). Tl_{2}F^{+}, in particular, is formed at threshold with considerable internal excitation (∼1.8 eV). The low cross sections for both TlF and Tl_{2}F_{2} and the high internal excitation of Tl_{2}F^{+} at threshold are consistent with a collision model in which only very dynamically constrained collisions result in the extraction of the light F^{−} ion from either TlF or Tl_{2}F_{2}.

NMR relaxation study of molecular motions between unequal potential wells in solid t r a n s,t r a n s‐muconodinitrile
View Description Hide DescriptionWe report observations of extremely unusual proton NMRrelaxation rates in solid t r a n s,t r a n s‐muconodinitrile (TMD, N≡C–CH=CH–CH=CH–C≡N). In particular we measured, over the temperature range 77–423 °K, proton dipolar relaxation timesT _{1D } and spin lattice relaxation timesT _{1} (at 24 and 58 MHz). The relaxation pattern is characterized by the following features: (a) very long motional T _{1} and T _{1D } even at their respective minima, (b) no detectable motional narrowing of the line even at the T _{1D } minimum, (c) unequal slopes at temperatures below and above the minimum of T _{1} (and T _{1D }) vs 1/T, and (d) significant deviations from the usual linear dependence on resonance frequency of the values of the relaxation times at their respective minima. We extended an earlier NMRtheory to the case of spin lattice relaxation due to molecular reorientations between the extremely unequal potential energy wells of TMD. We were able to explain all features of the above data in terms of this theory. By comparing our data to the results of several calculations of intermolecular potential energy which used different interatomic force parameters, we were able to rule out some of these, thereby determining the best choice for the parameters in this crystal. The detailed structure of this potential profile (i.e., relative depths of the wells and energy barriers hindering rotation) was then determined from the T _{1} and T _{1D } data. We thus have observed and characterized in TMD a low concentration of orientational defects which occur when a molecule occupies a higher energy well. Our observations are probably the first of such extreme NMRrelaxation effects due to motions between significantly inequivalent sites.

Experimental evidence of chaotic states in the Belousov–Zhabotinskii reaction
View Description Hide DescriptionExperimental results are reported which show strong evidence that the Belousov–Zhabotinskii reaction proceeds in an intrinsic chaotic (sustained time‐dependent, nonperiodic) manner over a range of residence times in a continuous‐flow stirred reactor. Outside of that range the experimental states reach a sustained periodic condition in some cases and a stable steady nonperiodic condition in others. A suggested theoretical basis for the observed behavior is discussed.

X‐ray photoelectron spectroscopy of S_{2}N_{2} and the solid state polymerization of S_{2}N_{2} to metallic (SN)_{ x }
View Description Hide DescriptionAn x‐ray photoelectron spectroscopic(XPS) study of a thin film of S_{2}N_{2} at −100 °C, involving the valence band, core‐level and core‐level shakeup, and energy‐loss spectra, is reported. The results are analyzed in terms of a molecular orbital model and previous optical data. In addition, the thermally induced solid state polymerization of S_{2}N_{2} to metallic (SN)_{ x } was studied by recording the XPSspectra at −40, 0, and 20 °C. The valence band data show changes of the highest filled molecular orbitals of S_{2}N_{2}, consistent with the process of polymerization to the metallic state.

NMR study of proton transfer interactions in the system pyridine +HCl (0%–95%)
View Description Hide DescriptionPyridinium chloride, which has proven useful in a number of molten salt studies where it serves as a strong chloride donor Lewis base, is freely soluble in both excess acid and excess base. To probe the proton transfer interactions involved, proton NMR studies have been performed on pyridine+HCl solutions in the composition range 0%–95% HCl at temperatures ranging from −100°C to 200°C. This system is rich in examples of the way in which competing hydrogen bonding interactions can affect the magnetic environment of the involved protons. The most obvious of these is the increased magnetic shielding that develops in the vicinity of the N–H^{+}proton of the pyridinium cation as excess HCl competes for the Cl^{−} ions, initially to form HCl_{2} ^{−} anion and later to form more extended HCl⋅⋅⋅HCl^{−} _{2} aggregates. As excess pyridine is added to PyHCl a shift in the opposite direction occurs, due either to the formation of symmetrical [Py–H–Py]^{+} species, to the repression of PyHCl autodissociation, or to a combination of both effects as expressed by (PyHCl)_{2} dimer formation. Less obvious but equally interesting is the deshielding of the proton in the HCl_{2} ^{−} anion of the PyH^{+}–HCl_{2} ^{−} melt which accompanies addition of pyridine. This results from a competition between Py with Cl^{−} for the HCl proton and a consequent tendency to produce the [PyH⋅⋅⋅Cl⋅⋅⋅HPy]^{+} species implied by the stoichiometry of certain crystalline compounds. Finally the ring protons themselves reflect the competition of excess HCl for the Cl^{−} of PyHCl and the consequent shifts in ring electron density which accompany the inward movement of the N–H^{+}proton. The trends are such as to bring the observed ring proton chemical shifts relative to pyridine into better accord with theoretical predictions for the isolated PyH^{+} cation. The trend is continued when excess HCl is replaced by the stronger Lewis acids ZnCl_{2} and AlCl_{3} and in the case of excess AlCl_{3}, agreement with theory is almost quantitive except for the α proton shifts. For the latter, the observed shifts are not even qualitatively correct.

A b i n i t i o molecular orbital calculations on the reaction path of the ketocarbene–ketene rearrangement
View Description Hide DescriptionAn a b i n i t i o type SCF MO study using a double zeta quality basis set has been carried out on the formylmethylene–ketene rearrangement reaction which is the last step of the Wolff rearrangement–decomposition sequence of α‐diazoketones and α‐diazoesters. The ketene structure is computed to be 74.3 kcal/mole more stable than the isomeric formylmethylene and the reaction features a computed activation energy of 5.7 kcal/mole, corresponding to a bridged activated complex. The computed geometry of the ketene molecule is in good agreement with the experimental geometry.

Kinetic energy and path curvature in bound state systems
View Description Hide DescriptionThe effect of path curvature on kinetic energy in bound state systems has been investigated by solving the Schrödinger equation for a particle confined to an annular region of uniform width. In the one‐dimensional limit of a narrow annulus the angular behavior of the particle can be described by linear motion with an effective potential. This potential is related to the radius of curvature R by V _{eff}=−(h/^{2}/2m)(1/4R ^{2}). Thus, for a particle confined to a narrow channel high path curvature produces an effective stabilizing influence. An interpretation of this phenomenon is offered and several examples are examined.

Accurate characterization of the transition state geometry for the HF+H′→H+H′F reaction
View Description Hide DescriptionThe potential surface for the exchange reaction HF+H′→H+H′F has been investigated with various multiconfiguration self‐consistent field (SCF) and configuration interaction (CI) wavefunctions. For the first time, nonlinear geometries have been considered. The calculations demonstrate the importance of diffuse functions on the fluorine for describing nonlinear geometries. A qualitative model is presented to explain the need for diffuse functions. The energy barrier for the exchange reaction is calculated to be ∼45 kcal/mole, which is comparable to the values obtained in previous a b i n i t i o calculations on the collinear reactionsurface (Refs.1 and 2). More importantly, the calculations show that the saddle point region is very flat, the barrier changing by only 1–2 kcal/mole between collinear (180°) and perpendicular (90°) geometries. The optimum angle for the transition state geometry is calculated to be 106°. Dynamics calculations on the HF+H′→H+H′F reaction have employed semiempirical London–Eyring –Polanyi–Sato (LEPS) surfaces that had artifically small energy barriers, as has been pointed out previously. The present calculations show that not only were the barriers for exchange too low, but that the basic shape of the LEPS surfaces was inappropriate. The implications of this result for future dynamics calculations are discussed.

Vaporization kinetics of sodium chloride
View Description Hide DescriptionThe vaporization rates of pure and calciumdopedsodium chloride single crystals have been measured in vacuum (<3×10^{−7} torr) and oxygen (10^{−5} torr). In initial vacuum sublimation,calciumdoping was found to increase vaporization rates and decrease the activation energy of free sublimation with respect to pure sodium chloride. Introduction of oxygen into the system was found to decrease vaporization rates and increase activation energies with calciumdoped specimens whereas the kinetics of pure sodium chloride vaporization remained unchanged. The effect of oxygen could also be produced by long vacuum sublimation times. These results could be explained in terms of kinetic rate control at the desorption step of sublimation.

High resolution Raman spectroscopy of gases with laser sources. XI. The spectrum of cyanogen
View Description Hide DescriptionThe pure rotational and rotation–vibrational Raman spectra of cyanogen, C_{2}N_{2}, were photographed under high resolution. The spectra were excited with a single mode argon laser operating at λ=4880 Å. The pure rotation spectrum shows a partially resolved hot band structure that is assigned to the ν_{5} ^{1} and 2ν_{5} vibrationally excited states. The l‐type doubling in the pure rotational spectrum of molecules in the ν^{1} _{5} state is sufficiently well resolved at high J values to allow a determination of the l‐type doubling constant. The ν_{1}(Σ^{+} _{ g }) and ν^{1} _{4}(Π_{ g }) fundamental rotation–vibration bands were also photographed. Both fundamentals are overlapped by vibrational hot bands originating in low‐lying vibrational levels. Molecular constants obtained in the present work are, in units of cm^{−1}, The constants for the ν^{1} _{5} and 2ν_{5} ^{0,2} states were obtained from the pure rotation spectrum. The vibrational constants were found to be The ground state constants B _{0} and D _{0} and their uncertainties were determined by an extrapolation procedure. For all other constants the quoted errors are one standard deviation and only represent the internal errors generated in the least squares analysis of the data. Vibrational constants determined from Q‐branch measurements only are indicated by (Q).