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Volume 65, Issue 1, 01 July 1976

The semiclassical coupled states method
View Description Hide DescriptionA semiclassical method, in which only the translational degree of freedom is treated classically, is presented. The coupling scheme is reduced by neglecting the intermultiplet transitions. Thus, the method is the semiclassical version of the CS (coupled states) method. Some calculations on the He–H_{2} system are carried out. These calculations show that vibration to rotation energy conversion is dominating at low collision energies.

A molecular theory of interfacial phenomena in multicomponent systems
View Description Hide DescriptionThe van der Waals theory of surface tensions is generalized to multicomponent systems. The local free energy density consists of a ’’local equilibrium’’ free energy (i.e., equilibrium free energy of a uniform mixture having species densities equal to the local species densities) plus a quadratic form in the gradients of the species densities. The coefficients in this quadratic form depend on the local species densities through the density dependence of the second moment of the local multicomponent direct correlation function. The requirement that the free energy be a minimum yields a system of partial differential equations (one for each component). A particular linear combination of the differential equations is the condition for mechanical equilibrium. It can be interpreted as a microscopic statement of the multicomponent Young–Laplace equation for the pressure variation across a curved interface. For two component systems the theory is a generalization of the treatment of Cahn and Hilliard in that it allows for pressure variations. If the local pressure fluctuations are suppressed, the differential equation for the concentration is very similar to theirs, except that the total density may vary across the interface. Similarly, when the theory is applied to liquid–vapor equilibrium in a binary system, the differential equation for the total number density reduces to that of a single component system when the local chemical potential difference (μ=μ_{1}−μ_{2}) is held constant.

Dielectric constant in terms of atom–atom correlation functions
View Description Hide DescriptionA general formalism developed by us earlier is used to obtain an expression for the dielectric constant of a diatomic polar fluid in terms of atom–atom correlation functions. These functions are then shown to be of comparatively short range, decaying line r ^{−6} for large r for almost all densities and temperatures.

Anomalous temperature dependence of the frequency and damping constant of phonons near T _{λ} in ammonium halides
View Description Hide DescriptionThe mechanism which gives rise to the anomalous temperature dependence of nonsoft phonons near the lambda transition point in ammonium halides is discussed. The orientation of an ammonium ion in its unit cell is treated as a pseudo‐Ising spin, and the Hamiltonian of a pseudospin–phonon coupled system is derived from simple assumptions. Perturbation theory is used to evaluate pseudospin–phonon scattering terms in the Hamiltonian. The resulting expressions for the frequency and the damping constant of phonons are seen to include a long‐range order parameter and a correlation function of the pseudo‐Ising spins, which are well known to show characteristic temperature variations near a lambda point. The results qualitatively explain the anomalous temperature variation in the frequency and the damping constant of nonsoft optical phonons near the lambda point, as measured by means of Raman scattering experiments in NH_{4}Cl and NH_{4}Br. The difference between the temperature dependences of the frequency in these two materials is also discussed.

Ultrasonic and hypersonic properties of ionic hydrate melts
View Description Hide DescriptionUltrasonic and Brillouin scatteringmeasurements have been used to establish the relaxation properties of zinc chloride, zinc nitrate, and calcium nitrate hydrate melts in the frequency range 5 MHz to 12 GHz. A distribution of relaxation times is observed for these melts which is generally much broader than for a single relaxation. The width of this distribution decreases with increasing temperature and water content. Deuteration of the hydrate melts produces a significant increment in the low frequency absorption and also an increment in the mean relaxation time. The experimental data have been compared with the Isakovich–Chaban and Montrose–Litovitz theories of viscoelasticrelaxation. The mean relaxation times predicted by the I–C theory are generally longer than the experimental values, and the shape of the predicted distribution is different. The data can be closely fitted to the M–L treatment with proper choice of the two adjustable parameters in the theory. A multiple state chemical model is proposed for the hydrate melts. Under such circumstances this model can be reduced to a form which falls within the mathematical framework of the M–L treatment.

Triplet state radiationless transitions in polycyclic hydrocarbons
View Description Hide DescriptionThe zero‐field EPRtransitions and spin sublevel intersystem crossing rates for the lowest triplet states of tetracene, perdeuterotetracene, 1,2‐benzanthracene, and 1,2,3,4‐dibenzanthracene have been measured in n‐alkane solvents at 2°K by optical detection of magnetic resonance techniques. The rates of spin sublevel intersystem crossing are primarily nonradiative, and an analysis of these molecules, as well as the triplet state dynamics of several groups of polycyclic hydrocarbons, is presented with conclusions applicable to planar aromatic organic systems in general. Comparison of the triplet state intersystem crossing rates of the polycyclic hydrocarbons suggests that nonradiative transitions for the individual spin sublevels of the lowest triplet state may be qualitatively understood and predicted by a determination of the symmetry‐selected one‐center spin‐orbit coupling mechanism available to each triplet sublevel.

Decoupling scheme for a semiclassical treatment of electronic transitions in atom–diatom collisions: Real‐valued trajectories and local analytic continuation
View Description Hide DescriptionThe semiclassical theory of electronically nonadiabatic transitions in atom–diatom collisions is modified by the introduction of a decoupling approach to the nuclear dynamics. The probability of switching surfaces is calculated locally by integrating in the complex plane over a nuclear coordinate which couples most strongly to the electronic transition. A substantial computational simplification results when this approach is implemented. The power of the method lies in the fact that the potential energy surfaces need be analytically continued locally rather than globally. Thus the trajectories can be maintained on the real axis except for the one point where the surfaces are switched. Computational results are presented and discussed for two model collinear nonreactive systems, F+H_{2} and Br+H_{2}. It is shown that when the possibility of an E–Vresonant energy transfer exists, the vibrational as well as the electronic degrees of freedom must be treated quantum mechanically.

Solvent and temperature effects on natural radiative lifetimes of some substituted polyenes
View Description Hide DescriptionThe extent to which the concept of a natural radiative lifetime (τ_{0}) can be used as an indicator of what is taking place on the molecular level as the solvent or temperature changes is considered. The observation is made that since the universal solvent shift can be explained by perturbation theory, this indicates that the fluorescing state is really a mixture of states of the isolated molecule. With this as a basis, a simplified coupling model is introduced and resolvent techniques are used to solve for the time‐dependence of the fluorescing state as a function of the solvent–solute interaction strength. The results indicate that much of the dependence of τ_{0} on the solvent and temperature for the retinols and diphenylpolyenes may be due to the state mixing introduced by the solvent perturbations. In these molecules as the strength of solvent induced state mixing increases, τ_{0} decreases. The temperature effect is such that τ_{0} decreases as T decreases because of an increase in solvent perturbation correlated to density increase.

Trapped electrons in crystalline D_{2}O ice at 4°K
View Description Hide DescriptionThe ir absorption band and EPRspectrum of ΔH _{ p p }=1.3 G at g?2 observed in irradiated D_{2}O crystalline ice at 4°K have been assigned to trapped electrons. The ir band and EPRspectrum decayed with τ_{1/2}=35 min in pure D_{2}O ice at 4°K. The trapped electrons were not observed in H_{2}O ice at 4°K. Addition of 1.5% H_{2}O in volume in D_{2}O reduced the trapped electron yield to about 60% and shortened τ_{1/2}. Effect of NH_{4}F and AgNO_{3}doped in D_{2}O ice has been examined. The trapped electrons were stable in 10M LiCl⋅H_{2}O–D_{2}O glass at 4°K. Stability of the trapped electrons in ice has been discussed.

On the accuracy of the ’’decoupled l‐dominant’’ approximation for atom–molecule scattering
View Description Hide DescriptionCross sections for rotational excitation and spectral pressure broadening of HD, HCl, CO, and HCN due to collisions with low energy He atoms have been computed within the ’’decoupled l‐dominant’’ (DLD) approximation recently suggested by DePristo and Alexander; these are compared with accurate close coupling results and also with two similar approximations, the effective potential of Rabitz and the coupled states of McGuire and Kouri. These collision systems are all dominated by short‐range repulsive interactions although they have varying degrees of anisotropy and inelasticity. The coupled states method is expected to be valid for such systems, but they should be a severe test to the DLD approximation which is expected to be better for long‐range interactions. Nonetheless, DLD predictions of state‐to‐state cross sections are rather good, being only slightly less accurate than coupled states results. DLD is far superior to either the coupled states or effective potential methods for pressure broadening calculations, although it may not be uniformly of the quantitative accuracy desirable for obtaining intermolecular potentials from experimental data.

Cage effects and steric hindrance in van der Waals solids, with application to alkyl iodide photolysis in rare gas hosts
View Description Hide DescriptionMolecular luminescence in the near ir is produced by 259–290 nm pulsed ’’photodissociation’’ of CH_{3}I, CD_{3}I, and perfluoroalkyl iodide guests in rare gas hosts at 4.2 °K. For CD_{3}I and CH_{3}I in Ne, the 15 member progression observed is assigned as fluorescence into high lying (near v ^{″}=37) vibrational states of the methyl–iodide stretch in the ground electronic state. Photoselection studies confirm the transition dipole lies along the methyl–iodine bond. The photodissociation cage effect is near complete, with only a minor quantum yield of permanent dissociation. Detailed analysis of the spectra suggests that the 0^{+} ’’repulsive’’ excited state is actually slightly (<2000 cm^{−1}) chemically bound, and that the ground state potential is negligibly perturbed from its free molecule shape. A simple semiquantitative theory of the cage effect is proposed. In the impulsive limit, the excited state dynamics reflect a strong cage effect. However, in the adiabatic limit, the absorption and emission spectra reflect only a weak, van der Waals cage effect. The theory is applied to known examples of photodissociation in solids, and to rearrangements of larger molecules. A cage potential experiment of Schnepp and Dressler is reinterpreted.

The three components of the thermomagnetic force in NO and O_{2}
View Description Hide DescriptionThe three components of the thermomagnetic force were measured on disks with their surfaces perpendicular to the heat flux. The study was done in the paramagnetic gases NO and O_{2} for conditions approximating those assumed by recent theory. Comparison has been made with theory as well as previous experimental work.

Infrared absorption spectra of gaseous HD. II. Collision‐induced fundamental band of HD in HD–Ne and HD–Ar mixtures at room temperature
View Description Hide DescriptionThe collision‐induced infrared absorption spectra of the fundamental band of HD in binary mixtures of HD with Ne and Ar at room temperature have been studied with an absorption path length of 105.2 cm for different base densities of HD in the range 8–20 amagat and a number of total gas densities up to 175 amagat. The observed features of the profiles of the enhancement of absorption in these mixtures resemble closely those of the corresponding profiles of the fundamental band of H_{2} in binary mixtures with Ne and Ar. The binary absorption coefficients of the band obtained from the measured integrated intensities are (1.84±0.06) ×10^{−35} and (4.41±0.06) ×10^{−35} cm^{6} s^{−1} for HD–Ne and HD–Ar, respectively. The characteristic half‐width parameters, δ_{ d } and δ_{ c } of the overlap transitions and δ_{ q } (and δ_{ q′}) of the quadrupolar transitions, are obtained from an analysis of the profiles of the enhancement of absorption in both these mixtures. The quantity δ_{ c } which is the half‐width of the intercollisional interference dip of the Q branch increases with the density of the perturbing gas Ne or Ar, and for HD–Ne it varies in a manner similar to that for HD–He as described in Paper I of this series.

Crystal field parameters for Eu^{3+} in KY_{3}F_{10}
View Description Hide DescriptionThe fluorescencespectrum of KY_{3}F_{10}: 1% Eu in powder form was recorded at 77 and 4.2°K between 4600 and 7000 Å, and 89 fluorescence lines arising from levels ^{5} D _{0}, ^{5} D _{1}, ^{5} D _{2}, and probably ^{5} D _{3} were observed. The spectrum agrees with with a C _{4v } symmetry, and it is possible to determine the irreducible representation of the group associated with the Stark components of ^{2S+1} L _{ J } levels. The set of crystal field parameters agreeing best with the experiment, on a basis of 200 kets ‖^{7} F≳, ‖^{5} D≳, and ‖^{5} G≳ of the 4f ^{6} configuration, is B ^{2} _{0}=−551 cm^{−1}, B _{0} ^{4}=−1360 cm^{−1}, B ^{4} _{4}=+345 cm^{−1}, B ^{6} _{0}=394 cm^{−1}, and B ^{6} _{4}=234 cm^{−1}.

On the nonequilibrium distribution of adatoms resulting from dissociative adsorption of a diatomic gas
View Description Hide DescriptionKinetic equations governing the distribution of adatoms resulting from irreversible, dissociative adsorption of homonuclear diatoms onto a two‐dimensional lattice are derived. Desorption and atomic skating are ignored, which allows the problem to be conveniently formulated from a molecular viewpoint. The rate constant for adsorption is assumed to be of an Arrhenius form with an activation energy which consists of an additive contribution from the interaction of the adsorbing molecule with each adatom on the surface. Special attention is paid to the relationship between the molecular distribution resulting from irreversible adsorption and the equilibrium molecular distribution. The kinetic equations are solved as a power series in the covering fraction; the coefficients involve molecular cluster diagrams similar to those in equilibrium, virial expansions. Comparison of the nonequilibrium and equilibrium covering fraction expansions of the molecular pair distribution functions is made, and an illustrated example is considered for a case where the functions and their expansions can be evaluated exactly. Finally, the effect of the nonequilibrium distribution of adatoms on the configurational contribution to the thermodynamic properties of the adsorbate is discussed.

Rayleigh light scattering from concentrated solutions of polystyrene in cyclohexane
View Description Hide DescriptionThe Rayleigh light scattered at 90° by concentration fluctuations in solutions of polystyrene with cyclohexane, in the mass concentration range 0.18–0.56 of polymer, is observed to mix with a heterodyne efficiency close to unity with light scattered elastically by dust particles. A technique is described where by using a digital photon correlator the absolute intensity of the Rayleigh light is measured and the elastic modulus of the uncross‐linked polymergel deduced. The results are in satisfactory agreement with values found in the literature. The measurements of the relaxation time of the concentration fluctuations allow the friction constant between the solvent and the polymer matrix to be calculated.

Evaluation of molecular integrals over Gaussian basis functions
View Description Hide DescriptionThis paper is concerned with the efficient computation of the ubiquitous electron repulsion integral in molecular quantum mechanics. Differences and similarities in organization of existing Gaussian integral programs are discussed, and a new strategy is developed. An analysis based on the theory of orthogonal polynomials yields a general formula for basis functions of arbitrarily high angular momentum. (η_{ i }η_{ j }∥η_{ k }η_{ l }) = Σ_{α=1,n } I _{ x }(u _{α}) I _{ y }(u _{α}) I*_{ z }(u _{α}) By computing a large block of integrals concurrently, the same I factors may be used for many different integrals. This method is computationally simple and numerically well behaved. It has been incorporated into a new molecular SCF program HONDO. Preliminary tests indicate that it is competitive with existing methods especially for highly angularly dependent functions.

Overtone emission spectroscopy of HF and DF: Vibrational matrix elements and dipole moment function
View Description Hide DescriptionMeasurements of the emission intensities for overtone bands of HF and DF from a chemical laser source have been used to determine the dipole moment function for the ground electronic states of HF and DF for internuclear separations from 1.25–3.1 bohr. Vibrational matrix elements and Einstein coefficients have been determined for the fundamental through fifth overtone bands for all transitions from upper vibrational levels below v=10 for HF and v=13 for DF. The results are compared with recent a b i n i t i o and semiempiricaldipole moment calculations.

Magnetic and thermodynamic properties of potassium ferricyanide from 0.4 to 4.0 °K in magnetic fields up to 22 000 G directed along the crystallographic a axis
View Description Hide DescriptionThe heat capacity of K_{3}Fe(CN)_{6} has been measured in fields of 0, 1400, 2800, 7000, 12 000, 16 300, and 21 500 G, from 0.4 to 4 °K, along with observations of intensity of magnetization and of the course of both temperature and magnetization along isentropes. These data are presented along with values of the entropy of the salt, as a function of field and temperature, derived from them. All properties show the effects of strong antiferromagneticinteractions.

Static and dynamic structure factors for interdimensional systems. II. Layered crystals
View Description Hide DescriptionThe displacement–displacement space–time correlation functions and the static and incoherent dynamic structure factors are calculated for a layered harmonic lattice. The continuous transition from 3D to 2D behavior of the various quantities as functions of the interlayer coupling is analyzed. Criteria for probing the 2D behavior are obtained along with suggestions and predictions for relevent scattering experiments.