Index of content:
Volume 68, Issue 8, 15 April 1978

Vibrational relaxation of N_{2} by H_{2}O
View Description Hide DescriptionThe vibrational relaxation of N_{2} by H_{2}O has been measured behind incident shock waves in the temperature range from 1600 to 3100 °K. The H_{2}O concentration was measured with a calibrated capacitancehygrometer. The vibrational relaxation was monitored by redundant diagnostics: interferometric measurements of the gas density and infrared emission measurements of the CO fundamental band using CO as a tracer species to reflect the N_{2} vibrational energy. The experimental results support the slowest published measurements of von Rosenberg e t a l. Taken together with existing low‐temperature data, the deactivation of N_{2} by H_{2}O can be expressed in the form pτ_{ N2–H2O}=exp(21T ^{−1/3}−1.35) μsec‐atm.

Intermolecular potentials by the inversion of differential cross sections. V. ArKr
View Description Hide DescriptionThe differential cross section for ArKr is measured at the energy of E=64.9 meV. Rainbow and fast oscillations are well resolved. The data are directly inverted to the potential by the procedure described in Paper I [J. Chem. Phys. 54, 1923 (1971)] of this series. The potential with the minimum parameters ε=14.4 meV and R _{ m }=3.88 Å is able to reproduce both the measured integral cross section and the second virial coefficient in an excellent manner.

Collisionless formation and rovibronic relaxation of CH and OH from the ir multiphoton photolysis of CH_{3}OH
View Description Hide DescriptionA CO_{2} TEA laser has been used to initiate the collisionless multiphotondissociation of CH_{3}OH between 1000 and 10 mtorr. The appearance of OH(X ^{2}Π_{ i }) 50±20 nsec after the laser pulse, independent of initial CH_{3}OH pressure (50–200 mtorr), suggests the primary dissociative channel CH_{3}OH+n hν→CH_{3} +OH(X ^{2}Π_{ i }); although CH_{3} could not be correspondingly confirmed. The appearance of CH(X ^{2}Π_{ r }) 70±20 nsec after the OH(X) appearance, independent of initial CH_{3}OH pressure (70–400 mtorr), suggests secondary collisionless dissociation. Initial rovibronic distributions of OH(X) and CH(X) were determined, as well as characteristic decay time constants. The observation of the relaxation of OH(X) over a 10 μsec time interval after radical onset, allowed the separate characterization of collisional rotational relaxation and translational diffusion.

Energy transfer in atom–diatom collisions: Vibronic excitation
View Description Hide DescriptionProduct state distributions from charge‐transfercollisions between Ar^{+}–N_{2} and H^{+}–O_{2} as well as collision‐induced excitation involving N^{+} _{2} on He, Ar, and Xe are presented. These data, obtained from collision‐produced emission spectra, are compared with a Franck–Condon model for the excitation‐radiation process; significant deviations are observed and explained on the basis of a qualitative curve‐crossing model formulated to treat such vibronic excitation processes.

Dynamical effects on nearly degenerate electronic levels in solids
View Description Hide DescriptionWe consider the optical absorption of a model system consisting of a two‐level ’’ion’’ interacting with a continuum of lattice vibrations. The two‐level system represents localized electronic energy levels such as are found on transition metal ions. The separation of the electronic energies is taken to lie within the phonon band and the interaction with the lattice vibrations is linear. For a single band of phonons the absorption is shown to consist of three peaks—a homogeneously broadened central peak flanked by two sharp lines. The existence of three absorption peaks is in contrast to the predictions of either a static crystal field or of the two‐level system interacting with a single harmonic oscillator. Our results reduce to the latter case when the phonon bandwidth becomes very narrow and to the former when the phonon bandwidth becomes very large.

Effect of vibrational excitation on the molecular beam reactions of Ca and Sr with HF and DF
View Description Hide DescriptionThe reactions of Ca and Sr with HF and DF are studied using a beam–gas configuration as a function of reagent and product vibration to obtain state‐to‐state reaction rates. A beam of alkaline earth metal atoms enters a scattering chamber containing hydrogen fluoride. The HF and DF reagents are pumped from v=0 to v=1 by a pulsed HF or DF laser; the alkaline earth monofluoride products are detected by a pulsed tunable probe laser. The product internal state distribution is determined from the laser excitation spectrum. While no products could be detected for reactions with DF(v=1) or DF(v=0), the rate constant for the Ca and Sr reactions with HF(v=1) are both at least four orders of magnitude larger than the reactions with HF(v=0). The implications of these results on bond energies and the fate of the excess energy of reaction are discussed.

Electronic to vibrational energy transfer from I (5 ^{2} P _{1/2}). I. HCl, HBr, and NO
View Description Hide DescriptionDeactivation of I* (^{2} P _{1/2}) by HCl, HBr, and NO is directly observed to produce vibrationally excited states of the diatoms. The total deactivation rates are determined from either the decay of I* fluorescence or the rise of diatom fluorescence to be k ^{ E } _{HCl}= (4.46±0.77) ×10^{2}, k ^{ E } _{HBr}= (3.51±0.12) ×10^{3}, and k ^{ E } _{NO}= (3.88±0.32) ×10^{3} sec^{−1} torr^{−1}. By comparing the intensity of I* fluorescence to that of the diatom it is found that the average number of vibrational quanta excited per deactivation of I* is 1.7±0.5, 2.3±0.5, and 3.4±0.7 for HCl, HBr, and NO, respectively. These findings are discussed in terms of recent models for E→V transfer.

Detection and assignment of the far infrared LMR spectrum of SeH (X ^{2}Π_{3/2})
View Description Hide DescriptionLaser magnetic resonancespectra of SeH(X ^{2}Π_{3/2}) have been detected at 184 μm. Transitions in ^{76,77,78,80,82}SeH have been identified, and assigned to Zeeman components of the J =5/2→7/2 transition.

Infrared study of diluted solutions of polyatomic molecules. I. Band shape of fundamentals associated with nondegenerate normal modes
View Description Hide DescriptionA theory is proposed to analyze the band shapes of the simplest class of ir band profiles of polyatomic molecule solutions. The following theoretical points are explored in detail: dependence of vibrational correlation functions on the nature of normal modes involved, calculation of vectorial correlation functions for a classical ensemble of free asymmetric rotators, construction of extended diffusion models for asymmetric tops, and use of the ordered cumulant expansion techniques to study anisotropic rotational diffusion in liquids. The theory predicts a large variety of complex, often highly irregular, band profiles. A catalogue of representative band profiles is presented which orders them according to the symmetry of the active molecule.

Series solution of the HNC and PY equations: The simple chain recursion way
View Description Hide DescriptionThe function t _{HNC}(1,2) that appears in the HNC equation when written in the form t _{HNC}(1,2) =ln g _{HNC}(1,2)+βu (1,2) can be analyzed by graphical expansion and topological reduction to obtain a series solution of the form t _{HNC}(1,2) =A _{1}(1,2) +A _{2}(1,2)+⋅⋅⋅, where each A _{ n } is graphically represented by a simple chain sum. A similar analysis yields a solution of the same form for the function t _{PY}(1,2) that appears in the PY equation when written in the form t _{PY}(1,2) =g _{PY}(1,2) e ^{βu(1,2)}−1. The graphs in a given A _{ n } are formed recursively from those of lower n. Truncation of the series at different n values provides an infinite number of well‐defined approximations to the pair correlation functiong (1,2). The series method also represents an efficient computational method for solving the HNC and PY equations that offers some advantages over methods involving the iterative or variational solution of the integral equations. The whole procedure is readily adapted to systems with long‐range forces, systems with several species of particles, and to systems suitably related to some reference system with known correlation functions.

Molecular‐dynamics investigation of solid–liquid coexistence
View Description Hide DescriptionMolecular‐dynamics simulation of a crystalline fcc solid–liquid interface has been carried out for the first time for a three‐dimensional model system with interparticle interaction described by a purely repulsive pair potential: φ (r) =4ε[(σ/r)^{12} −(σ/r)^{6}]+ε for r?2^{1/6}σ, and φ=0 for r ≳2^{1/6}σ. We have shown that the profile of potential energies versus layers [parallel to (100) plane] varies steeply in the interfacial region. The time variation of the profile has also been calculated for different temperatures including the overheating and supercooling states of the solid and liquid phases.

A b i n i t i o calculations of the vertical electronic spectra of NO_{2}, NO^{+} _{2}, and NO^{−} _{2}
View Description Hide DescriptionMCSCF/CI calculations of the vertical electronic spectra of NO_{2}, NO^{+} _{2}, and NO^{−} _{2} were carried out at the NO_{2} and NO^{−} _{2} ground state experimental equilibrium conformations. These calculations extend previous calculations of the same type in that polarization functions are included in the basis set and various limitations on the number of open shells and on the number of configurations in the MCSCF and CI calculations are removed. Calculations were also carried out on NO^{−} _{2} with a basis set augmented by diffuse s and p functions.

Determination of the long range nonreactive anisotropic potential of H+Cl_{2} and H+Br_{2} from nonreactive scattering experiments
View Description Hide DescriptionTotal differential and integral cross sections have been measured for the nonreactive scattering of H atoms from Cl_{2} and Br_{2}. The differential cross sections were measured with a velocity selected beam at two center of mass energies, 0.17 and 0.78 eV, and the integral cross sections covered the center of mass energy range 0.01 to 1.2 eV. The results can be reasonably well explained by a spherically symmetric Lennard‐Jones (12,6) potential for which the well depth and location are determined. The experimental results are shown to be in definite disagreement with cross sections calculated for the currently accepted LEPS potential surface. The fit of the experimental data is improved by including the effect of the anisotropy, which is accounted for by using the infinite order sudden approximation. A remaining discrepancy in the integral cross sections at high collision energies can be explained by introducing a plateau in the repulsive part of the Lennard‐Jones potential to take into account the distortion due to the chemical potential. This new potential model is used to predict new cross section features outside the range of the present experiments.

Fine structure due to magnetic dipole coupling in the low temperature EPR spectrum of Rb_{2}Cu(SO_{4})_{2}⋅6H_{2}O
View Description Hide DescriptionA study of the EPR spectrum of single crystals of Rb_{2}Cu(SO_{4})_{2}⋅6H_{2}O over the temperature range 290 to 115 K is reported. Below ∼240 K unusual fine structure occurs for certain orientations of the magnetic fieldH, consisting of eight equally spaced lines when H is approximately along the z molecular axis and five equally spaced lines when H lies along the y molecular axis of the Cu(H_{2}O)_{6} ^{2+} ion. The fine structure may be explained largely in terms of a magnetic dipole coupling with four neighboring copper (II) ions, each of which produces an approximately equal splitting of the EPR lines at the central copper (II) ion; the five line pattern occurs when the hyperfine interaction with the copper nucleus is small, while the eight line pattern results from a hyperfine interaction which is essentially equal to the magnetic dipole interactions (these each being ∼120 G). Spectra were simulated by considering the point magnetic‐dipole interactions with the ten nearest Cu(H_{2}O)_{6} ^{2+} ions using the expression =g _{1} g _{2}β^{2} (1–3 cos^{2}ϑ)/r ^{3}, where g _{1} and g _{2} are the g values of the two interacting ions, r is the distance between them, ϑ is the angle between the internuclear vector and the magnetic field, and β is the Bohr magneton. The resulting line shapes are in reasonable agreement with experiment for most orientations of the magnetic field in the (001) and (010) crystal planes. The agreement is significantly improved if the interaction with the two nearest copper (II) ions is ∼20% greater than that calculated using the simple magnetic dipole model, and it is shown that this is consistent with the unpaired electron density being represented as a quadrupole, as is required by the shape of the d _{ x } ^{2} _{ y } ^{2}ground state orbital, rather than as a point charge. Further improvement occurs if a weak exchange coupling of J=+30 and J=−15 G takes place with the nearest and next‐nearest copper ions, respectively, and if an anisotropic component to the background half‐width is introduced.

A solution to the rotational diffusion equation to describe molecular orientation due to a time dependent torque
View Description Hide DescriptionWhen aqueous solutions of macromolecules are placed in a square, pulsed, orienting electric field they frequently become dichroic and birefrigent. By following the rise of the optical anisotropy as a function of time after application of the pulse one can frequently distinguish between permanent and induced dipole orientation modes. Occasionally, molecules which for symmetry or other reasons are known to have no permanent dipole moment mimic permanent moment orientation. A possible explanation for this phenomenon is that the induced dipole is time dependent. Here we present a formal solution to the rotary diffusion equation for a molecule subjected to a time dependent torque due to an induced dipole mechanism. A new method of solution which can have broad application has been employed. The results are seen to be a viable explanation for the subject in question.

Depolarized Rayleigh scattering from benzonitrile
View Description Hide DescriptionThe depolarized Rayleigh light scatteringspectrum of benzonitrile has been studied from −10 to 20°C and a corresponding range of 0.070–0.019 for q ^{2}η/ρΓ. Over this temperature range the central Rayleigh dip is clearly resolved, and the value of the rotational–translational coupling parameter R is determined. For benzonitrile, R=0.36±0.03, and is constant over this temperature range. This result is similar to that of all other liquids studied thus far. The temperature dependence of the depolarized linewidth is also studied and the pair molecular relaxation time determined. It is found that the slip model of rotational diffusion agrees with the pair molecular relaxation time when the static pair correlations are taken into account.

Energy relaxation of a system of harmonic oscillators
View Description Hide DescriptionThe evolution of the vibrational energy of gas mixture under nonequilibrium conditions is studied using the evolution operator formalism. For a mixture of different harmonic gases we obtain a result that partially corrects the defects introduced by the linearization of differential equations.

Vibrational transitions in N_{2}–O_{2} collisions: A theoretical treatment and comparison with computer calculations
View Description Hide DescriptionVibration–translation and vibration–vibration–translation energy transfers during an N_{2}–O_{2} collisions are studied using a semiclassical treatment. The comparison with recent computer calculations confirms the validity of our approach and enables us to judge the effect of the simultaneous influence of different perturbations. Translational distorsion appears to have a considerable influence.

Photoelectron spectrum of Xe_{2} and potential energy curves for Xe^{+} _{2}
View Description Hide DescriptionThe photoelectron spectrum of the Xe_{2} van der Waals molecule was determined at 584 Å with a resolution of 20 meV, using an apparatus which combines a supersonic molecular beamsource with a hemispherical photoelectron spectrometer. This experiment gives new information on the potential energy curve for the bound Xe^{+} _{2}ground state at large internuclear separation. An optimum potential was determined for this state by fitting the observed photoelectron peak to a calculated Franck–Condon distribution. The calculations show specifically that the Morse function is not an adequate approximation to the potential at large internuclear distances. This experiment also gives new information on the potential energy curves for the weakly bound Xe^{+} _{2}excited states in the region of their potential minima, thus complementing Xe–Xe^{+} scattering experiments which probe these potentials in the region of their repulsive walls. Potential energy curves for all of the Xe^{+} _{2} states dissociating to Xe(^{1} S _{0})+Xe^{+}(^{2} P _{3/2} or ^{2} P _{1/2}) are constructed primarily from experimental results and are compared with recent theoretical calculations by Wadt. Photoelectron spectra of heavier xenon clusters were also determined and are discussed briefly.

Vibrational Raman spectra and intramolecular potential function of solid solutions of dimethyl ether‐d _{0} and dimethyl ether‐d _{6}
View Description Hide DescriptionVibrational Raman spectra of dilute solid solutions of dimethyl ether‐d _{0} and dimethyl ether‐d _{6} were recorded at liquid nitrogen temperatures. These data were used to develop a variety of modified internal valence force fields for specifically reflecting intermethyl potential energy coupling terms. A final 18 parameter force field was generated by applying a backward elimination statistical procedure to the least‐squares refinement computation for the force constants. This force field emphasizes the importance of a methyl–methyl interaction term between out‐of‐plane H–C–O bending displacement coordinates. Vibrational assignments for the dimethyl ether‐d _{0}, ‐d _{3}, and ‐d _{6} isotopic species were determined from the potential energy distributions calculated from the 18 parameter force field. The effects of both the tilt of the methyl group and inequivalence of the H^{in‐plane}–C–O and H^{out‐of‐plane}–C–O angles upon the normal coordinate analysis frequency fits were assessed.