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Volume 52, Issue 1, 01 January 1970
52(1970); http://dx.doi.org/10.1063/1.1672652View Description Hide Description
A functional‐integral representation of the quantum‐phase‐space transformation function is postulated and various expansion representations for this function are generated. The binary‐collision expansion is discussed in some details, and it is shown how dynamics of the system can be described in terms of the quantum irreducible cluster operators. The developed formalism is applied to the derivation of the kinetic equations for free electrons in the conduction band of the simple liquids and dense metallic vapors. It is proved that equations postulated on the ground of intuitive arguments can be regained if the multiple electron–neutral‐atom scattering and the interference between electron–electron and electron–neutral‐atom scattering are neglected. A brief discussion of the relation of presented formalism to Ziman and Edwards theoretical descriptions of disordered systems is also included.
Infrared Spectrum of Matrix‐Isolated Cyanate Ion. I. Vibrational Analysis, Bandwidths, and Absolute Intensities in Potassium Halides52(1970); http://dx.doi.org/10.1063/1.1672726View Description Hide Description
Solid solutions of the cyanate ion in KCl, KBr, and KI matrices have been prepared by heating standard infrared pressed disks. The infrared spectra of these disks have been measured from 5000 to 400 cm−1 and analyzed. Our frequency data are in excellent agreement with those obtained from dopedsingle crystals by earlier investigators. Anharmonicity constants, harmonic frequencies, and force constants have been calculated for the isotopic species 16O12C14N−, 16O12C15N−, 16O13C14N−, 16O13C15N−, and 18O12C14−. The anharmonicity constants are essentially independent of the matrix, and only quadratic force‐constant changes appear necessary to account for the frequency shifts of the fundamentals as the matrix is varied. The temperature dependence of the bandwidths and peak frequencies of the fundamentals have been studied in the range from 95 to 530°K. The fundamentals in all matrices can be represented well by Lorentz band shapes. The absolute band intensities have also been measured. In addition to bands arising from the internal modes of the cyanate ion, combination bands of the intense cyanate fundamentals with external modes of the cyanate and with lattice modes of the host matrix have been observed.
Irradiation of Isobutene with 8.4‐, 10‐, and 11.6–11.8‐eV Photons. Decomposition of Neutral Excited Isobutene and Reactions of C4H8 +52(1970); http://dx.doi.org/10.1063/1.1672679View Description Hide Description
Isobutene has been irradiated with 8.4‐, 10‐, and 11.6–11.8‐eV photons in the presence and absence of scavengers such as O2, NO, and H2S. Over the entire energy range, 80% of the neutral excited iso‐C4H8 dissociates as follows: iso‐C4H8*→C3H4+CH3+H. Minor primary fragmentations include: iso‐C4H8*→C3H6+CH2 and iso‐C4H8*→CH4+C3H4. Isotopic analysis of the products formed in the photolysis of (CD3)2CCH2 and iso‐C4H8–iso‐C4D8 mixtures throws some light on the mechanistic details. At 10 and 11.6–11.8 eV, iso‐C4H8 + ions are formed, with photoionization quantum yields of 0.26 and 0.31, respectively. Thirty percent of these ions react to yield isobutane as a product. The mechanism seems to involve internally excited ions which take part in a proton‐transfer reaction: C4H8 ++C4H8→C4H9 ++C4H7. When iso‐C4D8 is irradiated in the presence of alkanes (AH2), the following H2‐transfer reaction is shown to occur: C4D8 ++AH2→(CD3)2CHCD2H+A+. Experiments performed with a partially deuterium‐labeled isopentane demonstrate that the latter reaction is highly stereospecific.
52(1970); http://dx.doi.org/10.1063/1.1672694View Description Hide Description
A uniform and adherent layer of β‐UD3 was formed on uranium when uranium reacted with deuterium in the temperature range 175–350°C and pressure range 100–10 270 torr. The rate of reaction was controlled by diffusion of deuterium across this product layer. Reproducible results were obtained only with D2 of very high purity because low‐level impurities had a profound effect on the rate of reaction. It was concluded that molecular diffusion with sorption was the predominant method of mass transport, but atomic diffusion may also be occurring. The activation energy for molecular diffusion with Langmuir sorption of D2 on UD3 was determined to be 9.8 ± 0.5 kcal/mole D2. The activation energy for atomic diffusion was determined to be 4.4 ± 0.3 kcal/g‐atom of D.
52(1970); http://dx.doi.org/10.1063/1.1672713View Description Hide Description
A model is presented for electron–phonon coupling in molecular crystals and its effect on transport of excitons and charge carriers in aromatic hydrocarbon crystals. The model differs from the usual ones in that the coupling is taken quadratic instead of linear in the vibrational coordinates. It is shown that this coupling dominates in aromatic hydrocarbons, leading to large frequency shifts in out‐of‐plane molecular vibrations on electronic excitation or ionization. The present study is limited to weak intermolecular electronic coupling, implying quasilocalized excitons (or electrons). There are then two limiting modes of diffusion, governed by the rate either of exciton transfer between molecules or of phonon transfer. In either limit, at high temperatures, transport occurs by incoherent jumps between adjacent molecules (hopping) and increases or decreases gently with temperature, while at low temperatures, coherent transport decreasing rapidly with increasing temperature occurs. The diffusion coefficient is larger for normal than for deuterated aromatic hydrocarbons except for hopping transport in the slow‐exciton limit. The observed temperature dependence and deuterium effect of triplet excitondiffusion in the direction of anthracene are reproduced by the model in this case. The transition from hopping to coherent diffusion is not readily observable for anthracene, but may be observable for naphthalene or benzene. Preliminary results indicate that the model also accounts satisfactorily for the magnitude and temperature dependence of charge‐carrier mobilities in anthracene.
52(1970); http://dx.doi.org/10.1063/1.1672723View Description Hide Description
The lattice dynamics are discussed, using the method of Green's functions, for a linear chain of homonuclear diatomic molecules, one of which has a different force constant from the others. The model can represent a molecular crystal in which one molecule is electronically excited. The frequencies of the antisymmetric normal modes can be deduced from the frequencies of the symmetric modes of a chain of alternating masses, in which one of the lighter atoms is replaced by an isotopic impurity, and vice versa. The alternation of symmetry arises because, in the present model, the defect consists of two atoms instead of one. A localized mode in the bandgap or above the optical band is obtained.
52(1970); http://dx.doi.org/10.1063/1.1672724View Description Hide Description
Various configuration‐interaction wavefunctions for the Be ground state built up from Slater‐type orbitals are reported. Their 1‐ and 2‐matrices are examined in detail and compared with those previously reported in the literature. It is shown how the quality of a basis set and the omission of just a few configurations noticeably alter the density matrix structure. Further, it is pointed out that the occupation numbers of some important natural states are in general quite sensitive to the goodness of the wavefunction. In the choice of configurations to be included in a truncated CI expansion over an extended basis set by performing stepwise full CI expansions over small basis sets, the role played by singly excited configurations is emphasized. The use of density matrices as a global representation of the wavefunction is also stressed.
52(1970); http://dx.doi.org/10.1063/1.1672725View Description Hide Description
In this paper we present the results of an experimental study of the absorptionspectrum of benzene and deuterated benzenes in solid Ar, Kr, Xe, and N2 in the spectral region 2800–1700 Å, with special reference to the 2100‐ and to the 1850‐Å transitions. Our main results are:
(a) On the basis of the observed vibrational structure the second excited singlet state of the benzene molecule is assigned to the rather than to the excitation.
(b) Theoretical calculations of the dynamic electronic–vibrational coupling between the and the states support the assignment of the 2100‐Å transition.
(c) The vibrational structure of the 1850‐Å transition was resolved.
(d) No experimental evidence for Jahn–Teller coupling in the state was observed, in agreement with theoreticalanalysis.
(e) Information on site splittings for the higher excitation of benzene in rare‐gas solids has accumulated.
(f) Analysis of matrix shifts for the and transitions indicates that the “solvent effect” is dominated by dispersion interactions.
(g) Information on deuteration effects on the and energy levels was obtained.
(h) Qualitative information on intramolecular radiationless decay in the two higher excited states of the benzene molecule has been inferred from the linewidths in the absorptionspectrum.
52(1970); http://dx.doi.org/10.1063/1.1672653View Description Hide Description
Rayleigh–Schrödinger perturbation theory has been used through second order to obtain an analytic representation for the ground‐state wavefunction of H2 +. Values of the electronic energy and other molecular properties computed with this approximate wavefunction are compared with the corresponding exact values, and they demonstrate its high accuracy.
52(1970); http://dx.doi.org/10.1063/1.1672654View Description Hide Description
The time dependence of benzene vapor fluorescence is studied as function of vapor pressure for excitation in the neighborhood of 2600, 2530, and 2470 Å. At pressures above about 20 torr the decay appears exponential and independent of excitation wavelength. At lower pressure, deviations from exponential decay are observed for 2530‐ and 2470‐Å excitation. The decay times obtained under different conditions are combined with steady‐state data available in the literature and several rate constants derived. The result is related to discussions of the mechanism of deactivation of excited benzene molecules.
52(1970); http://dx.doi.org/10.1063/1.1672655View Description Hide Description
This paper explains and advocates the use of a Laplace‐transform steepest‐descent method for the computation of energy‐level densities by inversion of the partition function. The earlier Lin–Eyring approach, based on the Darwin–Fowler method, is shown to be unnecessarily obscure and in part redundant By use of a much‐simpler formulation due to Kubo, it is shown that the first‐order steepest‐descent approximation to the inversion integral follows straightforwardly from a knowledge of the relevant partition function, its energy, and specific‐heat relations. In this way several explicit equations for and its integral are derived, including two for anharmonic vibration and internal vibration–rotation. The relationship of the S–D method to Tolman's classical formula is discussed and some thermodynamic implications pointed out. Numerical results agree closely with those obtained by the direct counting of energy levels and, with certain exceptions, the indirect computations of other authors.
52(1970); http://dx.doi.org/10.1063/1.1672656View Description Hide Description
Wavefunctions and interaction energies are calculated for the helium‐atom–hydrogen‐molecule system at a wide range of internuclear separations. Letting represent the distance measured along a line drawn from the helium nucleus to the midpoint of the hydrogen molecule, the H2bond distance, and the angle between and , results are reported for , and . The orbital basis set consisted of Slater and orbitals, and all integrals are accurately evaluated. The wavefunctions are constructed by each of the two major approaches to molecular bonding; the self‐consistent‐field molecular‐orbital method of Roothaan and the configuration‐interaction method. The value of the two methods in atom–diatomic‐molecule interactions is compared extensively. For each individual method, the effect of the size of the basis set on the resultant interaction energy is examined. The values for the He–H2interaction energies obtained by the self‐consistent‐field and configuration‐interaction method are very similar. The self‐consistent‐field method appears adequate for the calculation of interaction energies for closed‐shell noninteracting systems except at large center‐of‐mass separations. The interaction energies are accurately fit to an analytic expression for the intermolecular potential. Configuration‐interaction calculations performed at large center‐of‐mass separations fail to locate the He–H2 van der Waals minimum.
52(1970); http://dx.doi.org/10.1063/1.1672657View Description Hide Description
Dielectric constants for the polar gases CFH3, CF3H, CClF3, and CCl3H in the range 50–143°C, and for CCl3F at 96.3°C, have been measured as a function of pressure and density in the pair interaction range of densities. Accurate values of dipole moment and polarizability of the first four molecules have been derived from the limiting temperature dependence at zero density, and dielectric and pressure second virial coefficients from the variation with density. The pressure coefficients are in good agreement with other compressibility data. The dielectric coefficients are very large and positive for CF3H, very large and negative for CFH3 and CClH3, and positive with approximately the values predicted for spherical polarizable dipoles in the case of CClF3 and CCl3F. The deviations from simple theory indicate major effects of molecular shape, but they are not satisfactorily explained by Buckingham and Pople's anisotropic short‐range pair‐potential model.
52(1970); http://dx.doi.org/10.1063/1.1672658View Description Hide Description
Dielectric and pressure second virial coefficients of five mixtures and the pure gases have been determined at 49.7°C, the values for CO2 at 29.4°C. The pressure coefficients are in reasonably good agreement with values predicted from combining rule Lennard‐Jones parameters derived from viscosities of the pure gases. The large effect of quadrupole interaction energy on the dielectric coefficient of pure CO2 has been calculated numerically, and analytical treatments of the smaller effects of reaction fields of induced moments, quadrupole‐induced dipole energy, and anisotropy energy have also been made. These result in a calculated molecular quadrupole moment of CO2 of 4.3 × 10−26 esu cm2 from the data for pure CO2. For CO2–Ar pairs, the effects in addition to the direct quadrupole‐induced dipole contribution are much smaller, and the value 4.1 × 10−26 esu cm2 for the quadrupole moment of CO2 is derived from the dielectric coefficient. Both values are in good agreement with the Buckingham–Disch result and with other less direct estimates from infrared and microwave absorption and from pressure virial coefficients.
52(1970); http://dx.doi.org/10.1063/1.1672659View Description Hide Description
Infrared and Raman spectra have been recorded for fluoroacetyl fluoride, chloride, and bromide. The data show that each compound exists as an equilibrium mixture of two isomers in the vapor and liquid states. Normal coordinate analysis calculations based on a Urey–Bradley potential function indicate that the two preferred conformations are a trans and a staggered conformation which is close to the cis. In all three compounds the trans isomer is found to be the more stable in both liquid and vapor phases, with its stability being relatively diminished in the vapor state. Approximate, but nearly complete vibrational frequency assignments are made for each isomer. The vapor phase enthalpy difference was measured as − 2.05 ± 0.25 kcal/mole for fluoroacetyl bromide.
52(1970); http://dx.doi.org/10.1063/1.1672660View Description Hide Description
The most powerful and efficient pulsed chemical lasers produced to date have resulted from the simple exothermic reactions between halogen atoms and hydrogen halides. These reactions have been initiated by flash photolysis. One such reaction is A kinetic model has been developed for this laser system which calculates the intensity profile of the laser pulse as a function of time. The input data for the model include estimates of the reaction rate into the zeroth and first vibrational level of HCl and cross sections for collisional deactivation by the different chemical species in the laser medium. The rate of reaction into the second vibrational level of HCl is assumed to be zero. Any small finite rate into the second level would have a negligible effect on the calculated performance of the laser which operates only on the fundamental transition of HCl. The theoretical model also requires as input data the photolysis flash intensity profile, the cavity geometry, and the losses. A discussion of the model is given, and a comparison is made between experiment and theory. The model is able to predict quantitative variations of the laser pulse characteristics as a function of flash intensity, cavity losses, and reagent partial pressures. The quantitative calculations are in reasonable agreement with experiment. It is concluded that (a) the most important single contribution to deactivation in the system is and (b) the rate of reaction to produce is at least as large as that to produce .
Anomalous Temperature Dependence of the Emission Spectra of 2Cr(en)3Cl3·KCl·6H2O and Cr(en)3Cl3·3H2O52(1970); http://dx.doi.org/10.1063/1.1672661View Description Hide Description
The photon‐induced luminescencespectra and emission lifetimes of crystalline 2Cr(en)3Cl3·KCl·6H2O (en=ethylenediamine) at temperatures down to 5°K are reported. The emission occurs at 14 880 cm−1 with vibronic structure to lower energy. At temperatures below 200°K accumulation of a new chromium(III) center during illumination partially quenches this emission, and a broader emission band due to transitions within the new chromium center appears at ∼14 500 cm−1. An equilibrium is set up between the number of these centers and the normal chromium sites, the position of the equilibrium being dependent on the temperature and the intensity of the incident light. Below 100°K equilibrium is attained only slowly. Cr(en)3Cl3·3H2O shows similar behavior, but the emission band is not quenched to the same extent. The nature of the new chromium centers and of the various relaxation processes is discussed.
52(1970); http://dx.doi.org/10.1063/1.1672662View Description Hide Description
The absorption and fluorescence spectra of Eu3+ in Gd2O3single crystals were investigated at 4.2°K. This study demonstrated that the Eu3+ ion occupies three nonequivalent sites of symmetry in this crystal extending previous crystallographic investigations. Unambiguous polarization of the absorption spectra allowed this determination.
52(1970); http://dx.doi.org/10.1063/1.1672663View Description Hide Description
Total cross sections for the production of slow heavy negative ions and of free electrons in collisions of O2 −, O−, OH−, and H− ions with O2 molecules have been measured over the primary‐ion KE range from a few electron volts to 350 eV. The experiments are of the ion‐beam gas‐scattering type and utilize a radio‐frequency filter to give separately the currents of detached electrons and slow product negative ions. The cross sections for slow ion formation, , were appreciable at all energies studied, for all four collision systems. The dominant contributions to could in most cases be attributed to simple charge transfer, although in the H−–O2 and OH−–O2 systems at low energies, the data indicate that ion–molecule reactions also contribute. With exception of the H−–O2 system, the electron detachment cross sections were similar in magnitude and in behavior with collision energy to those which have been measured previously for other systems.
52(1970); http://dx.doi.org/10.1063/1.1672664View Description Hide Description
Total cross sections for the electron detachment process have been measured for the collision systems O−–He, O−–Ne, O−–Ar, O2 −–He, and OH−–He, in ion‐beam gas‐scattering experiments which extend from primary ion energies of 400 eV down to several electron volts. Detached electrons were separated from other negative reaction products either by a radio‐frequency electron filter, or by electrostatic‐retardation analysis. Particular emphasis was placed on the low‐energy region near detachment threshold; the data obtained in this region was found to conform fairly well to predictions of theoretical threshold laws. The cross sections obtained at higher energies are, for the most part, in good agreement with previous measurements.