Volume 52, Issue 4, 15 February 1970

Laser‐Induced Fluorescence of BaO
View Description Hide DescriptionFluorescence spectra of the system of BaO excited by seven visible Ar ion laser lines have been observed over a wavelength region from the exciting lines to beyond 1000 nm. The strongest fluorescence was observed from , excited by 488.0 nm and , and 7 excited by 496.5 nm. The rotational and vibrational assignments of the various excitation transitions have been made, and rotational and vibrational constants for the lower electronic state were obtained. A rotational perturbation in of the upper electronic state was found. Studies have been made, from 0.4 to 40 torr, of the collisional energy transfer to other rotational and vibrational levels of the state after optical pumping by laser lines. The lifetime of the state of BaO was found to be 12 ± 3 × 10^{−6} sec. The BaO molecules were produced by gas‐phase chemical reactions between O_{2} and Ba vapor in an inert gas at room temperature. A weak chemiluminescence of the system of BaO was observed.

Calculation of the Vapor‐Pressure Ratio of the Isotopes of Solid Ne and Ar
View Description Hide DescriptionThe improved self‐consistent phonon theory of Goldman, Horton, and Klein for the Helmholtz energy of anharmonic crystal is used to calculate the vapor‐pressure ratios of the common isotopes of Ne and Ar. For both substances, a Mie–Lennard‐Jones nearest‐neighbor potential with parameters chosen to fit the zero‐temperature latent heat and molar volume is found to give reasonable agreement with experiment.

Some Propensity Rules in Collision‐Induced Rotational Quantum Jumps
View Description Hide DescriptionWhen a mixture of lithium vapor and argon is irradiated with the light from an argon ion laser and the resulting fluorescence of the band system is examined under high resolution, a pattern of collision‐induced satellite lines is observed to accompany the parent resonance fluorescence series. Under conditions of low pressure these satellite lines originate from single inelastic events which alter the rotational state of the excited Li_{2} molecule. The relative intensities of the satellite lines are found to be markedly different depending on whether the collision‐induced transition originates from the upper or lower component of the doublet of the state, referred to as or , respectively. An increase in is favored over a decrease for jumps whereas is favored over for jumps. On the other hand changes that preserve the character of the component, i.e., and , occur with nearly equal probability for the same value of . This behavior has been observed for the satellite lines corresponding to , and in some cases ± 3 for levels , and of ^{7}Li_{2} and of ^{6}Li ^{7}Li. In ^{7}Li_{2} only collisional transitions between symmetric or between antisymmetric levels are allowed. For ^{6}Li ^{7}Li, which does not have this symmetry, more satellite lines are observed. However, these additional lines are significantly weaker since the ^{6}Li ^{7}Li molecule is nearly homonuclear. A simple classical model is suggested which may help to explain the different rotational quantum jump propensities for the two components.

Nitroxide Radical–Metal Chelate Interactions
View Description Hide DescriptionWe have investigated the interaction of some nitroxide radicals with a series of transition‐metal acetyl‐acetonate complexes by monitoring the linewidth of peaks in the ESR spectra of the radicals as a function of chelate concentration. The effect of the chelates on the NMR spectra of some diamagnetic materials was also investigated. The linewidths are found to vary with the number of spins on the metal and the geometry of the complexes.

2491‐Å Absorption System of NO_{2} and a Double‐Minimum Potential
View Description Hide DescriptionThe 2491‐Å absorption system of N^{16}O_{2} and the corresponding system of N^{18}O_{2} have been photographed at temperatures up to 600°C. For each molecular species measurements yield the ground‐state frequencies as well as the excited‐state frequencies . A large isotope shift observed for the (0–0) band is found to be consistent with the assignment even though this frequency is quite small compared to the frequency . Two facts which demand explanation are the isotope shift of the frequency , and the relative intensity of the cold band involving . These facts cannot be explained in terms of harmonic potential in the antisymmetrical coordinate , but can be explained in terms of a double‐minimum potential in this coordinate. The barrier of this potential is about 722 cm^{−1} and the inversion doubling is near 103 cm^{−1}. At vibrational equilibrium the calculated N–O bond lengths are 1.426 and 1.202 Å.

Influence of Brownian Rotations and Energy Transfer upon the Measurements of Fluorescence Lifetime
View Description Hide DescriptionThe depolarization of the fluorescence of solutions by either Brownian rotations or intermolecular energy transfer may be simply described by a system of first‐order linear differential equations containing as only parameters the rate of fluorescence emission and the rate of transport of the excitation from one orthogonal component of the emission to another. The steady‐state solution has the form of Perrin's equation describing the depolarization by Brownian rotations, and the time‐dependent depolarization following a unit light impulse is that originally described by Jablonski. The solution for sinusoidal excitation is novel in that: 1. It shows the difference in lifetime between the polarized components of the emission to be a sensitive function of the ratio of the modulation frequency to the emission rate . For the difference between the polarized lifetimes may become many times greater than that observed after a unit light impulse. 2. It permits the determination of both the rate of transport of the excitation and the limiting polarization of the fluorescence from observations at one fixed temperature and viscosity. 3. It allows the definition of conditions under which the true or exponential decay of the fluorescence may be measured. Experimental tests of the theory by phase fluorometry are described: These include observations upon dilute solutions in media of limited viscosity where Brownian motion is the only cause of depolarization and observations upon concentrated frozen solutions where depolarization is due to energy transfer alone.

Electronic Spectra of Cesium Fluoride Complexes of Pentavalent Neptunium
View Description Hide DescriptionThe absorption spectra of magenta‐colored CsNpF_{6} both as a mull of the crystalline solid and as a solution in CsF·2HF were obtained under various conditions. The room‐temperature spectra were unique to the electronic energy levels of the seven Russell–Saunders states for the configuration, split by spin–orbit coupling into 13 free‐ion levels; this confirms the chemical evidence for the presence of pentavalent neptunium. At liquid‐nitrogen temperatures the spectra of CsNpF_{6} mulls were interpreted in terms of the free‐ion transitions of Np^{5+} split by an crystal field. Term assignments to the following experimental energy levels obtained at room temperature were made on the basis of the observed Stark splitting in the low‐temperature spectra, and agreement with calculated energy levels (in cm^{−1}): . All levels above the ground state were observed except . A least‐squares fit of these experimental energy levels was made to the Racah Coulomb interaction parameters, ; the spin–orbit coupling parameter ; and the configuration‐interaction parameters, and . The position of the levels of Np^{5+} on the intermediate coupling diagram compared to the levels of the isoelectronic series Pr^{3+}, Nd^{4+}, Th^{2+}, U^{4+}, and Pu^{6+} (in PuF_{6}) was intermediate between U^{4+} and Pu^{6+} as expected.

New Model for the Study of Liquid–Vapor Phase Transitions
View Description Hide DescriptionA new model is proposed for the study of the liquid–vapor phase transition. The potential energy of a given configuration of molecules is defined by , where is the volume covered by interpenetrating spheres each of volume and each centered on one molecule, and where is an arbitrary positive energy. This continuum model proves to have a line of symmetry comparable with those found hitherto only in lattice models. The line is that of the diameter, or mean orthobaric density , below the critical point, and continues through the one‐phase region to infinite temperature. The existence of this line allows some of the properties to be obtained explicitly, the most unusual of which is that the diameter has a singularity comparable with that in ; hence the law of the rectilinear diameter is not obeyed. An exact solution of the model is obtained in one dimension, in which there is no phase transition, and a mean‐field solution in three dimensions. The latter preserves the symmetry. The model is shown to be thermodynamically equivalent to a two‐component system in which the pair potential between molecules of like species is zero, while that between molecules of unlike species implies a mutually excluded volume of . In this transcription the symmetry of the model becomes obvious.

Separation of Xenon Isotopes in the Thermal Diffusion Column
View Description Hide DescriptionThermal diffusion column coefficients were measured for the separation of the isotopes of natural xenon, a mixture of nine stable species, in a 7.32‐m hot wire column at wire temperatures of 790 and 1073°K. For the two remixing coefficients good agreement was found between experiment and the theory of the thermal diffusion column. Measured values of the initial transport coefficient, however, were in poor agreement with theory when the theoretical calculations were based on measurements of the thermal diffusion factor of xenon taken from the literature. The agreement was considerably improved by the use in the theory of isotopic thermal diffusion factors evaluated from a corresponding states correlation of data for other noble gases. On this basis the average ratio of the experimental initial transport coefficient to the corresponding theoretical value was found to be 1.10 ± 0.07.

Non‐Markovian Contributions to Rate Equations. IV
View Description Hide DescriptionThe magnitude of the non‐Markovian contribution to the rate of a reaction is investigated for systems interacting through a potential having a finite extension in space. The investigation is carried out within the context of the field‐theoretic Green's function approach to kinetics.

Ion Impact Spectroscopy: Inelastic Scattering of 150–500‐eV H^{+} and H_{2} ^{+} from N_{2}, CO, C_{2}H_{2}, and C_{2}H_{4}
View Description Hide DescriptionA high‐resolution ion impact spectrometer has been constructed to measure the energy lost by ions which have been inelastically scattered from molecular targets. Inelastic collisions between 150–500‐eV H^{+} and H_{2} ^{+} and N_{2}, CO, C_{2}H_{2}, and C_{2}H_{4} were observed in which the energy lost corresponded to electronic transitions in the target molecules. Most of the observed energy losses were assigned to known transitions in the targets. The cross sections for the observed electronic excitations are large. Ion impact excitation in the cases studied appears to be a very specific process because only certain types of transitions are excited in molecules which have a large number of available electronic states. Proton impact was found to excite only singlet–singlet transitions while H_{2} ^{+} impact preferentially excited certain types of singlet–triplet transitions. The implications of the specific nature of the observed excitation as well as the general spectroscopic utility of the method are discussed.

Proton Magnetic Resonance of Ammonia at Low Temperatures
View Description Hide DescriptionProtonrelaxation times were measured for liquid and solid ammonia from 50 to 280°K. Second moments were determined from the melting point (195°K) to 10°K. In the liquid due to spin–spin coupling of the proton and nitrogen‐14. The spin–spin interaction is modulated by chemical exchange above 220°K which has an activation energy of 1.9 kcal mole^{−1}. decreases discontinuously by an order of magnitude at the melting point with decrease in temperature and reaches a minimum at 119°K. The activation energy for the threefold axis reorientation of the NH_{3} molecule is 2.41 kcal mole^{−1} and the intramolecular H–H distance is 1.63 Å. decreases with increase in temperature from about 160°K to the melting point. This corresponds to self‐diffusion in the solid with an activation energy of 4.94 kcal mole^{−1}. increases from 14 G^{2} above 90°K to 20 G^{2} below 70°K but does not attain the calculated rigid lattice value of 48 G^{2}. This effect appears to be due to quantum‐mechanical tunneling at low temperatures with a frequency of about 60 kHz. The self‐diffusion observed in the solid is interpreted with reaction rate theory models. It is necessary to introduce a orientational transmission factor that is equal to 5 × 10^{−3} in order to account for the magnitude of the observed self‐diffusion coefficients and jump times.

Range Relaxation. IV. Optimal Series Expansion Coefficients for Molecular Potential Curves and Surfaces
View Description Hide DescriptionA simple many‐dimensional (multiple) perturbation–variation scheme is invoked to generate the coefficients in the expansion of an energy curve or surface about some origin, to arbitrary small order. These expressions appear in a form in which it is unnecessary to start with a full set of eigenvectors and eigenvalues of the Hamiltonian. This permits their use in conjunction with large‐scale configuration‐interaction calculations. The relaxation of both linear and nonlinear parameters in the wavefunction from their values at the origin is taken into account. The expansion can be used as a basis for the development of both range and pass relaxation functions. The approach abridges the more conventional two‐step procedure of calculating the energy at a set of points which must subsequently be fitted to a polynomial. It eliminates thereby the repeated laborious solution of the eigenvalue problem. For the particular case of a one‐dimensional coordinate representing a uniform scaling of the nuclear positions it is trivially easy to generate matrix‐element derivatives by scaling. In application to several small molecules using a Gaussian‐type basis in both SCF–MO and CI frameworks such simple scaled matrix elements are shown to provide a reasonably good basis over a useful range of coordinates. In the particular case of a 20 configuration wavefunction for H_{2} ^{+} the scaled and conventional curves are partically indistinguishable over a range 0.25–15.0 a.u. The results are reproduced over a more limited section of the curve using the perturbation expansion in the inverse of the internuclear distance.

Ultraviolet Absorption Spectrum of Carbonyl Sulfide
View Description Hide DescriptionThe absorption coefficients of gaseous carbonyl sulfide have been measured in the spectral region 2000 to 2650 Å. Band structure has been observed superimposed on apparently continuous absorption. The bands can be arranged into four progressions, one of which arises from population of an excited vibrational level of the ground electronic state. It is concluded from the temperature dependence of the long wavelength portion of the spectrum that the “continuous” absorption is due to a transition to a bent upper state of OCS, namely .

Lifetime Studies of and Produced by Photodissociation and Quenched by Halogens
View Description Hide DescriptionThe time dependence of fluorescence produced by pulsed, far‐ultraviolet photodissociation of NaI vapor at 600°C has been directly observed via the method of single‐photon counting. The experimental apparatus and procedure are described. Sodium iodide molecules photodissociate in a time much less than 1 nsec, and the fluorescence decay is exponential with . No evidence of collision‐induced fluorescence is seen, and quenching of the fluorescence by NaI vapor itself is not observed. Quenching by iodine vapor is studied as a function of pressure, and I_{2} molecules are shown to be at least 30 times more effective quenchers than I atoms. The velocity dependence of the I_{2} cross section in the range ∼ 12 − 25 × 10^{4} cm/sec is studied by varying the photodissociation pulse wavelength. The fluorescence of following photodissociation of NaBr and of following photodissociation of TlI are also observed. An average cross section for the quenching of by Br_{2} is reported. Both TlI and I_{2} are observed to quench quite strongly, with I_{2}. having a cross section of ∼ 490 Å^{2} at ∼ 4 × 10^{4} cm/sec. The quenching process is discussed, principally in terms of the “harpooning” mechanism. Comparison is made with analogous molecular beam experiments.

ESR Study of Quantum Tunneling of a Methyl Group: A Simple Tunneling Model
View Description Hide DescriptionThe ESR absorption of the intermediate radical CH_{3}⋅CHR from l‐alanine was studied at 4.2°K. It was found that the methyl group spectrum for the axis was different than that for the axis. While Freed's theory J. Chem. Phys. 43, 1710 (1965)] failed to explain this fact, a simple quantum‐tunneling model was found to account for the observations satisfactorily, attributing the observed difference to an anisotropic dipole–dipole interaction. It was shown that an hfs splitting having any functional dependence on the angle of twist Θ results in the characteristic splitting of the states. A methyl proton which has the cos^{2}Θ dependence assumed by Freed was found to be a special case exhibiting this state splitting.

Low‐Energy Electron Reflection Spectrometry for Thin Films of n‐Hexane, Benzene, and Ice at 77°K
View Description Hide DescriptionA simple low‐energy electron‐reflection spectrometer is described. It constants of a 10^{−9} torr chamber fitted with an electron gum, an ultrathin film of vacuum evaporated sample, supported on a metal block at 77°K, and a Faraday cup to measure the backscattered electron current, . Plots of vs the incident electron energy eV exhibit some structure, more clearly exhibited by plots of which show clearly defined peaks and appear to correspond to near‐resonant energy losses. For benzene these peaks are matched by spectroscopicallymeasured electronic energy levels, including triplets. For an ice film there is a strong peak at 4.2 eV which, supported by several other recently reported measurements using other devices, is attributed to the state of H_{2}O. For n‐hexane the two lowest peaks occur at ∼ 3.9 and ∼ 4.6 eV.

Theory of the Hyperfine Splittings of Pi‐Electron Free Radicals. II. Nonempirical Calculations of Methyl Radical (Planar)
View Description Hide DescriptionNonempirical calculations of the ground‐state electronic wavefunction, energy, and proton and carbon‐13 contact hyperfine splittings of methyl radical in its planar configuration are performed using the spin‐restricted SCF method and configuration interaction including all spin configurations involving up to double replacement of space orbitals. Two minimum basis sets of Slater‐type orbitals are employed, one in which orbital exponents are chosen according to Slater's rules (unoptimized) and the other in which they are optimized through minimization of the SCF energy. Some calculations are made which involve double‐zeta basis sets. Considerable progress toward the goal of accurate ab initio calculations of hyperfine splittings is reported [S. Y. Chang, E. R. Davidson, and G. Vincow, J. Chem. Phys. 49, 529 (1968), paper I in this series]. The proton splittings computed using the unoptimized (unopt.) (1) and optimized (opt.) (2) minimum basis sets and a double‐zeta set (3) (free atom exponents on carbon and are − 33.1, − 43.8, and − 38.2 G, respectively (− 23 G exptl.). A “hybrid” minimum‐basis calculation using the optimized exponents on carbon and yields − 27.5 G. Carbon‐13 hyperfine splittings computed with the minimum basis sets are + 142.4 (unopt.) and + 140.5 G (opt.) (+ 38 G exptl). Spin polarization of the valence shell dominates the splitting. Much better agreement with experiment is obtained using the double‐zeta set, i.e., + 25.7 G. In this case the contributions arising from inner‐ and valence‐shell excitations are comparable in magnitude and opposite in sign. Other features of this work include (1) calculation of SCF energies and contributions to the correlation energy for the three basis sets identified above, namely − 39.415 (1), − 39.487 (2), and − 39.547 a.u. (3) (− 39.60 ± 0.02 a.u. estimated HF limit), and − 0.054 (1), − 0.061 (2), and − 0.106 a.u. (3) (− 0.2 a.u. estimated correlation energy), (2) a population analysis of the minimum basis wavefunctions, and (3) transformation of the minimum basis canonical SCF–MO yielding equivalent sigma bonding and antibonding orbitals. hybridizations deviate significantly from , namely (unopt.), and (opt.). A detailed analysis of the contributions of the various configurations to the hyperfine splittings is presented. This analysis leads to the conclusion that a good approximation in computing the proton splitting can be obtained from the SCF results for and and a first‐order perturbation theory calculation of the mixing coefficient for the configuration representing the excitation. Calculations of the electron‐nuclear coalescence cusps for the SCF–MO's and spin and charge densities are reported. The spin‐density cusp at the proton is correlated with the protonhyperfine splitting. Comparison is made with previous calculations of CH_{3}· and with our approximate calculation of the proton splitting of CH· fragment (paper I). The results of I are found to be in very good agreement with those of the ab initio calculations of CH_{3}·.

Transition Probabilities in Molecular Collisions: Computational Studies of Rotational Excitation
View Description Hide DescriptionExact numerical solutions are presented for the coupledstate formulation of a rigidrotor–structurelessatom collision, and are compared with qualitative ideas and semiquantitative decoupling approximations for the system. The advantages of using an adiabatic basis for the internal states of the system are demonstrated, in distortedwavetype computations and in accounting for the direct part and the resonance energies in slow inelastic collisions, in the absence of curve crossing. The diabatic regime is also considered, and a diabatic basis is used for a curvecrossing problem. For these slow, headon collisions, the Franck–Condon factors are not exponentially small, and significant (>10^{−1}) transition probabilities are possible.

Vibrational Relaxation of Anharmonic Oscillators with Vibration–Vibration and Vibration–Translation Energy Exchanges
View Description Hide DescriptionThe vibrational relaxation of a system of anharmonic oscillators with high initial vibrational energy into a low‐temperature heat bath was studied. It was assumed that the vibration–vibration quasisteady population distribution was instantly established, and during the longer time scale the level population distribution was controlled by a continuous equilibrium vibration–vibration exchange‐dominated process or by a vibration–translation exchange‐dominated process. Although large differences occurred in upper level populations of the two processes, no significant difference was found in the de‐excitation rate. The effect of an‐harmonicity did enhance the de‐excitation rate in the early stage of the relaxation process. This rate fell off quickly to a value close to the excitation rate obtained for the harmonic oscillator. No large order of magnitude differences in the de‐excitation rates of this investigation and previously established excitation rates were found.