Volume 35, Issue 1, 01 July 1961
Index of content:
35(1961); http://dx.doi.org/10.1063/1.1731873View Description Hide Description
The vibrational excitation of a CO2 molecule in collision with another CO2 molecule is investigated. A derivation of the cross section by means of the method of the distorted waves and the rate of total energy transfer are presented. There are two relaxation processes with different relaxation times related to direct excitation of the bending mode and excitation in series of the valence mode. Experimental results obtained by the author, to be published separately, confirm this conclusion. The experimental relaxation time for the bending vibration was about one‐half of the calculated value, which may be considered a fair agreement in view of the uncertainty involved in the interaction potential and of other approximations which had to be introduced into the calculations.
35(1961); http://dx.doi.org/10.1063/1.1731874View Description Hide Description
The kinetics of atom recombination by homogeneous and heterogeneous reaction are examined. The analysis includes the combined effects of first‐order surface reaction and third‐order gas‐phase reaction in a system undergoing diffusive and convective flow. On the basis of this model the rate constants for the homogeneous rate of recombination of oxygen atoms and of hydrogen atoms are derived from published experimental measurements.
35(1961); http://dx.doi.org/10.1063/1.1731889View Description Hide Description
A perturbation solution of an assumed Boltzmann‐type equation for bimolecular chemical reactions in a homogeneous gas phase consisting of molecules with or without internal degrees of freedom, leads to the conclusion that the law of mass action as well as the usually assumed phenomenological rate expressions for chemical reactions, is strictly valid only in lowest order of the perturbation. Higher order perturbations introduce an affinity and time dependence in the rate coefficient and the law of mass action becomes inadequate to the extent of the contribution of the effects of the perturbations.
A transition state formation of rate coefficients for bimolecular gas‐phase reactions is presented under less restrictive sufficient conditions than reported previously.
35(1961); http://dx.doi.org/10.1063/1.1731902View Description Hide Description
An orbital level diagram and assignments of electronic spectra are given for the benzene‐chromium compounds. These are based principally on symmetry arguments, atomic spectra and dichroism measurements. The problem of the energy involved in distorting benzene rings is also discussed.
35(1961); http://dx.doi.org/10.1063/1.1731913View Description Hide Description
Expansions in powers of Planck's constant are utilized in a discussion of isotope effects on the thermodynamic properties of fluid systems. Theoretical calculations of the differences in the equations of state of the hydrogen isotopes and of the helium isotopes are presented and comparison with experimental results are made. Agreement between theory and experiment is excellent.
35(1961); http://dx.doi.org/10.1063/1.1731931View Description Hide Description
The Bloch equations for the nuclear magnetic resonance of a single nuclear species which is transferred between state environments having different relaxation times (T 1 or T 2) and different resonance frequencies have been solved for rf pulse experiments. Expressions have been obtained for the free precession signals in two‐pulse experiments. A theoretical study of the signal envelopes has been made for several specific instances. In particular, the effect of the frequency difference between the two states on transverse (T 2) relaxation has been investigated; the predicted effect is large in some cases. The longitudinal (T 1) relaxation is independent of the frequency separation. A reduction of phase dispersion by the second pulse which is similar to that in molecular diffusion is also predicted.
35(1961); http://dx.doi.org/10.1063/1.1731932View Description Hide Description
The free radicals formed in solid n‐propanol by radiolysis were examined by electron paramagnetic resonance(EPR) techniques and compared to radicals in photolyzed propanol‐hydrogen peroxide mixtures. Identification of the radicals is based on modifications in the EPR hfs introduced by substituting deuterium for hydrogen at selected positions in the molecules. Radiolysis leads to radical formation by removing a hydrogen atom from the α carbon while photolysis apparently favors hydrogen abstraction from the β carbons. Mass spectrographic analysis of the gas liberated during irradiation gave corroborative evidence regarding the hydrogen atoms; however, the analysis also showed that some hydrogen escaped from other than the α and β carbon positions. The experimental EPR hf spectra are compared to a series of constructed spectra obtained by summing Gaussian absorption curves according to the interactions indicated by the proposed models of the radicals.
35(1961); http://dx.doi.org/10.1063/1.1731933View Description Hide Description
The structure of vanadyl bisacetylacetonate has been determined from three‐dimensional x‐ray diffraction data. The crystals are triclinic, space group , with a=7.53±0.02 A, b=8.23±0.03 A, c=11.24±0.04 A, α=73.0°, β=71.3°, γ=66.6°, Z=2. The structure consists of discrete molecules of VO(C5H7O2)2. Each vanadium atom has five oxygen neighbors at the corners of a rectangular (nearly square) pyramid, with vanadium near its center of gravity. The vanadium‐oxygen distances are 1.56 A to the apex atom (vanadyl oxygen) and 1.96, 1.96, 1.97, and 1.98 A to the others. Other bond distances average 1.28 A for C–O, 1.40 A for C–C (ring), and 1.52 A for C–C (methyl). Standard deviations are 0.01 A for V–O bonds and 0.02 A for C–O and C–C bonds. Each acetylacetone skeleton is planar, and this plane makes an angle of 163° with the plane of the other acetylacetone skeleton of the same molecule.
35(1961); http://dx.doi.org/10.1063/1.1731934View Description Hide Description
The ratio of the vapor pressures of Ne20 and Ne22 have been measured in the temperature range 16–30°K. An accuracy of about 1% in the logarithm of the vapor‐pressure ratio has been achieved. The latter is checked by comparisons of (1) triple‐point pressures, (2) equilibrium fractionation experiments, and (3) the entropy difference of the condensed phases with thermal measurements.
The Debye temperature for the solid derived from the ratio of the vapor pressures, 74.6°K, is in good agreement with values derived from the Debye‐Waller temperature factor and theoretical calculations by Bernardes. The discrepancy between the characteristictemperatures derived from measurements of free energy with those from heat capacities is attributed to the role of the anharmonicity of the lattice.
It is shown that the difference in the thermodynamic properties of solid and liquid neon in the vicinity of the triple point can be attributed to the change in coordination number.
35(1961); http://dx.doi.org/10.1063/1.1731935View Description Hide Description
It is shown that, if two functions Λ A (1, 2, 3,...p) and Λ B (1, 2′, 3′,...q′) describing two groups A and B of electrons are orthogonal with respect to electron 1 then there exists a complete orthonormal set of one‐electron functions Φ k (1) such that the functions actually occurring with nonvanishing coefficients in the expansion of one of the functions cannot simultaneously occur in the expansion of the other function. This is a generalization of a separation theorem recently found by Arai.
35(1961); http://dx.doi.org/10.1063/1.1731936View Description Hide Description
Approximate expressions for the self‐diffusion coefficients of spherical molecules in solid, liquid, and gas phases are obtained from the relationwhere D is the diffusion coefficient and ρ(s) is the velocity correlation function of the spherical molecules. The correlation function is approximated by the function cosαδs/coshαs and the parameters α and δ are expressed in terms of molecular properties for liquids and gases. The approximate diffusion coefficient is found to obey an Arrhenius relation in the solid phase and a Sutherland equation for the gas phase. The results of a crude calculation of the self‐diffusion coefficient for liquid neopentane are within a factor of two of the experimental diffusion coefficients. The temperature coefficient of the calculated diffusion coefficients is also within a factor of two of the observed temperature coefficient.
35(1961); http://dx.doi.org/10.1063/1.1731937View Description Hide Description
The transfer of excitation energy between molecules of different compounds in solutions is investigated as a function of temperature and viscosity of the solution. In all cases an increase in transfer efficiency with increasing diffusion is observed. The fluorescence of the donor molecules in the absence of acceptor molecules is studied as a function of temperature and the possible influence of the respective changes on the observed transfer efficiencies is discussed.
35(1961); http://dx.doi.org/10.1063/1.1731875View Description Hide Description
The exchange of boron between BF3(g) and BF3·phenol(l) was studied. The single‐stage isotopic fractionation factor varied according to the equation, logα= (10.315/T) —0.02423, over the temperature range —8°C to 37°C. B10 is concentrated in the liquid phase. Vapor‐pressure measurements of dilute and concentrated solutions of BF3 in phenol were made at various temperatures from —10°C to 40°C. The freezing point of the BF3·phenol complex was approximately —15°C; that for the BF3·2 phenol, —5°C.
Electronic Structure, Spectra, and Magnetic Properties of Oxycations. III. Ligation Effects on the Infrared Spectrum of the Uranyl Ion35(1961); http://dx.doi.org/10.1063/1.1731876View Description Hide Description
A series of uranyl complexes K x UO2L y (NO3)2, where L is the variable ligand (or ligands), has been prepared; it has been shown that a ligand series may be defined using the antisymmetric stretching frequency of the uranyl entity, and this series exhibits a remarkable parallelism with the spectrochemical series defined by Δ in octahedral complexes of transition metals of the 1st and 2nd series. This parallelism has been rationalized using a mixed ligand fieldtheory in which the uranyl ion is considered subject to bonding with ligands which are arranged hexagonally in a plane equatorial to the O–U–O axis. It is shown that the large changes of ν3 and ν1 are due primarily to electron population of the φ u and δ u atomic orbitals of uranium. Such population is physically equivalent to the reductions AmO2 + +→AmO2 + and N p O2 + +→NpO2 +, which cause a decrease of approximately 100 cm—1 in ν3. It is further shown that = — electrostatic effect — σ(L→M) — π(L→M) ± π(M→L), where in the last term the plus sign is the more probable, and the results obtained have been rationalized using this equation.
Some evidence in favor of linearity of the UO2 + + has also been induced, and a general criterion for distinguishing the difficulty observable ν1 has been reestablished. It has also been shown, although not discussed extensively, that the stability of uranyl complexes should increase, roughly as (or ) decreases. The discussion of similar effects in vanadyl, titanyl, chromyl, and other oxycations has been deferred to a later time.
35(1961); http://dx.doi.org/10.1063/1.1731877View Description Hide Description
The electron paramagnetic resonance spectra of a gamma‐irradiated single crystal of α‐glycylglycine have been measured at 9, 24, and 29 kMc/sec for various orientations of the crystal in the external magnetic field. From analysis of the spectroscopic splitting factors and the hyperfineinteraction constants, the free radical produced by gamma irradiation is found to be:[Complex chemical formula]The electron spin density on the —ĊH carbon atom is evaluated as approximately 0.75.
General Relation between Potential Energy and Internuclear Distance for Diatomic Molecules. III. Excited States35(1961); http://dx.doi.org/10.1063/1.1731878View Description Hide Description
A previously proposed internuclear potential function has been used to calculate the dissociation energies for the excited states of a large number of diatomic molecules. From these results and the Wigner‐Witmer rules the dissociation products are determined, and it is shown that in many cases it is possible to estimate independently, the dissociation energy of the ground state. The three‐ and five‐parameter forms of the proposed function lead to nearly equal values for dissociation energies suggesting an equivalence of the two forms. This leads to a relation between the anharmonicity and the vibrational‐rotational coupling constant which is slightly superior to the Pekeris relation. Equations derived from this relation are given relating the parameters a and b of the five‐parameter functions to the anharmonicity or vibrational‐rotational coupling constant. The parameter b and to a lesser extent a was found nearly constant for the excited states of all diatomic molecules.
35(1961); http://dx.doi.org/10.1063/1.1731879View Description Hide Description
The microwave spectrum of cis 2,3‐epoxybutane was investigated in the region from 8000 to 29 000 Mc. The spectrum consists of singlets and triplets. The ground torsional state shows a pseudo rigid‐rotor spectrum with rotational constants 8057.71, 4461.36, and 3468.60 Mc. The triplets yield a barrier to internal rotation of 1607±150 cal/mole independent of a range of assumptions concerning the coupling of the two methyl groups. The dipole moment was found to be 2.03±0.02D with 2.01±0.02D in the plane of the ring. A group theoretical discussion of double rotors with one rotor on each side of a plane of symmetry is given.
35(1961); http://dx.doi.org/10.1063/1.1731880View Description Hide Description
ESRspectra of copper complexes have been interpreted by means of molecular orbital theory, and the ``covalent'' character of both σ and π bonds have been discussed for a variety of compounds. Overlap integrals have been considered in a consistent manner in treating σ bonds. Particular attention has been given to Cu phthalocyanine and several of its derivatives. The in‐plane π bonding may be as important in determining the properties of a Cu complex as is the in‐plane σ bonding.
35(1961); http://dx.doi.org/10.1063/1.1731881View Description Hide Description
The study by Sands of ESR line shapes of polycrystallinecopper complexes has been extended and various ``anomalies'' discovered in the line shapes. The spectrum of copper phthalocyanine dissolved in concentrated H2SO4 has been studied at 77°K. The hyperfine line has a behavior very different from that discussed by Sands. Isotropic extra hyperfine structure, arising from the presence of the ligand nitrogens, is easily discernible even in the glass.
35(1961); http://dx.doi.org/10.1063/1.1731882View Description Hide Description
Phthalocyanine complexes of paramagnetic metal ions show ESR spectra characteristic of the metals; phthalocyanine complexes of diamagnetic metal ions show strong single ESR lines characteristic of free radicals. The source of this latter resonance is not understood. Intimate molecular mixtures of ``paramagnetic''copper and ``dimagnetic'' zinc phthalocyanines exhibit exchange between the copper unpaired electron and the ``free radical'' electron in the zinc phthalocyanine. Nickel and zinc phthalocyanine also exhibit a single sharp resonance in dilute solutions of concentrated sulfuric acid.