Volume 27, Issue 1, 01 July 1957
Index of content:
27(1957); http://dx.doi.org/10.1063/1.1743644View Description Hide Description
The quadrupole coupling constants of B11 in some boroncompounds are investigated in detail. A Townes‐and‐Dailey type of interpretation for boron trimethyl gives better agreement with experiment than a detailed molecular orbital calculation, but it is pointed out that this agreement is to be regarded as fortuitous. It is concluded that if localized LCAOMO functions are formed from undistorted atomic orbitals to describe a bond, they lead to an underestimation of the field gradient at the nucleus due to the electrons. For borine carbonyl, an estimation of the ionic character of the BC bond is made from the observed quadrupole coupling constant of B11. With this estimate, the dipole moment associated with the BH3 group is obtained from the observed dipole moment of the whole molecule. The dipole moment of the BH3 group is also calculated using localized LCAOMO's for the BH bonds. This calculation gives the correct sign of the observed dipole moment, but overestimates its magnitude. Some comments are made on the quadrupoleinteractiontensor for B11 in kernite using a molecular orbital approach.
27(1957); http://dx.doi.org/10.1063/1.1743647View Description Hide Description
A group theoretical analysis is given for the symmetry of the crystal structure and Brillouin zone of tellurium and selenium. This is of particular interest because of the presence in the crystal of a threefold screw axis. Character tables for the group of the wave vector are given for various points of the Brillouin zone. Both the single group and the spin double group are treated. Compatibility relations are given.
Nuclear Relaxation by the Hyperfine Interaction with the Ion Core Spins in Ferromagnetic and Antiferromagnetic Crystals27(1957); http://dx.doi.org/10.1063/1.1743659View Description Hide Description
The hyperfine interaction of the nucleus with the ion core spins in magnetic crystals provides a relaxation mechanism for the nuclear spins since energy conservation can be obtained by a change in the spin wave energy. In nonconducting magnetic crystals this mechanism may be dominant in the relaxation of the nuclei of the magnetic ions. The relaxation time is calculated for such a nucleus in an antiferromagnetic crystal.
27(1957); http://dx.doi.org/10.1063/1.1743669View Description Hide Description
Properties of π electrons in allyl anion, cation, and radical are calculated by including interaction between antisymmetrized products of molecular orbital functions. Detailed results in the form of energies and orbital composition of π‐electron state functions for the anion as well as transition intensities and energies for all three molecules, including and excluding configurational interaction, are presented. The extent to which a valence bond type wave function resembles an obtained state function is investigated by the computation of overlaps between the two functions. The overlaps and energies of various valence bond type functions are presented and suggest a relatively greater applicability of the valence bond approach in the case of the neutral radical compared to that of the ions.
27(1957); http://dx.doi.org/10.1063/1.1743677View Description Hide Description
The small angle x‐ray scattering from solutions of lithium,sodium, and potassium in liquid ammonia has been measured using molybdenumK radiation. Scattering curves were obtained for a series of concentrations of lithium solutions at —75°C, for one concentration at —45°C and —75°C, for potassium,sodium, and lithium solutions of approximately the same molarity, and for lithium and sodium solutions near saturation. The scattering data indicate the presence of scattering centers of dimensions of the order of 15 A, with at most a few types of centers in a given solution, and with the type of center depending on the metal ion. There was no evidence for the simultaneous presence of cavities with diameters of the order of 8 A. Calculations indicate these cavities probably would have been observed if present. These results are in good qualitative agreement with the theory of Becker, Lindquist, and Alder. The ``hole theory'' developed by Lipscomb and by Kaplan and Kittel would require modification to account for the observed scattering.
27(1957); http://dx.doi.org/10.1063/1.1743689View Description Hide Description
An approximate solution to the Fick equation for free diffusion is derived in terms of the error integral and its first derivative for the case when the diffusion coefficient shows exponential variation with the concentration of the diffusing species. The results are discussed with reference to the skewed character of the concentration gradient.
27(1957); http://dx.doi.org/10.1063/1.1743710View Description Hide Description
The role of induced polarization in statistical theory of the dielectric constant of polar molecules is examined using the classical harmonic oscillator model of induced displacements by external and intermolecular fields. In the absence of translational fluctuations and anisotropy of polarizability, the theory leads to the results of Kirkwood and Onsager. Reasons for different results obtained by other developments are discussed.
27(1957); http://dx.doi.org/10.1063/1.1743715View Description Hide Description
An investigation of the compressibility factors of gaseous mixtures of carbon dioxide and helium has been carried out at 30°C, using the Burnett method. The pressuremeasuring system included a visual high‐pressure manometer. Results are expressed in an empirical regression formula from which approximations to the virial coefficients can be obtained. The interaction coefficient characteristic of bimolecular encounters between helium and carbon dioxide is in reasonably good agreement with the value calculated by Lunbeck and Boerboom from the properties of the pure gases alone.
27(1957); http://dx.doi.org/10.1063/1.1743716View Description Hide Description
An alternate method of computing the influence of vibration‐rotation interaction on the intensities of lines in the band spectra of molecules from that discussed by Herman and Wallis and by Herman and Rubin is presented. The method consists of transforming the Hamiltonian of the molecule by a contact transformation so that the wave functions remain those for a harmonic oscillator‐rotator. The electric moment must then also be transformed by the same contact transformation before the matrix elements of the electric moment are computed. The method is applied to a diatomic molecule and gives the same results as those stated by Herman and Wallis.
27(1957); http://dx.doi.org/10.1063/1.1743717View Description Hide Description
Methods and detailed algebraic expressions are given for the normal‐coordinate analysis of ethylenic molecules. In the following paper they are applied to the calculation of potential constants, normal modes, and vibrational frequencies for a series of perhalogenated ethylenes. A force field of the Urey‐Bradley type is used for the planar vibrations, and a simple valence‐type potential function is applied to the nonplanar motions. The force constants established for the molecules with Vh symmetry are to be used with only linear interpolation and no further adjustment to calculate the fundamental frequencies and modes of all the remaining, less symmetrical ethylenes. For the Vh molecules the vibrational secular equations are set up in the customary GF matrix fashion. The other ethylenes require a somewhat different form which is more readily adapted to calculation by an electronic digital computer. In order that the force constants determined for the Vh molecules be as good as possible a method is given for their adjustment by a least‐squaring process.
27(1957); http://dx.doi.org/10.1063/1.1743718View Description Hide Description
The methods described in the preceding paper have been applied to the normal coordinate analysis of the fundamental vibrations of 27 perhalogenated ethylenes which contain F, Cl, or Br. Force constants for the planar modes of the key molecules, C2F4, C2Cl4, and C2Br4, have been obtained by an adjustment procedure based on the method of least squares. The agreement between the calculated and observed fundamentals is quite good. The constants established for the key molecules were then used, either directly or with a simple interpolation scheme, to calculate the fundamentals of the remaining 24 ethylenes. Comparisons with experimental results have been made where possible and indicate good agreement for the out‐of‐plane as well as inplane vibrations. The planar normal modes of C2F4, C2Cl4, and the 5 fluorochloroethylenes are depicted.
Analysis of Spin‐Spin Interaction in the Nuclear Magnetic Resonance Spectra of Symmetrical Molecules27(1957); http://dx.doi.org/10.1063/1.1743719View Description Hide Description
Some techniques are given for utilizing molecular symmetry in setting up the equations for spin‐spin coupling in molecules in the liquid state. Applications of group theory to factoring the secular equation, determining selection rules, etc. are similar to those developed for the problem of molecular vibrations. Symtrifluorobenzene is used to illustrate the procedures.
27(1957); http://dx.doi.org/10.1063/1.1743720View Description Hide Description
A variational method employing the unperturbed ground‐state wave function for the molecule is used to calculate the shielding of the proton in the hydrogen and hydrogen halide molecules. Surprisingly good results are obtained in view of the approximations employed in the calculation. The computations show that the shielding depends on the ionic character of the bond, the bond distance, and the number of electrons on the atom to which the hydrogen is bonded.
27(1957); http://dx.doi.org/10.1063/1.1743721View Description Hide Description
Higher approximations for the transport properties of binary gas mixtures are derived: (1) by the method of Chapman and Cowling; (2) by an extension of a method due to Kihara. Particular attention is paid to diffusion and thermal diffusion because of their importance in obtaining information on the forces between unlike molecules. The results can be used to test the convergence and accuracy of the theoretical formulas for various molecular models, and to supply higher correction terms if needed.
27(1957); http://dx.doi.org/10.1063/1.1743722View Description Hide Description
Mass spectrometric study of the gaseous species effusing from a Knudsen cell filled with WO3 has shown that WO3(s) sublimes to form the gaseous molecules W3O9, W4O12, and W5O15. From the measured partial pressures for these species and their variations with temperature, ΔH, ΔF 0, and ΔS 0 of sublimation are obtained.
27(1957); http://dx.doi.org/10.1063/1.1743723View Description Hide Description
The molecules vaporizing from V2O5(s) and VO(s) have been determined employing a mass spectrometer to analyze the vapors effusing from Knudsen cells containing these materials. The vapor over the V2O5 loaded cells was found to contain V4O10(g), V6O14(g), V6O12(g) with some evidence for V4O8(g) and V2O4(g). Since both the composition and the partial pressures varied with time no quantitative data could be obtained for these molecules. By contrast, both the composition and partial pressures of the vapor over VO(s) were essentially constant with time. The molecules observed were V(g), VO(g), and VO2(g). A thermodynamic treatment of the data yields 6.4±0.2 ev and 12.8±0.2 ev, respectively, for the atomization energies of VO and VO2.
27(1957); http://dx.doi.org/10.1063/1.1743724View Description Hide Description
A definition for the time lag L in the Zeldovich modified Becker‐Döring theory of nucleation is introduced which is in accord with the commonly used definition of L in diffusion theory. This L can be obtained exactly without solving for the transient concentration of embryos of the new phase. L is found to be the time required to set up the steady‐state distribution of embryos from a given initial distribution by means of the steady‐state flux of embryos. The numerical evaluation of L from various initial distributions, for at least vapor‐liquid transition, exhibits the importance of the homophase fluctuations in the initial embryo distribution in allowing us to observe the transition within the experimental observation time. The implications of this result for the general theory of phase transitions and for ``memory'' effects in nucleation are discussed.
27(1957); http://dx.doi.org/10.1063/1.1743725View Description Hide Description
The O–H stretching mode of hydrogen bonded methanol has been studied by the matrix isolation technique using solid nitrogen at 20°K as a matrix. The bands are narrow and permit assignment of absorptions at 3660, 3490, 3445, 3290, and 3250 cm—1 to the species, respectively, monomer, dimer, trimer, tetramer, and higher polymers. The results correlate with the room temperature concentration dependence of the H bonded O–H stretching mode of methanol in solution. The dependence of frequency upon polymer size suggests that methanol dimers and trimers have cyclic structures and higher polymers have open (chain) structures. In the cyclic structures, the strain associated with the bent H bond is assumed to account for the low‐frequency shift of dimers and trimers compared to higher polymers.
27(1957); http://dx.doi.org/10.1063/1.1743645View Description Hide Description
In order to study the effects of hindered internal rotation of a methyl group for a high barrier case, the microwave spectrum of propylene oxide has been observed. Rotational transitions have been assigned up to J=30 in the ground torsional state and to J=10 in the first excited torsional state. The structure of the molecule was partially determined by combining the rotational constants derived from the spectrum with the known structure of ethylene oxide. From Stark effect measurements, the dipole moment was determined to be 2.00±0.02 debye.
The theory of the interaction of internal rotation with over‐all rotation is discussed, including the necessary extension of the theory of Wilson, Lin, and Lide for a molecule having no symmetry. Because the tunnel effect splits each torsional state into two levels, the rotational lines appear as doublets. The threefold barrier hindering internal rotation of the methyl group is fitted to the doublet separations. For the ground state, the splitting of the lines was observed only for high J rotational transitions. A barrier of 2710 cal/mole was obtained. For the first excited torsional state, the splittings are about fifty times larger, and are observable for low J transitions. These yield a barrier of 2560 cal/mole. The causes of this apparent difference in barrier height and the errors in the method are discussed.
27(1957); http://dx.doi.org/10.1063/1.1743646View Description Hide Description
The microwave spectrum of methyl silane has been reinvestigated. Seven symmetric top and ten asymmetric top isotopic species have been studied. These molecules, together with the six symmetric tops studied by Lide and Coles, yield a total of thirty‐three rotational constants. A least‐squares analysis of these constants gave the following structural parameters:Analysis of the spectra of the isotopic species CH2D–SiH2D and CH2D–SiHD2 shows conclusively that methyl silane in its equilibrium configuration has the methyl group staggered with respect to the silyl group.
Certain transitions in the asymmetric top isotopic species, e.g., CH3SiH2D, are split into doublets because of coupling of over‐all and internal rotation. These splittings were used to determine the barrier to internal rotation. The form of the potential hindering internal rotation was taken to be V = ½V 3(1 — cos3α)+½V 6(1 — cos6α), giving the result V 3 = 1700±100 cal, V 6∼0–150 cal. This is in reasonable agreement with the result of Kivelson's analysis of the J = 0→1 torsional satellites of CH3–SiH3.