Volume 43, Issue 7, 01 October 1965

Discontinuous Change of Binding Type in the Series of Monohydrides. III. Regularities and Irregularities of Internuclear Distances and Force Constants
View Description Hide DescriptionThe recently attempted correlation of internuclear distances of the monohydrides of all elements by linear plots of logr vs logZ (atomic number) for each of the two octaves and of the three long periods is not satisfactory. The equations r_{e} =2.2240 n ^{−0.426} and r _{0}=2.7793 n ^{−0.371} (n is the total number of valence electrons in the hydride) apply merely from HF to BH and from HCl to AlH, respectively. The marked deviations from these equations shown by the hydrides M (I) H and M (II) H are related to a discontinuous change of binding type. In the long periods, r increases for the hydrides of the heavy metals from M (I) H to M (III) H, due to the decrease of polarizability and penetrability of the cations with an 18‐electron (s ^{2} p ^{6} d ^{10}) outer shell, e.g., from AgH to InH. It is emphasized that the knowledge of spectroscopic data for molecule ions of the hydrides of long period elements is necessary in order to decide at which places discontinuous changes of binding type occur.

X‐Ray‐Diffraction Study of Zinc Bromide Solutions
View Description Hide DescriptionX‐ray studies of solutions of zinc bromide show four coordination for the zinc ion. In concentrated water and acetone solution, zinc is coordinated by two bromines and two oxygens, on the average. If the bromine/water ratio is increased by adding hydrobromic acid,zinc becomes totally coordinated by halide. These solutions are too concentrated, however, to speak of the existence of discrete ZnBr_{4} ^{=} ions. Crystal radii serve to interpret contacts between species in solution.

Microwave Spectrum, Structure, and Dipole Moment of 2,4‐Dicarbaheptaborane (7)
View Description Hide DescriptionThe microwave spectra of all monosubstituted carbon and boron isotopic forms, and one disubstituted boron isotopic form of 2,4‐dicarbaheptaborane(7) have been analyzed. The skeletal boron and carbon atomic coordinates determined from the rotational constants show that the molecule is a pentagonal bipyramid. The two carbon atoms lie in the pentagonal base plane and are separated by one boron atom. The two apex boron atoms appear to lie on, or very near the C axis which is perpendicular to the pentagonal base. A molecular‐dipole moment of 1.32±0.03 D is oriented along the planar symmetry axis.

^{3}Π Levels and Predissociations of N_{2} near the 12.135‐eV Dissociation Limit
View Description Hide DescriptionThe two predissociations in the second positive bands, C ^{3}Π_{ u }→B ^{3}Π_{ g }, have been re‐examined in the light of recent spectroscopic studies of the N_{2}spectrum. It is concluded that the predissociation of Büttenbender and Herzberg is due to a ^{5}Π_{ u } state and not to a ^{3}Π_{ u } state as formerly believed. However, a few details of the predissociation are not yet clearly explained. The second, less well‐known predissociation of Hori and Endo is interpreted as being in all probability due to the C′ ^{3}Π_{ u } state (the upper state of the Goldstein—Kaplan bands). This explanation requires that the C′ state have a maximum in its potential curve at an internuclear distance of about 2.0 Å. The behavior of the C and C′ potential curves, which should apparently intersect at about 1.4 Å, is interpreted as a noncrossing rule interaction. The vibrational structure in the region of the interaction is discussed and in particular the level reported by Pannetier et al. and that reported by Tanaka and Jursa are attributed to a mixture of v=5 of C and v=1 of C′. The level formerly tentatively assigned to v=1 of C′ is now considered to be primarily v=2 of the same state. Some low‐temperature afterglow mechanisms are discussed in terms of the new interpretations of the C and C′ states. The ^{5}Π_{ u } and ^{3}Π_{ u } states which are to be expected in the energy range of interest are discussed theoretically by the application of both the molecular orbital and the Heitler—London methods and the conclusions are found to be consistent with the present interpretation of the experimental results.

Cyanate Ion in Alkali Halides: New Vibrational Levels and Interpretation of Localized Lattice Modes
View Description Hide DescriptionThe infrared absorption of alkali halide single crystals containing NCO^{−} impurity at concentrations up to about 1 mole % has yielded new information about the internal vibrational levels of the cyanate ion. Satellite lines near ν_{3} and its combinations have been shown to arise from neighbor pairs of cyanate ions in the host lattice. Absorptions of the type ν_{3}±ν_{ k }, where ν_{ k } is of the order of 80 to 180 cm^{−1} and is strongly dependent upon the host lattice, have been observed; and the relation of ν_{ k } to the impurity‐induced localized lattice modes is discussed.

Vibronic Interaction of Nearly Degenerate States in Substituted Benzene Anions
View Description Hide DescriptionThe pseudo‐Jahn—Teller effect, the vibronic interaction of nearly degenerate electronic states, arises in the same manner as the Jahn—Teller effect itself. An iteration method, suitable for desk calculation, has been developed to allow computation of the vibronic wavefunctions and energies of a system with two closely spaced electronic states. A calculation on benzene anion compares favorably with previously published results. The method, in combination with semiempirical evaluation of the necessary parameters, has been applied to various substituted benzene anions and the ESRspectra of these anions predicted. The results compare satisfactorily with experiment and indicate that the spectra are the net result of three principal factors, configuration interaction among the simple molecular orbital electronic states, vibronic coupling, and thermal equilibrium between at least two vibronic states.

Nuclear Magnetic Shielding of Alkali Ions in Crystals and Dilute Aqueous Solutions
View Description Hide DescriptionThe formulation for the Kondo—Yamashita overlap mechanism for the nuclear magnetic shielding in alkali halides developed earlier, is applied to the rubidium nucleus in RbCl, RbBr, and RbI crystals. The pertinent average energy denominators of perturbation theory are obtained using experimental pressure data on the magnetic shielding. Using these energy denominators, the calculated values of σ_{Rb}, the chemical shifts for the rubidium nucleus in the crystal with respect to the free ion, are −2.17×10^{−4}, −2.14×10^{−4}, −2.11×10^{−4} for RbCl, RbBr, and RbI, respectively. When combined with Baron's experimental data on the chemical shifts with respect to dilute aqueous solutions, we obtain for σ_{Rb} ^{aq}, which represents the chemical shift between the Rb^{+} ion in aqueous solution and the free ion, the values −0.88×10^{−4}, −0.63×10^{−4}, −0.60×10^{−4} from the RbCl, RbBr, and RbI data, respectively. These values are in fair agreement with the result σ_{Rb} ^{aq}=−0.65×10^{−4} that we have derived using a model of six oriented water molecules around the Rb^{+} ion in dilute aqueous solutions.

Microwave Spectrum and Barrier to Internal Rotation in Methylsilylacetylene
View Description Hide DescriptionThe microwave spectrum of CH_{3}CCSiH_{3} shows a complex fine structure caused by internal rotation with a very low potential barrier. The major part of this structure can be explained on the basis of completely free internal rotation. However, small perturbations are found which suggest that the barrier may not be identically zero. Subject to reasonably firm assumptions, an upper limit of 3 cal/molecule can be placed on the barrier height. The theory for treating this type of spectrum is developed, and some implications of the results are discussed.

Diffusion Along Dislocations
View Description Hide DescriptionThe Smoluchowski pipe model for diffusion along dislocations is modified so as to allow an exact solution of the two‐dimensional diffusion equation. Using the continuously variable diffusion coefficient: D=D _{0}/r ^{2}, where r is the radial coordinate perpendicular to the dislocation, rather than a step function, yields a diffusion profile proportional to: (D _{0} t)^{−¼} exp[−2z/a(D _{0} t)^{¼}], a=Γ(¼)(2π)^{−½}≃1.45 for large z, where z is the coordinate perpendicular to the surface from which diffusion occurs. Near the surface, where the Smoluchowski theory fails, the penetration is predicted to be anomalously high.
A characteristic diffusion coefficient for a grain boundary composed of parallel dislocations was calculated on the present model and found to be inversely proportional to the spacing of the dislocations.

Spin—Orbit Interaction Terms for the p ^{4}—nd Configuration
View Description Hide DescriptionSpin—orbit interaction matrices for the configuration (p ^{4} LS)—nd are given in the LS coupling scheme.

Spin‐Polarized Orbitals for Localized States in Crystals
View Description Hide DescriptionUsing the concept of different orbitals for different spins, in conjunction with the tight‐binding approximation, it is possible to construct a set of spin‐polarized orbitals (SPO's) in which electrons with different spins are localized on different crystal atoms. Thus, SPO's allow for the correlation between electrons with different spins and, for a pure crystal, are very similar to Löwdin's alternant crystal orbitals. For one‐dimensional crystals, an analysis which resembles that for linear mixed crystals reveals that, for α‐ or β‐spin electrons, the energy levels of the nonlocalized SPO's form two bands, while those of the localized SPO's lie either outside these bands or in the gap between them. Finally, Green's matrix method is employed to examine the effect on the SPO's of the perturbation produced by interior impurity atoms in the crystal, or chemisorbed atoms at the surface.

On the Ordered State of Nickelous Formate Dihydrate
View Description Hide DescriptionThe behavior of the magnetic ions in nickelous formate dihydrate, Ni(HCOO)_{2}·2H_{2}O, below its transition temperature is discussed theoretically. Expectation values of the spins at the two inequivalent sites in this crystal are calculated and expressions for paramagnetic and antiferromagneticsusceptibilities are derived. Crystal‐field parameters and the exchange integral which appear in the spin Hamiltonian for the present system are estimated from experimental data. If the same approximation as was used in the case of dihydrated formates of Mn^{++} and Fe^{++} is adopted, it is concluded that the spins for Ni(HCOO)_{2}·2H_{2}O at the two inequivalent sites in its antiferromagnetic state have different expectation values, 0.75 and 0.40. The coexistence of both paramagnetic and antiferromagnetic states is shown to be impossible.

X‐Ray Determination of the Structure of Liquid Methane
View Description Hide DescriptionX‐ray diffraction measurements from liquidmethane at four conditions of temperature and pressure ranging from near the triple point to the critical point indicate a structure of molecules in the liquid resembling close packing of spheres. The first peaks in the density functions are asymmetric and have areas and positions which range from 11.4 nearest neighbors at 4.24 Å and 96°K to 7.2 nearest neighbors at 4.35 Å and 186°K. The methane x‐ray form factor is derived from gaseous scattering experiments.

Two‐Dimensional Second Virial Coefficients of Methane and Tetradeuteromethane on Graphitic Carbon
View Description Hide DescriptionSpecific two‐dimensional second virial coefficients are obtained from low‐coverage adsorption isotherms for CH_{4} and CD_{4} on graphitic carbon between 220° and 290°K. These data are analyzed in terms of both classical and quantum‐statistical models employing a Lennard‐Jones potential, and corrections for non‐planarity of the adsorbed phase are also included. The sign of the quantity [ε(H)—ε(D)]/ε(D) cannot be unambiguously determined, but this quantity is somewhat smaller than in the corresponding three‐dimensional case. The measured nonadditivity of pair potentials amounts to about 15% of the gas‐phase energy, and is in good agreement with independent theoretical predictions.

Kinetics of the Thermal Decomposition of C_{2}F_{6} in the Presence of H_{2} at 1300°—1600°K
View Description Hide DescriptionThe thermal decomposition of hexafluoroethane in the presence of hydrogen has been studied in a single‐pulse shock tube in the temperature range 1300° to 1600°K. The reactants were highly diluted with argon, the composition ratios being Ar:H_{2}:C_{2}F_{6}≃7500:17.4:1. The principal reaction products containing carbon were fluoroform and tetrafluoroethylene. A reaction scheme which accounts for these products is proposed and the first‐order rate constant for the primary step C_{2}F_{6}→2CF_{3} is deduced: k _{1}=4.3×10^{17} exp(−94 400±4000)/RT sec^{−1}.
Accepting an activation energy of about 1 kcal/mole for the recombination of CF_{3} radicals leads to D(CF_{3}–CF_{3})≃93±4 kcal/mole.

Dipole Moments in Relation to Configuration of n‐Alkane Chains Bearing α, ω Dipolar Substituents
View Description Hide DescriptionThe dipole moments of α,ω‐dibromo‐n‐alkanes Br–(CH_{2})_{ n−1}–Br have been treated by exact methods applicable to a linear sequence of bonds each constrained to choice among several discrete rotational states, due account being taken of neighbor dependence in assignment of statistical weights to the various configurations. Computations have been carried out on the basis of threefold potentials with one trans and two gauche states (±120°) for each bond. Successive gauche states of opposite sign are excluded by steric overlaps. An energy of 500 cal mole^{−1} has been assigned to gauche relative to trans, in keeping with spectroscopic evidence for n‐alkanes and the scheme successfully applied to the mean‐square dimensions of polymethylene chains. Nonbonded interactions in which a Br atom is involved have been assigned statistical weights consistent with van der Waals radii and with evidence from Raman and infrared studies on n‐alkyl bromides. The mean‐square dipole moments averaged over all configurations are appreciably affected by the dipole—dipole interaction energy for n−1<6, but not for longer chains. Calculated values are in good accord with experimental results for n−1=3 to 10, inclusive. The applicability of the rotational‐isomeric state‐approximation to chains of comparatively short length is thus demonstrated.

Electron Spin Resonance Studies of the Onset of Metallic Character in Metal—Ammonia Solutions
View Description Hide DescriptionAsymmetric electron spin resonance spectra are described for moderately concentrated solutions of the alkali metals in liquid ammonia as functions of temperature, metal concentration, and concentration of added electrolytes. Both the asymmetry and the linewidth increase markedly above a critical temperature, corresponding to a thermal promotion of electrons from trapping sites to a conduction band. The g factor of the asymmetric resonance is strongly dependent on the concentration of added iodides.

Effect of High Pressure on the Lattice Parameters of Al_{2}O_{3}
View Description Hide DescriptionThe effect of pressure to 300 kbar has been measured on the lattice parameters of Al_{2}O_{3}. Corundum has a rhombohedral unit cell and is relatively incompressible (∼9% in 300 kbar). Perhaps the most intersting feature involves an increase of the rhombohedral angle of about 0.5° over this pressure range.

Effect of High Pressure on the Compressibilities of NaI, LiF, and NaF
View Description Hide DescriptionThe effect of pressure to several hundred kilobars has been measured on the compressibilities of NaI, LiF, and NaF. For NaI and LiF the semiclassical Born—Mayer—Huggins theory gives a good fit over the entire pressure range. For NaI this is not necessarily expected as the large size of the I^{−} ion relative to Na^{+} would indicate that next‐nearest‐neighbor interactions could be important. The equation is quite unsatisfactory for NaF, which is quite surprising as this should be a typical ionic crystal.

Irreducible Cartesian Tensors
View Description Hide DescriptionThis paper considers certain simple and practically useful properties of Cartesian tensors in three‐dimensional space which are irreducible under the three‐dimensional rotation group. Ordinary tensor algebra is emphasized throughout and particular use is made of natural tensors having the least rank consistent with belonging to a particular irreducible representation of the rotation group. An arbitrary tensor of rank n may be reduced by first deriving from the tensor all its linearly independent tensors in natural form, and then by embedding these lower‐rank tensors in the tensor space of rank n. An explicit reduction of third‐rank tensors is given as well as a convenient specification of fourth‐ and fifth‐rank isotropic tensors. A particular classification of the natural tensors is through a Cartesian parentage scheme, which is developed. Some applications of isotropic tensors are given.