Volume 37, Issue 7, 01 October 1962

Infrared Intensities of Silane
View Description Hide DescriptionThe integrated intensities of the fundamental absorption bands of SiH_{4}, SiD_{4}, and SiD_{3}H have been measured using the Wilson—Wells—Penner—Weber method. These data indicate that the derivatives of the molecular dipole moment with respect to the bond‐stretching and bond‐bending coordinates are of opposite algebraic sign.

Adsorption of Hydrogen on a (110) Nickel Surface
View Description Hide DescriptionHydrogen adsorption at room temperature on a clean (110) surface of a nickelsingle crystal is accompanied by reconstructive rearrangement of the surfacemetal atoms to form a (2×1) surface structure. It is possible to remove this adsorbed hydrogen and obtain a planar surface by heating the crystal slightly above room temperature. A determination of the temperatures and equilibrium hydrogen pressures necessary to remove this adsorbed hydrogen yields an isosteric heat of adsorption of 1.2 eV.
Oxygen displaces the hydrogen in the (2×1) structure from the surface and results in the formation of the (1×2) structure characteristic of adsorbed oxygen. This oxygen can be removed from the surface, however, by heating the crystal to 200°C in hydrogen.

Classical Model for Vibrational and Rotational Excitation of Diatomic Molecules by Collision. II. Interaction with Arbitrary Potential Functions
View Description Hide DescriptionTwo classical models for vibrational energy transfer between a diatomic harmonic oscillator A‐B and an atom C are examined in detail. The first model corresponds to a harmonic repulsion between B and C with a smooth cutoff at zero interaction. It can be solved exactly. The second corresponds to a Morse‐like potential between B and C. In this case, the orbits for colinear collisions are followed on a digital computer, and ΔE_{v} the inelastic energy transfer is ``measured'' from this numerical solution for the equation of motion. The results can be transformed into probabilities by defining excitation as the condition: 2hν>ΔE_{v} ≥hν. ΔE_{v} is a strong function of the phase angle of the oscillator. The probability function for excitation is transformed into a rate constant by averaging over the temperature‐dependent distribution functions for energies.
In contrast to other ``classical'' solutions, it is found that P, the probability of excitation (or de‐excitation), has a nearly Arrhenius type of dependence on temperature. The activation energy of P is quadratically sensitive to the range of the repulsive interaction between B and C. This arises from the result that the excitation probability P(E_{R} ) goes very sharply to zero as E_{R}, the relative collisional energy, approaches some small limiting value. This is in marked contrast to present theories for which P(E_{R} ) goes asymptotically to zero with E_{R}.
Features of the classical model are discussed in some detail and comparisons are made with experimental data from shock tubes. Because of the extreme sensitivity of the model to the value for the range parameters, no absolute predictions of de‐excitation probabilities are possible. However, it is possible to fit the temperature dependence reasonably well with physically acceptable Morse parameters.

Theory of Relaxation Phenomena near the Second‐Order Phase‐Transition Point
View Description Hide DescriptionOne may expect that the observables connected with nonequilibrium processes will show abrupt changes if a substance undergoes a second‐order phase transition, since the equilibrium thermodynamic quantities appear to do so. In order to study these phenomena in a connected way the assumption is made that the long‐range order parameter and the short‐range order parameter can be treated as fluxes and forces in the sense of Onsager's theory of irreversible thermodynamics. Actual calculations are performed for two cases: an order—disorder system with short‐ and long‐range order and a system with two modes of long‐range order (antiferromagnet). The absorption of sound is calculated and its behavior near the critical temperature is analyzed. The function is continuous with a discontinuity in the slope provided the phenomenological constants are smooth functions of the temperature.

Thermodynamic Stability of Polymer Crystals. II. Torsional Vibrations of Chain Molecules
View Description Hide DescriptionBy taking into account the decrease of interchain potential barrier for longitudinal displacement as a consequence of incoherent longitudinal vibration of adjacent chains, the free‐energy density exhibits a minimum at a finite number N ^{*} of monomer units in the straight section of the macromolecule between the (001) surfaces. Crystals with N ^{*} are thermodynamically stabler than those with N≠N ^{*}. The agreement with experimental data can be very much improved by considering torsional vibrations. Starting with the known interaction energy between two CH_{2} groups and considering the influence of the six adjacent polyethylene chains only the lattice force field was derived and the torsional fluctuation amplitude calculated. The resulting N ^{*} fits very well with measurements of Fischer and Schmidt on crystals grown at different temperature from dilute xylene and butyl acetate solution when the surface energy is assumed close to 40 erg/cm^{2}. With this value the theory does not predict stable crystals with finite N ^{*} above 110°C; thus the growth tendency of polyethylene crystals during annealing has no limits at least until the macromolecules are completely stretched.

Crystal Structure of Copper Ammonium Oxalate Dihydrate, Cu(NH_{4})_{2}(C_{2}O_{4})_{2}·2H_{2}O
View Description Hide DescriptionThe crystal structure of copper ammonium oxalate dihydrate (space group ) has been derived from a refinement of the two‐dimensional (hk0) and (0kl) x‐ray data using the atomic coordinates of the isomorphous salt CuK_{2}(C_{2}O_{4})_{2}·2H_{2}O as the starting point of the analysis. In contrast to the chromium complexes of oxalic acid the C–C bonds in both the two nonequivalent oxalate ions in the unit cell are single bonds (1.58 and 1.61 Å) consistent with the conclusion of Jeffrey and Parry that the carboxyl groups of the oxalate ion are separated by a pure σ bond with little or no π conjugation across the molecule. Both the oxalate ions are slightly nonplanar. The copper ions occupy the special positions (0, 0, 0) and 0, ½, 0) and their coordination is of the distorted octahedral type with four nearest oxygen neighbors (≈2 Å) at the corners of a square and two more distant atoms along the octahedral bond direction. The environment of the NH_{4} ^{+} ions consists of eight nearest oxygen atoms at a mean distance of 3 Å.

Approximating Two‐Electron Atomic Energies Using Scaled Eigenfunctions : Semiempirical Coulomb‐Repulsion Integrals
View Description Hide DescriptionIf all electron coordinates in an exact atomic eigenfunction are multiplied by a scaling factor, the kinetic, potential and total energies are modified. Exact equations are derived for these changes. The one‐electron energy for a two‐electron atom is approximated using scaled one‐electron eigenfunctions leading to a semiempirical estimate of the (1s1s:1s1s) Coulomb‐repulsion integral. Finally, two‐electron atomic energies are approximated using scaled eigenfunctions for the corresponding one‐electron atom and a two‐electron atom of different nuclear charge.

Theoretical Vibrational Energy Levels of H_{2} Associated with Various Combinations of Molecular‐Orbital Configurations
View Description Hide DescriptionA theoretical examination has been made of the influence of various MO configurations on the spacing of the vibrational levels of H_{2}. Eleven previously determined potential curves for the H_{2}ground state, based upon LC STO MO wavefunctions with configuration interaction, have been used to calculate vibrational‐energy levels and their first differences ΔG. Comparison of the 11 curves of ΔG vs vibrational quantum number ν shows that only when the wavefunction contains the configuration (σ_{u}1sσ_{u}1s′) does the ΔG curve have a shape similar to that of the experimental ΔG curve. The combination of (σ_{g}1sσ_{g}1s′) and (σ_{u}1sσ_{u}1s′) provides left—right correlation or variable ionicity and this ionicity is found to vary in the same manner as the curvature of the ΔG curve. The addition of (σ_{g}2sσ_{g}2p), which gives in—out correlation, and (), which provides angular correlation, to the wavefunction raises the ΔG curve especially at large ν. The use of ΔG curves obtained from simple wavefunctions to estimate dissociation energies is discussed.

Sedimentation Constants of Broken Chains and Wormlike Coils
View Description Hide DescriptionThe sedimentation constant of two stiff‐chain models has been calculated by the method of Kirkwood. The broken chain consists of straight rigid segments of equal length connected by universal joints. The wormlike chain is that described by Kratky and Porod. In the limit of large contour length, both models have the same slope in a plot of S against n ^{½}, where n is the number of straight segments in the one case and the number of Kuhn statistical lengths in the other. The intercept of this plot at n=0 is sensitive to the model chosen as well as to the chain diameter and the statistical segment length.

Classification of Rotational Energy Levels for Symmetric‐Top Molecules
View Description Hide DescriptionIt is shown that the rotational energy levels of a symmetric‐top molecule can be classified according to symmetry species of the full symmetry group of the molecule. Useful selection rules for electric‐dipole transitions between rotational energy levels thus classified are presented. It is shown that the rotational energy levels can be labeled in addition by a convenient quantum number G, which is essentially a generalization of the +l, —l labels. Selection rules for this quantum number are presented, which, together with those for the symmetry species, allow one to determine easily the allowed branches for a transition between any two vibronic states in a symmetric‐top molecule.

Vibrational Energies of the CO_{2} Molecule
View Description Hide DescriptionThe vibrational energy levels of the eight most abundant isotopic species of carbon dioxide have been calculated. Over 1800 energy levels are given for each isotope. The calculations included terms to the third order in the vibrational quantum numbers and took account of the Fermi resonance. The matrices were diagonalized by an eigenvalue routine of great accuracy.

Calorimetric Determination of Isothermal Entropy Changes in High Magnetic Fields at Low Temperatures. CoSO_{4}·7H_{2}O
View Description Hide DescriptionAn apparatus has been described for the detailed calorimetric measurement of the entropy increase accompanying isothermal demagnetization from high magnetic fields. Integrated automatic heat input controlled by a helium gas thermometer, in thermal contact with the sample, divided by the selected temperature, gives a detailed description of the entropy increase. Investigation of a powdered sample of CoSO_{4}·7H_{2}O has shown that application of fields of the order of 100 kOe near 1°K extracts an entropy of R ln2 as an upper limit from the electronic system of this substance. No irreversible effects were found. The entropy was found to be a function of H _{ i }/T, over the range 1.236 to 4.211°K and from 0 to 94 500 Oe. H_{ i } refers to the magnetic field inside the sample. The resistance of a Pt(91–92%)—W(9–8%) alloy wire used for the noninductively wound calorimetric heater was investigated. The magnetoresistance was positive, very small, and linear with field at all fields. (1/R) (dR/dT) = —5×10^{—5} deg^{—1} and (1/R) (dR/d H) = +2.5×10^{—9} Oe^{—1}, range 1.2 to 4.2°K and from 0 to 95 kOe. Equations for the effect of a magnetic field on the helium gas thermometer are given.

Solubility of Naphthalene in Compressed Gases
View Description Hide DescriptionThe influence of hydrostaticpressure upon the equilibrium between solid naphthalene and its vapor in various inert gases has been measured over pressure ranges extending from 1 to 1100 atm and temperature ranges of 20° to 75°C, using spectrophotometric techniques.
The variation of naphthalene vapor concentration with the diluent gas density has been used to evaluate second virial coefficients representing diluent—naphthalene interactions for the following diluent gases: He, H_{2}, Ar, N_{2}, CH_{4}, and C_{2}H_{4}. Although the virial coefficients thus obtained vary from large negative values for the systems involving the hydrocarbon gases to small positive values for the helium—naphthalene system, attractive 6–12 intermolecular potentials may be fitted to all the data.

Use of Electrostatic Variation Principles in Molecular Energy Calculations
View Description Hide DescriptionThe Thomson and Dirichlet principles of electrostatics have been applied to the evaluation of electron‐interaction terms occurring in molecular‐energy calculations. A suitable choice of certain trial electric fields and electrostatic potentials permits these terms to be approximated both from above and from below. These approximate calculations of electronic interaction terms may often be considerably easier to perform than the exact evaluations required when molecular energies are obtained in the usual way through the minimum‐energy principle. At the same time, when the upper and lower bounds obtained by the present method are properly inserted into the total‐energy expression, the validity of the minimum‐energy principle is preserved, so that any parameters appearing in the trial wave function can still be evaluated by the usual energy minimization procedure. For illustration, the method has been applied to the calculation of the ground‐state energy of molecular hydrogen.

Monte Carlo Procedures for Generation of Nonintersecting Chains
View Description Hide DescriptionA new method is described for high‐speed computer generation of non‐self‐intersecting random walks for use as models of coiling‐type polymer molecules. Previous methods for the unbiased generation of self‐avoiding random walks have proved to be statistically inadequate when certain intramolecular interactions are assumed to exist. This situation arises because energetically important configurations may have a very low probability of occurrence in a normal sample. With this problem in mind, a method of generating samples in a biased fashion has been developed. The procedure allows energetically important configurations to be generated in such a way that the actual amount of bias can be calculated and compensated for, and the samples so obtained can be incorporated with those obtained in a normal, unbiased way. Data are presented to show how the attrition attending the generation of samples depends on bias.

Temperature Dependence of Spin—Spin Splitting in the Hindered Rotator CHCl_{2}–CF_{2}Cl
View Description Hide DescriptionThe effective H^{1}–F^{19} spin coupling in CHCl_{2}–CClF_{2} changes from 5.40 cps at —40°C to 5.60 cps at +100°C. This variation has been analyzed to obtain the difference in potential energy between the two energetically distinct staggered rotational isomers. The result is that the isomer possessing a plane of symmetry is either 2.0 kcal/mole more stable or 1.8 kcal/mole less stable than the other pair. The consequences of this result for the theory of spin—spin splitting are briefly discussed.

Raman Spectral Studies of Molten Selenious Acid
View Description Hide DescriptionPhotoelectric Raman spectra of molten selenious acid, obtained in the temperature range of about 70° to 175°C, provide evidence for the existence of a new species H_{2}Se_{2}O_{5}. Comparisons of Raman bands of molten selenious acid with those of very concentrated aqueous solutions of sodium biselenite indicate common frequencies. In concentrated aqueous solutions, the equilibrium 2HSeO_{3} ^{—} = Se_{2}O_{5} ^{2—}+H_{2}O provides Se_{2}O_{5} ^{2—} ions in considerable concentrations. Similarly, in molten selenious acid the reaction 2H_{2}SeO_{3} = H_{2}Se_{2}O_{5}+H_{2}O produces H_{2}Se_{2}O_{5} molecules in quantity. Raman lines common to the two spectra arise from vibrations which are characteristic of the Se_{2}O_{5} grouping. Such vibrations are those produced by the bending and stretching motions of the Se′–O–Se′ linkage.
When the stoichiometric composition of the melt is between 50 and 66.6_{7} mole% SeO_{2} in H_{2}O, (H_{2}SeO_{3})_{2} and H_{2}Se_{2}O_{5} are important species. At the higher compositions, however, one weak band of the melt was observed which is close in frequency to an intense band of solid selenium dioxide. The complexity of the Raman spectrum of that solid suggests considerable polymerization. Accordingly, (SeO_{2})_{ n } may make an increasing contribution as the composition is increased above 66.6_{7} mole% SeO_{2} in H_{2}O, although the contribution of that species to the Raman spectra of the melt is considered to be small at the lower compositions.

New Orthorhombic Phase in the Ru–B and Os–B Systems
View Description Hide DescriptionBy the use of single crystal and polycrystalline x‐ray diffraction techniques, isomorphous orthorhombic lattices (space group No. 59) have been found in the Ru‐B and Os‐B systems having lattice parameters of a _{0}=4.6443±0.0003 Å, b _{0}=2.8668±0.0008 Å, c _{0}=4.0449±0.0004 Å and a _{0}=4.6832±0.0001 Å, b _{0}=2.8717±0.0002 Å, c _{0}=4.0761±0.0001 Å, respectively. The probable empirical formulas are RuB_{2} and OsB_{2}, with two formula weights per unit cell.

On the Ionization Potential of the CH_{2} Radical
View Description Hide DescriptionA marked difference has existed between the ionization potential of the methylene radical as measured by flash photolysis (10.396 eV) and by mass spectrometry (11.7_{5} eV). A reinvestigation of the mass spectrometric experiment, undertaken to resolve the discrepancy, did not confirm the value previously reported. No evidence could be obtained for the formation of CH_{2} ^{+} from CH_{2} formed by pyrolysis of CH_{2}N_{2}, although the formation of CH_{3} ^{+} from CH_{3} formed by pyrolysis of (CH_{3})_{2}Hg could be readily detected.

ESR Investigation of Some Thiazine and Oxazine Dye Radicals
View Description Hide DescriptionESR spectra of semiquinone radicals, formed as intermediary reduction products in reversibly reducible thiazine and oxazine dyestuffs, have been investigated in acid as well as in alkaline solution.
In acid solutions at relatively high concentration of the dye the spectra consist of four lines. In alkaline solutions at high concentration there are three lines. At lower concentrations most spectra could be resolved further into many components.
A tentative interpretation of the spectra is given.