Volume 41, Issue 12, 15 December 1964

Accurate Adiabatic Treatment of the Ground State of the Hydrogen Molecule
View Description Hide DescriptionAccurate ground‐state energies of the hydrogen molecule have been computed using wavefunctions in the form of expansions in elliptic coordinates and including explicitly the interelectronic distance. The computations have been made with 54‐term expansions (0.4≤R≤3.7) and with 80‐term expansions (0.5≤R≤2.0). For the equilibrium internuclear distance, the best total energies obtained in the two cases are —1.1744701 a.u. and —1.1744746 a.u., respectively, the corresponding binding energies being 38 291.8 and 38 292.7 cm^{—1}. Employing the 54‐term wavefunctions, the relativistic corrections and the diagonal corrections for nuclear motion have been computed for several internuclear distances. For equilibrium their contributions to the binding energy have been found to be —0.526 and 4.947 cm^{—1}, respectively. Thus the final theoretical binding energy for H_{2} amounts to 38 297.1 cm^{—1} and is a little larger than the experimental value 38 292.9±0.5 cm^{—1}. The discrepancy may be due to the adiabatic approximation.

Accurate Computation of Vibronic Energies and of Some Expectation Values for H_{2}, D_{2}, and T_{2}
View Description Hide DescriptionThe complete four‐particle nonrelativistic Hamiltonian and 147‐term wavefunctions have been used to compute the energies and the expectation values of several other operators for vibronic ground states and for the first vibrationally excited states of H_{2}, D_{2}, and T_{2}. For H_{2} and D_{2} the computed dissociation energies, with relativistic corrections, are by 0.6 and 1.3 cm^{—1}, respectively, larger than the experimental values.

Isothermal Diffusion in Systems with Glasslike Transitions
View Description Hide DescriptionFollowing Simon, we define fluid systems with a ``glasslike'' transition as systems which above the transition temperature T _{ξ} are, and below T _{ξ} are not in internal chemical equilibrium with respect to a set of unspecified internal parameters of even tensorial rank. We present the flow equations for the chemical components of such systems in various frames of references. In particular, in a mass‐fixed frame of reference, besides a variation in the Onsager coefficients, the flow equations below T _{ξ} are subject to a different set of subsidiary conditions (the ``new'' Gibbs—Duhem equations). We also investigate the consequences of the assumption of sorption equilibrium at the surface of our diffusion system. We find that below T _{ξ} these systems will possess history‐dependent diffusion coefficients and be subject to time‐dependent surface concentrations. We can relate these time dependencies to the relaxation of the internal parameters of the system below T _{ξ}.

Studies on Absorption Spectra of Ni^{++} Ion in NiCl_{2} in Different Organic Solvents
View Description Hide DescriptionThe absorption spectra of Ni^{++} ion in NiCl_{2} in six different organic solvents were studied with a Hilger Uvispek spectrophotometer from 10 000 to 3900 Å. A comparison between the calculated and observed values of oscillator strength strengthens our view that electric dipole transition coupled with vibration give rise to these bands.
From the lowering of the term separation the covalency factor is found to vary between 0.85 and 0.89 for the different solvents. The deduced g‐ and magnetic moment have almost the same value in all the solvents.
The cubic field coefficient in some solvents is found to be smaller than that in aqueous solution. The cluster about the Ni^{++} ion appears to be more anisotropic than in aqueous solution.

On the Kinetic Theory of Dense Fluids. XVIII. The Bulk Viscosity
View Description Hide DescriptionA formula for the bulk viscosity of a simple liquid has been obtained from the solutions of the kinetic equations proposed by Rice and Allnatt. The reliability of numerical results obtained is limited to about ±20% by uncertainties in the radial distribution function, its density dependence, and the pair potential. Nevertheless, the theory unambiguously predicts that the ratio of bulk to shear viscosity for liquid argon, at a density of 1.12 g·cm^{—3} and temperatures between 128° and 185°K, should be approximately 1.3.

On the Kinetic‐Energy Distribution of Fragment Ions Produced by Electron Impact in a Mass Spectrometer
View Description Hide DescriptionDistributions of initial kinetic energies have been measured for fragment ions that are produced in the breakup of the excited ions CO^{+}, H_{2}O^{+}, NH_{3} ^{+}, CH_{4} ^{+}, and C_{6}H_{6} ^{+}. These ions were formed by electron impact. The energy of the ionizing electron beam was 400 eV in the case of benzene and 200 eV for the other target gases. The initial‐energy distributions of the fragment ions from H_{2}O and CH_{4} were measured as a function of electron energy over the interval from 100 to 400 eV. No measurable change in the distributions was observed. Evidence presented indicates that the excess‐energy ion pair (masses 15 and 63) are formed simultaneously in the decay of doubly charged benzene ions. Included also in this paper are the details of an analytical method to correct measured energy distributions for kinematic effects and instrumental distortions. In this analysis the distributions of the internal energy converted into kinetic energy of the fragments are characterized by their moments.

Collisional Deactivation of the Excited Singlet Oxygen Atoms and Their Insertion into the CH Bonds of Propane
View Description Hide DescriptionReaction of the excited singlet oxygen atoms with propane was studied at room temperature and at pressures from 400 to 6400 mm. Three main processes were observed: (1) insertion of the excited singlet atoms into CH bonds, (2) abstraction of hydrogen atoms, and (3) fragmentation of the paraffin. The yields of the insertion products increased approximately linearly with the pressure, the abstraction products remained almost constant and the fragmentation products decreased. The primary step is the insertion of the excited singlet oxygen atoms into the CH bonds of propane to form ``hot'' alcohol molecules. When gases capable of deactivating the excited atoms are added, the insertion and fragmentation decrease and the secondary hydrogen atoms are preferentially abstracted. From the increased discrimination in hydrogen abstraction the following relative rates (k _{2}/k _{3}) of the electronic deactivation of the excited singlet oxygen atoms by different gases have been obtained: Xe 0.47, N_{2} 0.15, Kr 0.05, and He and SF_{6} close to zero.

Perturbed Hartree—Fock Calculations. IV. Second‐Order Properties of the Fluorine Molecule
View Description Hide DescriptionThe coupled Hartree—Fock method with a limited basis set has yielded values at the F nucleus and at the center of chargeC of the F_{2} molecule for the electric polarizability (α_{∥}=2.15 Å^{3}, α_{⊥}=0.77 Å^{3}), the magnetic susceptibility (extrapolated to —10.2 ppm), the magnetic shielding [σ=—276 at F or —200 at C (preferred value); σ_{expt1}=—210 ppm], rotational magnetic moment (extrapolated to —0.108 nuclear magnetons) and spin rotation constant [C _{F}=169 at F or 152 at C (preferred value); C _{expt1}=157±2 kc/sec]. The poor gauge dependence for the shielding and spin rotation constant is associated with the unusually high paramagnetic shielding at F which is due specifically to an interaction of the occupied π_{ u } orbital with a low‐lying excited σ_{ u } state. The susceptibility and rotational magnetic moment did not vary extensively with change of gauge.

Paramagnetic Resonance Absorption in Phenanthrene in Its Phosphorescent State
View Description Hide DescriptionElectron paramagnetic resonance absorption in phenanthrene in its lowest photoexcited triplet state has been investigated at the boiling point of N_{2}. The measurements have been made on phenanthrene molecules, oriented in diphenyl host crystals, at the frequency ∼2.3×10^{10} cycle sec^{—1} and also at lower frequencies at almost zero field (76 to 3 G). Taking the long principal magnetic axis in the plane of the phenanthrene molecule to be the x axis, the short axis in the plane to be the y axis, and the normal to the plane to be the z axis, the results have been described by the spin Hamiltonian,whereA preliminary investigation of the hyperfine structure has been made. These results have been compared with published calculations.

Intensity Distribution for the X ^{1}Σ^{+}→A ^{1}Π Transition in Carbon Monoxide Excited by Electron Impact
View Description Hide DescriptionThe envelope shape for the unresolved X ^{1}Σ^{+}→A ^{1}Π transition in carbon monoxide excited by electron impact has been experimentally determined at an incident electron energy of 508 V. The distribution has been compared with calculations using several published theoretical formulations from which the Franck—Condon factors may be obtained.

Knight Shifts and Relaxation Times of Alkali‐Metal and Nitrogen Nuclei in Metal—Ammonia Solutions
View Description Hide DescriptionKnight shifts of ^{7}Li, ^{23}Na,^{87}Rb, ^{133}Cs, and ^{14}N in alkali‐metal—ammonia solutions have been measured at 300°K and in the concentration range 0.03 to 1 mole liter^{—1}. ^{23}NaNMR has been observed at Na concentrations down to 0.003 mole liter^{—1} at 300°K and in the range 0.03 to 4 mole liter^{—1} at 274° and 240°K. ^{14}N shifts are reported for concentrations from 0.008 to 4 mole liter^{—1} at 300° and 240°K. Linewidths of ^{87}Rb and ^{133}Cs have been obtained at 300°K in the concentration range 0.03 to 0.8 mole liter^{—1}. At 0.35 mole liter^{—1} and 300°K the shifts of Li, Na, Rb, and Cs are 9, 72, 450, and 900 ppm, respectively, to lower magnetic field. Shifts of ^{14}N are nearly independent of metal at 300°K.
The concentration and temperature dependence of ^{23}NaKnight shift data at concentrations up to 0.4 mole liter^{—1} may be quantitatively interpreted by the following reactions: where M represents the ``monomer'' species and (2) is the spin‐pairing reaction. The ^{14}N spin density at unpaired electron is essentially independent of alkali metal and concentration up to 0.6 mole liter^{—1} and equal to 0.88±0.11 a _{0} ^{—3} at 300°K. The electron spin density at ^{23}Na is calculated to be ≥8×10^{—3} a _{0} ^{—3} approximately independent of temperature and concentration.
The lifetimes of the Rb and Cs monomers at 300°K and 0.06 mole liter^{—1} are ≤3 and ≤4 μμsec, respectively, as determined from NMRlinewidth measurements. The monomer lifetime decreases sharply with increase in metal concentration.

Spin Densities in Alkali‐Metal—Ammonia Solutions
View Description Hide DescriptionWavefunctions for the alkali metalmonomers of Li, Na, Rb, and Cs in liquid ammonia are calculated using a multipole expansion potential. The wavefunctions are made orthogonal to molecular orbital wavefunctions for the ammonia molecules surrounding the metal ion and spin densities at the metal, nitrogen, and hydrogen nuclei are calculated. A model is proposed for the cavity species which is exactly soluble within the same approximation. Spin densities are evaluated at nitrogen and hydrogen nuclei following orthogonalization to wavefunctions of ammonia molecules on the periphery of the cavity.Orthogonalization produces a large enhancement of spin density at nitrogen and a corresponding decrease in spin density occurs at hydrogen due to a node in the wavefunction produced by orthogonalization. The calculated spin density at the metal nucleus of the monomer and at nitrogen of the cavity species are in good agreement with experimental values. An explanation for the negative spin density at the protons is proposed.

Spin Hamiltonian for Cr III Complexes. Calculation from Crystal Field and Molecular Orbital Models and ESR Determination for Some Ethylenediammine Complexes
View Description Hide DescriptionThe spin Hamiltonians of Cr(en)_{3} ^{3+} and trans‐CrCl_{2}(en)_{2} ^{+} in single crystals of Co(en)_{3}Cl_{3}·3H_{2}O, Co(en)_{3}Cl_{3}·NaCl·6H_{2}O and trans‐[CoCl_{2}(en)_{2}]Cl·HCl·2H_{2}O have been determined from the ESRspectra. In the case of the trans‐CrCl_{2}(en)_{2} ^{+}, ion it was found that the major axis for the spin—spin interaction lay along the C _{2} axis which is in the plane of the nitrogen atoms and rotates one ethylenediammine ring into the other. D and E for trans‐CrCl_{2}(en)_{2} ^{+} were calculated from both a crystal field model and from the results of an extended Hückel molecular orbital calculation. It was found that both calculations give comparable results and give the best results when the spin—orbit coupling parameter of the free ion is used. In the case of the MO calculation, the results agree with experiment when the N–Cr–N bond angle in the ethylenediammine ring is chosen to be 84°. For trigonal complexes of Cr III, D was also calculated using a crystal field model and again it was found that the best results were obtained when the spin—orbit constant was that of the free ion. These calculations also showed that large changes in D and E can be expected for crystal field symmetries that allow for configuration interaction between the ground state and an excited quartet state. The theory for g in these complexes was also developed. In the case of the near octahedral complexes it has been shown that g can be simply related to the charge on the Cr atom in the e_{g} bonding orbitals.

Vibrational Spectra and the Structure of Crystalline Triethylenediamine
View Description Hide DescriptionThe crystal structure of the symmetric‐top molecule, triethylenediamine, is discussed in terms of the analysis of three‐dimensional x‐ray diffraction data in the space groups P6_{3}/m and P6_{3}. It was possible in the two cases to refine to slightly different structures with different molecular and site symmetries. The centrosymmetric structure with molecular symmetryD _{3h }— m2 was used as the basis for an analysis of the infrared spectrum of the crystal and the assignment of the prominent bands. The Raman spectrum of the molecule in solution and the infrared spectrum of a crystalline monohydrate are also reported.

Structure of InSb at High Pressures
View Description Hide DescriptionIt has been found by x‐ray diffraction studies at high pressure (∼30 kbar) that InSb occurs in a form other than the β‐Sn type which has been reported in previous studies. The new modification appears to have a simple orthorhombic structure with two atoms in the unit cell and can be derived from the β‐Sn structure by a simple shear process. While this structure may be a metastable one, it cannot be ruled out that it may be more stable than the β‐Sn form.
On the other hand, it is confirmed that the β‐Sn structure is readily obtained by quenching to 77°K and releasing the pressure, after the transformation has occurred in the vicinity of 30 kbar.

Polyelectrolytes : A Fuzzy Sphere Model
View Description Hide DescriptionThe expansion factor α of polyelectrolytes is calculated on the assumption that at least one member of each interacting pair of charged segments is immersed in a segment cloud having the average sement density, here given by a uniform distribution inside a sphere. The counterion concentration is assumed to be much larger inside the sphere than the byion concentration, and a binding parameter is introduced via an effective dielectric constant. As a consequence α^{3} is predicted to be linear in the reciprocal square root of ionic strength. The dominant source of expansion is repulsion between segments such that one member of an interacting pair is inside and the other outside the background cloud. This same repulsion makes the free energy a minimum when the polymer shape is spherical.

Guest—Host Interactions: An Examination of the Solvent‐Induced Spectral Shift in a Model System
View Description Hide DescriptionIn this paper we study the effect of a surrounding lattice of He atoms on the manifold of electronic states of the H_{2} ^{+} molecule‐ion. One‐center expansions of the molecular wavefunctions are employed, calculated by the Tibbs—Wannier method. The spherically averaged wavefunctions are in good agreement with the known exact solutions.
A detailed study of the environmental effect of the He lattice leads to the prediction of a blue shift of the first electronic transition, arising from a delicate balance between changes in the impurity excitation energy, Coulomb, exchange, van der Waals, and three‐center interaction terms. The signs of the various energy changes are rationalized in terms of the overlap charge density. These results are compared with previous treatments of environmental spectral shifts based on continuum models.

Electrical Conductivity of Low Dielectric Constant Liquids by dc Measurement
View Description Hide DescriptionWhen conductivities of electrolyte solutions are very low dc measurements may be necessary to determine them. A quantitative criterion for when dc or ac may be used is given. Then a linearized partial differential equation for the transport of electric charge in low‐dielectric‐constant fluids, developed earlier by the author, is applied to the problem of dc conductivity measurements. In the absence of overpotentials at the low current densities usually employed boundary conditions on the transport equation are formulated in terms of charge densities in the solution near an electrodesurface, and are related to potentials at the surface. The equation is solved to give expressions for the formation of the equilibrium double layer at the surface, and for the formation of the nonequilibrium double layer when the surface potential of one electrode is raised to cause current flow. From these the current—applied potential—time expression is derived. This consists of a transient polarization current which decays to a steady‐state current. The decay rate of the transient depends primarily upon the relaxation time of the solution. The steady‐state current obeys Ohm's law if the electrode spacing is large enough; conductivity may then be determined. If the spacing is too small diffusion enhanced transport occurs giving erroneously high apparent conductivities.

Nuclear Magnetic‐Dipole Coupling in Solid BF_{3}
View Description Hide DescriptionThe nuclear magnetic resonances of ^{11}B and ^{19}F have been studied in solid polycrystalline BF_{3} at 77°K. From a study of the ^{11}B resonance, the ^{11}B nuclear quadrupole coupling constant was found to be 3.045±0.060 Mc/sec. The ^{19}F resonance possessed an unusual asymmetric structure that is explainable in terms of a magnetic‐dipole interaction between a ^{19}F nucleus and its nearest‐neighbor ^{11}B nucleus. An analysis of this interaction revealed that the observed asymmetry of the ^{19}F resonance indicates that the ^{11}B quadrupole coupling constant is positive. Furthermore, the width of the ^{19}F resonance leads to a value of 1.29 Å for the distance between nearest‐neighbor boron and fluorine atoms in the solid in excellent agreement with the known values for BF_{3} gas.

Magnetic Properties of Gd–Sc Alloys
View Description Hide DescriptionMagnetic properties of some Gd–Sc alloys have been measured. Paramagnetic to antiferromagnetic to ferromagnetic transitions were observed in the 69 at. % Gd alloy. Alloys of higher Gd content were ferromagnets and those of lower Gd content were antiferromagnets. The paramagneticCurie temperatures decreased with decreasing Gd concentration. The effective number of Bohr magnetons per Gd atom showed a nearly linear increase with decreasing Gd concentration. Also the saturationmagnetic moment per Gd atom increased with decreasing Gd concentration in the case of the ferromagnets.