Volume 47, Issue 2, 15 July 1967

Relationships between AB_{2} and H_{ n }AB_{2} Molecular Spectra and Geometry: Accurate SCF MO and CI Calculations for Various States of HCOO^{−}
View Description Hide DescriptionA close relationship between the geometry of formate ion in various electronic states and that of isoelectronic‐symmetric AB_{2} molecules is demonstrated by means of accurate SCF MO calculations for ground and certain excited states of HCOO^{−} which are compared to corresponding calculations for O_{3}. Transition energies between several states of HCOO^{−} are calculated within a limited CI treatment and their relation to spectral lines of corresponding AB_{2} molecules is discussed. Such comparisons suggest that existing relationships between the geometry of AB_{2} molecules can be extended effectively to the study of isoelectronic H_{ n }AB_{2} systems of related symmetry even though these molecules may otherwise bear little similarity to the triatomic systems.

Correlation Energy and Molecular Properties of Hydrogen Fluoride
View Description Hide DescriptionA natural‐orbital—configuration‐interaction calculation has been carried out on the ground state of the hydrogen fluoride molecule at the experimental equilibrium internuclear separation (1.7328 a.u.). A non‐relativistic energy of −100.2577 a.u. was obtained with 39 configurations. Individual pair correlationenergies totaling to over 80% of the total correlationenergy were obtained by considering double excitations of each pair.

Rotational Isomerism in Bromoacetone and Fluoroacetone
View Description Hide DescriptionInfrared spectra in the region 60–4000 cm^{−1} were obtained for bromoacetone and fluoroacetone for the vapor and liquid (or solution) states and for the solid state in the region 600–4000 cm^{−1}. Spectra in the region 300–4000 cm^{−1} were obtained for solutions in carbon tetrachloride and acetonitrile. The spectra show that both these compounds exist as mixtures of rotational isomers, and that the less polar form is present in much higher amount in the vapor state than the more polar form. For bromoacetone, the more polar form is more stable in the liquid state, and is the only form present in the solid. For fluoroacetone, the two forms have about the same energy in the liquid, and both forms are present in the solid.

Temperature Dependence of the Nuclear Quadrupole Resonance Frequency of ^{35}Cl in KClO_{3} between 12° and 90°K
View Description Hide DescriptionA precise measurement of the temperature dependence of the NQR frequency of ^{35}Cl in KClO_{3} has been made at constant pressure in the range 12°—90°K. Analysis using the Bayer—Kushida theory predicts lattice modes at 60 and 126 cm^{−1}. A comparison is made with the Raman spectrum.

γ Radiolysis of Liquids at High Pressures. III. Aqueous Solutions of Sodium Bicarbonate
View Description Hide DescriptionThe γ radiolysis of deaerated aqueous solutions containing sodium bicarbonate and either glucose or isopropanol has been studied at ∼20° in the applied pressure range 0 to 7 kbar. For 0.05M bicarbonate and 0.036M isopropanol, G(H_{2}) increases from 0.89 to 2.43 as applied pressure increases from 0 to 6.9 kbar. A 100‐fold change (0.005–0.5M) in bicarbonate concentration has little or no effect on the pressure dependence of G(H_{2}). Because primary yields are invariant over the pressure range studied, the results are interpreted in terms of an effect of pressure on the competition between Reactions [2] and [3] with Reaction [3] followed by Reaction [4]Such an interpretation gives a difference in activation volumes of Reactions [2] and [3] as ΔV _{2} ^{‡}—ΔV _{3} ^{‡}≈18.4 ml mole^{−1} and a specific rate k _{3} ^{0}≈6×10^{5} M ^{−1}· sec^{−1} at atmospheric pressure. Assumption that Reaction [2] is diffusion controlled permits estimation of ΔV _{2} ^{‡}≈1.6 ml mole^{−1}, from the pressure dependence of waterviscosity. Thus, ΔV _{3} ^{‡}≈−16.8 ml mole^{−1}. The latter value, in turn, yields an estimate of V̄(e _{aq} ^{−}) in the range −10.9 to −6.5 ml mole^{−1} relative to V̄(H^{+})=0. Use of an absolute value of V̄ _{0}(H^{+})=−5.4 ml mole^{−1} gives an absolute value of V̄ _{0}(e _{aq} ^{−}) in the range −5.5 to −1.1 ml mole^{−1}. Approximate equality of the values for V̄ _{0} of the electron and of the proton is consistent with their having a negligible intrinsic volume and approximately equal electrostriction volumes.

Proton Spin—Lattice Relaxation Temperature Dependence in Ammonium Bromide
View Description Hide DescriptionThe lambda transition at 234.5°K in ammonium bromide has been detected by proton spin—lattice relaxation temperature dependence measurements. There is a small but detectable change in T _{1} at the lambda point. In order to obtain the maximum detail in this temperature region, a special probe was designed to minimize temperature gradients in the sample. Use of this probe allows evaluation of the change in T _{1} at the transition and determination of the apparent activation energy immediately below the transition. The previously reported x‐ray, dilatometric, extensometric, and acoustical data are best interpreted in terms of a conceptual picture of domains defined by the orientation of tetragonal axes in the region immediately below the lambda point and the indistinguishability of the domains above this temperature. The τ_{ c } data are consistent with this concept. The degree of order seems to be affected by the orientations of the tetragonal axes in the domains. Comparison of the acoustical data and the τ_{ c } data suggests that the elastic constants are much more dependent on the electrostatic changes due to the volume changes than is the temperature dependence of τ_{ c }. The latter seems to depend mainly on the degree of order in the crystalline lattice.

Mössbauer Hyperfine Interactions in Sodium Nitroprusside Single Crystals
View Description Hide DescriptionThe Mössbauer absorptionspectrum of ^{57}Fe in single crystals of Na_{2}[Fe(II)(CN)_{5}NO]·2H_{2}O has been studied. The angular variation of the ratio of intensities of the quadrupole‐splitted lines with the incident radiation has been measured at different crystal orientations. The results may be satisfactorily interpreted by considering the detailed symmetry of the crystal and the effects of the anisotropy of the recoilless absorption probability. It was found that an axially symmetric field gradient with its principal axis oriented along the Fe–NO directions, couples with the nuclear quadrupole moment of ^{57}Fe giving a positive interaction with the value eq=+0.585×10^{18} V/cm^{2}. This field gradient is assumed to originate from unbalanced d‐electron density and the electronic population calculated for the molecule agrees with that obtained by molecular‐orbital methods. The large total s‐electron density at the ^{57}Fe nucleus measured by the isomer shift is quantitatively related to the effective 3d‐electron population and to the 4s partial occupation. Estimates of the 4s density also agree with that reported from molecular‐orbital calculations.

Reinvestigation of the Structures of Ethanol and Methanol at Room Temperature
View Description Hide DescriptionDiffraction studies of ethanol and methanol indicate strong intermolecular hydrogen bonding between neighboring alcohol molecules at room temperature. Each oxygen has, on the average, two nearest oxygen neighbors at 2.7 Å in each alcohol. From an analysis of the radial‐distribution function of each alcohol, a reasonable accounting of the observed intermolecular interactions is made.

SCMO Calculations on the Tetramethyl‐p‐Phenylenediamine System
View Description Hide DescriptionSCMO calculations in the PPP approximation were carried out on the tetramethyl‐p‐phenylenediamine (TMPD) system. Comparison with experiment was made for TMPD, TMPD^{+}, and TMPD^{++}. In general good agreement for one set of parameters was obtained.

Magnetic Transition of Wurster's Blue Perchlorate. I. The Low‐Temperature Phase
View Description Hide DescriptionEvidence is given for the low‐temperature phase of Wurster's blue perchlorate being built up of bipositive ions and neutral molecules, the high‐temperature phase having undergone disproportionation according to 2 TMPD^{+}→TMPD+TMPD^{++}. The electronic as well as the ESR spectra can be explained on this basis. The actual transfer of charge required in the disporportionation can be observed as a conductivity peak in the transition range.

Magnetic Transition of Wurster's Blue Perchlorate. II. Theoretical Considerations
View Description Hide DescriptionA theoretical discussion is given of the low‐temperature phase of Wurster's blue perchlorate. The suggested disproportionation of the TMPD^{+} ions can be simulated by the introduction of an inequivalence potential in an SCMO calculation of the ionic dimer. The value of this potential, as well as its consequences for the electronic absorption spectra is discussed. A calculation of the energy difference between high‐ and low‐temperature phase is given suggesting this difference to be almost zero, thus making a phase transformation possible.

Magnetic Transition of Wurster's Blue Perchlorate. III. The Nature of the Transition
View Description Hide DescriptionThe anomalous magnetic susceptibility of the low‐temperature phase of Wurster's blue perchlorate can be explained on the model of the inequivalent ion pair. Quantitative agreement between the calculated and experimental susceptibilities, between the calculated and experimental heat of transition, as well as between the calculated and experimental integrated difference in enthalpy content of the high‐ and low‐temperature phase has been obtained. The statistics to be used depend on an assumption about the way in which triplets can be formed in this system. In general, a system in which any pair of ions can form a triplet is favored.

Crystal Structure of Tetramethylammonium Fluoride Tetrahydrate
View Description Hide DescriptionTetramethylammonium fluoride tetrahydrate is tetragonal, space group I4_{1}/a with a=10.853 and c=8.065 Å at −26°C. The crystal structure was determined from the crystal data and the Patterson synthesis and refined by least squares. It has a hydrogen‐bounded ionic/water framework composed of four‐coordinated fluoride ions and three‐coordinated water molecules. The tetramethylammonium ions are in voids within this framework.

Crystal Structure of Manganese (II) and Cobalt (II) Bromide Dihydrate
View Description Hide DescriptionThe crystal structures at 298°K of MnBr_{2}·2H_{2}O and CoBr_{2}·2H_{2}O have been refined by full‐matrix least‐squares methods using three‐dimensional MoKα intensity data. In these compounds, polymeric chains of metal and bromine atoms arranged in a near‐square planar arrangement with each bromine atom shared by two metal atoms parallel the c axis. The water molecules which fill the remaining octahedral positions about the metal atom provide hydrogen bonds to link adjacent chains.

Measurement of the Frequency of Torsional Vibration in the Ethane Molecule
View Description Hide DescriptionThe direct excitation of the torsional vibration of the two methyl groups in ethane was observed in a slow‐neutron inelastic‐scattering experiment. Theoretical curves fit to the data indicate that the energy of transition from the zero to first excited state of this oscillation is 0.0332 eV (268 cm^{−1}) if the potential is assumed to be harmonic or 0.0344 eV (277 cm^{−1}) if the potential is assumed to be represented by ½V _{0}(1+cos3θ). To observe the transition, the scattering at small angles was observed through an evacuated scattering chamber and with careful consideration of multiple neutron scattering.

Experimental and Theoretical Study of Sigma‐Bond Electronic Transitions in Alkanes
View Description Hide DescriptionSigma‐bond electronic transitions in alkanes have been investigated both experimentally and theoretically. Vacuum ultraviolet spectra of a large number of alkanes have been recorded in the range 50 to 94 kK and absorption intensities as well as frequencies have been determined. The implications of vapor‐phase conformational isomerism are discussed. A qualitative interpretation of the observed spectra has been developed using independent‐systems theory in connection with a simple model in which excitations in only C–C bonds are considered. A reasonably good topological matching between theory and experiment is achieved. A quantitative theory in which C–H bond excitations are included has also been developed. With this theory parameters are derived from the spectra of methane and ethane which prove sufficient to describe the higher alkanes without recourse to ``fitting.'' The theoretical procedures used are outlined in the text and described in greater detail in an Appendix.

Improved Design for the Trennschaukel: Measurement of the Thermal‐Diffusion Factors in Gas Mixtures
View Description Hide DescriptionA four‐tube all‐glass trennschaukel or swing separator, having several new features has been designed. Bulbs have been used at the hot and the cold ends of each tube to increase considerably the gas space in the isothermal regions. Thermocouples have been inserted into the top and the bottom end volumes to measure exact upper and lower temperatures. Two dummy tubes have also been placed on each side of the effective four‐tube arrangement to eliminate dilution of the gas sample from the rocking arrangement. This apparatus has been successfully employed to measure thermal‐diffusion factors of He–Ne, Ar–N_{2}, and H_{2}–CO_{2} mixtures over the temperature range from 275° to 390°K.

Thermal Diffusion in Hydrogen—Helium Gas Mixture
View Description Hide DescriptionThe composition dependence of the thermal‐diffusion factor for the hydrogen—helium system has been studied by a trennschaukel. Like thermal conductivity, the thermal‐diffusion‐vs‐composition curve for this particular system shows a pronounced minimum. It has been suggested that probably the effects of inelastic collisions are responsible for the apparently anomalous behavior.

Quantum Mechanics of One‐Dimensional Two‐Particle Models. Electrons Interacting in an Infinite Square Well
View Description Hide DescriptionSolutions of Schrödinger's equation for the system of two particles bound in a one‐dimensional infinite square well and repelling each other with a Coulomb force are obtained by the method of finite differences. For the case of a 4.0‐a.u. well, the energy levels are shifted above those of the noninteracting‐particle model by as much as a factor of 4 although the excitation energies are only about 50% greater. The analytical form of the solutions is also obtained and it is shown that every eigenstate is doubly degenerate due to the ``pathological'' nature of the one‐dimensional Coulomb potential. This degeneracy is verified numerically by the finite‐difference method. The properties of the model system are compared with those of the free‐electron and hard‐sphere models; perturbation and variational treatments are also carried out using the hard‐sphere Hamiltonian as a zeroth‐order approximation. The lowest several finite‐difference eigenvalues converge from below with decreasing mesh size to energies below those of the ``best'' linear variational function consisting of hard‐sphere eigenfunctions. The finite‐difference solutions in general give expectation values and matrix elements more accurately than do the other approximations.

Effect of Pressure on the Mössbauer Resonance in Ferrocene and Pyrite
View Description Hide DescriptionThe effect of pressure to 200 kbars has been measured on the Mössbauer resonance in ferrocene and pyrite. For both compounds a large increase in s‐electron density at the iron nucleus with pressure was observed. For ferrocene, calculations showed that the increase is primarily due to decrease in shielding of the 3s electrons by the 3d. To account for the change quantitatively it would be necessary to consider the change both in the occupation and radial extent (shape) of the 3d orbitals.
The quadrupole splitting in pyrites increased with pressure. Although both q _{lat} and q _{val} are probably important, the results could be accounted for in terms of the former component only.
For ferrocene a decrease in quadrupole splitting with increasing pressure was observed. A Wolfsberg—Helmholz type calculation gave a change in electric field gradient which accounted for the effect. The same calculation accounted for the change of the optical absorption frequency with pressure which was previously observed for the e _{2g }→e _{2g } ^{*} transition.