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Volume 36, Issue 1, 01 January 1962

Spin Relaxation Processes in a Two‐Proton System Undergoing Anisotropic Reorientation
View Description Hide DescriptionThe spin‐lattice relaxation timeT _{1} and the spin‐spin relaxation timeT _{2} for two identical spins I=½ have been calculated for anisotropic reorientation in which the spin pair reorients randomly about an axis which, in turn, tumbles randomly. The results are applicable to liquids and solids provided that the correlation time for tumbling of the axis is small compared to T _{2}. Although the two types of motion are independent, their contributions to relaxation are not. For nonviscous liquids,T _{1}=T _{2}. The results are generalized to multispin systems.

Hydrogen Formation in the γ Radiolysis of Ethylene
View Description Hide DescriptionThe radiolysis of ethylene‐d _{2} and C_{2}H_{4}–C_{2}D_{4} mixtures has been investigated in the gas, liquid, and solid phases. The data indicate that hydrogen may be formed by two distinct molecular‐elimination processes: CH_{2}CH_{2}→CH_{2}C+H_{2} and CH_{2}CH_{2}→CH≡CH+H_{2}. The effect of xenon and pressure on the yields of H_{2}, HD, and D_{2} in the gas‐phase radiolysis of CH_{2}CD_{2} has been investigated. The results for the (^{2} P _{1})Hg‐sensitized and the 1237 A‐photochemical decomposition have been compared with those for radiolysis.

Effect of Oxygen upon the Heat Capacity of Gadolinium between 1.3° and 5°K
View Description Hide DescriptionA specimen of gadolinium was oxygenated and the heat capacity measured at three levels of oxygen content. The broad low‐temperature anomaly reported by Kurti and Safrata was reproduced by the oxygenation. Entropy calculations show that the reported anomaly results from the magnetic ordering of the spin 7/2 Gd^{3+} ions of the Gd_{2}O_{3} molecules.

Charge Distributions in Positive Ions and Ionization Energies of Conjugated Hydrocarbons
View Description Hide DescriptionThe π‐electron ionization energies of conjugated hydrocarbons and charge distributions of the resulting positive ions are examined utilizing closed and open shell SCF theory with deformation of σ and π orbitals. Ionization energies: Koopmans' theorem is shown to be invalid for conjugated hydrocarbons to the extent of about 2–4 ev, the major breakdown occurring through the Σ and Π deformation effects and not through reminimization of the ionic configuration. It is shown that the sigma description is not the same for both the ground and ionized states. A first‐order correction to the Σ‐framework energy of the ion can be obtained by removing a π electron from a single carbon atom. Very good agreement is obtained between the calculated and observed onization potentials (average discrepancy 0.1–0.2 ev). Justification is given for the so‐called ``ω technique'' for the calculation of ionization energies by the Hückel procedure in that this method contains deformation corrections which approximate those derived in this work. Charge distributions: Both deformation effects and reminimization of the ionized state are important in consideration of the charge distribution in the ions. It is shown that certain sites of negative charge density are predicted in positive ions by the reminimization procedure, and that this is both a reasonable and necessary consequence due to the form of the ionic Hartree‐Fock Hamiltonian. The wave functions, and consequently the charge distribution, calculated by the ω technique, are shown to be poor approximations of the ionized state Hartree‐Fock eigenfunctions.

Charge Distribution in Negative Ions and the Electron Affinities of Conjugated Hydrocarbons
View Description Hide DescriptionIt is shown that the analog of Koopmans' theorem for the calculation of electron affinities yields poor results for conjugated hydrocarbons due mainly to neglect of atomic orbital deformation effects. Reminimization of the molecular ionic wave function yields a sizable increase of the electron affinity in several cases. It is further shown that the ground stateMO's give a poor description of the charge distribution in the negative ion. In particular, reminimized MO's yield sites of positive charge in some negative ions.

Electron Impact Study of CO Using a Lozier Apparatus
View Description Hide DescriptionA Lozier apparatus, modified in that a quasi‐monoenergetic electron beam is used, has been employed to study CO. Ionization efficiency curves for both positive and negative ions were collected. From a detailed treatment of these data we deduced the ions produced, the appearance potentials for ions formed with zero kinetic energy, the processes in which they were produced, and the states of excitation of the fragments formed. From an analysis of our results alone, the dissociation energy of CO and the electron affinity of oxygen were determined, and they agreed within experimental error with the spectroscopic value of D(CO) of 11.11 ev and electron photodetachment value for EA(O) of 1.465 ev. Using the accepted values for D(CO) and EA(O), the electron affinity of carbon was determined from two different sets of our data to be between 1.34 and 1.74 ev. The lower value is in better agreement with other experimental determinations and with most of the recent empirical calculations for the EA(C).

SCF‐MO Wave Functions for the Hydrogen Fluoride Molecule
View Description Hide DescriptionAn SCF‐LCAO‐MO ground‐state wave function is reported for the HF molecule at several internuclear distances. The basis set of Slater‐type orbitals (STO's) was chosen so as to obey the following four criteria: (a) be a balanced basis set, i.e., each atom should have a set of STO's equally extended relative to the number and kinds of occupied AO's in the free atom; (b) include in the set STO's for a balanced polarization; (c) optimize the orbital exponents; (d) avoid redundancy in the set. The computed total energy at the internuclear distances of 1.7328 a.u. is —100.05804 a.u. This should be about 0.004 a.u. above the Hartree‐Fock energy of the HF molecule. The significance of the STO's in the basis set adopted is illustrated by several parallel computations. The computed equilibrium distance is 1.74 a.u. and the experimental is 1.733 a.u. The dipole moment is computed for several wave functions and the value corresponding to the best wave function is 1.984 D (experimental is 1.74 D), whereas the best computed moment for another wave function is 1.970 D. The significance of this variation is discussed. The dμ/dr is estimated at 1.7 D/a.u. at the equilibrium distance (experimental is 0.954). The overlap population and gross charge Q are computed for several internuclear distances. The significance of the Q _{H} is discussed; the best value of Q _{H} at the internuclear distance is 0.479.
The ground‐state ^{2}Π and the excited‐state ^{2}Σ^{+} for HF are investigated. An SCF computation is made for the ^{2}Π^{+}excited state at several internuclear distances. Gross charges and overlap populations are given for different internuclear distances for the two ionic states. The reorganization effect due to the removal of one electron is discussed in relation to the total energy, population analysis, and gross charge Q _{H} for the ion. A discussion of the computed ionization potentialI(3σ) is given at the end of the paper.

SCF‐LCAO‐MO Wave Function for the ^{1}Σ_{ g } ^{+} Ground State of C_{3}
View Description Hide DescriptionThe ^{1}Σ_{ g } ^{+}ground statewave function for the C_{3} molecule is computed in the SCF‐LCAO‐MO approximation. Four wave functions derived from different basis sets of Slater type orbitals (STO's) are compared. Subject to the limitations of our available computer program we have investigated the effects of expanding a minimal basis set by adding extra functions which should allow for polarisation effects, and changes in optimum orbital exponents of atomic orbitals in the molecular environment.

Influence of the Excluded‐Volume Effect on the Average Square Length of a Normal Alkane‐Type Chain
View Description Hide DescriptionThe model used by Tobolsky for calculating the mean square end‐to‐end distance of a normal alkane‐type chain is modified so as to account for part of the excluded volume effect. All conformations containing cyclohexane‐type loops, and most configurations involving pentane‐type steric hindrances are excluded. The present model, as compared with that used by Tobolsky, is simpler mathematically and yields values of the average square length of short chains which are closer to the exact ones.

Crystal Structure of Cupric Fluoride Dihydrate at 298°K
View Description Hide DescriptionA neutron determination of the crystal structure of cupric fluoride dihydrate at 298°K has been made. The structure consists of puckered sheets of nearly square CuF_{2}O_{2} groups, linked together by hydrogen bonds of 2.715±6 A, with the sheets connected by longer Cu–F bonds to form distorted octahedra around the Cu^{2+} ions. Dimensions within the octahedra are, two Cu–O distances of 1.941±5, two Cu–F of 1.898±8 and two Cu–F of 2.465±6 A. The long F–Cu–F axis is inclined at 7½° from the normal to the plane containing the remaining CuF_{2}O_{2} group of the octahedron. The Cu–O bonds bisect the H–O–H angle of 115.5±0.4°. The O–H bond is 0.980±7 A and the O–H···F angle is 164.9±0.7°. The amplitudes of thermal displacement of the atoms along various directions are given. The nuclear scattering length of fluorine is revised to 0.529±13 (10^{—12} cm).

Crystal and Magnetic Structure of Cupric Fluoride Dihydrate at 4.2°K
View Description Hide DescriptionA neutron diffraction study of CuF_{2}·2H_{2}O below the Néel point has determined the crystal and magnetic structure. As compared with this crystal at 298°K, the long Cu–F axial bonds of the distorted octahedron around the Cu^{2+} ion are reduced in length from 2.465±6 to 2.391±4 A: the short Cu–F bond of 1.899±6 A and the Cu–O bond of 1.945±4 A are unchanged. The H–O–H angle is reduced from 115.5° at 298°K to 110.1±0.4° at 4.2°K, and the O–H distance from 0.980±7 to 0.959±5 A. The amplitudes of vibrational displacement of the Cu, O, and F atoms at 4.2°K are about one‐half that at 298°K: The hydrogen atoms have about the same motion, due to zero‐point energy. The magnetic unit cell is identical with the nuclear cell, but the spin on the body‐centered copper atom is antiparallel to that at the origin. The spin direction is very nearly along the c axis, although an alternative model with the spin along the long octahedral direction fits the magnetic scattering almost as well. The difference between the Néel temperature of 10.9° and that of 26°K at which the magnetic susceptibility is a maximum is consistent with the observed magnetic structure. The revised nuclear scattering length for fluorine of 0.529×10^{—12} cm found in the analysis of CuF_{2}·2H_{2}O at 298°K is in excellent agreement with the experimental value of 0.534±12 obtained in the present study.

Infrared Studies of Crystal Benzene. V. Reflection Spectrum and Absolute Intensities
View Description Hide DescriptionAn experimental procedure for obtaining the reflection spectrum in the infrared from solid benzene is described. The results are analyzed according to the method of Robinson and Price to give the index of refractionn and the absorption coefficient κ as a function of frequency. Integration of the latter gives the absolute intensity Γ_{ i } of the ith fundamental, without requiring a knowledge of the path length. Since the path length is the most uncertain variable in the evaluation of absolute intensities from absorption measurements in condensed phases, the intensity results even from these relatively crude reflection measurements are probably as accurate as those from absorption studies. Comparisons are made with other studies on benzene, and the discrepancies are discussed.

Correction of Electron Diffraction Data for Failure of the Born Approximation
View Description Hide DescriptionA simple objective method for correcting electron diffraction data for the effects of the imaginary part of the atomic electron scattering factor is presented. Expressions for the phase shifts of the form:valid for s up to 50 at 40 kv and z up to 98 are given. This analytical form was chosen since it provides a close fit (less than 2% average deviation) to tabulated values of η(s, z), calculated by Ibers and Hoerni, over the useful range of s and thus makes the inclusion of the cos[η_{1}(s)—η_{2}(s)] term in theoretical molecular intensity curves a routine matter. The Fourier transform of the complete constant coefficient molecular intensity curve including the cosine phase shift term has been obtained and simple analytical expressions for peak splittings and corrections to vibrational amplitudes are presented.

Symmetry of Configurational Entropy in Lattice Statistics
View Description Hide DescriptionAn investigation is made of the general conditions under which the configurational entropy of a binary solid solution is symmetrical with respect to composition about the 50–50 composition point. Spin coordinate and occupancy number representations of the configurational energy are discussed. When the sites of the site array are equivalent due to spatial symmetry, the configurational entropy is symmetrical for any pair interaction model. Asymmetry of the configurational entropy implies the presence of some n‐site interactions, n=3, 5, 7, .... Application of these results to order‐disorder alloy and physical adsorption systems is considered.

Far Infrared Spectra of Solid Methyl Halides
View Description Hide DescriptionThe infrared spectra of solid CH_{3}Cl, CH_{3}Br, CH_{3}I, CD_{3}Cl, CD_{3}Br, and CD_{3}I have been measured in the spectral region from 130 to 30 cm^{—1} at 78°K. Two sharp bands were found in the cases of the chloride and bromide, and three in the case of the iodide. These absorptions are interpreted as arising from lattice vibrational modes. The isotopic shifts exclude libration about the symmetry axis as a possible assignment for any of the bands, however, definite assignments to B‐axis librations or translational modes cannot be made with confidence.

Electrical Properties of Some Dilute Cubic Sodium Tungsten Bronzes
View Description Hide DescriptionThe preparation and electrical properties are described for cubic Na_{ x }WO_{3}single crystals of the compositions x=0.363, 0.291, and 0.234. Specimens were prepared by diffusing sodium from single crystals of Na_{0.687}WO_{3}. The composition and homogeneity of the crystals were established by x‐ray powder and back‐reflection Laue photographs.
The electrical resistivity‐temperature plots show a more complex electronic behavior than had been expected for dilute Na_{ x }WO_{3} on the basis of earlier work; Na_{0.291}WO_{3} and Na_{0.234}WO_{3} exhibit resistivity minima at about 150° and 320°K, respectively, with characteristics similar to that of degenerate semiconductors. A polycrystalline sample of Na_{0.025}WO_{3}, having a room‐temperature resistivity of 3×10^{—3} ohm cm and a Seebeck coefficient of —270 μv/deg, is also described.

Raman Spectral Studies of Aqueous Solutions of Selenious Acid
View Description Hide DescriptionPhotoelectric Raman spectra of aqueous solutions of selenious acid, obtained at various concentrations, and of dilute strongly alkaline and partially neutralized aqueous mixtures of sodium hydroxide and selenious acid, have yielded vibrational frequencies considered to be those of the species H_{2}SeO_{3}, SeO_{3} ^{2—}, and HSeO_{3} ^{—}, respectively. In aqueous solutions of selenious acid, the intensities of two strong bands were found to increase linearly with (stoichiometric) concentration over a wide range of concentrations. This fact suggests essential completeness in the reaction of SeO_{2} with water, and negligible dissociation of H_{2}SeO_{3} into its ions, in the solutions for which linearity is obtained.
Polarization studies of the various Raman bands, comparisons of the observed frequencies with those of molecules of known symmetry, intercomparisons of the frequencies of the species SeO_{3} ^{2—}, HSeO_{3} ^{—}, and H_{2}SeO_{3}, and information gained from reported x‐ray studies of solid selenious acid have allowed for provisional vibrational assignments on the assumptions of various symmetries.

Magnetic Susceptibility of Potassium Hexachlororhenate (IV) and Potassium Hexabromorhenate (IV) from 5° to 300°K
View Description Hide DescriptionThe Curie points of K_{2}ReCl_{6} and K_{2}ReBr_{6} obtained from magnetic susceptibility measurements are 12.4±0.5° and 15.3±0.5°K, respectively, which confirm that cooperative‐type transitions observed in the heat capacities of these compounds with maxima at 11.9±0.1° and 15.2±0.1°K, respectively, represent transitions to the antiferromagnetic state. Evidence is presented that the ratios of the next nearest‐neighbor to nearest‐neighbor superexchange interactions in the two compounds are approximately equal. An estimate of the spin‐orbit coupling constants in the crystals is given and compared with other estimates.

Experimental Determination of the Heat of Dissociation of N_{2}O_{4}→2NO_{2} from the Temperature Dependence of Absolute Infrared Intensities
View Description Hide DescriptionThe heat of dissociation of N_{2}O_{4} has been determined from measurements of the temperature dependence of the integrated absorption of NO_{2} and N_{2}O_{4} vibration‐rotation bands. Results have been obtained that are in acceptable accord with the earlier estimate of Giauque and Kemp.

Cubic Lattice Model Chain
View Description Hide DescriptionThe partition functions for conditions of constant force Z_{f} or fixed displacement length Z̃_{r} are derived for the three‐dimensional cubic lattice model chain having two possible positions of different energy for each link. The problem can be set up so that it reduces to a one‐dimensional Markov chain, thus Z_{f} can be obtained in closed form. The network treatment of Wang and Guth for non‐Gaussian chains is used to obtain the partition function for a network of cubic lattice chains. Qualitative comparison with experiment indicates that most of the deviations from Gaussian behavior which have been observed for cross‐linked natural rubber at low relative elongations may be ascribed to intramolecular rotational energy effects.