Volume 52, Issue 6, 15 March 1970

Dependence of Vicinal H–H Coupling Constants in Substituted Ethanes on the Potential Function Characteristics to Internal Rotation. Application to A_{2}B_{2} PMR Spectrum of Nonsymmetrical 1,2‐Disubstituted Ethanes
View Description Hide DescriptionBased on rotational averaging, a theory governing the change of the vicinal coupling parameters and in the A_{2}B_{2} PMR spectra of nonsymmetrical 1,2‐disubstituted ethanes, as evidenced in the studies of substituent effect and solvent effect, has been developed in terms of the potential function characteristics to internal rotation about the C–C bond. By taking the average over the entire period of dihedral angle with respect to an appropriate potential function for internal rotation of the compound, a refined Karplus equation for the vicinal H–H coupling constant as a function of dihedral angle, , could yield the expression for and/or in terms of hyperbolic Bessel functions which describes an explicit functional dependence of and/or on both the ethane barrier and the maximum dipole interaction potential between the two bonds C–X and C–Y. These expressions enable one to determine the physical parameters related to internal rotation upon measurement of and/or from NMRspectrum. The determined energy difference between rotamers for several 1,2‐disubstituted ethanes were found in good agreement with the literature values. Solvent effect on the A_{2}B_{2} PMR spectrum was discussed on the light of the theory. The NMR experimental relation was derived from the above expressions. This latter relation enables one to tell whether the trans or the gauche isomer is more stable for the given compound from measurement on and with respect to the neat sample or in the medium of various solvent, and it also enables one to evaluate the value of for each given compound.

Rotational Isomerization of Polymer Chains by Stretching
View Description Hide DescriptionA general theory is presented on the effect of elongation of a polymer chain on the apportionment of its bonds and bond sequences among various rotational isomeric states. The perturbation of the population of a state is found to be proportional to , where is the length of the chain vector, is the mean square of for the unperturbed chain, and is the same quantity subject to the condition that the bond or bond sequence is in the conformational state specified by . The theory is limited to the range of moderate deformations; it is inapplicable for lengths approaching full extension of the chain. Numerical calculations are presented for polymethylene chains and for syndiotactic vinyl polymers. The calculated effects are very small; unit increase in generally alters the conformation population of a given state by no more than about one bond (or sequence) per chain. The length of the given conformation and its susceptibility to orientation by stretching are the main factors governing the effect. The connection with strain dichroism is discussed.

Model Calculations of Cooperative Motions in Chain Molecules
View Description Hide DescriptionThis article describes model calculations of the so‐called “perpendicular mode” of dielectric relaxation in chain molecules. Particular emphasis is given to cooperative interactions between adjacent chain elements. An extension of Glauber's model for the time‐dependent statistics of the Ising chain is used for the purpose. A closed‐form expression is given for the dielectric relaxation of an isolated dipolar element in an infinite ring. The influence of chain length and variable mobility along the chain upon dielectric relaxation is also described.

Microwave Spectra, Barriers to Internal Rotation, and Dipole Moments of cis‐ and trans‐Propylene Phosphine
View Description Hide DescriptionThe rotational spectra of cis‐ and trans‐propylene phosphine have been observed in the region 8–35 GHz. The respective barriers of the cis and trans isomers were determined to be and . The dipole moments were measured to be and 1.29 D, respectively. The relative stability of the isomers was also estimated. The trans is favored by .

Widths of Rotational Lines of an Asymmetric‐Top Molecule SO_{2} I. Broadening by a Rare Gas
View Description Hide DescriptionWidths of six rotational lines of SO2 with ranging from 3 to 16 have been measured. Linewidths have been calculated theoretically on the basis of the Anderson theory, and an assessment of the relative importance of different interactions has been made. Calculations have also been done on the basis of the Murphy–Boggs theory. The theoretical and experimental linewidths are found to agree well.

Systematic Determination of the Slater Parameters for the First Transition Elements
View Description Hide DescriptionSlater's parameter and with have been determined systematically from the experimental atomic energy levels for the neutral atoms and singly through triply positive ions of the first transition elements in their , , , , and . configurations, by a least‐squares procedure. A procedure of obtaining the semiempirical values of , which have never been obtained from the data of atomic spectra, is given along the line suggested by Anno [J. Chem. Phys. 47, 5335 (1967)] involving the consideration of appropriate “electron‐transfer reactions.” Data on , the energy change in the course of the electron‐transfer reaction, are also given, which may be combined with and/or to obtain Ideal correlation lines, which correlate a particular kind of , , or with the atomic number and/or electron configuration in ideal situations where no anomaly due such as to CI or misassignment were present, are discussed and are given in such a way that they are most consistent with the actual data obtained to facilitate the semiempirical MO calculations on the transition metal compounds, in which the metal atom has a fractional charge and a fractional population in each of its AO's. As far as possible, the semiempirical data obtained in the present work have been compared with the data obtained with the nonempirical Hartree–Fock calculations.

Solubility of Phenanthrene in Compressed Methane, Ethylene, Carbon Dioxide, and Nitrous Oxide: The Correlation of Phenanthrene–Gas Second Cross Virial Coefficients Using Pseudocritical Parameters
View Description Hide DescriptionThe solubility of phenanthrene in compressed methane, ethylene, carbon dioxide, and nitrous oxide has been measured over pressure ranges of 1–60 atm at temperatures ranging from 37 to 142°C. Second cross virial coefficients representing phenanthrene–gas pair interactions have been evaluated from this data. It is shown that when allowance is made for the effect of molecular quadrupole moments on the critical temperatures of carbon dioxide and nitrous oxide, ordinary combining rules produce pseudocritical parameters which reduce these phenanthrene–gas cross virial coefficients to a single function of reduced temperature. The data are fitted to several potential functions which are shown to be consistent with the reduced behavior of these systems.

Single‐Crystal EPR Study of a Cu(II)dialkyldiselenocarbamate. An Example of Noncoinciding Principal Axes
View Description Hide DescriptionA single‐crystal EPR study of Cu(II)di‐n‐butyldiselenocarbamate magnetically diluted in the corresponding Ni(II) complex is reported. The directions of the principal axes of the ^{63}Cu and ^{77}Se hyperfine splittingtensors and the magnitudes of the electron‐spin–nuclear‐spin dipole–dipole interactions along these axes were found to agree satisfactorily with what is expected for a planar complex of approximately symmetry with one unpaired electron in an antibonding orbital. The Se hfs data were used to calculate the extent to which the Se and atomic orbitals participate in the orbital of the unpaired electron. It was found that two principal axes of the tensor do not coincide with the principal axes of the Cu hfs tensor. In addition, the anisotropy in value reaches a minimum in the plane where the anisotropy in the Cu hfs reaches a maximum. This indicates that the over‐all electronic structure of the complex differs significantly from the structure normally evoked to interpret the EPR parameters of planar Cu(II) complexes, notwithstanding the “normal” hyperfine data. The consequences of the noncoincidence of principal axes for the powder spectrum are discussed. It is shown that the peak positions in the recorded powder spectrum can be accounted for quantitatively using the single‐crystal EPR results.

Mössbauer Study of ^{57}Co Implanted in Diamond
View Description Hide DescriptionA Mössbauer source of ^{57}Co in diamond has been produced by implanting ^{57}Co with an isotope separator directly into a diamondsingle crystal. The Mössbauer spectra taken at 80 and 300°K and in the [100] and [110] orientations displays two peaks of equal intensity. These two peaks can be interpreted as quadrupole splitting caused by the displacement of the ironinterstitial from its site of tetrahedral symmetry.

Photoelectron Spectroscopy of HCl and DCl Using Molecular Beams
View Description Hide DescriptionA focusing field electrostatic energy analyzer was used to examine photoelectrons from HCl and DCl using the 584 Å line of helium and the 736–744‐Å doublet of neon. Ionization potentials for the and states of HCl^{+} and DCl^{+} were determined and found to be essentially in agreement with values obtained by spectroscopic methods. Relative transition probabilities to the molecular–ion states were measured and are in agreement with calculated values.

Transient Nuclear Magnetic Resonance Studies of Dilute Copper‐Base Alloys
View Description Hide DescriptionData are presented for the nuclear spin–spin and spin–lattice relaxation rates for the ^{63}Cu and ^{65}Curesonances in dilute copper‐base alloys with the following atomic percent of the solute metals: 0.1% Ag, 0.2% Ni, 0.25% Al, 0.25% Au, 0.4% Ni, 1.0% Ni, and 5.0% Ag. The data reflect the sizable electric field gradients due to local strains introduced by alloying and the spatial rearrangement of conduction‐band electrons in the vicinity of individual solute atoms.

Environmental Effects on Transitions. III. Spectral Intensities of Lanthanide Nitrate, Sulfate, and α‐Picolinate Solutions
View Description Hide DescriptionThe environmental effects of nitrate, sulfate, and α‐picolinate anions on transitions of lanthanide ions in aqueous solution were investigated. For the α‐picolinate complexes, LnP_{3}, it was possible to apply the Judd–Ofelt method to the evaluation of the spectral changes. The parameters were larger than for the aquoion spectra with showing the largest change. Results are presented for trivalent Pr, Nd, Sm, Dy, Ho, Er, and Tm.

Proton Dynamics in KH_{2}PO_{4} Type Ferroelectrics Studied by Infrared Absorption
View Description Hide DescriptionThe infrared absorptionspectrum of ferroelectric crystals analogous to KH_{2}PO_{4} was measured at several temperatures. Substantial changes in the intensity and width of the ir absorption peaks, especially in the low‐energy spectral region, were observed upon crossing the Curie temperature. Assignments of the ir absorption peaks for both phases were made on the basis of a systematic comparison of the spectra of compounds isomorphic to KH_{2}PO_{4} and containing isotopes of D and ^{18}O. Correlation charts were constructed for both phases, permitting harmonic interpretation of the ir selection rules. The structure of the ir absorptionspectrum of KH_{2}PO_{4} at temperatures above , and comparison of this spectrum with that of KD_{2}PO_{4}. suggests a dynamic hydrogen symmetrizing process along the H bonds. It also indicates the existence of strong coupling between certain PO_{4} modes and the soft longitudinal hydrogen modes, caused by the extremely anharmonic nature of the potential well along the H bond. The coupling results in a broadening of the PO_{4} lines involved. The partial broadening that remains in KH_{2}PO_{4} below indicates that the soft hydrogen modes persist to a small extent even in the ferroelectric phase of this crystal. The ir data are explained on the basis of the fluctuating double‐minimum‐potential‐well theory for the hydrogens.

Antiferroelectric Transitions in NH_{4}H_{2}PO_{4} and NH_{4}H_{2}AsO_{4} Studied by Infrared Absorption
View Description Hide DescriptionThe antiferroelectric phase transition of NH_{4}H_{2}PO_{4} and NH_{4}H_{2}PO_{4}, as well as of their deuterated analogs, were studied by observing the changes in the infrared absorption spectra (250–4000 cm^{−1}) accompanying the phase transition. The behavior of the spectrum of NH_{4}H_{2}PO_{4} and ND_{4}D_{2}PO_{4} while approaching suggests that the same hydrogen‐dynamics mechanism is responsible for the phase transition in both cases, and that the fluctuating double‐minimum‐potential‐well theory for the hydrogens applies here too. The differences observed at temperatures below indicate a different final arrangement of the hydrogens in the antipolar phase. There are more PO_{4} lines in the NH_{4}H_{2}PO_{4} low‐temperature spectrum, indicating that the hydrogens are arranged asymmetrically along the axis, thus inducing an antiparallel dipole network. The ir absorptionspectrum of a mixed crystal NH_{4}H_{2}(AsO_{4})_{0.95}(PO_{4})_{0.05} was measured at different temperatures in order to check the validity of the site‐group assignments in these crystals. The gradual reduction in the correlation field splitting on increasing the deuterium percentage in the antipolar phases of ND_{4}D_{2}PO_{4} compounds suggests a more distorted deuteron network. Possible assignment for the absorption peaks in both phases of NH_{4}H_{2}AsO_{4} and ND_{4}D_{2}AsO_{4} (60% D) are given.

Magnetothermodynamics of α‐MnCl_{2}·4H_{2}O. II. Heat Capacity, Entropy, Magnetic Moment, from 0.4 to 4.2°K with Fields to 90 kG along the Crystallographic Axis
View Description Hide DescriptionThis work is a continuation of our previous magnetothermodynamic measurements on a 3.934‐cm‐diam spherical single crystal of MnCl_{2}·4H_{2}O in which case the field was directed along the crystallographic axis. Here the heat capacity and magnetic moment have been measured between 0.3° and 4.2°K with stabilized solenoid fields of 0, 1, 5, 7.5, 10, 14, 18, 22, 25, 40, 65, and 90 kG, along the crystallographic axis. At 0.716°K and fields of 90, 80, and 70 kG. the electron system was magnetically saturated. The derived temperature‐independent magnetic susceptibility was found to be − 1.6 × 10^{−4} cm^{3} mole^{−1} and the saturation moment of the temperature‐dependent system is 27 974 G·cm^{3} mole^{−1}, equivalent to . At 90 kG the nuclear spins were found to contribute a heat capacity term of gibbs mole^{−1}. The amount of enthalpy required to remove quanta of angular momentum from the saturated condition at 90 kG was found to be 20.63 cal mole^{−1} of angular momentum. This is less than , the magnetic work, by 3.44 cal mole^{−1}, which is the amount of stored internal energy contributed to the saturated condition for this limiting process, and indicates antiferromagnetic interactions. Extrapolation of the magnetic moment–temperature curves to absolute zero yields the expression M = 1.056H + 9.0 × 10^{−7} H ^{2}G·cm^{3} mole^{−1} at 0°K. On this slightly curved line the saturation value, 27 974 G·cm^{3} mole^{−1}, is reached at a field of 25 920 G, and the work of magnetization, equals 8.73 cal mole^{−1} at 0°K. Temperature–field observations on 31 isentropes were used to correlate the entropies along 12 iso‐Oerstedic heat capacity series. The zero of electronic and lattice entropy was located from the low‐temperature values of the heat capacity series at 90 kG. The upper limit of the electronic entropy was found to be 3.559 gibbs mole^{−1}, compared to . Smoothed, correlated values of the heat capacity,entropy,enthalpy, internal energy, magnetic moment, iso‐Oerstedic temperature coefficient of the magnetic moment (which equals the isothermal derivative of entropy with respect to field), and the magnetic work have been tabulated.

Stability Conditions for the Solutions of the Hartree–Fock Equations for Atomic and Molecular Systems. II. Simple Open‐Shell Case
View Description Hide DescriptionThe stability conditions for the solutions of the Hartree–Fock equations for the simple open‐shell case, i.e., closed shell with one extra electron, are derived. It is shown that only “doublet stability” is relevant is this simple open‐shell case, the solutions being always “nondoublet unstable.” The doublet stability conditions are then derived using the mathematical methods of quantum field theory, namely, occupation number representation, Wick's theorem, and Feynman‐like diagrams. In order to familiarize the reader with the use of these concepts they are first used to rederive the singlet and nonsinglet stability conditions for the closed‐shell case. A general method of finding new Hartree–Fock solutions, in the case that the symmetry adapted Hartree–Fock solutions are unstable, is briefly discussed. The implications of the instability on the ground‐state correlation energy calculations and on the excitation energy calculations using time‐dependent Hartree–Fock theory are considered.

Investigations on the Unrestricted Hartree–Fock Method as a Tool for Computing Potential Surfaces
View Description Hide DescriptionThe possible uses of the ab initio spin‐unrestricted Hartree–Fock (UHF) method for computing potential energy surfaces have been investigated, expanding the molecular orbitals from a basis set of Gaussian functions. In order to approximate spin‐pure states, an exact spin projection operator, as well as an operator annihilating only the state of next higher multiplicity, has been used. Preliminary studies undertaken on the H_{2} and LiH molecules indicate that among the various methods employed, the unprojected UHF approach gives the most satisfactory shape for potential curves. The HNO molecule was then investigated, and five electronic states of the system were considered, namely , plus two states of symmetry. The ground state is . Its UHF energy was minimized by varying the three geometrical parameters independently. A value of of 0.32 was obtained at the experimental geometry. This system with an even number of electrons thus has the unexpected property of being unstable with respect to a splitting of the and orbitals. Application of the spin projection operator lowers the energy by 0.0265 a.u. The UHF wavefunctions give an excitation energy of 3860 cm^{−1}. When pure spin states are produced, it becomes 11 660 cm^{−1} (experimental value 13 150 cm^{−1}). The state practically coincides with the ground state in the UHF approximation, but after projection an excitation energy of 5850 cm^{−1} is obtained. A slight maximum is observed in the UHF potential energy curve of the states as a function of the N–H distance, which we associate with the predissociation observed in the spectrum of the compound. Based upon projection at the experimental minimum for the ground state, and at infinite N–H separation, a set of adjusted curves has been generated for the system H + NO. The features of these curves are discussed in relation with the mechanism of the recombination reaction between hydrogen atoms and nitric oxide.

Relative Electron Impact Ionization Cross Sections by a Double Crossed‐Beam Technique
View Description Hide DescriptionAccurate values of electron impact ionization cross sections of high‐temperature species are of importance in mass spectrometric investigations as well as a variety of other fields. However, the present experimental techniques are subject to many inherent difficulties or are limited in applicability and have yielded relatively few reliable values. Theoretical calculations are not sufficiently accurate. An experimental technique for accurate measurement of relative cross sections is described. The measurement depends only on one experimentally determined quantity, as well as the mass and temperature of the gaseous species, and is applicable to a wide variety of systems. The technique utilizes a mass spectrometer that is fitted with a Knudsen cell and employs electron impact ionization. A second, modulated electron beam intercepts the molecular beam, causing a slight modulation in the intensity of the molecular beam that is reflected in the output signal of the mass spectrometer. The relative attenuations of the various component species of the molecular beam are proportional to the relative total ionization probabilities of these species. The relative cross sections for Ca, Tl, Ag, and Pb have been measured and are compared with literature values obtained by other techniques. Preliminary application has also been made to the molecular species W_{2}O_{6} and W_{3}O_{9}.

“Appearance Energy” and Energy Dependence of the Recoil Product Yield in Indium Ethylenediaminetetra‐acetate by the In Reaction
View Description Hide DescriptionThe concept of the “appearance energy” has been proposed by observing the recoil product yield as a function of recoil energy in a solid system. The yield of ^{115m}In^{3+} ion following the In reaction in indium ethylenediaminetetraacetate (In–EDTA) was zero in the low‐recoil‐energy region and it increased from a threshold value of recoil energy, that was named the “appearance energy,” to a saturation yield in the higher energy region. The appearance energy of the ^{115m}In^{3+} ion in In–EDTA was about 60 eV with possible errors of factor 2. The meaning of the appearance energy has been discussed in comparison with the displacement energy in solid‐state physics. From the energy dependence curve it was suggested that the reaction of the recoil atom might be divided into three categories corresponding to the three parts of the recoil range.

Perturbation Theory for Intermolecular Forces Including Exchange
View Description Hide DescriptionGeneralized solutions to the Eisenschitz and London perturbation equations are derived. It is pointed out that the results obtained in the formalisms proposed by Hirschfelder (HAV), by Hirschfelder and Silbey, by Murrell and Shaw, and by Musher and Amos are special cases of the generalized treatment.