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Volume 28, Issue 1, 01 January 1958

Calculation of Atomic Valence State Energies
View Description Hide DescriptionGiven a molecular valence‐bond wave function (constructed according to the approximation of perfect pairing), the general theory is presented for calculating either (1) the energy following complete nonadiabaticdissociation of the atoms (hence, the promotional energy) or (2) the intra‐atomic energy of the molecule for equilibrium positions of the nuclei. It is found that existent methods and tables are generally sufficient for treating only molecules having less than two unpaired electrons and, if hybridization is admitted, only molecules having less than two bonds. Tables are here given which serve the needs with respect to all possible structures involving s‐ and p‐valence electrons. Promotional energies for the CH and CH_{2} molecules are derived for illustration.

Fragmentation of Methane by Electron Impact, and the Latent Heat of Sublimation of Carbon
View Description Hide DescriptionThe ions produced in the fragmentation of methane by electron impact have been found to be formed with initial kinetic energy. Taking this energy into account, the electron impact data on methane are shown to be compatible with the spectroscopically acceptable value of 171 kcal/mole for the latent heat of sublimation of carbon in agreement with the value obtained by direct measurement.

Vibrational Matrix Elements of NO
View Description Hide DescriptionA potential function meeting certain qualitative criteria is developed from the Lippencott potential, a seven term expansion of this function being actually utilized. A three‐term expansion of the dipole moment is used within the framework of familiar perturbation theory to obtain the vibrational‐matrix elements for the fundamental and first four overtone transitions arising from each of the first eleven levels. The results of this calculation are utilized for a further investigation of the potential function, and the approximations involved are considered. This calculation has been programmed and carried out on the IBM 650 electronic data processing machine, and is readily adaptable to other diatomic molecules for which the requisite empirical data are available.

Electrochemical Behavior of the Palladium‐Hydrogen System. I. Potential‐Determining Mechanisms
View Description Hide DescriptionThe potential of saturated α‐palladium in hydrogen‐stirred solution compared to a Pt/H_{2}electrode in the same solution is 0.0495±0.0005 v. The potential‐determining reaction on α‐palladium is independent of hydrogen pressure. The potential‐determining equilibrium is postulated to be, . Pure palladium spontaneously absorbs hydrogen in hydrogen‐stirred solution until the saturation limit of the α phase is reached. This limiting atomic ratio of H/Pd=0.025±0.005. Between a H/Pd atomic ratio of 0.03 to 0.36 both the α and β phases coexist and the mixed potential is determined by that of the α domains. In the H/Pd region 0.36 to 0.6, the potential is a function of the hydrogen content of the palladium.

Electrochemical Behavior of the Palladium‐Hydrogen System. II. Thermodynamic Considerations
View Description Hide DescriptionThe thermodynamic relationships between the potentials of the palladium‐hydrogen alloys and the known equilibrium properties of the system, palladium‐hydrogen gas, are derived and discussed. A value of 0.048 v for the potential of the saturated α alloy derived from the gas phase data is in substantial agreement with the observed value of 0.050 v. The spontaneous loss of hydrogen from the electrolytically charged alloy of composition, H/Pd∼0.6, to form an alloy of lower hydrogen content shows that there is an unusual free‐energy situation involved in this system. This is discussed and an explanation of the free energy scheme is suggested.

Electrochemical Behavior of the Palladium‐Hydrogen System. III. Gas‐Charged Palladium Alloys
View Description Hide DescriptionExperimental evidence is presented to support the proposed difference in electrochemical properties of the β‐ and β′‐palladium‐hydrogen alloys. It is shown that the β‐palladium‐hydrogen electrode is a true equilibrium hydrogen electrode. A consideration of the electrocapillary properties of pure palladium and the α‐palladium alloys in solution provides an explanation of the cessation of spontaneous absorption of hydrogen before complete equilibrium is attained.

Chemical Determination of the Oscillator Strength of F Centers
View Description Hide DescriptionThe concentration of F centers in additively colored KCl was determined by measuring the amount of hydrogen evolved when the colored crystal is dissolved in water. This method avoids the uncertainties inherent in previous experiments on the change in acidity occurring upon dissolution. The use of this concentration in the Smakula absorption equation gives the optical oscillator strength f. The value of f, based upon 12 independent experiments, was 1.17±0.15, which disagrees with previously reported values.

Nuclear Quadrupole Coupling in the Li_{2} Molecule
View Description Hide DescriptionThe method of deformed atoms in molecules is applied to calculate the electric field gradient q at a nucleus in Li_{2}, using the molecular wave function obtained by Arai and Sakamoto. The field gradient is composed of nuclear and electronic terms which almost cancel each other, so that its magnitude and even its sign are seriously affected by accuracy of wave functions used. It is nevertheless expected that the A. S. wave function, which gives a dissociation energy of 0.96 ev compared with the experimental value of 1.05 ev, is sufficiently accurate. Neglecting the shielding effect induced in the 1s shell by the nuclear quadrupole moment Q, the result obtained is q/2e=q′=—0.0034 au at an internuclear distance of 4.93 au. The nuclear quadrupole coupling constant eqQ found experimentally is positive (+0.060 Mc/sec). A negative value of the quadrupole moment Q(Li^{7}) thus is obtained, in agreement with the prediction of the nuclear shell model.

Application of the Method of Deformed Atoms in Molecules to the Li_{2} Molecule
View Description Hide DescriptionThe method of deformed atoms in molecules, proposed previously to remedy deficiencies in the method of Moffitt, is employed to calculate energies of the ground state^{1}Σ _{g} ^{+} and the lower excited states^{3}Σ _{u} ^{+}, ^{1}Σ _{u} ^{+}, and ^{1}II _{u} of the Li_{2} molecule. As basis for the molecular calculation, modified atomic functions are introduced to take deformation of atoms in molecules into account. These modified functions are constructed from atomic eigenfunctions in a manner which fully preserves correlation between electrons. Exact atomic energies are used to calculate the atomic energy parts of the matrix elements of the molecular calculation, while the energy defects due to deformation of atoms are determined by using approximate functions.
The modified atomic functions are made up so that their charge distributions are well described by the use of Slater orbitals with equal orbital exponents for all atomic states. Interatomic interaction operators, overlap integrals, and energy defects due to deformation of atoms are calculated using Slater orbitals. For the 1s)^{2}2s)2p) ^{3} P and ^{1} P states of the Li^{—} ion, the exchange correction due to binding a free electron into the 2p orbital is considered. The energy defects of Slater orbitals from Hartree‐Fock orbitals are found to have small effect on the dissociation energy of the ground state.
The calculations are performed for three sets of values for the orbital exponents. The dissociation energy obtained for one set of values is 0.96 ev, in good agreement with the observed value of 1.05 ev. The excitation energies obtained of 1.63 ev for ^{3}Σ _{u} ^{+}—^{1}Σ _{g} ^{+}, 2.05 ev for ^{1}Σ _{u} ^{+}—^{1}Σ _{g} ^{+} and 2.59 ev for ^{1}II _{u} —^{1}Σ _{g} ^{+} also agree reasonably well with the corresponding observed values of (1.35 ev), 1.76 ev, and 2.54 ev.
The calculation is discussed and compared with the orbital approach and Moffitt's method. Conclusions are stated regarding the nature of bonds and orbital exponents in Li_{2}.

Structure of Sodium Metaphosphate Glass
View Description Hide DescriptionThe x‐ray diffraction pattern of sodium metaphosphate glass (formula NaPO_{3}) has been determined. The radial distribution function determined from the diffraction pattern indicates that the structure consists of long chains of PO_{4} tetrahedra crosslinked to other chains by O–Na–O— bonds. This model agrees with the one advanced by other workers who applied high polymer techniques to the study of metaphosphates.

Spin Densities in the Perinaphthenyl Free Radical
View Description Hide DescriptionValence bond theory is used to calculate π‐electron spin densities (ρ_{ i }) on carbon atoms in the perinaphthenyl free radical,[Complex chemical formula]The results are ρ_{1}=—0.176, ρ_{2}=+0.321, ρ_{3}=—0.220, ρ_{13}=+0.262. The theoretical spin densities ρ_{1} and ρ_{2} are compared with the ``experimental'' values ρ_{1}=0.098, ρ_{2}=0.325 which are obtained from the equation a_{i}=Qρ_{i} and the absolute isotropic protonhyperfine splittings (a _{1}=2.2, a _{2}=7.3 gauss) which have been observed in the electron magnetic resonance of the perinaphthenyl free radical by Sogo, Nakazaki, and Calvin. Valence bond theory thus yields calculated spin densities in this odd‐alternate radical which are in reasonably good agreement with the ``experimental'' densities. Molecular‐orbital theory without configuration interaction predicts only positive spin densities and is therefore inadequate to describe experimental densities in the perinaphthenyl radical or in any other substance with large negative spin densities.

Crystal and Molecular Structure of Diboron Tetrafluoride, B_{2}F_{4}
View Description Hide DescriptionX‐ray diffraction study of a single crystal of B_{2}F_{4} indicates a planar, centrosymmetric molecule with B–B=1.67±0.04_{5} A, B–F=1.32±0.03_{5} A and angle F–B–F=120°. There are two molecules in a monoclinic unit cell of symmetry P2_{1}/n and parameters of a=5.49, b=6.53, c=4.83, and β=102.5°.

Molecular and Crystal Structure of B_{6}H_{10}
View Description Hide DescriptionThe approximately pentagonal pyamidal arrangement for boron atoms in B_{6}H_{10} has been shown to be attached to a hydrogen arrangement resulting in C_{s}‐mmolecular symmetry. There are four bridge hydrogens and no BH_{2} groups in the molecule. The boron framework is bonded, to a very rough approximation, by two electron‐pair bonds and two three‐center bonds. The electron‐pair bond perpendicular to the molecular symmetry plane is usually short (1.60 A). Comparison with other boron hydrides leads to some tentative conclusions about factors governing the relative stabilities of these compounds.

Theory of the Dielectric Constant of Imperfect Gases and Dilute Solutions
View Description Hide DescriptionGeneral statistical mechanical equations are derived for the polarization, Clausius‐Mossotti function, dielectric constant and electrostriction of an imperfect gas. Results are given in the form of series expansions which are closely related to the conventional virial expansion of a gas. The coefficients in the expansions for the polarization, etc., can be evaluated by a consideration of sets of only two, three, etc., molecules in the presence of the external electric field. A similar treatment of a binary solution is also included.

Discussion of Slater Parameters for Elements of the First Long Period
View Description Hide DescriptionSlater‐Condon parameters are calculated for elements of the first long period in terms of Slater functions. By comparison with the observed spectroscopic data it is found that the Slater rules predict reasonable values for the exponents of these functions, with certain important qualifications regarding the variation of the screening number with configuration. The exchange integral between the 3d and 4s functions is less satisfactory. By means of the derived results the reduction of Slater‐Condon parameters within complexes is attributed in part to a polarization of the 3d functions so as to achieve near equality of Slater exponents with those of the ligands.

Millimeter‐Wave Spectrum of Formic Acid
View Description Hide DescriptionThe investigation of the R^{a} branch of the formic acid rotational spectrum has been extended up to J = 9 around 1.5 mm wavelength. The centrifugal distortion corrections have been studied in some detail partly by means of sum rules and partly by power series expansions and other approximate methods.

Photon Impact Studies of Molecules Using a Mass Spectrometer
View Description Hide DescriptionA vacuum ultraviolet monochromator has been combined with a mass spectrometer, in order to study photoionization processes. A detailed description is given of this instrument. Photoionization efficiency curves for parent and fragment ions from a number of molecules have been measured, using a photonbeam with an energy spread of 0.05 ev. It is shown how the results can be interpreted in terms of potential surfaces and electronic transition probabilities. In favorable cases vibrational structure may be resolved.

Soft X‐Ray Absorption Edges of Metal Ions in Complexes. III. Zinc (II) Complexes
View Description Hide DescriptionThe K x‐ray absorption edges of the Zn^{+2} ion in various complexes have been measured with a two‐crystal spectrometer. The significance of the fine structure of these edges with regard to the stereochemistry and electronic structure of the complexes is discussed.

Viscosity of Dilute Solutions of Long Chain Polymer Molecules
View Description Hide DescriptionAn expression for the relative viscosity η_{ r } has been obtained on the basis of the ``theory of rate processes'' using an ``equivalent sphere'' model, which relates η_{ r } to parameters such as the shearing force, absolute temperature, and the volume fraction of the polymer. In the limit of zero rate of shear, a relation between the Flory constant φ and Huggin's constant k″ has been obtained. Some important applications of the derived equations have been discussed.

Statistics of Polymer Molecular Size Distribution for an Invariant Number of Propagating Chains
View Description Hide DescriptionA detailed study of the polymer statistics for a reaction system resembling the ethylene oxide initiator case is made allowing for different rates of initiation k_{i} and propagation k_{p}. The modified Poisson distribution that results necessitates evaluation of rather complicated summations in order to characterize the number x̄_{n} and weight average x̄_{w} molecular weights. It is found that r = k_{p}/k_{i} as large as 10^{6} still does not shift (x̄_{w}/x̄_{n} )_{max} beyond the range 1.3 to 1.4. But under any circumstance, depletion of monomer assures homogeneous polymers, regardless of r.