Volume 39, Issue 1, 01 July 1963

Use of Gaussian Functions in the Calculation of Wavefunctions for Small Molecules. I. Preliminary Investigations
View Description Hide DescriptionThe results are reported of calculations on H, H_{2}, He, Be, N, and NH in bases of Gaussian elementary atomic orbital functions. Such functions, though physically less satisfactory than the customary Slater exponential functions, have the advantage that all integrals can be evaluated exactly by closed analytical formulas. Some progress has been made with the problem of choosing the orbital parameters for bases of limited size. Predictions of total energy are understandably poor but the values obtained for bond length and binding energy are encouraging.

Use of Gaussian Functions in the Calculation of Wavefunctions for Small Molecules. II. The Ammonia Molecule
View Description Hide DescriptionThis paper reports further work on wavefunctions using Gaussian functions. Restricted optimization of the parameters in calculations on the nitrogen atom, using eight functions, and the ammonia molecule, using 14 functions, results in a calculated binding energy of 0.4774 a.u., although total energies are in error by about three times this. Suggestions are given for the simplification of calculations using large bases.

On the Theory of Torsional Vibrations of (CH_{3})_{3}—X Type Molecules
View Description Hide DescriptionTorsional vibrations of (CH_{3})_{3}—X type molecules having C _{3v } point group symmetry have been analyzed by using a periodic potential function, and by taking into account mutual top—top interaction terms. The energy scheme was calculated by perturbation methods, and the selection rules have been derived. For the high‐barrier case, two allowed transitions from the ground state to the first excited state can be predicted.

Correlation Effects in the Alternant Molecular Orbital Approximation
View Description Hide DescriptionExamination of the two‐electron density matrix in the alternant molecular orbital approximation for a large system in a singlet state reveals that there are both short‐ and long‐range correlations between the electrons of opposite spin. There is also a long‐range correlation between electrons of the same spin. These correlations are not found when the wavefunction for the system is approximated by a single determinant of alternant molecular orbitals.

Molecular, Crystal, and Valence Structures of B_{18}H_{22}
View Description Hide DescriptionA three‐dimensional x‐ray diffraction study of single crystals has yielded the molecular structure of B_{18}H_{22}. The molecule is centrosymmetric, has six bridge H atoms, and has the geometry of two decaborane‐14 cages sharing a common B_{9}–B_{10} edge. The space group is Pccn, and there are four molecules in a unit cell having dimensions a=10.844, b=12.107, and c=10.803 Å.
The valence structure has been studied in the two‐center and three‐center resonance approximation, which is comparable in its predictions to the Hückel molecular orbital method in the other boron hydrides. The charge distribution in B_{18}H_{22} has been obtained from an analysis of the 6506 resonance structures.

Investigation of the Bonding of Iron‐Group Ions in Fluoride Crystals. II
View Description Hide DescriptionThis paper describes an ESR investigation of the bonding of iron‐group ions with the configurations d ^{6}(Fe^{2+}) and d ^{7}(Fe^{+}, Co^{2+}, Ni^{3+}) on cubic lattice sites in the crystals LiF, NaF, and KMgF_{3}. To aid the analysis of the bonding of d ^{7}ions, the optical absorptionspectrum of Co^{2+} was measured in LiF and KMgF_{3}. A discussion is given of the effects of lattice dimensions and the charge state of the impurity ion on the bonding parameters.

Unimolecular Decomposition of Chemically Activated Propyl Radicals. Normal Intermolecular Secondary Kinetic Isotope Effect
View Description Hide DescriptionThe vibrationally excited radical pairs n‐propyl‐d _{0}, n‐propyl‐d _{6} and isopropyl‐d _{0}, isopropyl‐d _{6} were produced at 25°C by the addition of H atoms to propylene‐d _{0} and propylene‐d _{6}. Decomposition of n‐propyl is by C–C rupture, whereas C–H rupture appears to be the predominant path for isopropyl decomposition, possibly to the exclusion of C–C rupture. The average rates of decomposition k _{ a } were determined relative to collisional stabilization by complete product analysis: for n‐propyl‐d _{0} C–C rupture, k _{ a } ^{ n }≃10^{8} sec^{—1}; for isopropyl‐d _{0} C–H rupture, k _{ a } ^{ i }(—1)≃10^{—2} k _{ a } ^{ n }. For vibrationally excited propane, formed by the addition of H atoms to isopropyl radicals, k _{ a } ^{pr}≃6.6×10^{5} sec^{—1}. The secondary kinetic isotope effect for n‐propyl unimolecular decomposition in this nonequilibrium system was found to be ∼5.0 at the low‐pressure limit, and ∼4.5 at the high‐pressure limit; that found for isopropyl decomposition is ∼6.
The Marcus—Rice specific rate expression was used with a quantum statistical harmonic oscillator model to calculate theoretical rate constants for the decomposition of n‐propyl radicals which are in good agreement with the experimental values. A loosened activated complex was assumed, in which all vibrational modes and internal rotations were taken as active. The effect of different treatments of the internal rotations on the distribution functionf(E)dE was demonstrated to be small.

Hole Theory of Liquids and Dense Gases. II. Internal Entropy, Energy, and Heat Capacity
View Description Hide DescriptionThe internal entropy, energy, and heat capacity of the inert gases in the liquid and dense gas states are calculated on the basis on the hole theory of liquids under the assumptions that the free volume increases linearly with the number of neighboring holes and that the holes and molecules are randomly distributed. The agreement with experiment is good in the dense gas region but becomes less satisfactory for the liquid state. The various assumptions inherent in this work are discussed and improvements are suggested.

High‐Resolution ESR Spectra of Photochemically Generated Free Radicals: The Viologens
View Description Hide DescriptionHigh‐resolution electron spin resonancespectra have been obtained for free radicals produced from methyl, ethyl, and benzyl viologen and 4–4′‐bipyridyl in ethanol—water solutions by irradiation with sunlight. From the analysis of these spectra we find that the hyperfine splittings for the protonsortho and meta to the nitrogen atoms are almost equal. The spin density distributions are discussed in terms of McLachlan's approximate SCF theory and we conclude that Q _{NHH }≈Q _{N CH3 H }≈25.

Optical Studies of Anisotropic Color Centers in Germanium‐Doped Quartz
View Description Hide DescriptionThe optical absorption induced by x rays in germanium‐doped quartz has been investigated using polarized light. The wavelength range was 220–800 mμ, and the behavior of the various bands was examined over the temperature range of 77°—600°K. Absorption bands polarized in parallel to the optical axis were observed at 250, 285, 296, 450, and about 620 mμ, and bands at 260, 272, 290, and 330 mμ were found to be polarized perpendicularly to the optical axis. The experiments also included a study of the optical bleaching of the bands and the effects of exchange of interstitial monovalent ions by electrical diffusion.
The results are discussed and correlated with results of electron paramagnetic resonance measurements carried out on the same specimens by J. H. Mackey.

EPR Study of Impurity‐Related Color Centers in Germanium‐Doped Quartz
View Description Hide DescriptionSince aluminum and germanium are two of the most easily incorporated impurities in crystalline quartz, the relationship of the color centers produced by x irradiation to these elements has been studied extensively. Previous work based on irradiation at 300°K has indicated that one type of electron‐deficient center is produced at aluminum, two kinds of electron‐excess centers are associated with germanium, and local charge neutrality is maintained by the insertion of an interstitialNa^{+} or Li^{+} ion at the germanium site. We have studied this system after irradiation at 77°K by conventional methods of EPRspectroscopy (9500 Mc/sec) and have discovered a new set of low‐temperature centers associated with these impurities. By identification of nuclear hfs and modification of the interstitial content through diffusion in an electric field, it is established that the same number of species is produced under these conditions but that the interstitial is located at the aluminum site. Detailed observations on the g tensors and hfs of the germanium centers are reported while observations on the aluminum centers are limited to the field orientation H ∥ c. By warming the crystals, efficient conversion of the low‐temperature centers to the high‐temperature forms is produced in crystals containing Na^{+} and Li^{+} for charge compensation. All low‐temperature forms are bleached completely by warming in samples in which the alkali ions have been replaced by H^{+}, which is known to have a small mobility. While detailed models of all centers are not suggested, enough information was obtained to establish the relationship between the low‐ and high‐temperature forms. The experiments are correlated with optical results presented in an accompanying paper.

Two‐Center Integrals over Solid Spherical Harmonics
View Description Hide DescriptionOne‐electron, two‐center integrals (and the corresponding one‐center case) are evaluated for integrals of the typearising in electromagnetic interactions. The Fourier convolution theorem method is employed and specific results are obtained for N′=0 and N′=2 in terms of an F function and recursion formulas. All cases up to L′=3 are evaluated in terms of the F functions and in terms of elementary functions.

Vibrational Analysis of the Heitler—London Potential of H_{2}
View Description Hide DescriptionThe vibrational levels associated with the Heitler—London potential of H_{2} have been found through use of the first‐order WBK approximation. The vibrational energies G as a function of quantum number v are accurately represented by G=—D _{0}(1—Av—Bv ^{2})^{ n }, where D _{0} is the Heitler—London dissociation energy and A, B, and n are parameters. The ΔG curve has negative curvature at all v. At high v the vibrational levels show the rapid convergence characteristic of covalent molecules. The Heitler—London ΔG curve has very nearly the same shape as the experimental curve for H_{2}; horizontally displaced to agree with experiment at low v, the Heitler—London ΔG curve predicts a dissociation energy which is 93% of the experimental value.

Application of the Second‐Order WBK Approximation to Radial Problems
View Description Hide DescriptionWhen the WBK approximation is applied to radial problems, difficulties are encountered at the origin. Previous work has led to the conclusion that the difficulties are removed by substitution of (J+½)^{2} for J(J+1) in the effective potential. The use of (J+½)^{2} is here shown to be justified for the first‐order WBK approximation only. The second‐order WBK wavefunction is found to approximate the exact one as r→0, if one substitutes K for J(J+1), where K obeys the equation K+1/(64K)=J(J+1). Moreover, the second‐order WBK energy levels can be made to coincide with the exact levels for the hydrogen atom and for the radial harmonic oscillator if the same substitution is made. Implications with regard to the rotating vibrator problem are discussed.

Vibrational Energy Exchange between N_{2} and CO. The Vibrational Relaxation of Nitrogen
View Description Hide DescriptionThe vibrational energy exchange N_{2}(v=1)+CO(v=0)=N_{2}(v=0)+CO(v=1) should be fast, due to near resonance of the energy levels. We have studied the rate of this exchange relative to the rate of energy transfer from translational to vibrational degrees of freedom in a shock‐heated mixture of 1% CO—99% N_{2}. Vibrational relaxation of the CO is observed by its infrared emission near 2000 cm^{—1}. The density change behind the incident shock is simultaneously observed with an interferometer and gives a measurement of the N_{2}relaxation time. In the 3200°—4200°K range both methods are applicable; they yield identical relaxation times within the data scatter of ±20%. In contrast, at 3600°K, the vibrational relaxation time of pure N_{2} is four times that of pure CO. The exchange reaction thus appears fast enough to make the vibrational temperatures of the N_{2} and CO equal during the vibrational relaxation of the mixture. In the 1900° to 5400°K range, our study gives vibrational relaxation times in seconds for pure N_{2} (p=1 atm), represented by log_{10} τ=102T ^{—⅓}—11.24. This agrees at high temperature with Blackman's data, but gives a somewhat different temperature dependence. Extrapolation of our data to lower temperatures indicates relaxation times an order‐of‐magnitude longer than given by ultrasonic experiments.

Thermodynamic Properties of a Monatomic Hydrogen Gas at High Temperatures
View Description Hide DescriptionA study is made of a gas in which the internal and intermolecular degrees of freedom are not separable. Expressions for the partition function and thermodynamic properties are derived for a gas of monatomic hydrogen. The number of bound states of the system is limited by interactions between the hydrogen atoms. The potentials of interaction of hydrogen atoms with protons, electrons, and other hydrogen atoms are estimated, and the partition function is evaluated at a series of densities from 10 to 10^{—5} amagats. The occupation numbers of bound states and the percent ionization are changed significantly by considering atom—atom and atom—proton interactions, but the value of the partition function is only slightly changed relative to that calculated by considering only the effect of interatomic forces upon the single‐atom energies.

Fluorescence and Lifetimes of Eu Chelates
View Description Hide DescriptionThe fluorescent lifetimes of a number of europium chelates were determined in solution and as the solid at a number of temperatures and a range of wavelengths of the fluorescent emission. They are compared with the lifetimes of europiumfluorescence in other compounds and it is suggested that the variation in lifetime is a result of the ligand—Eu interaction and that discrepancies in the results of different workers on the same compound is related to the manner of preparation of the chelate.

Photoelectric Phenomena in Hemoglobin and Dyed Gelatin
View Description Hide DescriptionHemoglobin shows photoconductivity with a threshold at about 3.9 eV. A similar phenomenon is found in dyed gelatin films. In the latter case, the response arises from light absorbed by the protein rather than by the dye, and it is suggested that the energy is transferred to the dye by a nonradiative resonance process involving the aromatic amino acid residues in the protein, and that the dye functions only as a relatively easily ionizable center in the solid. The same is presumably true of the porphyrin group in hemoglobin. No evidence for the existence of band‐model structure in these proteins could be inferred from the data.

Crystal‐Field Spectra of d ^{3,7} Ions. I. Electronic Absorption Spectrum of CoCl_{4} ^{=} in Three Crystalline Environments
View Description Hide DescriptionThe electronic absorptionspectrum of the CoCl_{4} ^{=} complex ion has been studied in crystals of the type R_{2}CoCl_{4}, where R is Cs, N(CH_{3})_{4}, or quinolinium ion. The measurements have been made with single crystals at various temperatures down to 4.2°K with high resolution in the near infrared, visible, and near ultraviolet regions of the spectrum. The data include transitions from the ground state to states arising from six of the seven terms of the free ion. Analyses of the bands have been made, as well as an attempt to sort out the effects of spin—orbit coupling, the site symmetry, and the vibrations of the excited states. It is concluded that the assumption of cubic symmetry for the crystal field is valid only for the determination of the approximate energies of the electronic states and not for the details of the splitting patterns of orbitally degenerate states. The usefulness of crystal‐field theory which includes spin—orbit coupling and two inter‐electronic repulsion parameters is discussed.

Entanglement Effects in Concentrated Polymer Solutions from Viscosity Measurements
View Description Hide DescriptionThe viscosity—molecular weight relation for the system polymethyl methacrylate—diethyl phthalate has been measured.Polymer concentrations of 0.10, 0.15, 0.20, and 0.25 g/cc have been used. No variation in entanglement molecular weight M_{e} in the range 30°—80°C was found. Theoretical predictions for the dependence of M_{e} on concentration have been confirmed. After correcting the data for variation in T_{g} with molecular weight, the dependence of viscosity on molecular weight predicted by theory is confirmed. Possible reasons are given for the discrepancy between the present conclusions concerning M_{e} and those arrived at from considerations of dynamic data on the same system.