Volume 47, Issue 3, 01 August 1967

Influence of Charge Compensation on uv Excitation of Rare‐Earth Fluorescence
View Description Hide DescriptionExcitation spectra for the fluorescence transitions of Tb^{3+}, Eu^{3+}, and DY^{3+}, were obtained at room temperature on single crystals of the tungstates and molybdates of Ca, Sr, Pb, and Cd, having the Scheelite structure, and on terbium‐doped crystals of CaF_{2} and SrF_{2}. Rare‐earth concentrations were nominally 1 at.% and charge compensation was provided by vacancy formation or interstitials, by substitution in cation sites or by anionic substitutions. Strong uv‐excitation bands were found for Tb‐ and Eu‐doped crystals and weaker bands for Dy‐doped matrices. The bands generally occur in the vicinity of the host‐lattice absorption edge but their intensities and energy positions are strongly influenced by the charge‐compensating defects in the vicinity of the active ion. The long‐wavelength peaks of the bands occur at energies coinciding with 4f‐level positions of the rare‐earth ions, thus suggesting a strong perturbation of 4f levels by charge transfer states. The short‐wavelength regions of the excitation bands are ascribed to exchange transfer from uv‐absorbing groups.

SCF—MO—LCAO—CI Treatment of the Pi‐Electronic Structure of Formaldehyde Using Ohno's Formula for β_{CO} and Constrained to Satisfy Koopmans' Theorem Exactly
View Description Hide DescriptionThe Pople—Pariser—Parr simplification of Roothaan's matrix formulation of the Hartree—Fock self‐consistent‐field (SCF) equations is applied to the pi‐electronic portion of the formaldehyde molecule as (1) a test of the use of Ohno's resonance integral formula as a basis for obtaining self‐consistent resonance integrals for heterobonds and (2) as a test of the effect of constraining the energy of the highest occupied orbital to satisfy Koopman's theorem exactly. The calculated spectroscopic intervals, dipole moments, and charge distributions are not too far different from those obtained by the self‐consistent‐electronegativity method of Brown and Heffernan, but there are indications that the present method may form a more satisfactory basis for extension to other heteroatomic conjugated systems.

Photodissociation as Studied by Photolysis Mapping
View Description Hide DescriptionWe describe a method, called photolysis mapping, which can determine the orientation of the transition moment for gas‐phase photodissociations. This method measures the flux of fragments at the wall of a hemisphere when plane‐polarized light photodissociates a molecular gas. If the fragments recoil perpendicular to the transition moment, the angular dependence of the flux at the wall is different than if the fragments recoil parallel to the transition moment. Photolysis‐mapping experiments for bromine and iodine photolyzed with visible light indicate that the atoms recoil perpendicular to the transition moment.

Internal Rotation Barriers for Hydrazine and Hydroxylamine from Ab Initio LCAO—MO—SCF Wavefunctions
View Description Hide DescriptionLCAO—MO—SCF ab initiowavefunctions with atomic basis orbitals of double‐zeta accuracy have been constructed for N_{2}H_{4} and NH_{2}OH and the potential‐energy curves versus internal‐rotation angle have been determined. Similar wavefunctions for CH_{3}CH_{3}, CH_{3}OH, CH_{3}NH_{2}, and H_{2}O_{2}, reported previously, showed a quantitatively useful correlation with experimental barrier heights and shapes. Since experimental information on the N_{2}H_{4} and NH_{2}OH barriers is incomplete or unknown, the theoretical results presented here may help guide experimental work. Decomposition of the total energy into one‐ and two‐electron components has been found previously to help elucidate the physical origin of the rotational barrier, and results for the species studied here are given. The wavefunctions presented here (and those reported previously for the species noted above) are the most accurate available for molecules possessing a rotational barrier about a single bond, and comparison is made with the results of the other existing ab initiowavefunctions.

Simple AMO Function for the Lithium Molecule
View Description Hide DescriptionAn AMO calculation for the ground state of the Li_{2} molecule is described. The calculations are very simple, but quite satisfactory results are obtained. Connections with other calculations are pointed out and certain interesting problems connected with the Li_{2} molecule and related molecules for which the AMO method might be useful, are discussed.

Molecular Schrödinger Equation. V. A Correlated Polyelectronic Wavefunction
View Description Hide DescriptionOur earlier method for obtaining accurate solutions to the molecular Schrödinger equation for one and two electrons has been improved and extended, at least in principle, to the general polyelectronic case. The discussion includes development of the theory and examples of specific numerical results obtained with systems containing up to four electrons.

Molecular Schrödinger Equation. VI. Results for H_{3} and Other Simple Systems
View Description Hide DescriptionThe results of calculations on the ground state of the H_{3} system are presented, and potential‐energy surfaces are constructed for the linear and isosceles triangular configurations. The path of minimum energy along these surfaces for the H+H_{2}→H_{2}+H reaction passes through a maximum 7.74 kcal above the reactants at a linear symmetric configuration with an H–H separation of 1.76 bohrs. Calculations on the ground states of He_{2} ^{+}, He_{2} ^{++}, the lowest ^{1}Π state of equilateral triangular H_{3} ^{+}, and a number of one‐electron states of H_{3} ^{++} and He_{2} ^{+++} are also summarized.

Molecular Schrödinger Equation. VII. Properties of the Energy Variance Function: The Estimation of Energy Eigenvalues
View Description Hide DescriptionThe energy variance function U ^{2} is defined in terms of the eigenfunction expansion for a trial wavefunction ψ. The relationship of U ^{2} to certain upper‐ and lower‐bound formulas for the energy and purity functions associated with ψ is discussed. The concurrently allowed values of U ^{2} and the energy function ε fall within a bounded region, the shape of which depends partly upon the Schrödinger equation and partly upon those restrictions imposed by the incompleteness of the basis set used for the representation ψ. A number of exact relationships governing the behavior of ε, U ^{2}, and their derivatives along the boundary curve are worked out. The concept of the derivative wavefunction along the boundary is introduced, and an explicit prescription for its computation is given. Ways and means for the estimation of the true energy eigenvalue from the properties of an imperfect wavefunction are presented and discussed.

Theory of Radiation Chemistry. VIII. Ionization of Nonpolar Liquids by Radiation in the Absence of External Electric Field
View Description Hide DescriptionA theory of separated ion pairs in the x and γ irradiation of nonpolar liquids is presented. In this theory consideration is made of the mechanisms involved in the thermalization of electrons, and it is shown that a very significant portion of the prethermalization electron range occurs while the electron is in the subvibrational energy region (∼0.4 eV to thermal energy). The temperature dependence of the yield of separated charges arises in a perfectly natural manner. ``Thermalization lengths'' turn out to be 80–90 Å. Good agreement with experimental observations is obtained with reasonable values of the three adjustable parameters. The theory is also applied to the special case of ^{37}Ar, where most of the effect is due to 2.4‐keV conversion electrons. Calculated results are in reasonable agreement with experiment in this case. A small temperature effect is predicted.

Vibrational Spectrum of Cyclopropene
View Description Hide DescriptionThe infrared spectra of gaseous cyclopropene and a partially deuterated cyclopropene, and the Raman spectrum of liquid cyclopropene have been determined. The majority of the fundamentals and several overtones and combinations have been assigned. Some force constants based on a simple valence‐force potential function have been calculated.

NMR Studies of Inorganic Fluorides. III. Si_{3}F_{8}
View Description Hide DescriptionA high‐resolution NMR study of octafluorotrisilane, Si_{3}F_{8}, is reported. The chemical shifts of ^{19}F and ^{29}Si, relative to SiF_{4} as a reference, are given. Coupling constants, including in every case the relative sign, are given for isotopic species containing not more than one ^{29}Si atom. The results are compared with the corresponding values for SiF_{4} and Si_{2}F_{6}.

Effective Field Parameters in Iron Mössbauer Spectroscopy
View Description Hide DescriptionRelatively simple computational methods for interpreting Mössbauer spectra, in which there are simultaneously static quadrupole and hyperfine interactions, have been developed. Our explicit calculations are restricted to the case when either the source or absorber is a ``single line'' and the nuclear levels are the same as in the ^{57}Fe 14.4‐keV transition. Experimental spectra for powdered RbFeF_{3} and FeCr_{2}S_{4} have been obtained and are analyzed using these methods. Our results show that although the quadrupole interaction ΔE_{Q} is zero above the transition temperatures of both RbFeF_{3} and FeCr_{2}S_{4} it is rather large below, i.e., in FeCr_{2}S_{4}, ΔE_{Q} =0.78 mm/sec at 77° K and in RbFeF_{3}, ΔE_{Q} =3.00 mm/sec at 4°K. The isomer shift, the effective internal magnetic field, and its orientation with respect to the principal axes of the electric‐field‐gradient tensor in these substances at various temperatures are also obtained.

Calculation of the Barrier to Internal Rotation in Ethane with Improved Exponential Wavefunctions
View Description Hide DescriptionA minimum set of Slater exponential orbitals is used to construct molecular orbital wavefunctions for staggered and eclipsed ethane. The orbital exponents chosen are those which are optimum for methane, rather than those obtained from Slater's rules, as were used previously. The value of the internal rotation barrier is calculated to be 3.5 kcal/mole. Comparison with other calculations indicates that the barrier is fairly insensitive to choice of basis functions and to the value of the total energy.

Raman and Infrared Spectra of the ^{10}BF_{3} and ^{11}BF_{3} Complexes with Dimethyl Sulfide and the Isotopic Exchange of This Complex with BF_{3}
View Description Hide DescriptionThe Raman and infrared spectra of liquid BF_{3}·dimethyl sulfide have been recorded for both the ^{10}B and ^{11}B compounds. Assignments of the observed bands have been made using analogies with those of BF_{3}·dimethyl ether. The isotopic data have been used to calculate theoretical equilibrium constants for isotopic exchange between the complex and BF_{3}. The calculated values are compared with published experimental values.

Uniform Localization of Atomic and Molecular Orbitals. I
View Description Hide DescriptionA general procedure for a nonarbitrary external localization of atomic and molecular orbitals given in the form of a general LCAO expansion is introduced by imposing an extremum principle on the sum of certain local orbital populations which are required to be localized in given regions of space, in particular around atoms or between pairs of atoms in the molecule. The localization, which is uniform insofaras these local electron populations are simultaneously maximized in all the available orbitals, yields well‐defined inner‐shell, lone‐pair and bond orbitals. The orthogonal transformation which maximizes the localization function is obtained through an iterative sequence of 2 × 2 rotations between all N (N − 1)/2 possible pairs of molecular orbitals. Convergence was found to be excellent. The method turns out to be exceedingly simple, the coefficients in the LCAO expansion and the overlap integrals between the basic atomic orbitals only being required, and general enough to be valid for the localization of atomic orbitals as well of molecular orbitals, either for exact LCAO—SCF—MO's or for approximate LCAO—MO's constructed from nonorthogonal as well from orthogonal basic sets. The localized orbitals obtained in this paper starting from some unsymmetrically orthogonalized atomic orbitals and from the minimal‐basis‐set LCAO—SCF—MO wavefunctions given by Ransil for LiH, BH, NH, FH, LiF, BF, CO, Li_{2}, Be_{2}, N_{2}, F_{2} prove to be very close to the energy localized orbitals recently obtained by Edminston and Ruedenberg by maximizing the sum of the orbital self‐repulsion energies.

Infrared Transmission Spectrum and Lattice Vibration Analysis of Some Perovskite Fluorides
View Description Hide DescriptionInfrared absorption spectra of the perovskite fluorides KMF_{3}(M:Ni, Mg, and Zn) and NaNiF_{3} have been measured in the region 700 to 50 cm^{−1} at room temperature and liquid‐nitrogen temperature. Three absorption bands for KMF_{3} were observed and these have been assigned to the f _{1u } lattice modes. A normal‐coordinate analysis of the crystal as a whole has been performed and the interatomic force constants in the crystal have been obtained. The forms of the normal modes of the lattice vibrations have been fully described on the basis of the normal‐coordinate treatment. Vibrational assignments have been supported from the experimental ground (temperature effect) and the theoretical side. The compound NaNiF_{3} reveals a much more complicated spectrum than those of KMF_{3}, which suggests a structure of an appreciable deformation from the regular cubic perovskite. The analysis of the lattice vibrations for the rutile counterparts has been made based on the normal‐coordinate treatment by the use of the force constants transferred from the corresponding perovskite. The result gives another evidence for the lattice vibration assignments of the perovskite fluorides.

Crystal Structure of Ferric Chloride Hexahydrate
View Description Hide DescriptionThe crystal structure of ferric chloride hexahydrate has been determined from three‐dimensional single‐crystal x‐ray‐diffraction data. In the crystals two chloride ions and four water molecules are arranged around each ferric ion to form octahedral trans‐[FeCl_{2}(OH_{2})_{4}]^{+} ions with C _{2h }−2/m symmetry. Fe–Cl and Fe–OH_{2}interatomic distances in the complex ion are 2.30±0.02 Å and 2.07±0.02 Å, respectively. The crystals are monoclinic, space group C _{2h } ^{3}—C2/m, with a=11.89±0.02, b=7.05±0.01, c=5.99±0.01 Å, and β=100.5±0.2°. The unit cell contains two [FeCl_{2}(OH_{2})_{4}]Cl·2H_{2}O units. The arrangement of the [FeCl_{2}(OH_{2})_{4}]^{+} ions, chloride ions, and water molecules in the crystals indicates hydrogen bonding in addition to the electrostatic forces between oppositely charged ions.

Molecular Beam Kinetics: Reactions of K, Rb, and Cs with Br_{2} and I_{2}
View Description Hide DescriptionCrossed‐beam studies have been made of the reactions of K, Rb, and Cs atoms with Br_{2} and of K and Cs with I_{2}. It is found that for all these systems: (1) The reaction cross sections are remarkably large, ≳150 Å^{2}. (2) Most of the alkali halide product recoils into the forward hemisphere with respect to the incident alkali atom beam, with scattering angle θ≲60° (in the center‐of‐mass system). However, there also appears to be considerable intensity (∼20% of the forward peak) throughout the backward hemisphere, 90°<θ<180°. (3) The angular distribution (in the c.m. system) of alkali atoms scattered without reaction falls off much more rapidly at wide angles than for collisions between unreactive molecules of comparable size. (4) The shape of the angular distributions of both the reactive and nonreactive scattering is the same for various alkali metals, but differs appreciably for Br_{2} and I_{2}. (5) Most of the chemical energy released appears as internal excitation of the products. This could include substantial rotational and/or electronic excitation, but other evidence shows that vibrational excitation of the newly formed bond is dominant. All these properties can be accounted for by a model (suggested originally by Polanyi and Magee) which assumes that the attacking alkali atom transfers its valence electron to the halogen at large distances (≳7 Å), so that these are in effect ion‐recombination reactions.

Energy of Interaction between Two Hydrogen Atoms by the Gaussian‐Type Functions
View Description Hide DescriptionThe interaction of two hydrogen atoms in their ground states is investigated with a Hirschfelder—Linnett type of wavefunction in which the exponentials are replaced by Gaussian‐type functions. It is found that these functions do not properly describe the long‐range interaction, although the same functions reasonably approximate the molecular energy near the equilibrium separation. The explicit formulas for the atomic integrals are tabulated.

Raman Effect of Corundum
View Description Hide DescriptionThe Raman effect of corundum (sapphire) was measured with an Ar^{+} laser source. The seven expected Raman active phonons were found and their symmetry characters determined. Assignment of the internal and external vibrations of the crystals was made and the effect of birefringence in the Raman selection rules is discussed.