Volume 55, Issue 10, 15 November 1971

Germanium‐Hydrogen‐Lithium Center in α‐Quartz
View Description Hide DescriptionA new center, denoted by GeHLi_{2}, has been observed by EPR to be present in alpha‐quartz containing germanium, after room temperature x irradiation. The spin Hamiltonian at 8909 MHz and 300°K has been measured, yielding the Zeeman splittingtensorḡ and the hyperfine coupling tensorsĀ (^{73}Ge),Ā (^{1}H), Ā (^{7}Li_{1}), and Ā (^{7}Li_{2}). From the principal values and axis directions, a model for the center of the form Ge^{3+}H^{−}(Li^{+})_{2} has been derived. This postulates germanium to be present substitutionally at a silicon site, with the hydride and two lithium ions occurring interstitially nearby. The unpaired electron is thought to be in a Ge orbital , with and , with considerable spin density also at the hydrogen. The center may be formed from a diamagnetic precursor Ge^{2+}(Li^{+})_{2} by reaction with a hydrogen atom.

One‐Center r_{ij} Integrals Over Slater‐Type Orbitals
View Description Hide DescriptionExpressions are derived for the integrals which arise in calculations of atomic wavefunctions of four or more electrons, utilizing the method of explicit introduction of interelectronic distances r_{ij} into a configuration interactionwavefunction (subject to the restriction of at most one r_{ij} per configuration). The approach followed in the derivations is similar to one followed by Öhrn and Nordling for three electron integrals; however, in extending the Öhrn and Nordling scheme to four electrons for a basis of s, p, and d Slater‐type orbitals, numerical snags are encountered which have been obviated by an Euler transformation on certain of the auxiliary integrals.

Approximate Numerical Hartree—Fock Method for Molecular Calculations
View Description Hide DescriptionCalculations are presented which show that the atomic orbitals which result from approximate numerical Hartree—Fock calculations (by the Xα method) are as close to the Hartree—Fock limit for atoms as are those calculated using a double‐zeta basis. Arguments are given which show that the exchange is treated with sufficient accuracy by the Xα method. With the additional ``muffin‐tin'' approximation, which is widely used in solid state calculations, the ``multiple scattering'' formalism can be used for molecules to solve this model Hamiltonian without any further approximation. The exchange is treated with sufficient accuracy, therefore this approach should give the electronic energies as well as the usual type of ab initio calculation, whenever the ``muffin‐tin'' approximation is good, but with 2 or 3 orders of magnitude less computational time.

Diffusivity of ^{3}He, ^{4}He, H_{2}, D_{2}, Ne, CH_{4}, Ar, Kr, and CF_{4} in (C_{4}F_{9})_{3}N
View Description Hide DescriptionAn earlier paper from this laboratory reported that diffusion coefficients of gases in CCl_{4} multiplied by their molecular cross sections are the same for gases heavier than Ne, but that they increase linearly from D_{2} to ^{4}He with the square of the de Boer quantum parameter A^{*}. The present study of gases in (C_{4}F_{9})_{3}N includes ^{3}He. For relative cross sections we use, instead of uncertain values of σ^{2}, the power of the critical volumes, V_{c} , accurately known from critical densities. Measured values conform to the equation . Diffusion coefficients in CCl_{4}, multiplied by yield . The relative steepness of the two quantum lines is , exactly the same as the ratio of the internal pressures of the two liquids, 3350/2160.

Trajectory Studies of Atomic Recombination Reactions
View Description Hide DescriptionThe radical molecule complex (RMC) theory for bromine atom recombination in the presence of an inert gas M has been tested by computing 3D classical trajectories for collisions. The dissociation energy of BrM was taken to be of the order of one kcal/mole. Monte Carlo methods were used to select random initial conditions of the BrM molecules with bound and metastable states included. The largest cross sections for the recombination reaction were with deep potential wells and small collision diameters for the interaction. Heavy third bodies were slightly more effective than light third bodies in promoting the reaction. The velocity averaged cross sections decreased with temperature as T ^{−0.4} for M=Xe, T ^{−0.6} for M=Ar and T ^{−0.9} for M=He. Recombination rate constants,k_{r} , were calculated at 300, 600, 1000, and 1500°K. For argon, with a well depth of 1.0 kcal/mole, the absolute magnitude and temperature dependence of k_{r} agreed with experiment. For helium and xenon agreement of the calculated and experimental k_{r} values at 300°K was obtained with the same well depth, 1.0 kcal/mole. The temperature dependence of k_{r} was reasonable for Xe but for He the calculated value of k_{r} at 1000°K was more than a factor of two smaller than the experimental value. The limitations of the RMC model are discussed in the light of these findings. The energy distributions for the bromine molecules formed in the recombination reaction show that the mean total internal energy is close to the dissociation energy but that there are wide spreads of rotational and vibrational energies; recombination does not take place predominantly into a few vibrational levels near the dissociation limit. The trajectory results are compared with the findings of Blake, Browne, and Burns [J. Chem. Phys. 53, 3320 (1970)] who used a Sutherland potential model for the interaction.

Optical and Magnetic Studies of Tripositive Thulium in Octahydrated Sulfate Crystals
View Description Hide DescriptionThe optical absorptionspectra of single‐crystal and Tm^{3+} in have been studied in the range from 2500 to 8000 Å at 4.2 and 77°K. Nine [SL]‐J levels were identified including ^{3} P _{2,1,0}, ^{1} I _{6}, ^{1} D _{2}, ^{1} G _{4}, ^{3} F _{2,3,4}. The vibronic, electronic, and temperature‐dependent absorption lines of these multiplets were identified and tabulated. The spectra were studied as a function of magnetic field strength and as a function of orientation in the magnetic field.Zeemanabsorption, paraelectric resonance, and zero‐magnetic field optical absorptionspectra all indicate a nearly accidental degeneracy in the ground state of tripositive thulium in the octahydrated sulfate salts. The magnetic moment was found to lie in the rectangular plane formed by the crystal's macroscopic habit and inclined at an angle of 46° with respect to the crystal's major habit direction. The crystalline lattice of these salts was found to possess magnetically inequivalent sites. The optical spectra arising from thulium ions in both sites are indistinguishable, but the application of an external magnetic field revealed that the local ionic magnetic moments in these two kinds of sites are inclined at a relative angle of approximately 60°. The observed splitting factor for thulium ions in both sites was found to be 13.4 Lorentz units. The principle features of the magnetic properties of these salts were confirmed by anisotropicparamagneticsusceptibilitymeasurements.

Location of Energy Barriers. IV. Effect of Rotation and Mass on the Dynamics of Reactions
View Description Hide DescriptionIn Paper I of the present series a study was made of the effect of barrier location on the dynamics of thermoneutral reaction, for which the atomic masses were m _{A}=m _{B}=m _{C}. Two contrasting potential‐energy hypersurfaces were used; on ``surface I'' the crest of the 7 kcal mole^{−1} energy barrier was slightly displaced into the entry valley of the collinear energy surface, whereas on ``surface II'' the crest of the barrier was displaced by the same amount into the exit valley. Precisely the same potential‐energy hypersurfaces have been used in the present work as were used in Paper I. The present work was undertaken to examine the effect (a) of the inclusion of a small but significant amount of rotational energy in the reagents, and (b) of a change in reagent masses from the extreme case to the opposite extreme . [These mass combinations were identified as extreme cases, the former giving rise to the ``light‐atom anomaly'' and the latter to a maximum of ``mixed energy release,'' in earlier work, see J. Chem. Phys. 44, 1168 (1966)]. The qualitative generalizations introduced in Paper I are found to remain valid despite the introduction of variables (a) and (b), above. Of these generalizations the most important is that reagent translational energy favors reaction on surface I, whereas reagent vibration is the most favorable to reaction on surface II. If barrier location on the ``diagnostic'' collinear potential‐energy surface is to be used as an approximate quantitative guide to reactiondynamics, then the diagnostic surface should be the scaled collinear surface appropriate to the particular mass combination.

Spin—Spin Coupling in Magnetically Condensed Complexes. XII. The Ground State of Tetrakis (N, N′‐dimethylglyoximato) dicopper (II)
View Description Hide DescriptionThe ground state of tetrakis (N, N′‐dimethylglyoximato) dicopper (II) is shown to be of triplet multiplicity with the first excited state being a singlet, at 29.8 cm^{−1} higher in energy. EPR measurements confirm the existence of spin—spin interactions, and a value of D=0.0340 cm^{−1} was obtained from the half‐field line, H _{min}. The other g values obtained from the triplet state spectra were and . Cryomagnetic measurements in the low‐temperature range (4.2–55°K) in conjunction with a best fitting procedure yielded the following values for the magnetic parameters: and . A superexchange mechanism via the σ orbitals of the bridge is proposed to account for the experimental findings. This mechanism includes both intra‐atomic direct exchange and interatomic electron transfer.

Pressure‐Consistent Integral Equations
View Description Hide DescriptionThe behavior of the Hurst and Rowlinson—Carley—Lado pressure‐consistent equations for the Lennard‐Jones (6–12), hard‐sphere, and Gaussian potentials and their dependence on the adjustable parameters m and φ are discussed. Numerical solutions of the Hurst and Rowlinson—Carley—Lado equations are compared with the Percus—Yevick, PY2, hypernetted chain, and Monte‐Carlo results. It is shown that the pressure‐consistent equations are more satisfactory for the hard‐sphere potential than the Lennard‐Jones potential.

Moments of NMR Absorption Lines from the Free Induction Decay or Echo of Solids
View Description Hide DescriptionA new method is presented for determining the moments of nuclear magnetic resonance absorption lines from the shape of either the free induction decay or that of the echo. Unlike previously used techniques, this method does not require the assumption of an analytic function for the line shape or the fitting of the experimental decay with a polynomial. A fast, suitably precise and numerically stable algorithm has been developed for performing the integration required by the new method.

Water Cluster Formation Rates of NO^{+} in He, Ar, N_{2}, and O_{2} at 296°K
View Description Hide DescriptionReaction rates of NO^{+} and its hydrates, , with water were measured in a flow system. The mechanism for conversion of NO^{+} hydrates to H_{3}O^{+} hydrates was confirmed, and rate constants for the sequence of six clustering, redissociation, and rearrangement reactions were determined for each of the four carrier gases He, Ar, N_{2}, and O_{2}.

Non‐Steady‐State, Hot Wire, Thermal Conductivity Apparatus
View Description Hide DescriptionA non‐steady‐state, hot wire apparatus has been constructed to measure the absolute or relative thermal conductivities of fluids. With the use of a four‐lead bare wire probe, a precision of 0.1%, and an absolute accuracy of have been obtained. A quartz‐coated film sensor is used to obtain relative thermal conductivity data for salt water solutions with a precision of 1% and an over‐all accuracy of . A comparison is made with experimental data available from the literature. For toluene, a comparison is made with the extrapolated values of Poltz and Jugel from which errors due to radiation have been eliminated for the parallel plate apparatus. The values agree within experimental error.

Low‐Frequency Vibrational Light Scattering in Viscous Liquids
View Description Hide DescriptionThe theory of Raman scattering from the vibrations of amorphous materials is applied to the spectra of B_{2}O_{3}glass and its melt. Experimental evidence is obtained indicating that low frequency scattering in the melt liquid is also due to first order scattering from intermolecular vibrational states. The relationship among several scattering mechanisms in liquids is discussed.

Vibrational Frequencies and Force Constants for Tetrahedral (X=Cl, Br, and I) in Melts
View Description Hide DescriptionRaman spectra are reported for the species present in melts (X=Cl, Br, and I) with X^{−1}/Mg^{+2} mole ratios near 4.0. The observation of one polarized band and three depolarized bands for each halide melt is consistent with the existence of the tetrahedral complexes , , and . All the observed frequencies are calculated within 1 cm^{−1} using a Urey—Bradley force field which consists of an stretching constant, an bending constant, and an repulsion constant.

Variational Methods in the Wave Operator Formalism. A Unified Treatment for Bound and Quasibound Electronic and Molecular States
View Description Hide DescriptionThe wave operator formalism of Löwdin, heretofore used to describe states belonging to the discrete energy spectrum, has been extended to unify the treatment of bound and quasibound (or decaying) states. The approach makes use of an arbitrary reference function that may be chosen to approximate the physical state at short distances. Real and complex eigenvalues are obtained, respectively, for bound and quasibound states from an implicit equation, valid for all coupling strengths. Resonance positions and linewidths are explicitly independent of energy. Variational principles of the Lippmann—Schwinger type are presented which apply to states with either bound‐state or decay boundary conditions. Particular cases leading to minimization or maximization principles for real energies are discussed. The formalism is considered in connection with decaying electronic states of atoms and decaying molecular states.

Electronic Splitting between the ^{2} B _{1} and ^{2} A _{1} States of the NH_{2} Radical
View Description Hide DescriptionTheoretical calculations are reported for the ground and first excited states of NH_{2}. A contracted Gaussian basis of four s, two p, and one d functions is centered on the nitrogen atom, while for hydrogen two s and one p functions are used. Both self‐consistent‐field (SCF) and multiconfiguration first‐order wave‐functions have been computed, the latter using the iterative natural‐orbital method. Two new theoretical ideas were tested and found useful: (a) Bunge's partitioning of degenerate spaces and (b) a procedure for generating uniform sets of starting orbitals for multiconfiguration calculations. For the ^{2} B _{1} state the SCF, CI, and experimental geometries are θ=105.4°, r=1.019 Å; θ=102.7°, r=1.055 Å; , . The analogous results for the ^{2} A _{1} state are θ=141.9°, r=0.997 Å; θ144.7°, r=1.010 Å; , . For the upper ^{2} A _{1} state the barrier to linearity is 1370 cm^{−1} in the SCF approximation, 1030 cm^{−1} from the correlated wavefunctions, and experimentally. The ^{2} B _{1}—^{2} A _{1} splitting T _{e} is predicted to be 12 800 cm^{−1} (SCF) and 14 500 cm^{−1} (CI), whereas the experimental value is thought to be . Potential curves are shown and electronic structure considerations discussed.

Irradiation Damage and Semiconducting Properties of CdF_{2}:Eu
View Description Hide DescriptionThermoluminescence data have been used to unravel the fluorescencespectrum of Eu^{3+} in the insulating . Optical absorption and EPR measurements of semiconducting CdF_{2}:Eu are the bases of a model of this semiconductor.

Kinetic Salt Effects on the Aquation Reaction of the Azidopentaaquochromium (III) Ion and Predictions of the Mayer Theory
View Description Hide DescriptionThe rate of the reaction of aquation of the azidopentaaquochromium (III) ion has been measured at two different concentrations of hydrogen ion in the presence of a number of salts. The values of k _{1} and k _{0} of the equationwere calculated and both show positive salt effects and obey the Olson‐Simonson rule. Calculations performed using the Mayer theory in the approximation `` '' have shown that at high dilution both these effects can be rationalized using appropriate values of the distances of closest approach. The possibility of using this form of the Mayer theory for extrapolation purposes is suggested. The use of different distances of closest approach for different pairs of ions does not lead to any inconsistency.

On a Generalized Einstein Theory for the Thermodynamics of Planar Surfaces and Microcrystallites
View Description Hide DescriptionWe present a generalized Einstein theory to predict the thermodynamic properties of planar surfaces and microcrystallites which Nishioka et al. have obtained from numerical normal mode calculations. An important aspect of our model is that it identifies the important physical features governing the structure of the vibrational free energy as a function of microcrystallite size.

Energy‐Transfer Processes in Monochromatically Excited Iodine Molecules. V. Rotational Energy Transfer in Argon‐Excited I_{2}
View Description Hide DescriptionRotationally resolved energy‐transfer rates have been measured for I_{2} excited to and 15 of of the state by the argon laser line at 5145 Å, for accompanying changes in v′ of 0, , , and , in collisions with ground‐state I_{2}, H_{2}, He, and Ne. In all of these collisions, there is a persistence of rotational state, being favored; however, broader distributions are found, as expected, for collisions with larger Δ v's or with heavier collision partners. The microscopic rate constants are asymmetric to , as expected for .