Volume 52, Issue 12, 15 June 1970

New Partitioning Perturbation Theory. I. General Formalism
View Description Hide DescriptionBy the use of partitioning techniques, a general formalism is developed for considering degenerate, almost‐degenerate, and electron‐exchange perturbation problems. In effect, we generalize the Van Vleck–Kirtman approach to arbitrary orders and arbitrary normalization and obtain three types of approximations: In the modified Kirtman treatment the functions through the Nth order are fully normalized and the energies are obtained as the roots of the secular equation. The DE–FOP–VIM approximation is the same except that the normalization of the functions is energy optimized. The Kirtman approximation uses the same functions as the modified Kirtman but the energies are obtained as the roots of a much simpler secular equation which results from a factorization of the original secular equation (except for terms of order ). The Kirtman energies are not upper bounds. Löwdin's formalism is equivalent to the Modified Kirtman with the exception that Löwdin uses intermediate normalization. Electron exchange problems are considered more explicitly in a companion paper with the use of symmetry considerations.

New Partitioning Perturbation Theory. II. Example of Almost Degeneracy
View Description Hide DescriptionA system of two coupled simple harmonic oscillators where many of the energy levels are almost degenerate doublets serves as an excellent “guinea pig” for testing many perturbation techniques including the modified Kirtman, Kirtman, and DE–FOP–VIM treatments discussed by Certain and Hirschfelder in a companion paper. These methods are compared with the “usual” approach to almost‐degenerate problems which makes the zeroth‐order energies of the doublet pair degenerate by a suitable choice of the zeroth‐order Hamiltonian. In addition, four types of Rayleigh–Schrödinger expansions are considered. The best values of the energy are given by the Kirtman treatment. However, the DE–FOP–VIM and the modified Kirtman procedures give values almost as good, and have the added advantage that they give upper bounds to the energy of the states which are considered.

New Partitioning Perturbation Theory. III. Applications to Electron Exchange
View Description Hide DescriptionA new partitioning perturbation technique provides a rigorous derivation and generalization of the Hirschfelder–Silbey formalism for treating electron exchange problems. A new method of solving the first‐order perturbation equation is introduced. The first‐order wavefunction is the sum of the polarization function which describes van der Waals correlations and an exchange function which introduces ionic terms. The exchange function is determined variationally for both the ground‐state H+H^{+} and H+H interactions. In the many‐electron case, the first‐order equation reduces to a set of one‐ and two‐electron equations.

Crystal Structures of the Three Modifications of Nitrogen 14 and Nitrogen 15 at High Pressure
View Description Hide DescriptionWe have determined from x‐ray diffraction photographs that high‐pressure N_{2} is tetragonal with two molecules per unit cell in special position of space group . At an average pressure and temperature of 4015 atm and 20.5°K, respectively, the unit cell dimensions are and , giving a molar volume in good agreement with that from measurements. The N_{2} solid modification, which is contiguous with the melting curve, remains hexagonal up to at least 4125 atm and 49°K where the unit cell constants are and . Over the pressure range investigated, the ratio is very close to the ideal value for closest packing of hard spheres. The atomic positions in hexagonal N_{2}, which are known to be highly disordered at low pressure, show no evidence of ordering at the highest pressures studied. The third allotrope, N_{2}, is cubic at 3785 atm and 19.6°K with four molecules in a unit cell 5.433 Å on a side. Both the and space groups, which have been reported at zero pressure, appear to be spatially possible at limiting high pressures for N_{2}. However, from our diffraction measurements on the cubic solid at all pressures, we were unable to prove the existence of the structure. The measurements on pure ^{30}N_{2} show that this isotope also exists in the same three solid modifications as ^{28}N_{2} with cell dimensions that are similar for both isotopes. However, the transition to N_{2} at 20°K for the mass‐15 isotope occurs 400 atm lower than that for the mass‐14 isotope.

Ionic Collision Processes in Water Vapor
View Description Hide DescriptionSome ionic collision processes in water vapor have been studied by the techniques of high‐pressure single‐source mass spectrometry. Rate coefficients for reactions resulting from collisions of H_{2}O^{+} with H_{2}O, and of OH^{+} with H_{2}O have been studied as a function of primary‐ion translational energy over the energy range of 0–8 eV. For purposes of calibration and comparison, the reaction leading to CH_{5} ^{+} production in methane gas has also been studied over the same primary‐ion energy range. The rate coefficient for H_{3}O^{+} production from H_{2}O^{+} / H_{2}O collisions was found to drop from a value of 26 × 10^{−10} cm^{3} molecule^{−1}·sec^{−1} for thermal ion reactions to a value of less than half of this for ions with a maximum energy of 4 eV. H_{3}O^{+} production from OH^{+} / H_{2}O collisions was found to proceed with a rate coefficient of 20 × 10^{−10} cm^{3} molecule^{−1}·sec^{−1} for ions of thermal energy, but this coefficient had dropped to zero as the maximum ion energy was increased to 0.8 eV. Evidence is presented to support the contention that although H_{3}O^{+} production decreases as the OH^{+}energy increases, the rate of removal of OH^{+} continues with high cross section The results indicate that in the ion energy region above 0.8 eV, OH^{+} is removed exclusively by charge transfer to H_{2}O.

Effect of Pressure on Naphthalene‐d_{8} Phosphorescence in Durene Crystals
View Description Hide DescriptionThe phosphorescence lifetime of C_{10}D_{8} in durene mixed crystals has been studied in the temperature range 77–320°K and under pressures of 0–30 kbar. Matrix compression to 30 kbar shortens the triplet lifetime at 77°K about 20%. At higher temperatures where thermally activated quenching is evident, the triplet decay is very sensitive to pressure and becomes nonexponential with increasing pressure. Compression decreases the activation energy and high concentrations of defects increase the pre‐exponential factor. The phosphorescence quenching is ascribed to charge‐transfer interaction with the host molecules at structuraldefects in the crystal lattice.

Shock Wave Compression of Benzene, Carbon Disulfide, Carbon Tetrachloride, and Liquid Nitrogen
View Description Hide DescriptionHugoniot data to several hundred kilobar have been obtained for benzene, carbon disulfide, carbon tetrachloride, and liquid nitrogen. Standard high explosive techniques were used for generating the shock waves. Experimentally measured quantities were transformed to pressure and volume data by the impedance match method. The shock‐particle velocity data for the liquids are described by a linear relationship, however, a quadratic in particle velocity also provides an adequate representation of the data for carbon tetrachloride and liquid nitrogen. Benzene undergoes a transition at 133 kbar and carbon disulfide at 62 kbar. These transitions are accompanied by a volume decrease of approximately 16%. A double shock‐wave structure, observed in many solids which undergo a transition, was not observed in benzene and carbon disulfide. There is some evidence that carbon tetrachloride and liquid nitrogen undergo a transition at 165 and 135 kbar, respectively. Hugoniot curves calculated from a Lennard‐Jones and Devonshire (6‐9) and a modified Buckingham exp‐6 intermolecular potential fit the liquid nitrogen experimental Hugoniot curve between 20 and 170 kbar.

Hyperfine Structure Constants of HF and DF
View Description Hide DescriptionThe radio frequencyspectrum of HF and DF is measured by the molecular‐beam electric resonance method. The measurements are in the lowest vibrational state and first rotational state . The constants obtained are: The electron coupled spin–spin interaction, .

Nuclear Quadrupole Coupling Tensors of ^{27}Al in Andalusite (Al_{2}SiO_{5})
View Description Hide DescriptionThe nuclear quadrupole coupling tensors of ^{27}Al at the two crystallographically nonequivalent Al^{3+} sites in andalusite, Al_{2}SiO_{5}, have been determined from nuclear magnetic resonance measurements. For this, the Hamiltonian matrix for the mixed magnetic and electrostatic interaction was diagonalized and a minimization technique based on the least‐squares principle was used. The quadrupole coupling constants and asymmetry parameters are: The site assignment which cannot be made from NMR data alone is based on point charge calculations (point multipole model). Previous assignments concluded from EPR data of Fe^{3+} and Cr^{3+} impurities at the Al^{3+} sites are confirmed. The principal axes of the magnetic Fe^{3+} and Cr^{3+}tensors deviate from the ^{27}Al tensor axes by 1°–10°.

Electron Injection into Quinone Crystals
View Description Hide DescriptionPhotostimulated electron injection from an ethanol or water electrode into single crystals of tetrahalo‐substituted p‐benzoquinones was observed. The electron transfer processes involve the excited quinone molecules. By the addition of appropriate electron donor molecules such as p‐phenylenediamine to the electrode,electron injection in the dark could be observed. Excited chlorophyll molecules also caused electron injection to be enhanced.

Gol'danskii–Karyagin Effect in Dimethyl Tin Difluoride
View Description Hide DescriptionThe temperature dependent asymmetry in the intensity of the two components of the Mössbauer resonance doublet in dimethyl tin difluoride can be related to the mean‐square amplitudes of vibration parallel and perpendicular to the cylindrical molecular symmetry axis, and hence to the anisotropy of the Mössbauer–Lamb faction (the Gol'danskii–Karyagin effect). With an assignment of the and transition in the Mössbauer spectrum based on a simple bond character description, an asymmetry ratio of 0.78 ± 0.06 is derived from the Mössbauer data. This is in good agreement with the value derived from precision x‐ray diffraction data on (CH_{3})_{2}SnF_{2} and constitutes an independent check on the presence of the Gol'danskii–Karyagin effect in such solids.

Test of the Monte Carlo Method: Fast Simulation of a Small Ising Lattice
View Description Hide DescriptionA very fast stochastic procedure is used to generate samples of configurations of a 4 × 4 periodic Ising lattice in zero field. Running on the IBM 7094, we require only 15 μsec to process each site (cf. Yang who required 300 μsec on the 7090) and hence we generate 4000 completely new configurations each second. Our main results are based on samples of 10^{6} configurations at each of 10 temperatures; we also took samples of 10^{7} configurations at three temperatures. The 4 × 4 lattice can be solved exactly without much difficulty. Hence our data give information about the Monte Carlo method itself, especially its rate of convergence. We define the statistical inefficiency (SI) in a variable as the limiting ratio of the observed variance of its long‐term averages to their expected (Gaussian) variance. (Thus, if the SI is 3, then averages of the variable taken over Monte Carlo runs of three million configurations will be as accurate as averages over one million configurations drawn randomly from the true ensemble. The SI accounts for correlations between configurations closely following one another in the Monte Carlo run.) We find that for this lattice the SI in energy never exceeds , and that its maximum occurs slightly above the temperature which is critical for the infinite lattice. We confirm earlier statements that the influence of the initial configuration is lost very quickly, except when two phases coexist.

Magnetic Susceptibility of IrO_{2} and RuO_{2}
View Description Hide DescriptionWe have measured the magnetic susceptibility of IrO_{2} and RuO_{2} in the temperature range 4.2–300°K using the Faraday technique. We find for RuO_{2} at 300°K and , and for IrO_{2} at 300°K and . Our results are discussed and compared with the behavior of the susceptibility of some of the transition metals. The temperature dependence of in RuO_{2} is quite similar to that for some transition metals. The temperature dependence of in IrO_{2} below 30°K is quite different possibly owing to trace impurities.

Some Ion–Molecule Reactions of H_{3} ^{+} and the Proton Affinity of H_{2}
View Description Hide DescriptionThe flowing afterglow technique has been used to study the reactions of H_{3} ^{+} with a number of neutral reactants at thermal energies. Proton transfer was the only primary reaction observed with N_{2}, CO, CO_{2}, N_{2}O, NO, CH_{4}, C_{2}H_{2}, H_{2}O, and NH_{3}. Both proton transfer and dissociativecharge transfer were observed with C_{2}H_{4} and C_{2}H_{6}, while dissociativecharge transfer is the exclusive primary process with NO_{2}. Secondary reactions were observed with NO, C_{2}H_{6}, C_{2}H_{4}, and C_{2}H_{2}. Cluster ions were formed between NO^{+} and NO_{2} and H_{2}O, between H_{3}O^{+} and H_{2}O, CO_{2}, and CO, and between NH_{4} ^{+} and NH_{3} and H_{2}O. Proton transfer was also observed between HN_{2} ^{+} and CO_{2}, N_{2}O, CH_{4}, and H_{2}O, and between HO_{2} ^{+} and H_{2} and N_{2}. Rate constants were obtained for these reactions and are discussed. Limits could be placed on the proton affinity (P.A.) of H_{2} from the failure to observe rapid proton transfer to O_{2} and the observation of proton transfer to N_{2}. These indicate 4.2 < P.A. (H_{2})< 4.7 eV with a recommended value of 4.4 eV. The technique can be used to measure relative proton affinities of gases.

Correlation Effects on Transition Energies in the Series of Linear Polyenes. III Dynamical Correlation Effects
View Description Hide DescriptionAn optimization of the atomic orbitals is rederived for the ground‐state energy of conjugated systems. Within some reasonable assumptions, this optimization (analogous to that proposed by Silverstone and Joy) allows the orthogonalized atomic orbitals to be considered as v rtual orbitals in the CI calculation when one starts from a SCF calculation performed in the minimal basis set of optimized atomic orbitals. The reorganization of the MO in the excited state leads to a spatial expansion in the singlet state and a spatial contraction in the triplet state. But this effect is less and less important when the dimension of the system increases, and the corresponding energetic correction decreases as . A less pronounced effect is obtained on the singly occupied orbital; the doubly occupied MO's are not significantly modified in the singlet state. The role of the atomic orbitals in the correlation effects on the transition energies is much more important. It is not mainly due to the monoexcited configurations (which only give a correction proportional to ) but to the doubly and triply excited states: Their correction tends towards a constant value which has been estimated.

Vibrational Spectra and Structure of Oxalyl Chloride in the Crystalline and Fluid States
View Description Hide DescriptionThe vibrational spectrum of oxalyl chloride, [COCl]_{2}, has been recorded between 33 and 4000 cm^{−1}. The infrared spectra of the oxalyl chloride molecule have been examined in the solid, liquid, and gaseous states. The Raman spectra of the solid and liquid have also been observed, and qualitative depolarization ratios have been measured. The vibrational spectrum of the crystalline material has been interpreted on the basis of molecular symmetry and space group symmetry. All 12 of the normal vibrations have been assigned, and the barrier to internal rotation around the C–C bond has been obtained. Nine bands appear in the infrared and Raman spectra of the liquid/gaseous states which do not appear in the spectra of the solid. In light of depolarization data and the frequencies for the vibrations of the trans isomer, these bands are interpreted as arising from a cis rotamer. A temperature study was made in order to determine the relative stability of the rotamers. The trans isomer was found to be 2.2 kcal/mole more stable than the cis form. A rough estimate of the equilibrium mixture at room temperature based on intensities and an assumed equilibrium constant gives a value of 15%–20% for the cis isomer.

Vibrational Spectra and Structure of Small Ring Molecules. XVI. Vibrational Analysis and Ring‐Puckering Vibration of 1‐Pyrazoline
View Description Hide DescriptionThe infrared spectrum of gaseous 1‐pyrazoline has been measured from 33 to 4000 cm^{−1}. The infrared and Raman spectra of the corresponding liquid sample have also been recorded. A vibrational assignment of the fundamentals is proposed which is consistent with the equilibrium configuration. The assignment is based on the gas‐phase band contours, the depolarization values, and group frequency correlations. A series of 13 pronounced branches was observed in the far‐infrared spectral region, and they have been attributed to the strongly anharmonic ring‐puckering vibration. Although the far‐infrared frequencies could be reproduced by two different potential functions, a double minimum potential of the form where is the reduced ring‐puckering coordinate provides the most satisfactory interpretation of all the spectral data. The height of the inversion barrier is calculated to be 113 cm^{−1}, and the equilibrium angle between the two dihedral planes of the puckered ring is 19.7° ± 1.0°. The results are compared with those obtained on cyclopentene.

Spectra and Structure of Small Ring Compounds. XIX. Vibrational Analysis and the Barrier to Pseudorotation of Germylcyclopentane
View Description Hide DescriptionThe infrared spectrum of germylcyclopentane in the gaseous state has been recorded from 4000 to 33 cm^{−1} and that of 1, 1‐dideutero‐1‐germylcyclopentane has been recorded from 4000 to 250 cm^{−1}. The Raman spectra of the two liquids have been recorded and depolarization values determined. The data rule out the planar configuration for the germylcyclopentane molecule and are shown to be consistent with the twisted molecular structure. The 39 normal modes have been assigned on the basis of their depolarization values, infrared band contours, isotopic shift factors, band intensities, and “group frequencies.” The ring‐bending mode was found at 113 cm^{−1} in the vapor phase of the “light” compound. The ring‐twisting mode for the and compounds was found at 273 and 269 cm^{−1}, respectively, in the Raman spectrum. The 113‐cm^{−1} band in the light compound was found to be the first of a series of branches running to lower frequency. This series has been interpreted in terms of a relatively high barrier to pseudorotation. From midinfrared sum bands a similar series of transitions were obtained for the pseudorotation of the compound. A potential function of the form was found to fit nine observed far‐infrared transitions of the ring‐puckering mode. The calculated barrier to pseudorotation was 5.9 ± 0.1 kcal/mole for the “light” compound, and the spectroscopically derived parameter was found to be 18.7 × 10^{−40} g·cm^{2}. The barrier in the corresponding compound is estimated to be 6.0 ± 0.3 kcal/mole. The barriers are considerably higher than one might expect from existing theories and data on torsional barriers.

Ozone Ultraviolet Photolysis. I. The Effect of Molecular Oxygen
View Description Hide DescriptionTo clarify the role of molecular oxygen in the photolytic decomposition of ozone,measurements of mixtures of ozone with helium, nitrogen, or oxygen were analyzed by the intermediate quantum yield method which separates effects due to fast and slow reactions by measuring the fast components shortly after flash photolysis. Analysis of the results gives the following rate constants (in liters/mole·second): . The efficiency of (4d) for forming is found to lie in the range . As a consequence of the high value of , which was previously neglected, rate constants reported previously should be revised as follows: . The quoted error limits are those which represent the fit of the data to the assumed mechanism with appropriate allowances for uncertainties due to minority processes.

5142‐Å Transition in Thiophosgene ; Rotational Analysis and Excited‐State Structure
View Description Hide DescriptionRotational structure is observed in the 2^{1} _{0}3^{1} _{0}4^{1} _{0} vibronic band of the lowest singlet transition of thiophosgene (5142 Å). Computer analysis gives three excited‐state moments of inertia, from which, assuming a value for the C–S bond length, an excited‐state structure may be determined.