Index of content:
Volume 43, Issue 2, 15 July 1965

Vibrational—Rotational Angular‐Momentum Coupling in Spherical‐Top Molecules. II. General Zeta Sums
View Description Hide DescriptionGeneral Coriolis zeta sums are derived for all molecules belonging to tetrahedral, octahedral, and icosahedral point groups. For all infrared‐active species, the zeta sum is given by , where m _{0}=1 or 0 depending on whether or not a central atom is present; m is the number of sets of equivalent nuclei on threefold or higher symmetry axes, but not on all symmetry elements; δ_{ r }=1 or 0 depending on whether or not the rigid rotations belong to the infrared‐active representation; and δ_{ g }=1 for Point Group T _{ h } and zero for all other point groups. Several related matters are considered, including the definition of the signs of individual zetas. The application of these zeta sums to the analysis of vibrational spectra is treated briefly, especially with regard to the contours of unresolved bands.

Vibrational Relaxation of HI, 1400°—2300°K
View Description Hide DescriptionThe vibrational relaxation of HI in a mixture of 10% HI in Ar has been studied by following the populations of the four lowest vibrational states as they approach their equilibrium values after the abrupt heating produced by a shock wave. The states v=1, 2, and 3 all relax approximately exponentially with the same rate constant, k _{ v }≅1.0×10^{−13} cc molecule^{−1}·sec^{−1} at 2000°K. As the temperature increases from 1400° to 2300°K, k _{1} approximately triples. This temperature dependence is very much smaller (a factor of ∼10^{−2}) and the rate is very much faster (a factor of 10^{2} to 10^{3} at 2000°K if the relaxation is due to HI—Ar collisions) than the values predicted on the basis of the Schwartz—Slawsky—Herzfeld theory or the empirical correlation of Millikan and White.

Vibration—Rotation Spectra and Structures of Germyl Halides
View Description Hide DescriptionThe rotational constantsA″ and ζ values have been determined by the analysis of the rotational structure of the perpendicular bands of GeH_{3}F, GeH_{3}Cl, GeH_{3}Br, and GeH_{3}I. By combining the microwave and the infrared data, the structural parameters of some of the germyl halide molecules have been refined. A strong rotational perturbation was observed in the GeH_{3} deformation fundamental v _{5} of GeH_{3}Br which has been interpreted as a second‐order Coriolis interaction between two fundamental vibrations (v _{2} and v _{5}) of different symmetry.

EPR Study of the Biphotonic Nature of the Solute‐Sensitized Photodecomposition of Polydimethylsiloxane
View Description Hide DescriptionThe photolysis of solutions of naphthalene in polymeric dimethylsiloxane (PDMS) has been examined by EPR(electron paramagnetic resonance)spectroscopy at 77°K. It was found that the naphthalene solute sensitizes the decomposition of the solvent by a stepwise two‐photon absorption process involving the first triplet state of naphthalene as an intermediate. The absorption of the second photon within the naphthalene triplet manifold of states is followed by an energy transfer process to the polymer which then decomposes. Decomposition occurs via Si–C and C–H bond rupture. The stabilities of the resultant radicals, ≡Si·, CH_{3}·, —CH_{2}·, and H·, which are identified by means of their EPR spectra (except for H· which is not observed at 77°K) are also discussed. The latter species presumably reacts immediately, possibly by a hotatom reaction, with a polymer molecule to form H_{2} and —CH_{2}·. It is shown that the CH_{3}· radical is also unstable at 77°K and decays by a hydrogen abstraction reaction to form CH_{4} and the —CH_{2}· radical with a half‐life of approximately 80 min.

Thermal Decomposition of 2,3‐Dimethylbutane in a Single‐Pulse Shock Tube
View Description Hide Description2,3‐Dimethylbutane has been pyrolyzed in a single‐pulse shock tube. The initial steps appear to involve the breaking of carbon—carbon bonds. At about 1100°K the decomposition mechanism is as follows:[Complex chemical formula]The Arrhenius parameters for the bond‐breaking steps are

^{13}C Nuclear Magnetic Resonance Spectroscopy. VI. Azines and Methyl Azines
View Description Hide DescriptionThe ^{13}C nuclear magnetic resonance spectra of the six known unsubstituted azines, pyridine, pyridazine, pyrimidine, pyrazine, s‐triazine, and s‐tetrazine have been obtained, as well as those of some of their methyl derivatives. The carbon shieldings have been compared with those calculated theoretically, and estimates of the effects of π and σ electron densities and of bond orders are attempted. Reasonably good agreement between theory and experiment is obtained if the σ bonds between carbon and nitrogen are assumed to be very slightly polar.

Probability Tables for Clusters of Foreign Atoms in Simple Lattices Assuming Next‐Nearest‐Neighbor Interactions
View Description Hide DescriptionConcentration dependent probabilities for clusters of impurities of one kind in simple cubic, body‐centered cubic, face‐centered cubic, and hexagonal close‐packed lattice structures are given. Polynomials which give the probabilities of singles, pairs, and different configurations of triads are tabulated for concentration values ranging from 10.0% to 0.01%. The existence of the next‐nearest‐neighbor and nearest‐neighbor interactions between impurities randomly distributed throughout the lattice is assumed. Results obtained by considering only nearest‐neighbor interactions are graphically compared with those of the present paper, and a significant reduction in the probability of singles, pairs, and triads is claimed in the present work. The inclusion of next‐nearest‐neighbor interactions produces a change in the number of single, pair, or triad clusters similar to that caused by increasing the concentration. Among other conclusions, it is noted that, for impurity concentrations below 3%, changes in the cluster probabilities are influenced by the consideration of interactions with more distant neighbors, while for higher concentrations it is wise to consider, in addition, clusters of four or more.

Bounds on the Configurational Integral for Hard Parallel Squares and Cubes
View Description Hide DescriptionUpper and lower bounds on the configurational integral for hard parallel squares and cubes are obtained. These bounds are valid over the entire density range and apply to infinite (thermodynamic) systems. Both the upper bound and the lower bound approach the free‐volume form at high density.
This strong result proves rigorously that the free‐volume form is correct for these systems in the thermodynamic limit.

Calculation of Virial Coefficients. Squares and Cubes with Attractive Forces
View Description Hide DescriptionA general combinatorial formulation of the star integrals occurring in calculations of virial coefficients is presented. The usefulness of the formulation is demonstrated by the exact calculation of the first five virial coefficients for gases of hard parallel squares and cubes with attractive forces.
For these gases the three‐, four‐, and five‐term virial series are examined, and each series is found to have a critical point. Most of the critical properties of these truncated virial series are sensitive to the number of terms included, but the product P_{c}V_{c} remains nearly constant as more terms are added.
It is shown that any two‐ or three‐dimensional square‐well virial coefficient is negative at low temperature. Despite this, the low‐temperature contribution of the complete star integral can be either positive or negative.

Spin Delocalization in Mixed Tetrahedral Ni II Complexes
View Description Hide DescriptionProtonmagnetic resonance spectra of a number of paramagneticNi II chelates of the type NiL_{1}L_{2} where L_{1} and L_{2} are different aminotroponeimine ligands have been examined. The proton resonances show large hyperfine contact interaction shifts due to delocalization of spin density from the metal to the ligand by dπ—pπ bonding. In the series of mixed chelates the amount of spin density delocalized to the different ligands varies markedly. Comparison with the spectra of the symmetric chelates shows that one ligand of each of the mixed chelates gains in spin density at the expense of the other ligand. The effect has been found to depend on the electron withdrawing or donating properties of the ligand substituents. The results for a number of ligands containing substituted phenyl groups have been correlated with the Hammett σ parameters. Two possible interpretations of these results are discussed, one proposed by Lin and Orgel and the other suggested by Jaffe's ideas of competitive π bonding in tetrahedral complexes. The latter is preferred for the Ni II aminotroponeimineates.

Gaussian‐Transform Method for Molecular Integrals. I. Formulation for Energy Integrals
View Description Hide DescriptionThe Gaussian‐transform method for the evaluation of multicenter nuclear‐attraction and electron‐repulsion integrals over one‐electron exponential orbitals is described. The basic formulas for 1s orbitals are developed, and machine methods for their extension to higher orbitals are outlined. Computational techniques for the implementation of the Gaussian‐transform method are given with emphasis on the requirements for accuracy and speed in the calculations. Possible improvements and extensions of the method are discussed.

Gaussian‐Transform Method for Molecular Integrals. II. Evaluation of Molecular Properties
View Description Hide DescriptionThe Gaussian‐transform approach to the evaluation of multicenter molecular integrals is developed for one‐ and two‐electron coordinate operators averaged over a wavefunction which is constructed from one‐electron orbitals composed of exponential basis sets. The general method is outlined and applied to a number of electric‐ and magnetic‐interaction operators. Formulas for these operators are given not only for exponential orbitals but also for Gaussian orbitals, which enter at an intermediate stage in the treatment of the exponential case. The complete analysis, supported by numerical data gathered from test programs, serves to demonstrate that the Gaussian‐transform method represents a possible approach to the determination of polyatomic wavefunctions and their properties.

Thermodynamics of the Rigid Rotor at High Temperature
View Description Hide DescriptionIt is shown that Q_{e} , the partition function for a rigid rotor summed over even levels and Q_{o} , summed over odd levels, have exactly the same asymptotic (power series in σ=ℏ ^{2}/2IkT) expansion. No information as to differences in thermodynamic properties due to spin and statistics can be obtained from this expansion. The exchange partition function, Q_{e}—Q_{o} , is calculated directly and used to give simple expressions for the differences in thermodynamic properties between the para, ortho, and equilibrium cases.

Heteronuclear Spin—Lattice Relaxation in Some Crystalline Aromatic Compounds
View Description Hide DescriptionNuclear spin—lattice relaxation has been studied in some crystalline aromatic compounds, the toluene derivative C_{6}H_{5}CF_{3}, and the xylene derivates m‐ and p‐CF_{3}C_{6}H_{4}CF_{3}, over the temperature interval between −185°C and the respective melting points. The decay of both the ^{1}H and ^{19}F nuclear polarization was investigated by pulse techniques. The relaxation data were supplemented by measurements of the proton and fluorine NMR second moments. Between −160°C and the melting point, the ^{1}H second moment of each compound indicated that the protons were immobile. The ^{19}F second moments indicated the effective reorientation of the CF_{3} group in all three compounds throughout the same temperature range. The relaxation of the ^{19}F polarization was found to occur more rapidly than the corresponding ^{1}H relaxation. Moreover, the relative rates of ^{1}H and ^{19}F relaxation also varied quite considerably with temperature. These results were analyzed by Solomon's treatment of heteronuclear relaxation. Semiquantitative agreement between theory and experiment was achieved for the C_{6}H_{5}CF_{3} relaxation data.

Isotope Effects on Vibrational Transition Probabilities. II. Electronic Transitions of Isotopic Nitrogen, Nitric Oxide, and Oxygen Molecules
View Description Hide DescriptionFranck—Condon factors are given for the major electronic transitions of the normal and stable‐isotope‐labeled molecules N_{2}, NO, and O_{2}, for vibrational levels up to 10 of the v″=0 and v′=0 progressions and for the (1, 1) transition. Appreciable isotope effects on vibrational transition probabilities are found in the O_{2} Schumann—Runge and Herzberg bands, in the O_{2} ^{+} second negative bands, in the NO beta and ``M'' bands, and in the N_{2} Vegard—Kaplan bands. The magnitude of isotope effects on Franck—Condon factors is determined by differences in reduced masses between two isotopic molecules, as well as by differences in equilibrium internuclear distances between the two electronic states involved. The ratio of Franck—Condon factors of the light and heavy molecules decreases in the v″=0 and v′=0 progressions with increasing quantum number. The isotope effect on r centroids is very small.

Mass‐Spectrometric Study of Ions at Near‐Atmospheric Pressure. II. Ammonium Ions Produced by the Alpha Radiolysis of Ammonia and Their Solvation in the Gas Phase by Ammonia and Water Molecules
View Description Hide DescriptionA new mass‐spectrometric method for the study of solvation of ions and of ion complexes is applied to the ammonium ion.
The major ion in the α‐particle radiolysis of NH_{3} is the clustered ammonium ion NH_{4} ^{+}·nNH_{3}. A study of the distribution of these clusters is made at room temperature and in the pressure range 0.05 to 200 Torr ammonia. Clusters up to n=20 can be observed. The intensity distribution of the ions shows that the inner solvation shell contains four molecules. Approximate free‐energy changes for inner‐ and outer‐shell solvation are obtained.
Studies of competitive solvation of the NH_{4} ^{+} ion by water and ammonia molecules confirm the inner four shell. Ammonia is preferentially taken up in the inner shell and water in the outer shell. The higher stability of the ammoniated inner shell requires a very small effective NH_{4} ^{+} radius. This requirement leads to an examination of the structure of the NH_{4} ^{+}·4NH_{3} ion.

Calculation of Absolute Raman Intensities of A _{1} Modes of Molecules and Ions from a Delta‐Function Potential Model
View Description Hide DescriptionA delta‐function potential model of molecular binding is used to derive an expression for α_{∥b }, the parallel component of the molecular polarizability from the region of a chemical bond, and , the derivative of the mean molecular polarizability with respect to a change in a bond length for the A _{1} stretching modes of diatomic and polyatomic molecules and ions. The final expression is , in which g is the delta‐function strength; Z, the effective nuclear charge; σ, the Pauling covalent bond character; a _{0}, the Bohr radius; n, the number of electrons in the bond region; and r is the equilibrium internuclear distance. There is shown to be good agreement between calculated and experimental values of both α_{∥b } and .

Electron Spin Resonance Spectrum of FCO
View Description Hide DescriptionThe electron spin resonance spectrum of the fluoroformyl radical (FCO) has been observed at 4.2°K in solid carbon monoxide. The radical was prepared by reaction between the CO matrix and fluorine atoms produced by in situ photolytic dissociation of fluorine oxide (OF_{2}). The fluorine hyperfine splitting of FCO is very large and approximately axially symmetric: A _{1}/h=1437.5, A _{2}/h=708.2, and A _{3}/h=662.0 Mc/sec. The large hyperfine splitting results from spin polarization of an exceptionally weak CF bond, and is consistent with the theory for the proton hyperfine interaction in HCO. This implies that FCO, like HCO, is a sharply bent molecule in which the unpaired electron occupies an in‐plane or σ orbital, a conclusion which is in agreement with theoretical predictions.

On the Nature of Stimulated Emission in Rigid Organic Solutions
View Description Hide DescriptionA dilute solution of an aromatic amine in a saturated hydrocarbon is frozen to a rigid state in liquid nitrogen and irradiated with ultraviolet light in the absorption band of the amine. The amine undergoes a one‐electron ionization to give its colored radical cation and an electron trapped in the matrix. Subsequent infrared illumination causes a burst of blue‐green luminescence called stimulated emission, which is investigated here. It is found to be a recombination luminescence composed of the fluorescence and phosphorescence bands of the amine, though the phosphorescence appears in much greater proportion than when the amine is excited by ultraviolet light. The kinetics of the two bands are analyzed and it is shown that the phosphorescing state and the fluorescing state are both populated directly by the recombination process, and through the same rate‐determining step. The recombination is also observed as a bleaching of the colored cation, which closely follows the kinetics of the stimulated fluorescence. It is shown that the system possesses electron traps of several different depths, ranging from shallow, thermally ionizable levels to depths of more than 3 eV.

Approach to Simple Exponential Decay in Vibrational Relaxation
View Description Hide DescriptionWhen diatomic oscillators are dilutely dispersed in an inert heat bath, populations of the various vibrational levels in an initial nonequilibrium distribution relax toward thermal equilibrium with a time dependence that is a sum of terms like exp (λ_{ mt}), where λ_{0}=0, all other λ_{ m }<0, and λ_{ m+1}<λ_{ m }. −1/λ_{1} ordinarily corresponds to the experimental relaxation time τ, since this term will dominate at long times. This work investigates cases in which the coefficient of the λ_{1} term, depending on the initial vibrational distribution and the heat‐bath temperature, may vanish or be so small that the final simple exponential decay corresponding to λ_{1} is never reached under experimental conditions.
For harmonic oscillators, if the initial distribution has its first n moments equal to the corresponding moments of the equilibrium distribution, then the first n coefficients in the sum of exponentials will be zero. Furthermore, there will be one or more values of the heat‐bath temperature, independent of the initial distribution, for which the normally dominant exponential decay will be missing in the expression for the time dependence of population in any particular level. Some of these results can be extended qualitatively to anharmonic oscillators and more general systems.