Volume 56, Issue 2, 15 January 1972

Theory of Optical Rotation by Helical Polymers
View Description Hide DescriptionThe theory of the optical rotation of infinite single‐stranded helical polymers is developed using the multipole Hamiltonian and the exciton approximation. The optical rotation formulas are obtained without using any sum rules. Contributions to the optical rotation from electric dipoles, magnetic dipoles, and electric quadrupoles of the monomers are considered explicitly.

Lifetimes of the , 1, 2 Levels of the A ^{2}Σ^{+} Electronic State of NO
View Description Hide DescriptionThe lifetimes of the , 1, 2 levels of the A ^{2}Σ^{+} state of NO have been measured by monitoring 17 transitions of the NO γ bands. A new cold cathode discharge tube was used in conjunction with the delayed coincidence technique for measurement of lifetimes. A nonlinear least squares program was used for data analysis in order to estimate cascade contributions. Values obtained for lifetimes are , , and . Using Morse potential Franck—Condon factors, the electronic transition moments are calculated to be 0.195, 0.197, and 0.208 a.u.

Path Integrals and Semiclassical Tunneling, Wavefunctions, and Energies
View Description Hide DescriptionThe semiclassical limit of Feynman path integrals is investigated in order to determine those classical trajectories which contribute to tunneling processes. The semiclassical bound state energies, wavefunctions, and scattering phase shifts are directly recovered from the poles and residues of the semiclassical Green's function in energy space. Some extensions to cases of tunneling and bound states for multidimensional nonseparable potentials are discussed.

Infrared Matrix‐Isolation Studies of BrCN and CICN: Fermi Resonance and Dimer Structure
View Description Hide DescriptionThe infrared spectra of CICN and BrCN in argon and krypton matrices at 20°K have been investigated. There is good evidence that for the monomeric species the bending mode is split by the matrix environment and that the first overtones of these two bending components form a Fermi resonant triad with the v _{1} fundamental. The frequencies and intensities of the unperturbed levels and the Fermi coupling constants have been calculated. The absorption bands due to dimeric species are consistent with a linear or nearly linear configuration for the dimer.

ESR Studies of Unsubstituted Cyclic Nitroxides in Solids
View Description Hide DescriptionA new photochemical method of producing nitroxides from nitramines is reported. Solutions of un‐substituted cyclic nitroxides from nine nitramines were studied in the ESR and splitting constants established. For two cases, single‐crystal studies of nitroxides produced in situ by this reaction permitted neighboring hydrogen interactions with the nitroxide electron to be compared with the nitrogen interaction.

Molecular Dynamics of Two‐Dimensional Gases and the Formation of Bound States
View Description Hide DescriptionMolecular‐dynamics programs which can solve equations of motion for dilute and moderately dense gases have been developed. In the molecular‐dynamics calculation for two‐dimensional argon gas, the formation and dissociation of classical bound pairs (dimers) have been observed. The chemical reactionrate constant for this process has been determined and compared with existing classical theoretical models.

On the Symmetry of the Hydrogen Bonds in Ice VII
View Description Hide DescriptionThe interaction of the hydrogen atoms with nearest neighbor oxygen atoms in the hydrogen bonds of ice VII are approximated by two equivalent Morse potentials. With the inclusion of a repulsive oxygen—oxygen interaction, the model predicts a transition to symmetric hydrogen bonding in ice VII at a pressure between 350 and 800 kbar.

An ESR Study of Anisotropic Rotational Reorientation and Slow Tumbling in Liquid and Frozen Media
View Description Hide DescriptionA careful study is described of the ESR lineshapes for the peroxylamine disulfonate (PADS) radical dissolved in 85% glycerol solution and in frozen water and D_{2}O. In the frozen media, spectra characteristic of rotational correlation times τ_{ R } ranging from to are obtained, while the range in glycerol is from to . The very rapid rotational motion in frozen water is taken to imply that PADS is rotating in a clathrate cage. The activation energies in ice and 85% glycerol are and , respectively, (from motional‐narrowing data). The value for ice is very similar to that obtained for other rate processes in ice. The lineshapes for are analyzed in terms of the familiar spin‐relaxation theories valid in the motionally narrowed region. These results are well fitted by the model of axially symmetric rotational diffusion with the symmetry axis in the plane of the N, O, and S atoms and parallel to a line passing through the two S atoms. Diffusion about this axis is found to be and times faster for frozen water and glycerol solvent, respectively than about the other axes over a wide range of values of average τ_{ R̄ }. It was possible to obtain these results, because accurate measurements of the g and A tensors for PADS in these media could be made from the well‐resolved rigid spectra at X band and 35 GHz; the intrinsic widths in D_{2}O are only about 1.5 G. The spectra in the slow‐motional region were simulated utilizing the slow tumbling formulation of Freed, Bruno, and Polnaszek appropriately generalized to include completely asymmetric g and A tensors. The simulated spectra are found, in general, to be in quite good agreement with experimental observations. The agreement is clearly improved by introducing axially symmetric rotational diffusion, as found for the motional‐narrowing region, into the simulations. Spectra are simulated for Brownian rotational diffusion as well as for simplified models of free diffusion, which includes inertial effects, and for diffusion by jumps of substantial angle. Improved agreement with experiment is found with some of these latter models. What appears to be a surprisingly small nonsecular linewidth contribution in the motional‐narrowing region is briefly discussed in terms of these models.

On the Calculation of the Coefficient of Self‐Diffusion
View Description Hide DescriptionSimple parametrized analytic expansions for both the velocity autocorrelation function and its associated memory function are presented. Two methods have been used to fix the parameters. One is to use the Maclaurin expansion of the velocity autocorrelation function through terms in t ^{4}. The other is to assume that the velocity autocorrelation function decays exponentially for long times and to use only the coefficients of t ^{2} in the Maclaurin expansion. The results are compared to the molecular dynamics calculations of Rahman and Levesque and Verlet.

Electric Dipole Moment of Diatomic Molecules by Configuration Interaction. III. Open‐Shell Molecules CO a ^{3}II and CS A ^{1}II
View Description Hide DescriptionThe CI technique developed for closed‐shell molecules is extended to open‐shell cases, retaining a 200 configuration limit, but including higher‐than‐double excitations and employing the iteration to natural orbitals as suggested by Bender and Davidson. For CO the effect of different initial molecular orbitals and different Slater‐type basis sets is examined. For CO a ^{3}II, the Hartree—Fock, CI, and experimental dipole moments (in debye) are 2.30, 1.55, and 1.38, respectively. The remaining error in the CI value is attributed more to inadequacies in the Slater‐type basis used than to the CI technique. For CS A ^{1}II the CI dipole moment of 0.63‐D C^{−}S^{+} is in excellent agreement with the experimental value of ; the Hartree—Fock value is 0.09 D in the wrong direction.

Classical Limit of Fredholm Theory for Elastic and Inelastic Scattering; Inability of Phase Space Integrals to Describe Inelastic Transitions
View Description Hide DescriptionUsing a classical phase space integral to approximate certain quantum mechanical operations, the classical limit of the Fredholm determinant for a general multichannel scattering system is derived. This statistical form of the classical limit of scattering is found to give exactly the same ``classical S matrix'' for the case of potential scattering as does a dynamical treatment of the classical limit. For inelastic scattering, however, the classical S matrix which results from this Fredholm determinant is only an approximation to that obtained by exact classical dynamics. Reasons for this failure of the statistical version of the classical limit for inelastic scattering are discussed.

EPR Studies of Copper‐Doped L‐Alanine Crystals: Ultraviolet‐Induced Conversion in Cu^{2+} Complexes
View Description Hide DescriptionCopper‐doped L‐alanine crystals exhibit an absorption band in the ultraviolet region. EPR observations indicate that as a result of this uv absorption, multiple conversion takes place in the Cu^{2+} complexes. In addition to the complexes originally formed by the impurity ions, two others were identified during uv irradiation at 77°K. These were distinguished by their tensor parameters and thermal stabilities, as well as an absence of ligand nitrogen hyperfine structures. The EPRspectra also indicated the formation of free radicals which, however, were not positively identified. On increasing the temperature, these underwent an irreversible transformation accompanied by the formation of yet another copper complex showing a quintet ligand hyperfine structure of 1:2:3:2:1 intensity ratio.

Theoretical Studies of the Binding Energy and Geometry of the Molecular Ion
View Description Hide DescriptionThe geometry and binding energy of the molecular ion have been examined by two different ab initio quantum mechanical variational methods. In the first a CI wavefunction was made from the 10 covalent valence‐bond structures which could be constructed from 1s orbitals at the nuclei, each 1s orbital being represented by a five‐term Gaussian expansion and having a variable scale factor. For geometries identical or similar to the D _{2d}geometry previously predicted from analogous calculations with cruder basis sets, we found no stability with respect to . Other geometries were examined, especially those arising naturally from the approach of and H_{2}; however, binding was never greater than a tiny 0.6 kcal/mole. We thus concluded that the method had failed adequately to describe , as it had for , and that it is probably unreliable for studying ions with small binding energies. The second method used the SCF MO model with a flexible basis set to account for distortion and polarization. This gave an geometry corresponding to an complex of over‐all C _{2v } symmetry, in which the H_{2} sits about 3 a.u. from the apex and perpendicular to the plane and to a line extending from the midpoint of the base of the , through the apex, and through the H_{2} midpoint. The calculated binding energy relative to is 4.25 kcal/mole. Because formation of such a loose molecular complex from two closed‐shell systems should produce very little extra correlation energy in the complex, and because of basis set reasons discussed in the text, these results are believed to be reliable.

Infrared Absorption Spectra of Isotopic Ozone Isolated in Rare‐Gas Matrices
View Description Hide DescriptionSome of the isotopic ozone molecules of different combinations of oxygen‐16 and oxygen‐18 have been synthesized and isolated in rare‐gas matrices at 20°K. Their infrared absorption bands have been identified. The isotope effects are calculated for symmetrical as well as unsymmetrical isotopic ozone molecules.

Determination of Optical Oscillator Strengths by Electron Impact Spectroscopy
View Description Hide DescriptionAn expansion of the square of the momentum transfer times the differential cross section, in powers of the momentum transfer, about the nonphysical point of zero momentum transfer, is carried out through terms of the order of the reciprocal of the square of the incident energy. The results confirm the view that the differential cross section can be regarded as a function of the square of the momentum transfer down to relatively low energies. Simple formulas are presented for calculating corrections to electron impact estimates of the intensity at zero scattering angle in order to obtain accurate optical oscillator strengths. Correction formulas are also presented for obtaining quadrupole transition probabilities from optically forbidden transitions. The case of spin forbidden but exchange allowed transitions is also considered. It is shown that certain second Born exchange corrections exist with the same dependence on the incident energy as that found for the leading term in the first Born approximation for exchange.

Molecular Beam Kinetics: Reactions of Deuterium Atoms with Halogen Molecules
View Description Hide DescriptionAngular distributions and velocity distributions have been measured for deuterium halides reactively scattered from crossed beams of D atoms and five halogen molecules, Cl_{2}, Br_{2}, I_{2}, ICl, and IBr. The D beam was obtained either from a tungsten furnace at or a microwave discharge at , the halogen beam from a supersonic nozzle source at . A small computer was employed as a multiscalar to record the time of flight spectrum of the product at each observation angle. Data of satisfactory quality (signal‐to‐noise ratio ) were obtained with rather short counting times () for reactive scattering signals of a few counts per second. Contour maps of the differential reaction cross sections are derived from an approximate transformation to the center‐of‐mass coordinate system. The main results found with D atoms at are as follows: (1) In the Cl_{2}reaction, most of the DCl recoils into the backward hemisphere with respect to the incoming D atoms; the angular distribution peaks beyond , nominally near 180°. For the Br_{2}reaction, the DBr is much less strongly pitched backwards, peaking near . For the I_{2}reaction, most of the DI scatters sideways, peaking near . (2) The angle and velocity dependence of the DX distributions is approximately separable, but the forward‐scattered part shows a distinct upward trend in velocity ( at 60°) as the scattering angle decreases. (3) The mean energy released into relative translation of the products is 25, 16, and 12 kcal/mole, respectively, for the Cl_{2}, Br_{2}, and I_{2}reactions, as compared with total available energy ( mean collision energy plus reaction exoergicity) of 55, 51, and 44 kcal/mole. (4) For the IBr reaction, the yields of DBr and DI are comparable. The distributions in angle and translational energy are different, for DBr resembling closely the Br_{2}reaction, for DI the I_{2}reaction. (5) For ICl, the yield of DI exceeds DCl by a factor of at least 3 or 4 despite the much lower exoergicity for forming DI (20 kcal/mole) rather than DCl (52 kcal/mole). The DI angular distribution peaks sideways, as for I_{2}; the DCl peaks backwards, as for Cl_{2}. However, the translational energy of DI is much lower (mean 7 kcal/mole) than for I_{2} and that of DCl much lower (mean ) than for Cl_{2}. With the D atoms at : (6) The reaction yield with Cl_{2}was not detectable, very small with Br_{2}, and comparable to that for hot D atoms with I_{2}. (7) In the I_{2} case, the product angular distribution shifts backwards by as compared to the hot D atom reaction. The mean energy released into product translation decreases substantially (from 12 to 9 kcal/mole) but about in proportion to the decrease in the total available energy due to the temperature change. Qualitative implications of these findings are discussed, with emphasis on the role of the rapid motion of D relative to X and Y and electronic structure aspects. The energy distributions indicate an impulsive interaction governed by repulsion between the halogen atoms. The angular distributions indicate that migration of D between the halogens does not occur and that the preferred reaction geometry changes from essentially collinear D‐X‐Y to strongly bent configurations as the central atom changes from Cl to Br to I.

Vibrational Spectra of Ammonium and Other Scheelite‐Type Perrhenates
View Description Hide DescriptionThe far‐infrared and laser‐excited Raman spectra of several scheelite‐type perrhenates have been recorded at 77°K and room temperature in order to obtain frequencies and symmetry assignments for the lattice modes. Both NH_{4}ReO_{4} and ND_{4}ReO_{4} were studied to separate ammonium‐ion translations and librations. At 77°K the ammonium‐ion librational mode is observed at 264 cm^{−1} in NH_{4}ReO_{4} and 194 cm^{−1} in ND_{4}ReO_{4}. Upon warming to 300°K, the ammonium‐ion librational mode disappears and is unobservable in both the far‐ir and Raman spectra. The Raman‐active ammonium‐ion fundamental modes have also been observed in both NH_{4}ReO_{4} and ND_{4}ReO_{4}. The temperature‐dependent changes in the intensities and linewidths of the ammonium‐ion fundamentals and lattice modes indicate that the ammonium‐ion motion undergoes a change between 77 and 300°K.

Energy‐Deposition Functions in Mass Spectrometry
View Description Hide DescriptionMethods for the evaluation of internal energy distribution functions resulting in ions from impact of energetic electrons are examined and their shortcomings are analyzed. It is shown that energy‐deposition functions can be estimated from photoelectron spectra and photoionization cross sections if the Bethe—Born treatment of collisions is employed, but allowance for autoionization and multiple ionization processes is not possible. Deposition functions are calculated for methane, ethane, and ethylene. Mass spectra obtained by folding the functions into breakdown graphs are in reasonable agreement with experimental fragmentation patterns for 70−eV electrons.

Triplet‐Triplet Spectroscopy of Polyacenes
View Description Hide DescriptionComplete triplet—triplet absorption spectra (2000–10000 Å) were measured in alcoholic solution at 113°K with naphthalene, anthracene, tetracene, and a few methylated derivatives. Several new bands were observed. Calculations of the higher ππ^{*} triplet states energies with the LCAO—MO—SCF Pariser—Parr—Pople method were improved by the use of large configuration interactions. These include many doubly excited configurations with respect to both the ground singlet state S _{0} and the lowest triplet state T _{1}, thanks to the systematic use of all monoexcitations with respect to S _{0} plus all monoexcitations with respect to T _{1}. The comparison of all experimental and theoretical results for the three polyacenes allows one to modify a few previous assignments and to give a general tentative assignment for all observed transitions.

On the Convergence of Multibody Expansions for Short Range Intermolecular Forces. A SCF Calculation of He_{3} and He_{4} Systems
View Description Hide DescriptionIn this paper we calculate the potential energy surface of He_{3} within the SCF—LCAO—MO approximation to test the pairwise additivity of intermolecular forces at short range. We obtain large nonadditive contributions at very close distances, but in general, in the neighborhood of the van der Waals well (), they are negligible. However the study of a few He_{4} configurations shows that four‐body effects can be important enough to question the convergence of many‐body expansions.