bluuebunny/crossref_metadata_2025 huggingface dataset:
Vibrationally Excited Ozone in the Pulse Radiolysis and Flash Photolysis of Oxygen
Authors: Hochanadel C. J. , Ghormley J. A. , Boyle J. W.
Published: February 2004

The kinetics of ozone formation have been studied in the pulse radiolysis and flash photolysis of gaseous oxygen by measuring the change in optical absorption following the pulse. The absorption spectrum of the ozone present immediately after the pulse is considerably broader and the peak is at longer wavelength (∼2860 Å) than that of ground state ozone (∼2560 Å). The initial absorption is attributed to ozone in the upper vibrational levels produced by O + O2⇋O3‡. It is clearly shown that the over-all third-order reaction O + O2+M→O3 + M occurs by a sequence of steps. The relaxation time for de-excitation from the upper vibrational levels to the ground state is ≥6 × 10−6 sec in O2 at 740 torr and 24°C. De-excitation requires at least 4.5 × 104 collisions, and assuming 20 vibrational levels, the average efficiency is about one quantum in 2200 collisions. The third-order rate constant based on O atom disappearance k(−O) is several times larger than that based on formation of O3 in the ground vibrational state k(O3, υ = 0). Neither rate constant can be evaluated accurately by optical absorption measurements. Measurements at 2800 Å, where all vibrational levels appear to have about the same extinction coefficient, gave a value 2.2 × 108M−2 sec−1. This value should approximate k(−O) for which Kaufman and Kelso determined 2.4 × 108M−2 sec−1 by direct measurement of O atom disappearance. Measurements at wavelengths below 2480 Å gave an upper limit for k(o3.υ = 0) of 1 × 108M−2 sec −1.
Test of a Melting Criterion for Cubic Metals
Authors: Gupta R. P. , Sharma P. K.
Published: February 2004

The electron gas model for the lattice dynamics of cubic metals propounded by one of us earlier has been used to test Lindemann's melting criterion by calculating the ratio γm of the mean-square amplitude of thermal vibrations to the square of the interatomic spacing at the melting point for a number of cubic metals belonging to different groups of the periodic table. The calculated γm has roughly the same value for elements belonging to one particular group, but the spread in γm values is quite large from one group to another. It is concluded that Lindemann's hypothesis of constant γm for all solids is inadequate.
Dissociation Energy of Copper Monofluoride
Authors: Hildenbrand D. L.
Published: February 2004

High-temperature gaseous equilibria in the Mg–Cu–F system were studied by mass spectrometry and the results were used to derive the dissociation energy of CuF. For the reaction MgF(g) + Cu(g) = Mg(g) + CuF(g), ΔH298 = 7.1 ± 2 kcal, leading to D°298(CuF) = 103 ± 2.2 kcal (4.47 eV). This result differs from those obtained on many other mono- and difluoride combinations in that D(Cu–F) > D(CuF–F). It can be shown, however, that this reversal of bond strengths in the Cu–F system is consistent with the valence-state concept of bonding.
Molecular Structure of XeF6. I. Analysis of Electron-Diffraction Intensities
Authors: Gavin R. M. , Bartell L. S.
Published: February 2004

A gas-phase electron-diffraction investigation of xenon hexafluoride has been carried out in an effort to obtain structural information which might shed light on the curious properties of the compound. Elaborate precautions were taken to prevent decomposition or contamination of the sample (99.8 mole % pure). Several innovations were introduced into the structure analysis to minimize difficulties encountered in conventional analyses of molecules containing both heavy and light atoms. Two different sets of analyses (I and II) employing two different levels of approximation in electron scattering theory were conducted to test the adequacy of the expressions usually adopted. Analysis I was based on Hartree–Fock x-ray elastic scattering factors, Heisenberg–Bewilogua inelastic scattering factors, and (modified) Born phase-shift corrections for Thomas–Fermi atomic fields. Improvements in Analysis II included the new electron elastic scattering factors and Born phase-shift corrections calculated by the partial wave method by Cox and Bonham, and Hartree–Fock inelastic scattering factors. The Hartree–Fock phase-shift correction was not in complete agreement with experiment but was markedly better than the Thomas–Fermi correction. The effect of ionic character on phase shift was investigated theoretically and shown to be significant. A mean Xe–F bond length of 1.890 ± 0.005 Å was found, but the radial distribution function for Xe–F bonds corresponded to that of a composite for nonequivalent bonds. Amplitudes of bending oscillations are notably large. The diffraction data are not compatible with a regular octahedral XeF6 molecule vibrating in independent normal modes. A more detailed exposition of alternative structures and internal motion is presented in Paper II.
Molecular Structure of XeF6. II. Internal Motion and Mean Geometry Deduced by Electron Diffraction
Authors: Bartell L. S. , Gavin R. M.
Published: February 2004

The distribution of internuclear distances in gaseous XeF6 exhibits unusually diffuse XeF6 bonded and F–F geminal nonbonded peaks, the latter of which is severely skewed. The distribution proves the molecule cannot be a regular octahedron vibrating in independent normal modes. The instantaneous molecular configurations encountered by the incident electrons are predominantly in the broad vicinity of C3υ structures conveniently described as distorted octahedra in which the xenon lone pair avoids the bonding pairs. In these distorted structures the XeF bond lengths are distributed over a range of approximately 0.08 Å with the longer bonds tending to be those adjacent to the avoided region of the coordination sphere. Fluorines suffer angular displacements from octahedral sites which range up to 5° or 10° in the vicinity of the avoided region.

Alternative interpretations of the diffraction data are developed in detail, ranging from models of statically deformed molecules to those of dynamically inverting molecules. In all cases it is necessary to assume that t1u bending amplitudes are enormous and correlated in a certain way with substantial t2g deformations. Notwith-standing the small fraction of time that XeF. spends near Oh symmetry, it is possible to construct a molecular potential-energy function more or less compatiable with the diffraction data in which the minimum energy occurs at Oh symmerty. The most notable feature of this model is the almost vanishing restoring force for small t1u bending distortions. Indeed, the mean curvature of the potential surface for this model corresponds to a υ4 force constant F44 of 10−2 mdyn/Å or less. Various rapidly inverting non-Oh structures embodying particular combinations of t2g and t1u deformations from Oh symmetry give slightly better radial distribution functions, however. In the region of molecular configuration where the gas molecules spend most of their time, the form of the potential-energy function required to represent the data does not distinguish between a Jahn–Teller first-order term or a cubic V445 term as the agent responsible for introducing the t2g deformation. The Jahn–Teller term is consistent with Goodman's interpretation of the molecule. On the other hand, the cubic term is found to be exactly analogous to that for other molecules with stereochemically active lone pairs (e.g., SF4, ClF3). Therefore, the question as to why the XeF6 molecule is distorted remains open. The reported absence of any observable gas-phase paramagnetism weighs against the Jahn–Teller interpretation.

The qualitative success but quantitative failure of the valence-shell–electron-pair-repulsion theory is discussed and the relevance of the “pseudo-Jahn–Teller” formalism of Longuet-Higgins et al. is pointed out. Brief comparisons are made with isoelectronic ions.
Effect of Intramolecular Twisting on the Fluorescence Spectra of Sterically Hindered Tetraphenylbutadienes
Authors: El-Bayoumi M. Ashraf , Halim F. M. Abdel
Published: February 2004

Absorption and fluorescence spectra of trans-1,1,4-triphenylbutadiene, trans-1,1,4,4-tetraphenylbutadiene (TPB), and trans-1,1,4,4-tetraphenyl-2-methylbutadiene (TPMB) were measured in an isopentane-methylcyclohexane mixture at room temperature and in rigid glass at 77°K. Absorption maxima exhibit a polarization red shift while fluorescence maxima exhibit a large blue shift upon freezing the samples at 77°K. Thus the intense blue fluorescence of tetraphenyl-2-methylbutadiene appears as a weak yellow fluorescence as soon as the rigid glass begins to melt. In these sterically hindered molecules the equilibrium configuration in the excited state is different from that in the ground state, and an intramolecular twisting relaxation process occurs before emission in fluid media. In rigid media and in the crystal, the twisting relaxation is slowed down, and emission originates from a Frank–Condon state which lies at higher energies. Quantum yield and energy of fluorescence of sterically hindered molecules in general are expected to be viscosity sensitive.
Inapplicability of the Born Exchange Scattering Amplitude for the He (11S→23S) Transition
Authors: Miller Kenneth J. , Krauss Morris
Published: February 2004

Differential cross sections are calculated for the He (11S→23S) transition within the Born–Oppenheimer approximation. The Bonham–Ochkur (OB) approximation is compared to the exact exchange scattering amplitude and it is found to yield semiquantitative agreement, especially at high incident energies. However, the theoretical results show qualitatively different behavior from recent experimental results. Experimental differential cross sections peak in the forward direction while theory predicts a maximum at large angles.
Force Constants of Nickel Carbonyl from Vibrational Spectra of Isotopic Species
Authors: Jones Llewellyn H. , McDowell Robin S. , Goldblatt Maxwell
Published: February 2004

The infrared spectra of gaseous Ni(13CO)4 and Ni(C18O)4 and the infrared and Raman spectra of CCl4 solutions of these isotopic molecules were recorded. General quadratic valence force constants have been calculated from the frequencies of the normal species and the two isotopic species. The resulting force constant solution is similar to that obtained previously assuming a pi electron interaction potential function. These results put the force constants of metal carbonyls on a firmer basis.
Nitrogen–Oxygen Phase Diagram
Authors: Barrett C. S. , Meyer Lothar , Greer Sandra C. , Wasserman J.
Published: February 2004

We have determined the phase diagram for the notrogen–oxygen system by examining the x-ray diffraction patterns of polycrystalline samples of the solidified mixtures over the temperature range 21°–50°K. The diagram exhibits a surprising complexity: a eutectic line divides the liquid and the two-phase region of (γ-O2 + β-N2), and a peritectoid line separates this two-phase region and a new phase, designated “x”, between 18% and 37% N2 and 34° and 45°K. The “x” region is flanked by a two-phase region with β-O2 on one side, and a wide two-phase region with β-N2 on the other side, and is terminated at its low–temperature end by a two-phase region (β-O2 + β-N2) between 32.5° and 34°K; this region extends over nearly the whole concentration range. Oxygen has a striking range of solubility in β-N2 of 53% at 50°K and only 15% at 40°K. The lattice constants of β-N2 at 47.5°K decrease essentially linearly on addition of up to 40% O2, then decrease very sharply between 40% and 50% O2; the volume of the β-N2 unit decreases by 10% on addition of 50% O2.
Potential-Energy Surface for H3
Authors: Shavitt I. , Stevens R. M. , Minn F. L. , Karplus M.
Published: February 2004

An a priori variational calculation of the H3 potential-energy surface has been made with complete configuration-interaction wavefunctions formed from optimized-exponent basis sets of six orbitals (1s, 1s′, on each nucleus) and 15 orbitals (1s, 1s′, 2px, 2py, 2pz, on each nucleus). Linear (180°) and nonlinear (150°, 120°) geometries were examined for a wide range of internuclear distances with particular emphasis on the minimum-energy path for each angle. The 15-orbital set yielded a linear-symmetric saddle point at an internuclear distance of 1.765 a.u. with an energy 11 kcal/mole above that of a corresponding calculation for an isolated hydrogen atom and hydrogen molecule. The H3 surface, details of which are presented in terms of tables, least-squares fits, and contour maps, is found to be similar in form to a semiempirical surface which has been used in quasiclassical analysis of the (H, H2) exchange reaction. However, there are quantitative differences, whose significance can be ascertained only by more refined a priori treatments and new dynamical calculations.
Infrared Spectra of Borohydride Ions in Alkali Halide Single Crystals
Authors: Coker E. Howard , Hofer Douglas E.
Published: February 2004

Solid solutions of NaBH4 in NaCl, NaBr, and NaI, of KBH4 in KCl, KBr, and KI, of CsBH4 in CsBr and CsI, of KBD4 in KCl, KBr, and KI, and of CsBD4 in CsBr and CsI have been prepared. The borohydride was diffused into the alkali halide single crystals as it was produced by action of the alkali metal and hydrogen upon the borates of a borosilicate glass capsule. The site symmetry was found to be tetrahedral for salts of both bcc and fcc structure. For NaX:BH4– and KX:BH4–, 2ν4 < ν3 < ν2 +  ν4 for KX:BD4–ν3 < 2ν4 < ν2 + ν4; and for CsX:BH4–2ν4 < ν2 + ν4 < ν3. These variations are accounted for by isotopic shifts and by the nature of the repulsive interaction of the borohydride ion with the solvent ions.
Method of Calculating Phase Shifts for Spherically Symmetric Potentials
Authors: Eu B. C.
Published: February 2004

A method of calculating the phase shifts for spherically symmetric nonsingular potential is presented. The radial Schrödinger equation is reduced to a Ricatti's equation which is solved in the form of a continued fraction. Illustrative calculations of S-wave phase shifts for an attractive exponential potential are made with the first and second approximants of the continued fraction in comparison with the exact and Born phase shifts. For the potential parameter chosen (Z = 2 and 2.6) the agreement with the exact value and the over-all behavior of the phase shifts as a function of the momentum is reasonably satisfactory in contrast to the Born phase shift. A brief discussion of the possible application of the method and its limitations are given along with a remark on the extension to singular potentials. The convergence of the continued fractions is discussed with an example of an exponential potential in the appendix.
Quantum Corrections to Time Correlation Functions
Authors: Hynes James T. , Deutch J. M. , Wang Chin Hsien , Oppenheim Irwin
Published: February 2004

The first quantum correction to a time correlation function is obtained by expanding the quantum-mechanical correlation function in powers of Planck's constant. Quantum corrections to time correlation functions are of interest because they may be used to obtain quantum corrections to transport properties. An application of the formalism to nuclear spin-lattice relaxation is included. A formal expression is obtained for the first quantum correction to the lattice time correlation functions. The effect of this correction on the relaxation time is indicated. The possibility of using the first quantum correction to calculate isotope effects on transport properties is discussed.
Approximate Analytical Wavefunctions for Certain States of Nd3 +
Authors: Synek M. , Corsiglia L.
Published: February 2004

Approximate analytical self-consistent field wavefunctions were calculated for the ground state and for certain excited states of the laser-active ion Nd3 +. The following states of the 4f3 configuration of Nd3 + were covered by our calculations: S4,D4,F4,G4,, and I4. For the purpose of this work we combined the minimum and the saturated basis set approximations. All the orbital exponents were accurately optimized. The d orbitals, and particularly the 4f orbital, were calculated unusually accurately. Except the optically unaffected orbitals 1s, 2s, and 2p, all the orbitals of the s, p, d, and f symmetries exhibited zero deviation (to five decimals) from the tail nodal extinction. The virial theorem was always satisfied to at least five significant figures.
Collision Theory of Relaxation Processes. II. Diatomics
Authors: Chen F. M. , Snider R. F.
Published: February 2004

A theory of nuclear magnetic relaxation for gases composed of diatomic molecules is developed starting from a quantum Boltzmann equation. Formal expressions for the relaxation times and collision induced chemical shifts due to intramolecular spin–rotation and dipole–dipole interactions are given in terms of the relaxation times for rotational polarization. The form of the resulting equations agrees with the Bloom–Oppenheim theory while also giving expressions for the rotational-polarization relaxation times in terms of the transition operator for the collision process.
Expansion of the Time-Dependent Wavefunction in Quasistationary Energy Eigenfunctions
Authors: Frey Robert B. , Thiele Everett
Published: February 2004

The motion of a wave packet moving in a potential well with a penetrable barrier is considered. A formally exact expression for the evolution operator is given as a sum over quasistationary energy eigenfunctions plus a remainder term. Numerical calculations are carried out for the square barrier potential. The approximation in which one neglects the remainder term is shown to be a useful and accurate one in computing properties of the particle which depend on the value of the wavefunction inside the potential well.
Fluid Flow of Liquid Plutonium Alloys in an Oscillating-Cup Viscosimeter
Authors: Wittenberg L. J. , Ofte D. , Curtiss C. F.
Published: February 2004

An oscillating-cup viscosimeter was utilized to measure the viscosity of three low-melting plutonium alloys. The derived relationship for the viscosity calculation was confirmed by measurements on standard viscosity oils and on liquid metals which covered wide ranges of viscosities. Abnormal behavior was detected for the three plutonium alloys. When the period of oscillation was greater than 11.0 sec for the three plutonium alloys, the logarithmic decrement passed through a maximum, then decreased as the temperature decreased; at the same time the period of oscillation increased greatly. When the period of oscillation was 2.7 sec, the plutonium alloys behaved normally but showed very large viscosities, which approached 25 cP. The cause of the anomalous behavior was not determined but indicated possible viscoelastic or non-Newtonian behavior.
Chemical Exchange and Transient Effects in an AB-Type NMR Spectrum
Authors: Gore E. S. , Gutowsky H. S.
Published: February 2004

A density matrix formulation is used to investigate the transient NMR effects which occur when the rf field H1 is changed discontinuously for a coupled AB system undergoing intramolecular chemical exchange. It is shown that the problem reduces to the solution of two matrix differential equations. Explicit solutions are obtained and discussed for two special cases: (i) H1 = 0 for t < 0, H1 = weak observing field for t > 0; and (ii) H1 = ∞ for t < 0, H1 = weak observing field for t > 0. For Case (I) it is shown that the Anderson–Weiss theory gives the same results. Also, our formulation is used to determine the conditions under which the absorption intensity can be calculated by assuming it to be proportional to the z component of the corresponding nuclear magnetization. Finally, the effect of inhomogeneities in the static field H0 is treated briefly. For a Lorentzian distribution of inhomogeneities, it is shown that the transient as well as steady-state broadening effects can be accounted for by replacing the linewidth parameter (1 / T2) with (1 / T20) + (1 / T2*), where (1 / T2*) gives the width of the inhomogeneity function.
Energetics of the Interaction of Molecular Oxygen with Organic Molecules
Authors: Khan Ahsan U. , Kearns David R.
Published: February 2004

The interaction of molecular oxygen with electronically excited organic molecules (M) has been examined theoretically and expressions for energies of the states of the [M···O2] complex have been derived. The results indicate that in [M···O2] complexes where the triplet state of the organic molecule, 3M, and the charge-transfer state of the complex are close in energy, (i) the O2 induced S→T absorption bands may be diffuse and red shifted relative to the positions of unperturbed bands; (ii) the quenching of triplet states by O2 will invariably be diffusion controlled; (iii) the [3M···3O2] complex has a significant binding energy (>300 cm−1); and (iv) complexes between a ground-state molecule and electronically excited oxygen molecules (either 1Σg+ or 1Δg) are dissociative.
Internal Rotation in Completely Asymmetric Molecules. IV. Energy Contributions from the α Dependence of the Torsional Kinetic Energy
Authors: Knopp J. V. , Quade C. R.
Published: February 2004

For molecules with asymmetric internal rotors, the reduced moment of inertia for the torsional motion depends explicitly upon α, the angle of internal rotation. General expressions have been obtained for this dependence from a model which considers one degree of internal freedom for molecules with one part planar and the other with a plane of symmetry. The formulas are functions only of the inertial parameters of the molecule. For those cases where the α dependence is small, the results are expanded in trigonometric series. In this case the α dependence of the torsional kinetic energy may be expressed as a variation in the effective potential hindering the internal motion. Torsional coefficients have been calculated for some representative molecules.
Raman Spectrum of Crystalline Sodium Nitrate
Authors: Rousseau D. L. , Miller R. E. , Leroi G. E.
Published: February 2004

Raman scattering from crystalline NaNO3 has been observed in all polarization orientations. Except for small intensity contributions in some orientations which are probably due to depolarization effects in the birefringent crystal, the polarizability activities of both internal and external modes follow the expected symmetry selection rules. From relative intensity considerations, the bands at 185 and 98 cm− 1 have been designated as the Raman-active librational and translational lattice modes, respectively. This assignment has been confirmed by the comparison of the lattice spectra of Na14NO3 and Na15NO3 at 35°K, where an isotope shift is observed only on the lower frequency band. No evidence of mixing between these Eg lattice modes has been observed.
Lowest Ionization Potentials of Some Nitrogen Heterocyclics
Authors: Yencha Andrew J. , El-Sayed M. A.
Published: February 2004

The photionization potentials of the highest occupied orbital of pyrazine (9.29 eV), pyrimidine (9.35 eV), pryidazine (8.71 eV), naphthalene (8.15 eV), quinoline (8.62 eV), isoquinoline (8.55 eV), quinoxaline (9.02 eV), cinnoline (8.95 eV), and phthalazine (9.22 eV) are determined. In addition, estimates of the second ionization potentials of cinnoline (∼9.1 eV) and phthalazine (∼9.3 eV) are obtained from the analyses of the spectral characteristics of the photoionization yield curves. A discussion of the observed and estimated values of the ionization potentials in terms of the type of the ionized electron (π vs nonbonding) is given. It seems that for all the molecules studied, except pyridazine and phthalazine, the π electron has a lower ionization potential than the nonbonding electron. The interchange of the type of the ionized electron in pyridazine and phthalazine is caused mainly by the strong repulsive interaction between the two lone pairs of electrons on the adjacent nitrogen atoms in these molecules as well as by the stabilization of the π electrons in these systems.
Infrared Emission as Studied through the Temperature Dependence of Integrated Intensities of a Molecular Crystal
Authors: Leles Byron K. , Neff Vernon D.
Published: February 2004

The expression for the integrated intensity of an infrared absorption band is normally obtained by neglecting spontaneous emission. At high temperatures, the emission term cannot be ignored, and in fact gives rise to a decrease in apparent absorption intensity with increasing temperature. We have studied this effect experimentally with the molecular crystal copper phthalocyanine at temperatures up to 600°C. Expressions based on the assumption of a harmonic potential function, and retaining only linear terms in the dipole-moment operator have been derived for the temperature dependence of the fundamental absorptions. These expressions compare favorably with the experimental data.
Dispersion Curves and Frequency Distribution of Polymers: Single Chain Model
Authors: Piseri Luigi , Zerbi Giuseppe
Published: February 2004

A general method for the calculation of dispersion curves for any single polymer chain in terms of internal coordinates is proposed. The method is immediately applicable to electronic computers. Dispersion curves and the corresponding frequency distributions have been obtained for polyethylene and deuterated polyethylene, hexagonal polyoxymethylene, and deutero derivative and orthorhombic polyoxymethylene. Spectroscoptically active fundamentals have been calculated and the normal modes described in terms of a valence force field. Experimental data from vibrational spectroscopy and inelastic neutron scattering have been compared and discussed in terms of that predicted by calculations.
Infrared Studies of the Rare-Earth Sulfates (4000–80 cm−1)
Authors: Postmus C. , Ferraro J. R.
Published: February 2004

The hydrates and the anhydrous salts of the rare-earth sulfates were studied by infrared techniques from 4000–80 cm−1. The environment of the sulfate group was followed as the hydrates were dehydrated. The change occurring in the symmetry of the sulfate group is discussed in terms of water effects and coordination to the metal. From deuteration studies, the various librational modes of coordinated water to rare-earth metals have been assigned for the first time.
Difference Bands in the Infrared Spectrum of Carbon Tetrachloride
Authors: Tegnelia J. A. , Powell F. X.
Published: February 2004

Experiments are reported which demonstrate the predominance of difference bands in the infrared spectrum of carbon tetrachloride. Special emphasis is placed on the band at 775 K. The conclusion reached is that the fundamental spectrum of this molecule is inaccessable at the temperature 195°K and above.
WKB Calculation of Vibrational Transition Probabilities in Molecular Collisions
Authors: Shin Hyung Kyu
Published: February 2004

A comparison is made between vibrational transition probabilities calculated by use of the WKB approximation with those obtained from other methods. For Cl2–Cl2, the transition matrix element for a purely repulsive exponential potential is within 1.5% of the Jackson–Mott exact value over the energy range from 1500k–3900k. For a “shifted exponential” potential, the WKB matrix element agrees satisfactorily with the exact value and with the Hartmann–Slawsky approximation at higher energies. It is also shown that the WKB matrix element for a Morse potential is larger than the Lennard-Jones (12–6) matrix element by a factor of 1.3–1.5 over the energy range from 900k–3900k for Cl2–Cl2. Both for the exponential and inverse-law potentials, the inclusion of attractive forces in the calculation leads to significantly larger matrix elements. Application of the WKB method to the calculation of the collision numbers of Cl2–Cl2 and O2–O2 gives results within a factor of about 2 of the experimental data up to temperatures 2000° and 4000°K, respectively, when the effect of molecular orientation on the transition is properly taken into account.
Moment Theorems for Vibronic Exciton Spectra of Molecular Crystals
Authors: Merrifield R. E.
Published: February 2004

The mean energy and second moment of an absorption band can be calculated exactly without a knowledge of the energies and eigenstates of the upper levels of the transition. Application of this theorem to exciton spectra of molecular crystals having two molecules per unit cell shows that the purely electronic part of the factor-group splitting is given by the difference of the mean energies of absorption in the two relevant polarizations and that the second moment of the absorption band is independent of the intermolecular coupling strength. These results are independent of the vibronic coupling strength and of whether or not the vibrations are harmonic. The finite-temperature form of the mean energy theorem is derived and is employed to discuss the broadening of exciton spectra resulting from interaction with lattice vibrations.
Vibrational Analysis of Random Polymers
Authors: Tasumi Mitsuo , Zerbi Giuseppe
Published: February 2004

The frequency distributions of some isotopically random polymers are calculated by applying Dean's negative eigenvalue theorem. It is shown that the results of calculation are in good agreement with the infrared spectra of polymers of cis-CHD = CHD and trans-CHD = CHD, giving strong confirmation to the previous view that the polymerization by a Ziegler-type catalyst occurs with the cis opening of the double bond. The spectra of copolymers of CH2 = CH2, CHD = CD2, and CD2 = CD2 are also discussed. The effects of randomness and deuterium content on the frequency distribution are studied.
Electronic Raman Effect. II. Asymmetry of the Scattering Tensor for Electronic Raman Transitions
Authors: Mortensen O. Sonnich , Koningstein J. A.
Published: February 2004

The theory of electronic Raman scattering for trivalent rare-earth ions in crystals is formulated in a general way. It is shown that vibronic coupling is unimportant. The antisymmetric part of the scattering tensor, which vanishes for vibrational Raman scattering, turns out to be dominant for several electronic Raman transitions. The implications of this with respect to selection rules and depolarization ratios are pointed out.
Origin of the Temperature Dependence of the Ultrasonic “Rotational Relaxation” Time
Authors: Raff L. M. , Winter T. G.
Published: February 2004

An investigation of the origin of the anomalous temperature dependence of the rotational equilibration time is reported. Systems of H2, D2, and N2 have been studied. In each case the rotational system has been represented as a multilevel ensemble. The transition constants kij for transitions j → i are obtained from a simple, line-of-centers collision model and contain one common adjustable parameter which is fixed by fitting room-temperature ultrasonic velocity dispersion data to the model. Equilibration rates are obtained via numerical solution of the master equation. Velocity dispersion curves are then calculated under the assumptions of gaseous ideality and rotational Boltzmann equilibrium at all times. The individual transition constants kij obtained in the formalism exhibit both positive and negative temperature coefficients depending upon the i–j spacing. Positive coefficients are associated with large rotational spacing while negative values result from small spacings. The calculated ultrasonic velocity dispersion curves correspond to experiment with near quantitative accuracy over a 700°K temperature range. The ultrasonic frequency at which dispersion occurs decreases with increasing temperature, and this effect does not appear to be due to the negative temperature coefficient exhibited by the transition constants for the low-J states. Likewise, the effect is not directly associated with a decrease in collision rate at unit pressure as T increases. In general, it is concluded that the apparent negative temperature coefficient associated with the over-all ultrasonic equilibration process is due to the multilevel character of the system and to the fact that the adjacent level spacing increases linearly with rotational quantum number. It is shown that the equilibration process can not be adequately described by a simple relaxation expression with a single time constant, and the misleading character of the term “rotational relaxation time” is pointed out.
Convexity of the H Function: The Weak-Coupled Master Equation
Authors: Harris S.
Published: February 2004

We show, for the weak-coupled master equation, that the choice of H function which preserves the usual relationship with the thermodynamic entropy is convex as a function of time.
Self-Consistent Methods in Hückel Theory
Authors: Harris Frank E.
Published: February 2004

A study is made of the equations defining minimum-energy molecular orbitals for Hückel-theory calculations in which the parameters depend upon the charge distribution. It is shown that these equations are not equivalent to iterative solution of the usual Hückel equations, as the latter equations do not properly describe the variation of the energy upon change of the charge-dependent parameters.
Triplet–Triplet Annihilation and Delayed Fluorescence in Isotopic Mixed Crystals of Benzene
Authors: Hatch G. F. , Nieman G. C.
Published: February 2004

The behavior of triplet excitations of a single isotopic guest in a benzene crystal (C6H6 in C6D6) is investigated as a function of temperature from 2° to 15°K by detailed measurements of the phosphorescence. It is found that even in dilute systems there is significant (∼20% for 0.2% guest) temperature-independent annihilation below 8.0°K. Above 8.0°K a thermally activated annihilation process dominates the phosphorescence quenching in an ultrapure sample. Thus while the first-order decay rate, which includes impurity quenching, increases by less than a factor of 2, the second-order annihilation rate increases by five orders of magnitude when the temperature is raised from 4° to 12°K with an activation energy equal to the known trap depth. The difficulty of fitting a nonexponential decay to the combination of first- and second-order decays is discussed and a new method is suggested which accomplishes this. Measurements of the temperature dependence of the phosphorescence decay, the steady-state phosphorescence intensity, and the steady-state delayed fluorescence intensity provide independent evaluations of the annihilation rate which are in good agreement with one another at all temperatures. The low delayed-fluorescence quantum yield in benzene is discussed.
Structure of Piperazine Hexahydrate
Authors: Schwarzenbach D.
Published: February 2004

Piperazine hexahydrate, C4N2H10·6H2O, forms monoclinic pseudo-tetragonal and usually strongly twinned crystals, melting at 44°C. The structure has been determined using x-ray counter data obtained at room temperature. The space group is P21 / n, with Z = 2, and cell dimensions are a = 6.309, b = 6.323, and c = 14.912 Å, β = 94.96°. The hydrogen-bonded water molecules form puckered layers of almost tetragonal symmetry composed of edge-sharing pentagons, which are joined into a three-dimensional framework by hydrogen bonds to the nitrogen atoms of the piperazine molecules. The twin laws are explained as stacking faults of the water layers. The hydrogen atoms are disordered within the water layers and ordered between the oxygen and nitrogen atoms. The bond lengths and angles of the piperazine molecule are normal. The structure is related to the clathrate hydrate structures because of the pentagonal geometry of the water structure.
Spin Polarization in an Aliphatic Fragment: Comparison between Proton Hyperfine Interaction and Spin–Spin Coupling
Authors: Luz Zeev
Published: February 2004

Expressions are derived for proton hyperfine interaction constants (hfs) in an aliphatic chain arising from a single unpaired pπ electron on the first carbon atom. The method used is the Dirac vector model. Only spin polarization is considered, while electron delocalization is neglected. The resulting expressions are very similar to those derived by Alexander for proton spin–spin coupling. This makes it possible to use experimental spin–spin data for a semiempirical estimate of the contribution of spin polarization to the aliphatic proton hfs. It is found that spin polarization contributes substantially to the hfs of protons removed up to five bonds from the pπ center. The contribution of spin polarization to α-proton hfs is positive and amounts to about 50% of the observed value. For β and γ protons spin polarization contributes, respectively, negative and positive spin densities of the order found experimentally. Deviations from the calculated values are discussed in terms of spin delocalization and conformational effects.
Energy Dependence of Charge-Transfer Reactions in the Thermal and Low-Electron-Volt Region
Authors: Wolf Fred A. , Turner B. R.
Published: February 2004

A method is presented for extrapolating to lower energies the cross sections for charge transfer which have been measured by beam techniques for incident kinetic energies greater than 1 eV. The method combines the Rapp and Francis resonance charge-transfer theory with the Langevin capture model, and is based upon a simple superposition of the “noncapture resonance” and “capture resonance” probabilities resulting in charge transfer. Also illustrated is a method for including nonrectilinear orbits in the Rapp and Francis model. Application of the theory to the negative-ion charge-transfer reactions O−, O2−, O3−, and OH− with NO2; the positive-ion charge-transfer reactions O+, O2+, N+, and N2+ with NO; and N+ with O2 is given, and comparisons with existing experimental data are made. The method appears to be a reasonable approximation provided that the relative probability of the charge-transfer channel emerging from the capture-formed complex is independent of the relative kinetic energy of the reactants.
Measurement of Line Strengths at Low Pressures—Application to the 2–0 Band of CO
Authors: Korb C. Laurence , Hunt Robert H. , Plyler Earle K.
Published: February 2004

The use of low pressures and a high-resolution spectrometer for the measurement of the absolute line strengths of gases in the near infrared is tested on the first overtone band of carbon monoxide. Measurements are made at pressures from 100 to 500 μ Hg, where the line profile has nearly a pure Doppler contour, and at pressures 2 to 7 cm Hg, where the effects of Doppler and collision broadening are both important. It is found that both wing and base corrections must be made in higher-pressure measurements, and these corrections are given for lines with combined Doppler and collision-broadened profiles. It is found that the use of the Doppler profile offers significant advantages for the accurate determination of line strengths, and a discussion of these advantages are included. It is shown that within the accuracy of the measurements, the true line profile at pressures from 100 to 500 μ Hg cannot be distinguished from the assumed Doppler profile. The band strength of the first overtone band of CO is calculated from the measured line strengths, and the best value obtained at a temperature of 273°K is 2.06 ± 0.07 cm− 2·atm− 1.
Hyperfine Splitting of the Interaction Energy in H + D and in D + D
Authors: Milleur Mac B. , Curtiss Larry A. , Twerdochlib Michael , Hirschfelder Joseph O.
Published: February 2004

The hyperfine interaction of a ground-state D atom with either a ground-state H or a ground-state D atom is treated. For H + D there are 24 hyperfine states with 12 potential-energy curves, and for D + D there are 36 hyperfine states with 22 potential-energy curves. At separations greater than 9a0 to 10a0, the electronic spins (for most of these hyperfine states) become partially decoupled and one can no longer refer to the molecule as being an electronic singlet or an electronic triplet.
Mechanism of Hydrogen Formation in the Radiolysis of n-Pentane
Authors: Horowitz A. , Rajbenbach L. A.
Published: February 2004

The radiolytic yields of trichloroethylene, hydrogen, and hydrogen chloride from solutions of tetrachloroethylene in n-pentane were determined. A mechanism for radiolytic hydrogen formation, which assumes the existence of three precursors of hydrogen, is postulated. The initially formed excited species C5H12′ is assumed to yield thermal hydrogen atoms. This species is scavenged at low tetrachloroethylene concentrations. Molecular (unscavengeable) hydrogen is assumed to be formed from the decomposition of another excited species, C5H12″, a process which is not affected by the presence of tetrachloroethylene. Hot hydrogen atoms are assumed to be formed mainly from charge recombination reactions. The reduction in hydrogen yield at concentrations above 10−2M tetrachloroethylene is due predominantly to electron scavenging by the solute. Kinetic treatment of the results gives the following G values for the hydrogen yield resulting from the decomposition of C5H12′ and C5H12″ and from charge recombination reactions: G(H) thermal = 1.0; G(H2) molecular = 1.6; G (H2) electronic = 2.3.
Molecular Theory of Flow Alignment of Nematic Liquid Crystals
Authors: Helfrich W.
Published: February 2004

A mechanism to explain flow alignment of nematic liquid crystals is proposed. It is based on the rodlike shape of the molecules of these substances. A model calculation is performed in which the molecules are assumed to be equally and rigidly oriented ellipsoids of revolution, colliding with each other like the molecules of a gas. The two coefficients governing the linear relationship between torque per unit volume and shear rate are derived. The theory is used to predict the degree of flow alignment (which is found to be incomplete and to be independent of the shear rate) and to establish a relationship between the viscosity and one of the shear–torque coefficients. Theory and experiment are compared for p-azoxyanisole, and good agreement is found.
Dynamics of the Reactions of N2+ with CH4 and CD4
Authors: Gislason E. A. , Mahan Bruce H. , Tsao Chi-wing , Werner Arthur S.
Published: February 2004

Product velocity vector distributions have been determined for the reactive and nonreactive scattering of N2+ by CH4, CD4, and Ne. In the most probable reactive events, N2H+ and N2D+ are scattered forward at almost exactly the velocity calculated from the ideal stripping model. At the higher projectile energies, the internal excitation of CH3 even for zero angle scattering is significant, and product internal excitation increases with increasing angle. A large isotope effect favoring abstraction of H over D was found. The nonreactive scattering showed the occurrence of highly inelastic collisions, even for small angle scattering, and a feature which may be due to the collisional electronic excitation of CH4 or of N2+ was discovered.
Variational Solution of the Chemical-Kinetic Boltzmann Equation
Authors: Present R. D. , Morris B. M.
Published: February 2004

Variational principles are formulated for the linearized molecular Boltzmann equation and it is shown that if a perturbation of the Maxwell distribution maximizes the nonequilibrium correction to the reaction rate, subject to an equation of constraint, it is a solution of the integral equation describing a gas-phase reaction. A corollary is that the Chapman–Enskog–Burnett subapproximations generate lower bounds for the nonequilibrium correction to the reaction rate. Since it has been shown previously that the Chapman–Enskog method is useless in the treatment of slow activated reactions because the Sonine polynomial expansion diverges, the variational method is applied to the same problem using a trial function that is not in polynomial form. We use the trial perturbation function ψ = A [exp(γc2) + ac2 + b] where a and b are fixed by the auxiliary conditions and A by the equation of constraint and γ is an adjustable variation parameter. An order-of-magnitude improvement and increase in the nonequilibrium correction over the previous two-polynomial approximation is obtained for ε* / kT = 20 → 30 where ε* is the activation energy; however, the correction is still negligibly small. Small improvements are obtained for fast activated reactions and for free-radical recombinations.
Vacuum-Ultraviolet Photolysis of N2O. II. Deactivation of N2(A 3Σu+*rpar; and N2(B 3Πg)
Authors: Young R. A. , Black G. , Slanger T. G.
Published: February 2004

Quenching of N2(A 3Σu+), produced during the photodissociation of N2O with 1470-Å radiation, was studied using the NO γ-band emission excited by the process N2(A 3Σu+) + NO → N2 + NO(A 2Σ+) as a monitor of N2(A 3Σu+). The relative quenching efficiencies of NH3, C2H2, C2H4, NO, C2N2, N2O, O2, CO, CO2, H2 CH4, N2, Ar, and He are 2.6, 2.3, 2.2, 1, 0.8, 0.091, 0.054, 0.036, < 4 × 10−4,≤ 10−4, < 10−4, < 10−4, < 10−4, and < 10−4. At 1236 Å the B 3Πg state of N2 is produced in N2O photolysis and the variation of the intensity of N2O first positive emission with N20 pressure was used to evaluate the quenching rate of N2(B 3Πg) by N2O. The value obtained was 1.6 × 10−10 cm3 molecule−1·sec−1. Quenching efficiencies for other gases were determined relative to N2O and hence absolutely. The values obtained for NO, CO2, O2, CO, H2, N2, Ar, and He are ∼2.4 × 10−10, 1.5 × 10−10, 1.1 × 10−10, 8.5 × 10−11, 4.6 × 10−11, 2.7 × 10−11, 1.6 × 10−12, and 8 × 10−13 cm3 molecule−1·sec−1.
Rotatory-Diffusion Broadening of Rayleigh Lines Scattered from Optically Anisotropic Macromolecules in Solution
Authors: Wada Akiyoshi , Suda Nobuhiro , Tsuda Toshio , Soda Kunitsugu
Published: February 2004

A technique for the spectroscopic detection of pure rotatory Brownian movement of anisotropic macromolecules in solution are developed in combination with a high-resolution optical heterodyne spectrometer. The line broadening originating in the translational diffusion of the solute macromolecule, which is a dominant factor in intensity in the Rayleigh component, is suppressed by taking the forward scattering. Then, only the depolarized light whose amplitude is fully modulated by the rotation of solute molecules is filtered off by the polarizer and received by a photomultiplier tube. The time-dependent component of the output from the phototube is analyzed by a wave analyzer to give a spectrum of the scattered light. From the spectral linewidth thus obtained, the rotatory diffusion coefficient of Tobacco Mosaic Virus in aqueous solution has been obtained and found to be 350 ± 20 sec−1. On the other hand, the optically isotropic polystyrene latex sphere has shown no broadening in this system. From these results and from the evidence of sharpening of the linewidth with increasing solvent viscosity, it is concluded that the observed broadening originates in the amplitude modulation of the scattered light by the rotatory diffusion of TMV. This “depolarized light mixing” technique is quite general and able to cover a frequency range from 101 to 107 Hz. And it is believed to be useful especially in the studies of rotatory diffusion and transconformation of anisotropic macromolecules, and in studies of chemical kinetics accompanying an anisotropic change of polarizabilities.
Densitometric Measurement of the Vibrational Relaxation of HCl and DCl in Shock Waves
Authors: Breshears W. D. , Bird P. F.
Published: February 2004

The vibrational relaxation of HCl and DCl has been studied behind incident shock waves in the temperature range 700°–2100°K. Relaxation was followed by time-resolved measurement of the postshock density gradient using a laser-beam-deflection technique. Hydrogen chloride is found to relax more rapidly than DCl. The relaxation times obtained at temperatures above 1000°K are summarized by the expressions (Pψ)HCl = (4.21 ± 0.14) × 10−7exp[(64.0 ± 5.7) (T−1/3 − 0.090)]atm·sec(1000°–2000°K), and (Pψ)DCl = (7.41 ± 0.09) × 10−7exp[(77.7 ± 2.1) (T−1/3 − 0.090)]atm·sec(1000°–2100°K). The values depart from Landau–Teller behavior at lower temperatures. These results are in serious disagreement with those of Borrell and with predictions of the SSH theory. However, they are in good agreement with the theory of Moore, suggesting that rotation–vibration energy transfer is important in the relaxation of HCl and DCl. Possible effects of strong dipole interactions are also discussed.