Volume 40, Issue 11, 01 June 1964

Resolution Enhancement for Spectra of Chemical and Physical Interest
View Description Hide DescriptionWhen a spectrum is composed of a superposition of lines with known shape and uniform width, the signal output of a spectrometer may be transformed into a spectrum whose effective resolution is significantly improved. If the line shapes are not precisely known or the linewidths not exactly uniform, it is still possible to achieve a worthwhile resolution enhancement. Decomposition and analysis of complex spectra is often aided by this transformation. The theory of filters which produce the desired transformation is developed. Digital and analog implementation for these filters is given as well as several examples.

Influence of Vibrations on Molecular Structure Determinations. III. Inertial Defects
View Description Hide DescriptionThe relationships between various types of moments of inertia and vibration—rotation corrections are developed from general theory, with emphasis on the qualitative physical features and the quantities which may be calculated without knowledge of anharmonic force constants. The inertial defects of planar triatomic and tetratomic molecules and nonplanar molecules with a plane of symmetry are considered, and it is found that simple approximations, which depend mainly on the one or two modes of lowest frequency, give results within 10%—20% of the experimental values. The application of inertial defect corrections in structure analysis is illustrated for the calculation of HH distances in CH_{2}Cl_{2}, SiH_{2}F_{2}, and CH_{3}CXO molecules (X = H, F, Cl, Br).

Absorption Spectra of H_{2} in the Vacuum‐Ultraviolet Region. I. The Lyman and the Werner Bands
View Description Hide DescriptionThe absorptionspectrum of the H_{2} molecule has been studied in the wavelength region 930–840 Å with a 6.8‐m grazing incidence vacuum spectrograph in combination with the helium continuum. The Lyman and the Werner bands have been extended to their dissociation limits. The results of the rotational analysis of these bands are given. Behavior of the C ^{1}Π_{ u } potential curve near the dissociation limit and predissociation found in the v = 13 level of the C state are also discussed.

Molecular Theory of Dissipative Processes in Gases
View Description Hide DescriptionThe velocity distribution function associated with a molecule entering a dilute gas, either in equilibrium or with a temperature gradient, is evaluated by solving a forward Boltzmann equation.
In the equilibrium case, the velocity distribution function associated with the molecules, other than the incoming molecule, is also evaluated and the contributions to the Kubo‐type coefficient of thermal conduction from both distribution functions are evaluated for Maxwellian molecules. These contributions give the coefficient of thermal conduction obtained by the Chapman—Enskog method.
The various mean accelerations experienced by a molecule moving in a gas are calculated using the above solutions of the forward equation and also the solutions of a backward Boltzmann equation. These expressions are then used to evaluate the friction coefficients, first introduced by Kirkwood, for both equilibrium and nonequilibrium gases.
An experimental procedure using radioactive particles injected into a gas is also suggested as a method of confirming the obtained results.

Phosphorescence in Nucleotides and Nucleic Acids
View Description Hide DescriptionAs a sequel to earlier work by Steele and Szent‐Györgyi, the phosphorescence of DNA, polyadenylic acids, and individual nucleotides in a water—glycerine glass at 77°K has been studied. Under these conditions, our experiments lead to the following conclusions: (1) Purine bases phosphoresce but pyrimidine bases do not, (2) the emission from DNA is the sum of independent emissions from guanine and adenine, and (3) if certain assumptions are valid, the triplet excitation is a delocalized exciton. Addition of paramagnetic ions to a polynucleotide results in quenching of the phosphorescence. If this effect is studied quantitatively, the diffusion coefficient of the exciton can be measured. This diffusion coefficient should be sensitive to the degree of order in the polynucleotides and to their composition.

Study of First‐Order Phase Changes in a Number of Organic Crystals
View Description Hide DescriptionThe change in the long lifetime τ_{2} for positron annihilation has been measured as a function of temperature for benzene, diphenylamine, cyclohexane, naphthalene, N‐phenylbenzylamine, p‐bromotoluene, and phenol. In each case, the temperature range covered a first‐order phase transition.

Theory of Adsorption of the Isotopic Hydrogen Molecules at Low Temperatures
View Description Hide DescriptionA theory of adsorption of the isotopic hydrogen molecules is developed where the potential of interaction of the adsorbed molecule with the plane surface is a function of two parameters. The Schrödinger equation is solved for the rotation—vibrational energy levels of the diatomic molecules in the adsorbed state. From these energy levels, isotopic and ortho—para separation factors and heats of adsorption are calculated by statistical thermodynamics. There is a reasonable correspondence between experimental separation factors and heats of adsorption derived from chromatographic experiments, and those computed from the theory for selected values of the potential parameters. The sequence of relative volatilities of the hydrogen isotopes and ortho—para species found experimentally is in accord with that predicted from the theory. Both the separation factors relative to para hydrogen and the heats of adsorption increase in the order; o‐H_{2}, HD, HT, o‐D_{2}, p‐D_{2}, DT, p‐T_{2}, and o‐T_{2}.

Vibrational Spectrum of Sodium Azide Single Crystals
View Description Hide DescriptionThe infrared and Raman spectra of a single crystal of sodium azide have been intensively investigated at 298° and 90°K using grating spectrometers. Selection rules for internal and lattice vibrations are determined by application of the unit cell (factor group) method of Bhagavantam and Venkatarayudu. The unit cell modes of the crystal belonging to irreducible representations of the unit cell group have been constructed to within a good approximation. Spectra in the infrared are characterized by the occurence of medium‐strength absorptions symmetrically spaced about the principal bands of the spectrum with a separation of 122 cm^{—1}. The observation of the Raman‐active rotatory lattice mode at this frequency confirms the assignment of the medium‐strength bands as sum and difference frequencies involving rotational motion of the azide ion as a rigid unit. Tentative assignments were made for all bands observed in the spectra and deduced frequencies for unobserved infrared lattice modes are presented. The spectra were found to be in good agreement with the accepted structure as described by the space group .

Self‐Consistent‐Field Theory. II. The LCAO Approximation
View Description Hide DescriptionIn Part I of this series, eigenvalueequations which apply to any electronic system were developed by means of a general coupling operator. These equations are here adapted to the method of linear combinations of atomic orbitals. The resultant matrix equations are applied to the helium atom for the configurations: ^{1} S, (1s)^{2}; ^{3} S, (1s) (2s); ^{1} S, (1s) (2s), using Slater 1s and 2s orbitals as basis functions.

Self‐Consistent‐Field Theory. III. General Treatment for Excited States
View Description Hide DescriptionThe general coupling operator defined in the first paper of this series is used, in conjunction with the modified variation method due to Weinstein and MacDonald, to formulate a general self‐consistent‐field scheme. In principle this permits the determination of the eigenfunctions and eigenvalues of any state of an electronic system with no restrictions on orbital occupancy, symmetry, or multiplicity. A tentative generalization of the concept of a Hartree—Fock function is given and the meaning of correlation energy, in the context of the modified variation method, is discussed.

Self‐Consistent‐Field Theory. IV. LCAO Approximation for Excited States
View Description Hide DescriptionThe pseudo‐eigenvalue equations previously obtained for any state of an electronic system are brought into the form required by the LCAO approximation. The matrix formulation involved is discussed and some practical methods for reducing the value of the maximum error of the evaluated energy are given.

Off‐Center Hydrogen Atom Calculations
View Description Hide DescriptionStudies are carried out of truncated expansions of a hydrogen‐atom 1s orbital in spherical harmonics at another center, with Coulson—Barnett and with Slater‐orbital radial factors.

Phase‐Space Theory of Chemical Kinetics
View Description Hide DescriptionA theory of the cross sections of three‐body gas‐phase reactions which proceed without activation energy is presented. It is based on the hypothesis that the decomposition of a collision complex is governed by the phase space available to each product under conservation of angular momentum and energy. Calculations on model ion—molecule systems show that the cross section is enhanced if the reaction is exothermic, the final reduced mass is large, and the final long‐range attractive forces are large. The theory gives a consistent explanation for the cross sections of the reactions between He^{+} and H_{2}, and He and H_{2} ^{+} which is in satisfactory agreement with experiment.

Partial Pressures in Equilibrium with Group IV Tellurides. I. Optical Absorption Method and Results for PbTe
View Description Hide DescriptionAn optical‐absorption method has been developed for measuring the partial pressures of Te_{2}(g) and MTe(g) in equilibrium with MTe(c), where M is Pb, Sn, or Ge. The partial optical densities of Te_{2}(g) at 4360 Å and of MTe(g) at 3650 or 3100 Å are obtained by a Beer's‐law analysis of the data, which use optical constants for Te_{2}(g) and MTe(g) found in calibration experiments. Published vapor‐pressure data are then used to calculate the partial pressures of Te_{2}(g) and MTe(g) from their respective partial optical densities.
This paper reports results obtained by the optical absorption method for the Pb–Te system. Between 725° and 924°C, the maximum melting point of PbTe, the partial pressure of PbTe(g) in equilibrium with solid PbTe is given by logp(Torr) = —11,430/T°K+10.612, corresponding to a heat of sublimation of 52.3±1.0 kcal/mole. The PbTe(g) partial pressure is independent of the composition of PbTe(c) within the limits of experimental error. The partial pressure of Te_{2}(g) varies strongly with the composition of the solid phase, as shown by data for Pb‐saturated and Te‐saturated PbTe. The maximum partial pressure of Te_{2}(g) in equilibrium with PbTe(c) is 12.5 Torr, which is attained between 796° and 832°C for Te‐saturated PbTe. At these temperatures the partial pressures of Te_{2}(g) in equilibrium with Pb‐saturated Te are about two orders of magnitude smaller. The partial pressures of PbTe(g) and Te_{2}(g) in equilibrium with PbTe(c) at its maximum melting point are 11.8 and 2.5 Torr, respectively.

Nuclear Magnetic Double Resonance Spectrum of Ammonia
View Description Hide DescriptionIf the magnitude of the second rf field is small, proton nuclear magnetic double resonance spectra of ammonia, recorded by sweeping the magnetic field, are in good agreement with a calculation based on a treatment of double resonance which neglects relaxation effects. To calculate the width of spectral lines it is assumed that one relaxation mechanism is dominant, and that linewidths are small compared to the separation of a given multiplet. With these assumptions, a linewidth can be associated with the lifetimes of states giving rise to that line. The calculation of field‐sweep double resonance spectra is discussed in detail, and calculated spectra are displayed by photographing traces formed on the on‐line oscilloscope of an IBM 7090 digital computer. For larger magnitudes of the second rf field, the treatment neglecting relaxation fails to describe adequately the observed field‐sweep double resonance spectra. A limited calculation based on the density matrix treatment of double resonance indicates that the effect of the second rf field on line shape is significant. The density matrix theory presented here has been extended to include exactly overlapping lines, but neither degenerate energy levels nor partially overlapping lines are considered.

Raman Spectral Studies of Water Structure
View Description Hide DescriptionRaman frequencies and polarizations and infrared frequencies of water and heavy water have been obtained, and the intermolecular vibrations of water have been related to a five‐molecule hydrogen‐bonded C _{2v } model consistent with x‐ray data. Observed variations of the integrated Raman intensity of the 175‐cm^{—1} hydrogen‐bond‐stretching vibration, with variations of temperature, have been interpreted in terms of the five‐molecule model. That interpretation leads to reasonable values for the enthalpy of hydrogen‐bond formation. Effects of electrolyte addition on the intensity of the 175‐cm^{—1} band are also described.

Effects of Pressure on the Resistivity of Some Organic Charge‐Transfer Complexes
View Description Hide DescriptionThe effect of pressure on the electrical resistance of samples of several organic charge‐transfer complexes was investigated over the range 1 to 15 kbars. The resistances decreased exponentially with increased pressure up to at least 6 kbars. At higher pressures, a different behavior was observed in only two complexes; their resistivities leveled off. These latter compounds had very low resistivities at atmospheric pressure.

Radial Distribution Functions from a Linear Integral Equation
View Description Hide DescriptionA linear integral equation derived by Mayer for the radial distribution function of fluids has been investigated numerically. To compare with other recent investigations of integral equations, a Lennard‐Jones 6–12 potential was used and the 55°C isotherm of argon investigated. Results for the pressure and the radial distribution function are less satisfactory than are obtained with other integral equations. An estimate of the validity of Kirkwood's superposition approximation in the range of the calculation was also made.

Photoionization of Aliphatic Ketones
View Description Hide DescriptionThe photoionization of a series of ketones, acetone, 2‐butanone, 2‐pentanone, 3‐methyl‐2‐butanone, 2‐hexanone, and 4‐methyl‐2‐pentanone was studied using mass spectrometric techniques. Adiabatic ionization potentials were determined. It was found that for the ketones the cross section above threshold is not constant, and a modified method of treatment of the results was developed in order to obtain information about fragmentation processes. The shifts in appearance potentials of fragments with increasing temperature were found to be close to the change in internally stored energy. Bond dissociation energies in ions were calculated. The adiabatic ionization potential of the acetyl radical was calculated to be 7.08 eV, which is considerably lower than reported by authors using electron impact where no effort was made to distinguish between adiabatic and vertical ionization potentials. A lower limit was calculated for the ionization potential of the n‐propyl radical leading to a value of the adiabatic ionization potential of 7.2±0.2 eV.

On the Relaxation Effect in the Electrical Conductivity of Plasmas and Electrolytes
View Description Hide DescriptionWe apply the general formalism developed by Prigogine and co‐workers to the problem of transport in plasmas and in electrolytes. Taking into account the collective effects due to the long range character of Coulomb forces, we obtain first an exact transport equation for a dilute plasma which we then generalize to an electrolyte, using a semiphenomenological description of the solvant. Special attention is given to the internal field effect which is shown to result from the interference between the external field and the collision processes. We show that, in very simple cases, good agreement is obtained with the Debye—Onsager limiting laws.