Volume 27, Issue 6, 01 December 1957
Index of content:
27(1957); http://dx.doi.org/10.1063/1.1743984View Description Hide Description
From the viewpoint of Kirkwood's theory, the general formula of rotatory dispersion is presented. This formula is then applied to the rotatory dispersion of protein. Under reasonable assumptions, the behavior of the critical wavelength λ C , which seems to be a measure of denaturation, may well be interpreted. The rotatory dispersion of DNA is also explained as the sensitive reflection of the structural characteristics of this molecule. In the case of the latter substance, special attention is focused on Condon's one‐electron effect.
27(1957); http://dx.doi.org/10.1063/1.1743985View Description Hide Description
The equations of Kirkwood and Salzburg for distribution functions are generalized to multicomponent systems. The generalized equations serve to derive a recurrence relation between the coefficients of powers of particle number densities in a Maclaurin expansion of the distribution functions. This recurrence relation is then used to derive the general term in the expansion of the distribution functions in terms of modified irreducible integrals in multicomponent systems, which includes the original one‐component expansion of Mayer and Montroll as a special case.
The corresponding expansion of the potentials of average force is derived. The use of the new expansion is illustrated by a relatively simple derivation of the Fuchs expansion of the grand potential in multicomponent systems.
Possible applications to ionic solutions, impurities in solids and x‐ray diffraction in solutions of several solutes are briefly discussed.
Some new formulas in the theory of cumulants (Thiele semi‐invariants) are presented.
MO‐Theoretical Approach to the Mechanism of Charge Transfer in the Process of Aromatic Substitutions27(1957); http://dx.doi.org/10.1063/1.1743986View Description Hide Description
An MO‐theoretical investigation on the mechanism of aromatic substitution is made. Supposing that the approaching reagent and the atom to be replaced can be treated as an atom (pseudoatom) which has a π‐type orbital in the course of reaction, an important role of hyperconjugation taking place between the pseudoatom and the aromatic compound is remarked. Since the electron density at the pseudoatom relates to the amount of charge transfer through this hyperconjugation and varies as the reaction proceeds, the proceeding of the reaction can be measured by this electron density. Then, the electron density is expressed, in the form of a contour diagram, in terms of the Coulomb integral of the pseudoatom and the resonance integral between the pseudoatom and carbon atom to be attacked. Thus, a reaction path can be represented by a locus plotted on this diagram. The discriminating property of frontier orbitals can be observed in this diagram. It has been confirmed that an electrophilic, or a nucleophilic, substitution takes place only when a certain condition is satisfied with respect to the energy of the reagent. By determining the transition state which corresponds to the end point of the locus, several reactivity indices, i.e., frontier electron density, superdelocalizability, its one‐term approximation and a generalized reactivity index are derived from the hyperconjugation energy at the transition state, which is also available as a generalized reactivity index. Correlation between these and the existing indices is examined.
27(1957); http://dx.doi.org/10.1063/1.1743987View Description Hide Description
The structure of chloropicrin was studied as a step in the investigation of several families of methane derivatives to determine variations in carbon bond angles and bond lengths in compounds having approximately tetrahedral carbon bonds. The results obtained showed the carbon‐nitrogen bond to be longer in chloropicrin than in either nitromethane or tetranitromethane.
The electron diffraction patterns were obtained in a camera in which high background intensity gradients were corrected by means of a rotating shutter intercepting the scattered electrons. Intensity curves derived from microphotometer traces were subjected to Fourier analysis to obtain a radial distribution function. Intensity curves were synthesized for a series of molecular models to make a refined determination of the molecular parameters for chloropicrin.
27(1957); http://dx.doi.org/10.1063/1.1743988View Description Hide Description
The heat capacity of high‐purity calcium has been measured over the temperature interval from 1.8 to 4.2°K. The electronic contribution is linear in T and the coefficient γ is 3.08±0.01 millijoules/(gram‐atom) deg2 corresponding to a density of states at the Fermi level of 0.653 momentum state per electron volt per atom. A Debye temperature of 239±2°K was obtained.
For purposes of testing the calorimeter, the heat capacity of copper was determined. In agreement with other recent measurements, the value obtained for γ is 0.691±0.006 millijoule/(gram‐atom) deg2 and θ D is 342±2°K.
27(1957); http://dx.doi.org/10.1063/1.1743989View Description Hide Description
The weak bands of formaldehyde extending from λ3500 A to λ2300 A are normally assigned to a 1 A 2←1 A 1, n→π transition (C 2ν symmetry) which is forbidden by electronic selection rules. The present paper gives a quantitative theoretical discussion of the total intensity of these bands in each of the three directions of polarization. Using approximate wave functions for the various electronic states involved, the theory shows that the intensity of the perpendicular bands can be accounted for by vibrationally‐induced mixing of excited electronic states. The calculated total intensity due to this mechanism is f=3×10—4. It is predicted that most of this intensity is produced by the out‐of‐plane bending vibration and is consequently polarized perpendicular to the C–O axis and in the molecular plane (B 1 polarized). The contribution due to in‐plane vibrations (CH2 wagging and antisymmetric C–H stretch), which would be polarized perpendicular to the molecular plane (B 2 polarized), is predicted to be much weaker. This is in agreement with experiment.
The weak parallel bands that have been observed cannot be interpreted in terms of vibrational‐electronic interaction. It is suggested that these derive their intensity by borrowing, induced by rotation around the C–O axis, from the strong 1 A 1←1 A 1, π→π transition. A quantitative theory of this effect gives f∼10—6 for the total oscillator strength of the parallel bands. Several predictions which might be tested experimentally are made on the basis of this hypothesis.
27(1957); http://dx.doi.org/10.1063/1.1743990View Description Hide Description
Nitrogen dioxide was photolyzed at trace concentrations in a carrier gas at a pressure of 1 atmosphere. The concentration of atomic oxygen could be estimated by using rate constants previously obtained [H. W. Ford and N. Endow, J. Chem. Phys. 27, 1156 (1957)]. An iterative method was used to calculate the concentration of atomic oxygen in the presence of trace amounts of hydrocarbons. Rate constants for the reactions of atomic oxygen with various hydrocarbons are reported, together with other closely related rate constants reported previously.
27(1957); http://dx.doi.org/10.1063/1.1743991View Description Hide Description
The dipole‐dipole part of the London‐van der Waals interaction energy of a system of N molecules is calculated in the general order of perturbation, using a model which represents each molecule as an isotropic harmonic dipole‐oscillator. The calculation assumes that the characteristic dispersion frequencies of the molecules are all equal. The advantages and limitations of the oscillator model are discussed.
27(1957); http://dx.doi.org/10.1063/1.1743992View Description Hide Description
The London‐van der Waals cohesive energy of a linear lattice is calculated in the dipole‐dipole approximation, including all orders of perturbation. This result is obtained by applying the Born‐von Kármán method to the electronic motions, using a model which represents each molecule as an isotropic harmonic dipole‐oscillator. The dispersion interaction energy of the lattice is expanded in powers of the parameter α/a 3 (where α is the molecular polarizability and a the nearest neighbor distance), and is computed up to the eighth order. For values of α/a 3 appropriate to actual molecular crystals, the main contribution to the energy comes from the second order. Among the higher order terms, the third order is always important, but for α/a 3≥0.06, contributes less than one‐half of the total correction to the second‐order energy.
27(1957); http://dx.doi.org/10.1063/1.1743993View Description Hide Description
A treatment is developed to interpret the observation that in corresponding regions of the ultraviolet the absorption spectra of sodium iodide and potassium iodide show a band system and a continuum, respectively. The former results from a bound excited state in which the form of the electronic wave function changes drastically with internuclear distance. The latter arises because the nuclear motion can no longer be considered adiabatic with respect to electronic motion, so that the noncrossing rule does not apply.
27(1957); http://dx.doi.org/10.1063/1.1743994View Description Hide Description
The mass spectrum of OF2 includes the ions OF2 +, OF+, O+, and F—. The ionization potential of the molecule and appearance potentials and excess kinetic energy are measured for the OF+ and F— ions. The known heat of formation of OF2 and the appearance potential of the F— ion permit calculation of the bonddissociation energiesD(FO–F) and D(O–F) and an estimate of the ionization potential,I(OF). Dissociation energies estimated for the OF2 + ion are consistent with those of the neutral molecule.
27(1957); http://dx.doi.org/10.1063/1.1743995View Description Hide Description
Paramagnetic‐resonance absorption has been observed in complexes of acetylacetone with the trivalent transition metalstitanium,chromium,iron,molybdenum, and ruthenium. The symmetry of the field perturbing the metal ion is predominantly axial. For the complexes of Ti+3 and of Ru+3, the axial potential is negative. Energy‐level splittings by the ligand field and g factors were obtained for the various complexes. Resonance was also observed in complexes of trifluoroacetylacetone with chromium and iron and in the complex chromium (III) hexafluoroacetylacetonate. Resonance could not be detected in the complexes vanadium (III) acetylacetonate, manganese (III) acetylacetonate and ferric (III) hexafluoroacetylacetonate, although magnetic‐susceptibility measurements on the last two compounds indicated that they were paramagnetic.
27(1957); http://dx.doi.org/10.1063/1.1743996View Description Hide Description
The infrared spectra of monomeric HCOOH, HCOOD, DCOOH, and DCOOD have been studied in the gaseous phase with emphasis on the 800 to 450 cm—1 region. New absorption bands were found for HCOOD at 541 and 512 cm—1, and for DCOOD at 538 and 489 cm—1. These bands are attributed to the a′ OCO bending and to the a″ O–D torsion motions, respectively. In HCOOH and DCOOH the bands arising from the corresponding vibrations apparently coincide at approximately 630 cm—1. An assignment of fundamentals for the four isotopic species has been derived. Excellent agreement is obtained with the Teller‐Redlich product rule. Also the calculated entropy agrees with the experimental value from the third law of thermodynamics.
27(1957); http://dx.doi.org/10.1063/1.1743998View Description Hide Description
27(1957); http://dx.doi.org/10.1063/1.1743999View Description Hide Description
The molecular structure of 1,3,5,7‐cyclooctatetraene has been studied by a sector‐microphotometer technique using data extending to very much larger scattering angles than were obtained in earlier investigations. An application of the method of least squares to sector‐microphotometer data in electron diffraction worked out by one of us (KH) has led in three refinement stages to unusually precise values for the parameters. The following are the more interesting parameter values with standard errors. It should be noted these results do not include a possible error of up to 0.2% in the scale of the molecule because of uncertainties in the electron wavelength, nor do they include the effect of correlations among the observations on the standard errors, which we estimate might increase the standard errors by as much as the factor 2½. Molecular symmetry.
Thermoluminescence and Coloration of Lithium Fluoride Produced by Alpha Particles, Electrons, Gamma Rays, and Neutrons27(1957); http://dx.doi.org/10.1063/1.1744000View Description Hide Description
The coloration and thermoluminescence produced in LiF by 2 Mev alpha particles, by 2 Mev electrons, by 1 Mev gamma rays from Co60, and by thermal neutrons are described. The energy initially required to produce an F center varies. It is about 700 ev for alpha, 140 ev for beta, 65 ev for gamma rays, and 65 ev for thermal neutrons.
The amount of thermoluminescence light produced and the number of thermoluminescence peaks increased with the exposure to each of these radiations. The larger the radiation dosage, the greater is the fraction of thermoluminescence emitted at the higher temperatures. All of the thermoluminescence is related to the emptying of F centers, but only one photon is emitted as visible thermoluminescence for every 104 electrons removed from F centers.
The optical and thermal decolorizations are discussed.
Investigations of the Detonation Properties of Condensed Explosives with Equations of State Based on Intermolecular Potentials. I. RDX with Fixed Product Composition27(1957); http://dx.doi.org/10.1063/1.1744001View Description Hide Description
An attempt is made to determine an average pair potential of intermolecular force for the mixture of product gases of the condensed explosive RDX (cyclotrimethylenetrinitramine) from measurements of the detonation velocity. The principal approximations are that the products of detonation consist of CO, H2O, and N2 in equimolar proportions and that the equation of state for this mixture can be calculated from theories of the free‐volume type with the use of an average intermolecular potential. It was found that the average intermolecular potential was fairly well determined at distances somewhat less than the crossover distance.
This result was almost independent of the choice of equation of state, although the calculated values of detonation temperature and pressure were not.
27(1957); http://dx.doi.org/10.1063/1.1744002View Description Hide Description
Compressed and uncompressed powders of several alkali halides (KCl, KBr, KI, CsI) have been colored by x‐rays and by chemical addition and their spectra measured. The x‐ray darkenability of pellets is greater than of single crystals, with respect to F, V 2, and V 3 bands. The F centers are relatively unstable optically; their bleaching is rapid and complete and does not give rise to appreciable K, M, R and N bands, in contrast to F centers in single crystals. After F irradiation the pellets still exhibit intense, well‐resolved V 2 and V 3 bands and, upon dissolving in water, liberate free halogen. The relative intensity of the F and V bands may be controlled by varying the x‐ray or F‐light exposure. KI pellets may be additively colored at room temperature with iodine. In general V bands may be produced by adsorbing halogen onto the crystalline surface and are more stable in the compressed pellets than the unconfined powder. By virtue of their different physical makeup from a single crystal the pellets exhibit the above color‐center phenomena to a larger degree than single crystals.
Effect of Change in Moment of Inertia on the Intensity Distribution in P and R branches of C∞v Molecules27(1957); http://dx.doi.org/10.1063/1.1744003View Description Hide Description
The effect of the change in moment of inertia part of the interaction between vibration and rotation on the intensities of parallel bands of linear polyatomic molecules has been determined to the first order. The results are quite similar to those of Herman and Wallis for diatomic molecules. The interaction term depends on among others a quantity, ξ k , different in general for each band. Perpendicular bands do not show a first‐order correction. A ``sum rule'' for the ξ k has been determined.