Volume 25, Issue 1, 01 July 1956
Index of content:
25(1956); http://dx.doi.org/10.1063/1.1742798View Description Hide Description
The free‐electron network model for conjugated systems is extended to include electronic interaction. The free‐electron wave functions are considered as molecular orbitals arising from an average one‐electron potential, and a configuration interaction treatment with these MO's is developed. The integrals occurring in this procedure, in particular the electron interaction integrals, are analyzed and a convenient method for their computation in the FE model is suggested. The integral evaluation requires certain semiempirical parameters which are determined from the benzene spectrum.
Electronic Interaction in the Free‐Electron Network Model for Conjugated Systems. II. Spectra of Aromatic Hydrocarbons25(1956); http://dx.doi.org/10.1063/1.1742804View Description Hide Description
A theoretical calculation is presented for the main uv transitions of the polyacenes, azulene, phenanthrene, the isomers of naphthacene and the peri‐condensed systems pyrene and coronene. A configuration interaction treatment, based on antisymmetrized products of free‐electron molecular orbitals, is carried out, using the methods developed for this purpose in the previous paper. Transition energies, intensities and polarizations compare well with experiment. Particular emphasis is placed upon illuminating the various factors influencing the spectra in the series of molecules considered.
25(1956); http://dx.doi.org/10.1063/1.1742841View Description Hide Description
An analysis of the published data on the pyrolysis of dimethyl ether shows that the reaction can be interpreted as a chain decomposition initiated by , terminated by CH3 radical recombination and accelerated by the chain transfer reaction CH3+H2→CH4+H. A simplified Rice‐Herzfeld mechanism then gives for the over‐all rate of reaction the expressionwhere k 0=k 2(k 1/k 10)½; k 2 representing H abstraction by CH3 from Me2O and k 10, CH3 recombination.
The data yield a value of k 0=4.31×10—3 (liter/mole)½ sec—1 at 777°K. Using published data on k 2 and k 10, an estimated activation energyE 1=81.1 kcal and an estimated value of ΔS 1 0=38 cal/mole‐°K one finds A 1=6.1×1016 sec—1 and for the reverse reaction to 1, A —1=7.0×109 liter/mole sec. The data do not permit evaluation of β while α is in the range 0.3 to 0.4 for both H2 and D2. Independent calculations of α yield the values 0.8 for H2 and 0.6 for D2, both calculations having a probable error of a factor of 2. For the over‐all activation energy of the ; order chain, E 0=50.0 kcal.
It is proposed that the observed exchange of Me2O with D2 is a heterogeneous reaction.
25(1956); http://dx.doi.org/10.1063/1.1742842View Description Hide Description
Thermal diffusion measurements have been carried out near the critical solution point by means of a new apparatus which will be described in another paper. The Soret coefficient D′/D for nitrobenzene+n‐hexane shows a large increase in the vicinity of this point. This is a strong argument in favor of the existence of a thermodynamical factor in the isothermal diffusion coefficient as predicted by the thermodynamics of irreversible processes.
25(1956); http://dx.doi.org/10.1063/1.1742843View Description Hide Description
The nuclear magnetic resonance spectra of powder samples of hydroxylamine hydrochloride and oxamide have been obtained. N–H bond distances were calculated to be 1.036±0.025 A in formamide, and 1.039±0.013 A in oxamide, assuming a 120° bond angle and a planar structure in each case. An attempt is made to correlate the N–H bond lengths with the hydrogen bond length by a modification of Lippincott's theory of the linear O≡O hydrogen bond.
The rigid lattice second moment of cyanamide was also measured. The result is not consistent with the assumption of an ammonia‐like N–H bond structure, but requires a larger H–H separation.
25(1956); http://dx.doi.org/10.1063/1.1742845View Description Hide Description
The J = 1 to J = 2 and J = 2 to J = 3 transitions for CH3NO2 and CD3NO2 have been assigned for several internal rotational states. The best values of the rotational constantsB and C were found to be 10 542.7 and 5876.7 Mc/sec for CH3NO2 and 8697.1 and 5254.3 Mc/sec for CD3NO2. The rotational constant for the NO2 group about the symmetry axis is 13 277.5 Mc/sec. These constants are determined assuming no inertial defect, slightly different values are calculated if other assumptions are made. Some of the assigned lines are a very sensitive function of the low barrier to internal rotation. The barrier term V 6 was determined to be 6.03±0.03 calories/mole for CH3NO2 and 5.19±0.03 calories/mole for CD3NO2. The term V 12 is less than 0.05 calorie/mole. The dipole moment of CH3NO2 is 3.46±0.02 Debye units.
25(1956); http://dx.doi.org/10.1063/1.1742846View Description Hide Description
Diffusivities of liquid alloys of Ge–Al, Ge–Au, and Si–Al have been measured by a new technique. Called temperature‐gradient zone melting, the technique involves passing extremely thin molten zones through a solid crystal by means of a temperature gradient. Preliminary values of the diffusivities fall in the 10—5 cm2/sec range at temperatures of 530°C to 700°C.
25(1956); http://dx.doi.org/10.1063/1.1742847View Description Hide Description
Three parallel fundamentals and one perpendicular overtone have been resolved with a grating spectrometer and the results analyzed. The ground state rotational constants are B″=0.371 cm—1 and A″—B″=8.64 cm—1, and the band origins are , , , and . The two skeletal bending bands have been observed with CsBr and KBr prisms and interpreted in terms of strong Coriolis coupling. The fundamental frequencies are approximately 408 and 422 cm—1.
25(1956); http://dx.doi.org/10.1063/1.1742848View Description Hide Description
The first (2—0) and second (3—0) overtones of DCl have been obtained with high dispersion in the 2.4 and 1.6 micron regions. Values for the rotational constantsB e , I e , and r e are essentially in agreement with those obtained by Pickworth and Thompson for the fundamental band. The molecular constants obtained are:These agree closely with the values calculated from the data for HCl.
Relaxation of Vibrational Nonequilibrium Distributions. I. Collisional Relaxation of a System of Harmonic Oscillators25(1956); http://dx.doi.org/10.1063/1.1742849View Description Hide Description
A theoretical study has been made of the collisional relaxation of a system of harmonic oscillators prepared initially in a vibrational nonequilibrium distribution. Using harmonic oscillator collisional transition probabilities we have obtained expressions which describe the relaxation of initial nonequilibrium δ‐function distributions and Boltzmann distributions to their final equilibrium state. Our results show that an initial Boltzmann distribution with ``temperature'' T 0 approaches the final equilibrium Boltzmann distribution at temperature T via a sequence of intermediate Boltzmann distributions with time‐dependent ``temperatures'' for the case T 0>T. The initial δ‐function distribution relaxes to the final equilibrium Boltzmann distribution via a sequence of nonequilibrium distributions. The study of the relaxation of the mean energy shows that this relaxation depends only upon the mean energy of the initial distribution, and is independent of the form of the initial distribution. The relaxation time for the mean energy was found to be 1/k 10θ where k 10 is the collisional transition probability per second for transitions between levels one and zero $$Word$$ where θ=hv/kT. The results obtained in this paper pertain to a system at sufficiently high pressure so that radiative transitions can be neglected as compared with collisional ones.
Relaxation of Vibrational Nonequilibrium Distributions. II. The Effect of the Collisional Transition Probabilities on the Relaxation Behavior25(1956); http://dx.doi.org/10.1063/1.1742850View Description Hide Description
In order to test the influence of the collisional transition probabilities on the relaxation behavior of initial vibrational nonequilibrium distributions, we have used collisional transition probabilities which increase exponentially with an increase in the vibrational quantum number. The results obtained for this set of transition probabilities are compared with the results obtained for the Landau‐Teller transition probabilities which increase linearly with an increase in the vibrational quantum number. Numerical calculations for the relaxation of various initial δ function and Boltzmann distributions show that the detailed relaxation behavior depends quite strongly on the form of the collisional transition probabilities.
25(1956); http://dx.doi.org/10.1063/1.1742851View Description Hide Description
The heat capacity of dysprosium has been measured over the range 15 to 300°K, and the thermodynamic functions have been calculated. Dysprosium had previously been found to exhibit two magnetic transitions and corresponding to these we have observed two maxima in the heat capacity, one at 174°K and a second at 83.5°K. Only the lower peak shows a dependence on the thermal history of the sample and this dependence was investigated. A correlation of the various contributions to the entropy at room temperature indicates that the magnetic contribution is R ln (2J+1). The value of S 0 298.16 is 17.87 cal (°K)—1 (g atom)—1.
25(1956); http://dx.doi.org/10.1063/1.1742852View Description Hide Description
The zero‐order wavelength of absorption, λ I , of a conjugated chain of N bonds with all bonds equal iswhere λ c is a universal constant, about 500 A per bond, and λ L , λ R are end‐group corrections. The corresponding energy, EI, is modified in second order by configurational mixing of the ground state with a certain excited state, to give within experimental error the observed transition energyThe derivation is a simplified adaptation of the ideas of Brooker, Herzfeld, and Sklar. The end‐group basicities, bL and bR, or stabilizations of alternative resonance structures, locate the electron density maxima in the chain and determine the bond density alternations and bond length alternations that probably produce the mixing. They are additive and consistent for over 50 end groups and can be derived theoretically in many cases. Their dependence on chain length and solvent is shown. Substituent groups have two parameters, λ, b, as in aromatic ultraviolet spectra.
The changes in transition band widths, vibrational structure, and intensity in changing solvents are accounted for. The strong convergence of polyene series spectra and the nonharmonic spacing of their higher states is attributed to their large b‐values, about 20 kK. The corresponding mixing of states is related to the probable character of the excited statewave functions and to the probable strong alternation of polyene bond lengths even in long chains.
25(1956); http://dx.doi.org/10.1063/1.1742799View Description Hide Description
The rates of decomposition of N2O and of formation of NO were measured simultaneously in a static system. NO yields at the beginning of reaction are as high as 50 to 60%, but NO quickly inhibits its own further formation. From initial NO yields, information about the reaction of oxygen atoms with N2O and about wall recombination was obtained. Limiting NO pressures for complete N2O decomposition were interpreted in terms of the reaction NO+O+M→NO2+M, and its rate constant was calculated. The effect of increased surface area and of added gases was studied. The halogens were found to be efficient inhibitors of NO formation.
The chemiluminescence of reacting N2O was observed and its dependence on temperature, pressure, and added gases studied. All evidence points to the reactionas its origin. Inhibition of NO formation and of chemiluminescence is shown to be closely related.
25(1956); http://dx.doi.org/10.1063/1.1742800View Description Hide Description
The polarized absorption and fluorescence spectra of anthracene have been measured in dilute solid solution in single crystals of naphthalene and phenanthrene at 20°K. The lowest singlet‐singlet transition is proven to be polarized along the short molecular axis, and hence 1 B 2u —1 Ag (1 La —1 A), in agreement with theoretical predictions. Vibrational frequencies are compared in the ground state and in the first excited state. The polarization of the fluorescence of anthracene in phenanthrene has also been studied as a function of temperature. The fluorescence is partially polarized at 300°K, but is depolarized at 20°K.
25(1956); http://dx.doi.org/10.1063/1.1742801View Description Hide Description
The absorption and fluorescence spectra of tetracene have been studied in substitutional solid solutions in naphthalene and in anthracene at 20°K. In agreement with theoretical predictions, the lowest excited singlet state at 20 246 cm—1 is 1 B 2u , 1 La, since the transition with the ground state is polarized along the short molecular axis. Vibrational frequencies of tetracene are compared in ground and excited electronic states, and are compared with the vibrations of anthracene and naphthalene.
25(1956); http://dx.doi.org/10.1063/1.1742802View Description Hide Description
The complex dielectric constant of highly purified nitrobenzene in the region of anomalous dispersion has been determined by measuring the input impedance of a variable length of a coaxial transmission line filled with the liquid. The measurements were carried out at frequencies from 0.65 kmcps to 3.00 kmcps in the temperature range between 15°C and 50°C. Good agreement was observed with an expression suggested by Cole and Cole, and the critical frequencies in this temperature region were found to be between 3 and 6 kmcps.
25(1956); http://dx.doi.org/10.1063/1.1742803View Description Hide Description
This paper develops a model for the dissipation of the tracks of high‐energy particles. It is assumed that all chemical effects are due to one kind of radical and that there are no effects of overlapping of neighboring tracks, i.e., that there is a sufficiently high concentration of scavenger to prevent such overlapping. The model of Samuel and Magee is used and extended to take into account the interaction of randomly distributed spurs along the track. Calculated values of the extent of scavenger reactions and radical reactions are presented in graphical form. General trends of experimental results to be expected according to the model are indicated. Quantitative correlation with experiments was not attempted because of the uncertainty in the values of various parameters used and because of the serious limitations of the one‐radical model of tracks.
25(1956); http://dx.doi.org/10.1063/1.1742805View Description Hide Description