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Volume 40, Issue 4, 15 February 1964

Electrical Conduction of a High Polymerized Sample of Sodium Salt of Deoxyribonucleic Acid
View Description Hide DescriptionThe electrical conduction of pressed pellets of a high polymerized Na‐DNA sample at various stages of drying has been studied. It has been found that in the early stages of drying, the resistance and activation energies are lower in comparison with those values obtained when the sample is further dried. The resistance of a Na‐DNA film has been measured at various relative humidities. The activation energies for the film samples in the dry state were also measured. The conduction of Na‐DNA is assumed to be due to electrons excited from impurity centers. The activation energy for photoconduction is interpreted as the barrier between neighboring DNA helices hindering the charge‐carrier transport.

Lifetime of Excited States in Solution by the Quenching Method
View Description Hide DescriptionThe fluorescence of naphthalene, benzene and twelve of its alkyl derivatives has been quenched by biacetyl in aerated normal hexane solution at 28°C. From the experimental quenching constants and the limiting rate constants computed for a diffusionally controlled quenching process, the lifetimes of the excited donors were obtained. These are shown to compare favorably with direct lifetime measurements (by phase shift) on the same materials.

SCF Theory of Localized Electron Sets
View Description Hide DescriptionThis paper describes a method within the LCAO—MO—SCF approximation for calculating pi electron localization energies for aromatic substitution reactions. Pilot calculations on butadiene, naphthalene, and azulene have been carried out using zero overlap (ZDO). A new result is that the relative reactivities of the unique positions in the azulene radical are found to be in agreement with experiment.
In the general theory we have divided a normally delocalized system into two or more sets of partially delocalized electrons. Each group of electrons is described by a unique set of molecular spin orbitals (MSO). Since, in general, it is impossible to guarantee that the wavefunctions of one set are orthogonal by symmetry to those of every other set, the resultant interset Lagrangian multipliers are taken into account by the introduction of interset coupling operators.

Nuclear Spin—Spin Coupling Involving Heavy Nuclei. The Coupling of Tl^{205} and Tl^{203} with H^{1} Nuclei in (CH_{3})_{2}TlX and (CH_{3}CH_{2})_{2}TlX Compounds
View Description Hide DescriptionThe nature of the spin‐coupling interaction between thallium nuclei and protons in (CH_{3})_{2}TlX and (CH_{3}CH_{2})_{2}TlX compounds has been examined. In aqueous solution where the corresponding cations R_{2}Tl^{+} are present, the coupling constants are characteristic of the alkyl group attached to thallium. In pyridine solution the coupling constants are dependent upon the nature of X and are larger than those in the parent cation. Using a simplified model for contact interaction employing optical hyperfine splitting constants, an estimate of the contact contribution to the total thallium—proton coupling constant has been made for the series R_{3}Tl, R_{2}Tl^{+}, and RTl^{++}. It is found that irrespective of the nature of R the observed proton—thallium coupling constants increase from left to right in the relative proportions predicted by the model. The results are consistent with the conclusion that the thallium and hydrogen nuclei are coupled mainly through the Fermi contact interaction.

High‐Density Equation of State for Hard Parallel Squares and Cubes
View Description Hide DescriptionHigh‐density systems of hard parallel squares and cubes enclosed in rigid containers are considered. Evaluation of the exact volume‐dependence of the configurational integral shows that such systems obey the free‐volume equation of state. Low order deviations from the free‐volume theory, found by Salsburg and Wood in an analogous calculation for hard circles and spheres, are not found for squares and cubes.

Fifth and Sixth Virial Coefficients for Hard Spheres and Hard Disks
View Description Hide DescriptionNew expressions for the fourth, fifth, and sixth virial coefficients are obtained as sums of modified star integrals. The modified stars contain both Mayer f functions and f̃ functions (f̃≡f+1). It is shown that the number of topologically distinguishable graphs occurring in the new expressions is about half the number required in previous expressions. This reduction in the number of integrals makes numerical calculation of virial coefficients simpler and more nearly accurate. For particles interacting with a hard‐core potential, values of the modified star integrals are shown to depend strongly on dimension; for example, several modified star integrals are identically zero for hard disks (two dimensions), but give nonzero values for hard spheres (three dimensions). Of all the modified star integrals contributing to the fourth, fifth, and sixth virial coefficients, the complete star integrals are shown to be the largest. Mayer's expressions for these coefficients made the complete star integrals the smallest contributing integrals.
The fifth (B _{5}) and sixth (B _{6}) virial coefficients of hard‐sphere and hard‐disk systems are obtained by Monte Carlo integration of the modified star integrals. The resulting values are where b is the second virial coefficient.
Estimated values of B _{7} obtained from a Padé approximation to PV ^{2}/(N ^{2} kT) — V/N are B _{7}/b ^{6}=0.0127 for hard spheres and 0.115 for hard disks. For hard spheres virial series calculations including terms through the sixth virial coefficient give values of PV/(NkT) which agree closely, for densities less than half of closest‐packing, with the molecular dynamics data of Alder and Wainwright. Furthermore the approximate Padé expression agrees within 2% with the molecular dynamics data for all densities on the fluid side of the solid‐fluid transition. This agreement indicates convergence of the virial series along the entire fluid branch of the hard‐sphere equation of state.

Some Dielectric Properties of Tantalum Pentoxide
View Description Hide DescriptionThe dielectric constant and dissipation factor of β‐ and α‐Ta_{2}O_{5}ceramics and of plates cut from a boule of α‐Ta_{2}O_{5} have been measured from 77° to 373° K over a frequency range from 100 cps to 100 kc/sec. β‐Ta_{2}O_{5}ceramics behave as typical dielectric materials. On the other hand, α‐Ta_{2}O_{5}ceramics exhibit large migrational losses, similar to those found in glasses, due to the migration of the tantalum ion through the structure. The activation energyQ of the process is estimated to be about 0.64 eV, in close agreement with 0.71 eV found from the formation of anodic films on tantalum. This and other facts suggest that anodic tantalum pentoxide is similar to that of the α form. A large relaxation peak is found in the data for boule α‐Ta_{2}O_{5} material having Q=0.2 ev and τ_{0}=10^{—10} sec. This peak must arise from a large deformation of the structure to account for such a large relaxation time and large dielectric constant peak.

Configurations of Triarylborons
View Description Hide DescriptionPotential energies were calculated for a series of methylated triarylborons considering interactions between all nonbonded atoms and pi‐electron resonance energies. All nonbonded interactions were estimated using modified Buckingham (exp‐six) potentials obtained from the literature; pi‐electron energies were calculated using simple molecular‐orbital theory. The resulting predictions of stable geometries were compared with those derived from proton magnetic‐resonance chemical shift data. All calculations were performed using a rigid geometric framework permitting only rotation of aryl groups. Reasonable agreement was found for several of the molecules studied; however, a number of discrepancies indicate certain inadequacies in the present treatment. In particular, future refinements must include the possibility of bond bending.
For tri‐1‐(2‐methylnaphthyl)boron, temperature dependence of the NMR spectra was indicative of rotational isomerism.

Heat Capacities of Cubic and Hexagonal Ammonium Hexafluosilicate from 25° to 300°K
View Description Hide DescriptionHeat capacities of cubic and hexagonal ammonium hexafluosilicate were measured between 25° and 300°K. The hexagonal heat capacity showed an anomaly at 38.6°K with an entropy of transition of R ln2. This was attributed to an order—disorder reorientation of the anion. These heat‐capacity measurements, when combined with heat of solution measurements, gave a third‐law verification with ΔS _{0}°=0.03±0.2 cal deg^{—1} mole^{—1} for the change in state (NH_{4})_{2}SiF_{6(hex)}=(NH_{4})_{2}SiF_{6(cub)}. The heat capacities were analyzed to determine the motions of the ammonium ions in the two polymorphs. These analyses showed that the ammonium ions in the cubic modification are undergoing torsional oscillation with a frequency of 235 cm^{—1}, and that the ammonium ions in the hexagonal modification are undergoing pseudofree three‐dimensional rotation at room temperature. The thermodynamic functionsC _{P}, S°, (H° — E _{0}°)/T, and — (F° — E _{0}°)/T were calculated. The values, in cal deg^{—1} mole^{—1} at 298.15°K are: 59.25, 67.99, 35.21, 32.78 for the cubic modification, and 54.52, 66.98, 33.93, 33.05 for the hexagonal. The entropy of the aqueous hexafluosilicate ion was determined to be 30.3±3 cal deg^{—1} mole^{—1}.

Cell Model for Quantum Fluids. I
View Description Hide DescriptionThe cell model of Lennard‐Jones and Devonshire is modified to include quantum effects. The energy levels are calculated by means of the WKB method with the effects of the first three shells of neighbors taken into account. The thermodynamic properties of hydrogen, deuterium, and tritium are calculated for the reduced volume v ^{*}=5/3.

Heat Contents of Molten Zinc Chloride and Bromide and the Molecular Constants of the Gases
View Description Hide DescriptionThe heat contents of zinc chloride and bromide were measured from room temperature to about 700°C. The heat capacities (cal/mole deg) of the solids were: 14.5+5.5×10^{—3} T and 12.6+10.4×10^{—3} T°K; those of the liquid were 24.1 and 27.2 cal/mole; and the heats of fusion were 2.45 and 3.74 kcal/mole. These thermal data, when combined with the entropies of evaporation of F. J. Keneshea and D. Cubicciotti [J. Chem. Phys. (to be published)], resulted in absolute gaseous entropies that were 5 eu larger than the values calculated from molecular constant data. The discrepancy can be resolved if the molecules are bent or have lower bending frequencies than the literature values.

Role of Multiple Quantum Transitions in NMR: A Three‐Spin System
View Description Hide DescriptionThe double and triple quantum (DQ and TQ) transitions in molecules containing three weakly coupled nuclei of spin ½ are examined theoretically and experimentally. Owing to the rapid growth and saturation of these transitions with increasing rf, it is practicable to observe each individual resonance only within a limited rf range. Based on the theory of Yatsiv, expressions at a given T _{1}=T _{2} are computed for the rf fields at which the various MQ absorption signals will attain their maxima and the intensity of these absorptions relative to the maximum intensity for SQ signals. It is pointed out that the usual MQ signal measured in liquids has a linewidth almost equal to that of a SQ signal, since a considerable saturation of the former is necessary for its easy observation. A frequency shift only significant for high‐rf MQ signals is also computed. The DQ spectrum of a camphor derivative containing three weakly coupled protons is examined and the experimental results for the observable peaks agree rather well with the theory. The geminal J is opposite in sign to the vicinal J's.

Infrared Spectrum of Carbon Dioxide, Enriched in Oxygen‐18
View Description Hide DescriptionThe infrared spectrum of a sample of carbon dioxide enriched to about 10 at. % with O^{18} was examined in the region 1620–5400 cm^{—1}, using an Ebert grating spectrometer with spectral slitwidths ranging from 0.2 to 0.4 cm^{—1}. Ten previously unreported bands were analyzed and assigned to various species of O^{18} substituted carbon dioxide and Courtoy's results for C^{12}O^{16}O^{18} in the 2‐μ region were confirmed. Courtoy's unexpectedly high value for the Fermi resonance constant of this species was confirmed by the separation of previously unreported Fermi‐resonant bands. The positions of the two bands assigned to C^{12}O^{18} _{2} suggest that the resonance constant for this species is larger still. A resonance interaction was found in C^{12}O^{16}O^{18}, dependent on the potential constant k _{113}.

Statistical Thermodynamics of the Lattice Model of a Polymer Molecule
View Description Hide DescriptionIntroduction of a potential energy of interaction between nonbonded neighbors of a lattice‐simulated random‐walk polymer enables us to study the thermodynamic properties of such a polymer. When the potential energy over a given range of intramolecular separations becomes infinitely large, the free energy and the entropy per unit step can be computed directly either from the attrition data using the Monte Carlo method of generating random walks, or from the exact numerical calculations for short chains. The transition to rodlike molecular configurations and the accompanying change in the free energy per unit step can be followed by gradually extending the range of the infinitely large intersegment interactions.
Instead of using computational methods for estimating the free energy of a polymer with a hard‐core potential energy, one can approximate the free energy by limiting the intramolecular interactions to the nearest neighbors only. These interactions are limited to configurations separated by the smallest number of steps needed to bring two polymer segments within a specified range of a hard‐core potential energy. The free energy can be calculated analytically, using certain recurrence relations constructed for the number of permissible configurations. A comparison is made of the results obtained on the basis of nearest‐neighbor approximation to the more accurate data obtained from the numerical calculations.

Kinetics of Pyrolysis of Alkyl Hydroperoxides and Their O–O Bond Dissociation Energies
View Description Hide DescriptionIt is shown that group additivity rules lead to very reliable estimates (±1 kcal) for the ΔH_{f} ° of both alkyl peroxides and hydroperoxides. Previously published data for t‐BuO_{2}H are unique in showing a discrepancy of 6.3 kcal/mole from the estimated data. From the ΔH_{f} ° for the ROOH and the activation energies of pyrolysis of ROOR it is shown that the bond dissociation energiesD(RO–OH) are about 42 kcal/mole for alkyl R. On this basis the direct split ROOH→RO+OH is shown to contribute negligibly to the observed kinetics of decomposition of t‐BuOOH in solution. Instead the decomposition is shown to be compatible with a chain involving t‐BuO_{2} and t‐BuO radicals via the fairly well established reaction: 2 t‐BuO_{2}→2 t‐BuO+O_{2}.
The rate law for such a chain is shown to lead to power dependence on t‐BuO_{2}H in good accord with the kinetic data. Absolute values of the chain rate are also in good accord with the data. It is further shown that very reactive solvents (olefins, etc.) may convert RO_{2} to RO directly, changing the rate to order with a lower activation energy (∼28 kcal). Published data from studies of tetralin‐OOH and cyclohexane‐OOH are shown to be in good accord with the proposed mechanism.
Allylic hydroperoxides are discussed briefly and considered from the standpoint of good H‐atom donors. The styrene induced decomposition of cyclohexane‐OOH is considered in detail and a new, fast initiation step is discussed:

Microwave Spectrum, Molecular Structure, and Quadrupole Coupling Constants of 2‐Chloropropane
View Description Hide DescriptionThe microwave spectra of (CH_{3})_{2}CHCl^{35}, (CH_{3})_{2}CHCl^{37}, (CH_{3})_{2}CDCl^{35}, (CH_{3})_{2}C^{13}HCl^{35}, C^{13}H_{3}CHCl^{35}CH_{3}, CH_{2}DCl^{35}CH_{3} (3 species), and CD_{3}CDCl^{35}CH_{3} have been examined and a complete structure has been obtained by the substitution method. The parameters obtained are as follows: r(CC) = 1.522 Å, r(CCl) = 1.798 Å, r(CH_{sec}) = 1.091 Å, r(CH_{methyl}) = 1.092 Å, ∠CCC = 112.7°, ∠CCCl = 109.4°, ∠CCH_{sec} = 109.9°, ∠CCH_{α} = 110.9°, ∠CCH_{β,γ} = 109.7°.
The quadrupole coupling constants in the principal axis system of (CH_{3})_{2}CHCl^{35} have been determined to be χ_{ aa } = —61.49 Mc/sec, χ_{ bb } = 34.81 Mc/sec, and χ_{ cc } = 26.68 Mc/sec. These values are consistent with χ_{ zz } = —69.61 Mc/sec assuming a cylindrical charge distribution near the Cl nucleus, or with χ_{ zz } = —67.82 Mc/sec and η = 0.0275 assuming that the z axis and the CCl internuclear line coincide.
From the absence of observable splitting in certain high J transitions in CD_{3}CDCl^{35}CH_{3}, it has been concluded that the potential barrier hindering internal rotation of the methyl groups is greater than 3450 cal/mole.

Molecular Structure of Cyclopropyl Chloride
View Description Hide DescriptionThe pure rotational microwave spectra of seven isotopic species of cyclopropyl chloride have been examined and rotational constants assigned. The data are sufficient for a complete structure determination by the substitution method. The bond distances and bond angles obtained are r(C_{1}C_{2})=1.513 Å, r(C_{2}C_{3})=1.515 Å, r(CCl)=1.740 Å, average r(CH)=1.08 Å, ∠CCCl=118.7°, ∠ClCH=115.8°, and ∠HCH=116.2°. The quadrupole coupling constants of C_{3}H_{5}Cl^{35} in the principal inertial axis system are χ_{ aa }=—56.64 Mc/sec, χ_{ bb }=36.72 Mc/sec, and χ_{ cc }=19.92 Mc/sec. These values are consistent with χ_{ zz }=—71.4 Mc/sec, and η_{bond}=0.029 if the z axis and the CCl internuclear line are assumed to coincide, and with χ_{ zz }=—73.5 Mc/sec if the charge distribution near the chlorine nucleus is assumed to be cylindrically symmetric.

Light Scattering by Linear Macromolecules Oriented in Laminar Flow. III. Perfectly Flexible Necklace Model with no Hydrodynamic Interaction
View Description Hide DescriptionOn the basis of the complete distribution function for the freely draining, ideal necklace model in laminar flow, the scattering intensity in the flow plane and in the plane perpendicular to the flow vector was calculated. The latter turns out to be independent of flow and the former shows a maximum and a minimum in the two directions of the main refractive index in the flow plane, respectively.

Statistical Theory of the Hydrogen Molecule‐Ion
View Description Hide DescriptionA version of statistical theory is applied to the hydrogen molecule‐ion, with good results for the electronic energies of the lowest attractive and repulsive states. For the former, a binding energy of 0.085 a.u. is obtained with an internuclear distance of 2.10 a.u., to be compared with 0.103 and 2.00 a.u. obtained from the exact solution of Schrödinger's equation. The method employed involves the use of hydrogen atomic orbitals, although when the latter refer to unbound states they are approximated by plane waves.

Determination of the Efficiency of Triplet Energy Migration in Benzophenone Crystals
View Description Hide DescriptionThe total emission—phosphorescence plus fluorescence—spectra of benzophenone crystals containing small quantities of 1,2‐benzanthracene (BA) are described. The electronic states of BA and benzophenone are such that the lowest triplet state but not the lowest singlet state of BA can be populated directly by energy transfer from the lowest triplet of benzophenone. The relative efficiencies of fluorescence and phosphorescence of the BA provide evidence that triplet exciton migration is occurring in the host lattice. The fact that the host‐crystal phosphorescence yield is temperature‐dependent provides another experimental probe into the energy transfer probabilities for this crystal. The combination of these two types of experiment gives some indication of the interaction energy between an excited molecule of benzophenone in the lattice and neighboring excited molecules.