Volume 31, Issue 2, 01 August 1959

Novel Perturbation Theory in Simple LCAO Treatment of Conjugated Molecules—Method of Perturbed Secular Determinant
View Description Hide DescriptionA new method of perturbation theory is developed in the simple LCAO MO treatment of conjugated molecules. Several useful equations are derived, giving orbital energy, electron density, and bond order of the perturbed system.

Chemical Bond. III. A One‐Dimensional Theory of the Energetics and Ionic Character of the Hydrogen Bond
View Description Hide DescriptionThe bondproperties of a first row element bonded to a hydrogen atom are calculated from one‐dimensional counterparts of the atomic orbitals. The potential energy function and the ionic character are found to be correctly predicted.
The hydrogen bond system O–H···O is described by means of the same atomic wave functions. The potential energy of the system is obtained for various positions of the hydrogen atom. Predicted properties are in good agreement with experiment. The existence of a second potential minimum is indicated. The contributions of the resonating structures of the system are obtained and are shown to lead to the observed value of dμ/dr for the hydrogen bonded OH system.

Hydrogen Bond: An Experimental Verification of the Double Minimum Potential
View Description Hide DescriptionThe spectra of alcohols in the region of the first and second OH stretching overtone in solvents of various bonding strengths reveal a pair of solvent dependent absorption bands. These bands are shown to arise from an energy level splitting resulting from a double minimum in the potential energy curve for the proton. The form that the potential energy curve must assume to yield the observed spectra is such that the second minimum lies in the region of the v=2 vibrational energy level for ordinary hydrogen bonding situations. The higher overtone bands, particularly in strongly basic solvents, are characteristic of the broad potential well.
This observed splitting of the absorption bands of hydrogen bonded alcohols confirms the theoretical predictions of a double minimum potential energy function for the proton.

Validity and Consequences of Schreinemakers' Theorem on Ternary Distillation Lines
View Description Hide DescriptionThe tangential behavior of distillation lines in a ternary mixture, as brought forward by Schreinemakers more than half a century ago, was denied some time ago by Redlich and Kister. We give another proof of the correctness of Schreinemakers' theorem. We define parameters Q _{0} governing the course of the distillation lines in each corner of the composition triangle. The Q _{0} values are, in principle, derivable from accurate binary boiling point curves. The occurrence of distillation lines with one or two points of inflection in a ternary system without complications from azeotropes or demixing is discussed at some length.

Physically Meaningful Concepts
View Description Hide DescriptionA statement on distillation lines, made by Schreinemakers and repeated by Korvezee and Meijering, lacks any physical meaning.

Theory of the Electron Spin Resonance of Benzene in the Triplet State
View Description Hide DescriptionThe splitting of the energy levels of the lowest triplet state of the benzene molecule has been calculated. The splittings were calculated with the aid of first‐order perturbation theory from antisymmetrized wave functions, which were composed of linear combinations of Slater orbitals. In the absence of an exterior magnetic field the triplet levels are split as a consequence of the spin‐spin interaction, the effect of spin‐orbit interaction may be neglected. The result is a doublet and a singlet; the separation of the two levels is 0.15 cm^{—1} for the ^{3} B _{1u } state and 0.09 cm^{—1} for the ^{3} B _{2u } state.

Theoretical Depolymerization Kinetics in Polymers Having an Initial ``Most Probable'' Molecular Weight Distribution
View Description Hide DescriptionThe kinetic equations describing a general chain mechanism of depolymerization are solved at steady state for a polymer having an initial ``most probable'' molecular weight distribution. Chain scission initiation, end group initiation, depropagation, intermolecular chain transfer, and several types of termination are considered.
In the past, solutions have been limited to special cases and approximations. Now general expressions for molecular weight change and rate of weight loss are available for polymers with an initial molecular weight distribution of wide interest. The relationships to the previously considered special cases are discussed.

Deuterium Positions in Lanthanum Deuteroxide by Neutron Diffraction
View Description Hide DescriptionThe deuterium positions in La(OD)_{3} have been determined by the neutron diffraction method. No hydrogen bonding was found in this structure. The close packing structure around the deuterium atom is characterized by the average distances of D—D = 2.29 A and D—O = 2.74 A. The infrared absorption spectra of La(OD)_{3} and La(OH)_{3} are briefly discussed.

Structures of Calcium Dicarbide and Uranium Dicarbide by Neutron Diffraction
View Description Hide DescriptionThe C–C distances of the C_{2} groups in calcium dicarbide and uranium dicarbide have been determined by the powderneutron diffraction method. The C–C distance in calcium dicarbide is 1.20±0.01 A, equal to the triple bond C–C distance, but not 1.4 A as reported previously. Uranium dicarbide is isostructural with calcium dicarbide and has the C–C distance of 1.34±0.01 A essentially that of a C–C double bond. The interatomic distances in calcium dicarbide, uranium dicarbide, lanthanum dicarbide, and lanthanum sesquicarbide are discussed in connection with the electronic configuration of the C_{2} group.

Thermodynamic Properties of Some Boron‐Oxygen‐Hydrogen Compounds
View Description Hide DescriptionThe heat capacity,enthalpy, and entropy of gaseous B, B_{2}, BH, BO, and B_{2}O_{2} have been calculated in the ideal gas state from 0 to 6000°K by standard methods of statistical mechanics with available spectroscopic data.

Field Desorption
View Description Hide DescriptionA theory of field desorption covering both covalent and ionic binding is presented. The mechanism corresponds to field ionization preceded by complete or partial ordinary desorption in the former and to direct ionic evaporation in the latter case. Comparison with experiment shows that field desorption of Ba can proceed via Ba^{+} or Ba^{+2}. It is pointed out that field desorption could be used to investigate the shapes of potential curves in adsorption.

Electron Spin Resonance of Ultraviolet Irradiated Compounds. I. Unsaturated Hydrocarbons
View Description Hide DescriptionTrapped radicals, formed by ultraviolet irradiation of pure, unsaturated aliphatic hydrocarbons, maintained at 77°K, have been observed with a 3‐cm electron spin resonancespectrometer at a g factor of two. Straight‐chain alkene radicals were characterized by well‐resolved hyperfine structure of four or more components. Branched‐chain alkene radicals showed more but poorly resolved components. Only those hydrogen atoms attached to carbon atoms at or adjacent to the location of the unpaired electron are found to contribute appreciably to the observed hyperfine structure. Their hyperfine coupling constants are approximately equal.
Radical formation and stabilization is attributed to the separation from the parent molecule of highly mobile hydrogen and methyl radicals which diffuse away from the remaining radical fragments, and eventually react with their environment or recombine. Stabilization of remaining fragments then occurs because of immobility and structural resonance. The number of radical spins detected was of the order of 10^{16} to 10^{18} in 1‐ml samples. Most radicals were stable for weeks at 77°K. Consideration is given to the existence of radicals resulting from secondary hydrogen addition reactions.

Effect of Pressure on the Absorption Edges of Certain Elements
View Description Hide DescriptionThe effect of pressure has been measured on the absorption edges of selenium, arsenic, white phosphorus, red phosphorus, and iodine. In all cases a red shift of the edge (decrease of the energy gap) occurs with increasing pressure. White phosphorus undergoes a transition to the conducting black phase near 30 000 atmos. The change in the gap with pressure for selenium is correctly predicted from conductivity measurements. An extrapolation of the gap to zero indicates that the gaps of these elements will have disappeared below 300 000 atmos. This compares with previous work on sulfur where the estimated pressure for zero gap is 400 000 atmos.

Growth Mechanism for Graphite Whiskers
View Description Hide DescriptionA mechanism is described which gives rise to the scroll habit which has been observed for graphitewhiskers. A supersaturation region exists which would favor the postulated growth mechanism.

On the Use of Harmonic Oscillator Wave Functions in the Treatment of Anharmonic Crystals
View Description Hide DescriptionAn analysis is made of the quantum‐mechanical treatment of a crystal as a perturbed harmonic oscillator. The relative magnitudes of the elements of the Hamiltonian matrix with harmonic oscillatorwave functions as a basis, are obtained for an anharmonic crystal. It is found that the harmonic oscillatorwave functions are extremely poor approximations (in the ordinary sense) to the true wave functions.

Proton Spin Relaxation in Aqueous Solutions of Paramagnetic Ions. II. Cr^{+++}, Mn^{++}, Ni^{++}, Cu^{++}, and Gd^{+++}
View Description Hide DescriptionNuclear magnetic relaxation times for protons in dilute aqueous solutions of chromic, manganous, nickel, cupric, and gadolinium ions were measured in the frequency range 1.9 to 60 Mc/sec. Results were interpreted in terms of Solomon's formulation of electron‐nuclear dipole‐dipole interaction and Bloembergen's expression for scalar coupling of electron and nuclear spins. In large magnetic fields relaxation times were found to be shorter than those expected on the basis of low field values, suggesting that the effective ion magnetic moments, electron spin relaxation times, and/or electron‐nuclear spin exchange constants are field‐dependent.

Statistical Mechanics of Rigid Spheres
View Description Hide DescriptionAn equilibrium theory of rigid sphere fluids is developed based on the properties of a new distribution functionG(r) which measures the density of rigid sphere molecules in contact with a rigid sphere solute of arbitrary size. A number of exact relations which describe rather fully the functional form of G(r) are derived. These are based on both geometrical considerations and the virial theorem. A knowledge of G(a) where a is the diameter of a rigid sphere enables one to arrive at the equation of state. The resulting analytical expression which is exact up to the third virial coefficient gives the fourth virial coefficient within 3% and the fifth, insofar as it is known, within 5%. Furthermore over the entire range of fluid density, the equation of state derived from theory agrees with that computed using machine methods. Theory also gives an expression for the surface tension of a hard sphere fluid in contact with a perfectly repelling wall. The dependence of surface tension on curvature is also given. The expressions obtained correlate nicely with those adduced by other thermodynamic and statistical mechanical theories. They also suggest that macroscopic consideration on surface tension can sometimes be successfully extrapolated to molecular dimensions.

Semiquantitative United‐Atom Treatment and the Shape of Triatomic Molecules
View Description Hide DescriptionThe united‐atom expansion of the potential energy of an electron in a molecular field is transformed into a Maclaurin series expansion containing a remainder term. It is shown that, if the center of nuclear charge is chosen to remain at the origin, the first nonzero terms of this expansion are quadratic in the nuclear separations. These terms determine the orbital properties as the nuclei in the united atom are slightly separated, and are useful in establishing correlation diagrams. Several such diagrams are given for triatomic molecules. The angular derivatives of the quadratic terms are used in an investigation of the angular stability of linear molecules composed of atoms from the second row of the periodic table. It is found that these derivatives themselves correctly indicate the linearity or nonlinearity of all except 26 electron systems, and that the nonlinearity of 26 electron systems is accounted for if internuclear repulsions are taken into account. Extensions and limitations of this result, and its implications with respect to theories of molecular shape are briefly discussed.

Expected Square of the Length of a Hydrocarbon‐Type Chain
View Description Hide DescriptionThree successive bonds along a hydrocarbon chain may be in a planar trans configuration or in two nonplanar gauche configurations. The energy of the trans configuration is taken as zero and the energies of the two gauche configurations are each taken as ε (per mole). The mean square length of a hydrocarbon‐type chain of n links each of length l _{0} is shown to be , where . The problem of excluded volume is not considered here.

Microwave Spectrum and Structure of Propynal (H–C≡C–CHO)
View Description Hide DescriptionThe moments of inertia I_{B} ^{0} and I_{C} ^{0} of fifteen isotopic species of propynal have been determined from the frequencies of certain lines in the type aspectra. With the aid of type b transitions, I_{A} ^{0} and the inertial defects Δ have been obtained for some of the isotopic species. Using equations relating the atomic coordinates to the change in the moments of inertia on isotopic substitution, three independent sets of molecular parameters have been obtained (two for C=O). The agreement between the three sets of data is within the probable experimental error. The mean values of the molecular parameters are as follows: r_{s} (C–H) (acet.) = 1.055_{3}A, r_{s} (C–H) (ald.) = 1.106_{4}A, r_{s} (C≡C) = 1.208_{9}A, r_{s} (C–C) = 1.444_{6}A, r_{s} (C=O) = 1.215_{0}A, ≰CCO = 123°47′, ≰CCC = 178°24′, ≰CCH (ald.) = 113°54′, ≰CCH (acet.) = 180°0′.
The error in the bond lengths is estimated to be ±0.001 A, and in the angles ±10′. A slight deviation from linearity (1°36′±10′) was apparent in the carbon chain.