Volume 56, Issue 9, 01 May 1972

Electrostatics of Diffuse Anisotropic Interfaces. III. Point Charge and Dipole Image Potentials for Air‐Water and Metal‐Water Interfaces
View Description Hide DescriptionWithin the framework of macroscopic continuum theory, the point charge and point dipole image potentials in the presence of a diffuse dielectricinterface are calculated. We consider the cases of both short and long range diffuseness for air‐water interfaces. In the first category we propose a model profile for which the charge image potential is devoid of singularities and is an integral over elementary functions. The calculated image potential goes through a maximum and minimum as the charge is taken from the high to the low dielectric constant medium. The heights of the maximum and minimum may be estimated in terms of a physical cutoff, characteristic of the gradient of the dielectric constant,D, in the diffuse region, using the crude model of an abrupt interface. For a diffuse layer, the very large but finite electrostatic barrier for an ion is determined by the ratio of a distance characteristic of the bulk electrolyte and a distance characteristic of the maximum gradient of D. The image potential for a point dipole, normal or tangential to the diffuse interface, is exhibited in the repulsive region, for the long range diffuse interface. For metal‐water interfaces, encountered in electrochemistry, the effects of diffuseness of the inner region, adjacent to the metal, are examined. One effect of diffuseness is to remove singularities in the image potential and to increase it in the relevant part of the inner region. The other effect is to decrease the effective attractive interaction between charges. For both the air‐water and metal‐water interfaces, the limitations of the commonly used constant dielectric profile are discussed.

Effect of Resonant Collisions on the Propagation of a Self‐Induced Transparency Pulse in SF_{6}
View Description Hide DescriptionEffect of the SF_{6} pressure on self‐induced transparency (SIT) in SF_{6} was investigated systematically. The study consists of measuring the shape, width, delay time, and intensity of the transmitted pulse (which is a SIT pulse at low SF_{6} pressure) as a function of SF_{6} pressure P. The SIT pulse was induced by the nonlinear interaction of a 20‐nsec P(20) CO_{2} laser pulse with the SF_{6}. A theory which includes the homogeneous broadening mechanism was developed for the pulse delay time. For a stationary propagating pulse, it was found that the pulse delay time is related nonlinearly to Q (the ratio of the transiently energy stored energy density to the rate of change of the energy flux density of the field). From the interpretation of the experimental results, it was concluded that, for , the resonant collision makes a significant contribution to the departure from SIT. The effect of level degeneracies associated with the high angular momentum of the involved resonantvibrational states is also discussed.

Microwave Spectrum, Structure, and Dipole Moment of Cyclopropylacetylene
View Description Hide DescriptionThe microwave spectra of cyclopropylacetylene and one deuterated species, , have been analyzed. With certain assumed structural parameters, the bond attaching the acetylenic group to the ring was found to have a length of 1.47 Å and the bond was 1.19 Å. These bond lengths are essentially indistinguishable from the corresponding distances in methylacetylene; the difference, if any, is in the opposite direction from that which would be predicted on the basis of either conjugative interactions or differences in hybridization. The dipole‐moment components are , and , nearly identical with that observed for pentyne.

Monte Carlo Trajectory Calculations of the Dissociation of HCl in Ar
View Description Hide DescriptionThe modified phase‐space theory of reaction rates is applied to the dissociation of HCl in a heat bath of argon atoms. Excellent agreement is obtained between the theoretical predictions and the shock‐tube measurements of the dissociation rate coefficient over the temperature range 2500–5000°K. The recrossing correction factor and nonequilibrium correction factor are obtained from Monte Carlo trajectory calculations for states near the dissociation limit. The trajectories were sampled within the reaction zone, with a weight proportional to the equilibrium reaction rate, and numerically integrated in both timewise directions to determine the complete histories of the collisions. A simple separable function for the equilibrium transition rate R(ε_{ i }, ε_{ f }) from initial states ε_{ i } to final states ε_{ f } was obtained to fit the numerical data with sufficient accuracy and was used to solve the steady‐state master equation. Important features of collisions of highly asymmetric diatomic molecules are discussed, and several typical reactive trajectories are shown to illustrate the importance of rotational motion in such collisions.

Phase Transitions Due to Softness of the Potential Core
View Description Hide DescriptionThis paper extends a previous demonstration [Hemmer and Stell, Phys. Rev. Letters 24, 1284 (1970)] showing that for a system in which the pair potential has a hard core plus a negative part, softening the hard core can produce a second transition if a first already exists. Detailed analytic and numerical results for one‐dimensional continuum fluids are given, and our discussion of the lattice gas is further developed. In particular interactions that are repulsive over next‐nearest neighbor cells as well as nearest‐neighbor cells are considered, and it is rigorously shown that as many as four first‐order phase transitions can occur for such potentials, even in one dimension. The relevance of our work to certain features found in real systems (e.g. the possible breakdown of the law of rectilinear diameters, and isostructural solid‐solid transitions) is also discussed, as is the novel critical behavior to be expected of certain two‐ and three‐dimensional lattice systems.

Superposition Assumption. II. High Density Fluid Argon
View Description Hide DescriptionThe triplet correlation function for high density fluid argon was calculated by the Monte Carlo(MC) method with a truncated cube as the basic box. This new box provides us a longer range for the triplet function than the conventional cubic box using the same number of particles; it also provides us better statistics for the same computing time. The MCg ^{(3)} at ρ^{*} = 0.80 was found to be very different from the SA prediction. Upon substituting both MCg ^{(3)} and SA g ^{(3)} into the Born‐Green equation, it is found that the result is fair for MCg ^{(3)} but very poor for the SA one. We conclude that the Superposition Assumption (SA) is poor at high density.

Density Localization of Atomic and Molecular Orbitals. I
View Description Hide DescriptionA new intrinsic method for the localization of atomic and molecular orbitals is presented, which will be called (charge) density localization method. This new procedure follows an earlier suggestion of Edmiston and Ruedenberg. It is based on the minimization of the sum of the charge density overlap integrals of the orbitals: being the charge density of orbitals Because of the physical relation between the exchange interaction of wave packets representing fermions and their mutual overlap it is expected that this method is related to the energy localization procedure of Edmiston and Ruedenberg. The density localization method is applied to the atoms Be and Ne, where the four outer shell localized orbitals point to the corners of a tetrahedron. The results are compared with those of other localization procedures. Good agreement is obtained. It is shown in the present and in forthcoming publications that the same physical situation can be described by different but physically equivalent pictures.

Conformational Equilibria in Isotactic Copolymers of Enantiomeric α‐Olefins
View Description Hide DescriptionThe conformational equilibrium in random isotactic copolymers of enantiomeric α‐olefins has been investigated. In particular, the conformational partition functions have been determined for copolymers of (R) and (S)‐4‐methyl‐l‐hexene (I), (R) and (S)‐3,4‐dimethyl‐l‐pentene (II), (R) and (S)‐5‐methyl‐l‐heptene (III). The molar ratio W_{l} of monomeric units left‐handed spiraled as well as the molar optical rotation [φ]_{ D } of the copolymers, have been determined as a function of the monomer optical purity P. In the case of (I) and (II), the dependence of [φ]_{ D } on P (and of W_{l} on P) follows a hyperbolic behavior, which is more pronounced in (II), whereas in the case of (III) it follows a linear pattern. The reason for this difference in behavior is discussed. In the case of (I), for which a hyperbolic dependence of [φ]_{ D } on P had been experimentally found, the comparison between calculated and experimental data is discussed with reference to the stereoselectivity of the copolymerization process. The temperature coefficient of optical activity is also calculated as a function of P and in the case of (I) and (II) it is shown to be highly enhanced with respect to that homopolymer, with a maximum occurring at a P value, which is different in the two cases.

Dielectric Relaxation of Aliphatic Amines in Cyclohexane Solution
View Description Hide DescriptionDielectric constants and losses have been obtained for n‐butyl‐, n‐hexyl‐, n‐nonyl‐, 2‐nonyl‐, 5‐nonyl‐, n‐decyl‐, n‐undecyl‐, N‐methyl‐n‐octyl‐, N, N‐dimethyl‐n‐octyl‐, and N, N‐diethyl‐n‐octylamines in cyclohexane solution at 25°C at up to 10 frequencies in the range 1.0–145 GHz. Static dielectric constants have also been measured at 2 MHz. Primary amines are characterized by short relaxation times which are almost independent of the size of the alkyl group and the location of the −NH_{2} group. Considerably longer values are obtained for the secondary and tertiary amines. The results are discussed in terms of the relative importance of dipole reorientation by intramolecular and whole molecule rotations.

Ground State of Gaseous CaO; a Study of the Matrix Spectra of Ca and CaO
View Description Hide DescriptionThe ^{1} P←^{1} S transition of Ca was studied in Kr and Xe at 20°K. The transition was shifted to the blue relative to the gas. The short‐wavelength component of the triplet shifted to the blue while the other two shifted to the red upon warming from 18 to 40°K. Codeposited Ca and Mg showed the same triplet structures with no shifts as when deposited individually in Xe thus confirming that the triplet structure is not due to long‐range interactions between metal atoms. CaO was synthesized in Kr and Xe by the reaction using ^{16}O_{2} and ^{18}O_{2}. CaO showed a band system with the band in Xe at 20 130 cm^{−1} and from the infrared spectrum. The matrix spectra do not correspond to any of the analyzed singlet systems of CaO. It is concluded that the X ^{1}Σ state is not the ground state of CaO, which is probably a triplet.

Point Charge‐Point Dipole Model for Vibrating Triatomic Molecules
View Description Hide DescriptionA point charge‐point dipole model for the electronic potential energy contribution to the Born‐Oppenheimer potential of triatomic molecules is proposed. The polyatomic virial theorem, with appropriate approximations, is shown to allow one to proceed by implicit rather than explicit inclusion of the kinetic energy. Bending force constants and cubic stretching constants for XY_{2} molecules are predicted.

Microwave Spectrum of BF_{2}OH
View Description Hide DescriptionThe microwave spectrum of BF_{2}OH has been observed and assigned. The rotational constants of the isotopic species , and have been determined. The inertial defects prove that the molecule is planar. Assuming the two BF bond lengths are the same, the bond distances and angles are found to be: r _{BF} = 1.32 Å, r _{BO} = 1.34 Å, r _{OH} = 0.94 Å, (this is the angle cis to the OH). The dipole moment is The dipole moment makes an angle of 50° with the BO bond with dipole moment line on the same side of the BO bond as the hydrogen.

Melting and Polymorphism of KHF_{2}, RbHF_{2}, and CsHF_{2} to High Pressures
View Description Hide DescriptionThe high‐pressure phase diagrams of KHF_{2}, RbHF_{2}, and CsHF_{2} were studied by means of differential thermal analysis and volume displacement. The tetragonal / Fm3m transition lines of KHF_{2} and RbHF_{2} rise steeply with pressure to meet the melting curves of the Fm3m phases near 2 kbar. The resulting melting curves of the tetragonal phases are almost immediately terminated by the appearance of new phases which appear to be similar to the high‐temperature forms with space group Pm3m of CsHF_{2} and the corresponding azides. In the case of KHF_{2} the tetragonal / Pm3m transition line meets the melting curve of the Pm3m phase at a triple point at 29 kbar, 451°C. A new high‐pressure phase CsHF_{2} IV appears above 2.7 kbar at 20°C. This phase may be similar to CsN_{3} III. The phase diagram of CsHF_{2} is closely similar to that of CsN_{3}.

Magnetic Structures of CeZn_{2} and TbZn_{2}
View Description Hide DescriptionCeZn_{2} and TbZn_{2} have the orthorhombic CeCu_{2}‐type crystal structure. CeZn_{2} becomes a simple antiferromagnet below the Néel temperature of 7.5°K. The magnetic unit cell is of the same size as the chemical cell. All moments are aligned along the b axis and the saturation moment per Ce at 4.2°K is μ_{ B }. In the range 60–75°K, TbZn_{2} exhibits a linear‐transverse‐wave moment alignment propagating along the c axis and polarized along the b axis direction. The wavelength of this static magnetization varies from 2.28 to 2.54 in units of c in this temperature range. The moment amplitude per Tb at 62.4°K is μ_{ B }. At below 60°K, a first‐order magnetic transition takes place and the resulting antiferromagneticstructure has a magnetic unit cell twice the size of the chemical cell, the c axis being doubled. All moments are aligned along the b axis and the saturation moment per Tb at 4.2°K is μ_{ B }. The magnetic structures of both CeZn_{2} and TbZn_{2} can be described as resulting from the stacking of ferromagnetic sheets of the rare‐earth ions in some antiferromagnetic fashion.

Molecular Model for Prenucleation Water Clusters
View Description Hide DescriptionA molecular model applicable to prenucleation water clusters is described. As an illustration the model is applied to water clusters having clathrate‐like structures composed of five‐membered rings. This work was motivated by the apparent inadequacies of the corrected liquid drop model which (in addition to applying bulk properties to small clusters) predicts nucleation rates which may be as much as 10^{17} larger than experiment. We present the ``energy of formation'' at a temperature of 277°K for our molecular model for clusters ranging in size from 5 to 57 molecules. These results agree qualitatively with experiment and, we believe, provide a motivation for further development of the molecular approach.

Unitary Transformations and Pair Energies. III. Relation to Perturbation Theory
View Description Hide DescriptionThe effect of unitary transformations among the occupied orbitals of the beryllium atom is discussed. It is shown that pair‐pair interaction energies become large for choices other than the canonical Roothaan‐Hartree‐Fock orbitals. The many‐body perturbation theory diagrams responsible for these effects are discussed.

Configuration Interaction Wavefunctions and Computed Inversion Barriers for NH_{3} and
View Description Hide DescriptionGround state LCAO‐MO‐SCF wavefunctions, using a large contracted Gaussian basis set, have been constructed for NH_{3} and . These wavefunctions were determined for four points along the inversion coordinates of the respective molecules, and were then improved by the method of configuration interaction (CI). In these CI calculations, the computed energies of NH_{3} and were obtained to within 0.18 hartree of their respective nonrelativistic limits. The inversion barrier, as computed with the CI wavefunctions, was 6.9 kcal/mole for NH_{3} and 2.8 kcal/mole for .

Radiative Lifetime of N_{2}(a ^{1}Π_{ g }) and the Formation of Metastable
View Description Hide DescriptionA model calculation has been carried out on the intrasystem cascading between the a ^{1}Π_{ g }, , and w ^{1}Δ_{ u } states of N_{2}. Input data to the calculation are spectroscopically determined energy levels and Franck‐Condon factors, experimentally determined radiative transition probabilities from each of the three excited states to the ground state, and reasonable estimates of the transition moments between excited states. A set of 21 coupled radiative decay equations is then solved for the populations of the excited state levels. The main conclusions are (1) the metastable state is efficiently populated by intrasystem cascade, (2) the a ^{1}Π_{ g } state decays nonexponentially, with an ``apparent'' lifetime shorter than that derived from the oscillator strength for the transition, (3) lifetimes of individual vibrational levels of the a ^{1}Π_{ g } state decrease with increasing vibrational quantum number, and (4) decay of a metastable molecular beam is nonexponential and shows an ``apparent'' lifetime which differs from that of the a ^{1}Π_{ g } state, due to formation of metastable molecules.

Configuration of the Water Molecule in Cupric Fluoride Dihydrate at 298°K
View Description Hide DescriptionThe crystal structure of cupric fluoride dihydrate at 298°K has been redetermined from three‐dimensional, single crystal,neutron diffraction data. Least‐squares refinement of 163 independent, observed reflections gave a final, weighted R index R_{w} = 0.038. The angle in the water molecule is , which, in contrast to the value found in an earlier study, is not significantly different from the tetrahedral angle of 109.5°. Thermal vibration is highly anisotropic, with much larger amplitudes perpendicular to infinite, hydrogen‐bonded sheets than parallel to the sheets.

Collisional Transition Probabilities for Rotational Levels of CN (B ^{2}Σ^{+})
View Description Hide DescriptionRotational relaxation of CN (B ^{2}Σ^{+}) formed by interaction of metastable argon atoms with CNBr was studied. The CN (B ^{2}Σ^{+}) initially is formed only in a few perturbed rotational levels for some vibrational states. Transfer out of the initially formed rotational levels via collision with argon took place with about the same rate for all rotational levels studied, although the magnitude of the rotational level spacings differed for the various cases that were investigated. Transition probability models were developed to simulate the observed pressure dependence of the spectrum. The best fit was obtained with a model having down transitions given by . For all models, it was essential to include a large probability of multiquantum () transitions in order to fit the data.