Volume 23, Issue 10, 01 October 1955
Index of content:
23(1955); http://dx.doi.org/10.1063/1.1740573View Description Hide Description
The Kirkwood and Fuoss theory of dielectricdispersion in polymer solutions is recalculated by including the Oseen hydrodynamicinteractions in the polymer'sdiffusiontensor. The theoretical results agree with experiment where comparison is possible. The recalculation gives root‐mean‐square molecular dimensions consistent with values calculated from viscosity and light scattering.
23(1955); http://dx.doi.org/10.1063/1.1740574View Description Hide Description
23(1955); http://dx.doi.org/10.1063/1.1740575View Description Hide Description
Dielectric constants and loss were measured from room temperature to —160°C for the pure liquids and mixtures with small amounts of water to facilitate supercooling. Two distinct dispersion regions were found below —100°C in the experimental frequency range from 1 cy/sec to 5 Mc/sec. The temperature dependences are similar and described by rate laws of the form found for similar measurements in 1‐propanol. An explanation of the multiple dispersions in terms of hydrogen bond breaking to permit reorientation of alkyl and hydroxyl groups is discussed.
23(1955); http://dx.doi.org/10.1063/1.1740576View Description Hide Description
Measurements of static dielectric constant were made for all except t‐butyl alcohol from the boiling points to —140°C; dispersion and loss were measured below 0°C in the range 20 cy/sec to 2 Mc/sec. Multiple dispersions were found as in other alcohols. The temperature dependences of static values are examined in terms of finite extent of chainwise molecular coordination by hydrogen bonding, and the rate laws of the dispersions are discussed.
23(1955); http://dx.doi.org/10.1063/1.1740577View Description Hide Description
Measurements of dispersion in the solutions show that at all concentrations the principal dispersion is a simple relaxation process, while the higher frequency behavior gives evidence of overlapping dispersions. As in other alcohols, the temperature dependences of relaxation times differ markedly from simple rate laws, especially for temperatures below 200°K. The significance of the results in relation to reorientation of hydroxyl and alkyl groups and intermolecular hydrogen bonds is discussed. Difficulties in measurements on solid methanol are described and their possible origins examined.
23(1955); http://dx.doi.org/10.1063/1.1740578View Description Hide Description
The apparatus for observing triplet‐triplet transitions in polyatomic molecules is the same as in part I except that resonance lamps are here replaced by a flash lamp. Triplet‐triplet spectra are reported for benzophenone, acetophenone, β‐bromo and β‐iodo naphthalene. No triplet‐triplet absorption was found in benzene, biacetyl, acetone dibromo benzene, or diisopropyl ketone. Detailed studies of the energy levels of benzophenone and acetophenone are reported.
23(1955); http://dx.doi.org/10.1063/1.1740579View Description Hide Description
The long‐range forces between large conjugated double bond molecules are highly directional and anomalously strong. This is the result of pi electrons moving freely from one end of the conjugated double bond system to the other, making the molecule behave like an extended oscillator. All three types of dispersion forces: σσ, σπ, and ππ are calculated for ethylene, acetylene, and the higher polyenes. In addition the ππ interaction energy is calculated for benzene. The free electron molecular orbitals are used for the π electrons and products of these orbitals are approximated by ``transition monopoles.'' Our treatment of the σ electrons and the use of the transition monopoles were suggested by London. The resulting energies are easy to calculate and easy to interpret. The ππ energy is proportional to the square of the energy of interaction of two real transition dipoles (real in the sense of the monopoles being separated by a finite distance). Previously, Coulson and Davies calculated the ππ interaction energy using LCAO orbitals and evaluating all integrals accurately; however, because of the complicated nature of their calculations it was not possible for them to obtain a simple understanding of the variation of the energy with the orientations of the molecules. The values we obtain for the ππ energy agree with those of Coulson and Davies except for a scale factor, our results being uniformly smaller. Such a scale factor corresponds to an adjustable parameter in either the Coulson and Davies treatment or ours. The σπ interaction energy has never previously been considered. For long polyenes, for which a simplified treatment is given, the ππ energy is larger than the σπ which is larger than that of the σσ. In the appendix, the free‐electron model is used to calculate the pi‐electron contribution to the polarizability and excellent agreement is obtained with the LCAO calculations of Davies.
23(1955); http://dx.doi.org/10.1063/1.1740580View Description Hide Description
The fractionation of oxygen‐18 in the reaction of copper with oxygen of natural isotopic composition has been measured over the temperature range 68—256°C. The oxide films (estimated thicknesses varying from 150—2500 A) were removed for O18 assay by treatment with hydrogen at 350°C. Using the CO2 equilibration technique, the O18/O16 ratios for the resulting water samples were determined mass spectrometrically and compared with the ratio for a reference sample of water prepared from the original oxygen gas.
The direction of the fractionation indicated that O2 16 reacts preferentially compared to O16O18. The isotope effect appeared to be independent of the oxygen pressure over the limited range studied (2—25 cm Hg). The magnitude of the fractionation factor was 2.0% at 150°C, with a small negative temperature coefficient. From this it was possible to estimate a value of ΔE act=17 cal/mole, which may be compared with the calculated isotopic zero‐point energy difference of 64 cal/mole. The theoretical implications of the experimental results are discussed.
Heat Capacity and Entropy of FeF2 and CoF2 from 11 to 300°K. Thermal Anomalies Associated with Antiferromagnetic Ordering23(1955); http://dx.doi.org/10.1063/1.1740581View Description Hide Description
The heat capacities of FeF2 and CoF2 have been measured between 11 and 300°K. Both salts show anomalies in heat capacity associated with the antiferromagnetic ordering of the magnetic ions. The heat capacity of FeF2 exhibits a sharp maximum of 17.8 cal deg—1 mole—1 at 78.35°K and that of CoF2 has a maximum of 5.64 cal deg—1 mole—1 at 37.70°K. Values of the heat capacity,entropy,enthalpy, and free energy are tabulated at selected temperatures. The values of the entropy and enthalpy at 298.16°K are: FeF2, S 0=20.79±0.04 cal deg—1 mole—1, H 0–H 0 0=3049±6 cal mole—1; CoF2, S 0=19.59±0.04 cal deg—1 mole—1, H 0–H 0 0=2978±6 cal mole—1.
23(1955); http://dx.doi.org/10.1063/1.1740582View Description Hide Description
Molecular orbitals made up of linear combinations of atomic orbitals, as well as orbital, total, and interactionenergies, have been calculated for the linear configuration of three He 1 — s atoms, with equal separation between the center and each outer atom. Roothaan's self‐consistent field matrix method was applied to this case. All electronic interactions were considered, their contributions appearing in the Hamiltonian used in solving for total energy. The assumption of additivity of the energies of all pairs of atoms in determining interactionenergy is shown not to be valid for internuclear separations approaching collision diameter of the 1 — s He atom, about 1 A. Deviation from additivity, as determined using the results of Wehner's MO calculation for the system He2 is about 30% for the smallest internuclear separation considered, around 0.93 A.
23(1955); http://dx.doi.org/10.1063/1.1740583View Description Hide Description
New calculations are presented for the thermodynamic properties of methanol which are based upon the most recent spectroscopic data. The molecular constants related to the internal rotation are now well established. The vibrational assignment is discussed and additional arguments are presented for the correctness of the selections of Herzberg and Plyler. The method of statistical calculation is essentially that of Halford, but avoids an approximation. Complete thermodynamic functions are tabulated for the range 100 to 1000°K. Agreement with experimental thermodynamic data is satisfactory.
23(1955); http://dx.doi.org/10.1063/1.1740584View Description Hide Description
The empirically determined values of the parameter Dq, which in transition‐metal complexes, measure the influence of the ligands on the metald‐orbitals are interpreted theoretically. A quantitative treatment of ``the magnetic criterion of the bond type,'' is given. Values of Slater‐Condon parameters for transition metal ions are tabulated.
23(1955); http://dx.doi.org/10.1063/1.1740585View Description Hide Description
23(1955); http://dx.doi.org/10.1063/1.1740586View Description Hide Description
Madelung constants of both simple and complex salts can be reduced to a common scale by taking the nearest‐neighbor distance as the unit distance and then dividing by half the sum of the squares of the charges of all the atoms in the stoichiometric unit. These ``reduced Madelung constants,'' α, can be predicted within a few percent by the relation α=1.89—1/m, where m is the harmonic mean coordination number. Madelung constants have been calculated for LaOCl, YOF, ReO3, and several perovskite structures for comparison with the predictions.
23(1955); http://dx.doi.org/10.1063/1.1740587View Description Hide Description
The absorption spectra of solutions of KCl, made luminescent by the addition of TlCl, have been analyzed with the assistance of dissociation constants for TlCl and TlCl2 — obtained from solubility measurements. Absorptivities for each of the absorbing species have been found at several wavelengths. Spectra of solutions having a wide variety of KCl and TlCl concentrations were calculated from the absorptivities and dissociation constants; these agree quite well with the observed spectra except at high Cl— concentration, where the disagreement is ascribed to the formation of more highly coordinated complexes. Decrease of dielectric constant of the solvent shifts the absorption band in the direction to be expected from an increase in the stability of molecular TlCl and the complex ions.
23(1955); http://dx.doi.org/10.1063/1.1740588View Description Hide Description
With increasing availability of good all‐electron LCAO MO (LCAO molecular orbital) wave functions for molecules, a systematic procedure for obtaining maximum insight from such data has become desirable. An analysis in quantitative form is given here in terms of breakdowns of the electronic population into partial and total ``gross atomic populations,'' or into partial and total ``net atomic populations'' together with ``overlap populations.'' ``Gross atomic populations'' distribute the electrons almost perfectly among the various AOs (atomic orbitals) of the various atoms in the molecule. From these numbers, a definite figure is obtained for the amount of promotion (e.g., from 2s to 2p) in each atom; and also for the gross charge Q on each atom if the bonds are polar. The total overlap population for any pair of atoms in a molecule is in general made up of positive and negative contributions. If the total overlap population between two atoms is positive, they are bonded; if negative, they are antibonded.
Tables of gross atomic populations and overlap populations, also gross atomic charges Q, computed from SCF (self‐consistent field) LCAO‐MO data on CO and H2O, are given. The amount of s‐p promotion is found to be nearly the same for the O atom in CO and in H2O (0.14 electron in CO and 0.15e in H2O). For the C atom in CO it is 0.50e. For the N atom in N2 it is 0.26e according to calculations by Scherr. In spite of very strong polarity in the π bonds in CO, the σ and π overlap populations are very similar to those in N2. In CO the total overlap population for the π electrons is about twice that for the σ electrons. The most easily ionized electrons of CO are in an MO such that its gross atomic population is 94% localized on the carbon atom; these electrons account for the (weak) electron donor properties of CO. A comparison between changes of bond lengths observed on removal of an electron from one or another MO of CO and H2, and corresponding changes in computed overlap populations, shows good correlation. Several other points of interest are discussed.
Electronic Population Analysis on LCAO–MO Molecular Wave Functions. II. Overlap Populations, Bond Orders, and Covalent Bond Energies23(1955); http://dx.doi.org/10.1063/1.1740589View Description Hide Description
LCAO molecular orbital overlap populations give in general much more flexible and widely useful measures of the non‐Coulombic parts of covalent bond energies than do LCAO bond orders. They are immediately applicable to both π and σ bonds, including bonds involving hybrid AOs of all kinds, and they take account directly of the effects of variations in bond length on bond strength. In the last section of this paper, a number of ways of defining LCAO bond orders are reviewed, and their advantages and disadvantages discussed.
If all LCAO parameters β are assumed proportional to corresponding overlap integrals S times suitable mean atomic ionization energies Ī, a simple general approximate formula for covalent resonance energies is obtained in terms of partial overlap populations and Ī's, including one or two empirical coefficients. This formula indicates that forced hybridization (see III of this series) due to inner shells should make important negative contributions to bond energies. The application of the formula to H2, CO, and H2O is discussed.
The assumption of proportionality of β values to SĪ values may be useful also in estimating unknown β values.
23(1955); http://dx.doi.org/10.1063/1.1740590View Description Hide Description
The adsorption isotherm of water vapor on nonalkali glass cloth was obtained at 25°C, and its dielectric power factor was measured also in the frequency range of 80 kc/sec∼11 mc/sec.
The power factor of glass cloth and surfacedc conductivities of nonalkali glass, soda glass, fused silica, Teflon, and polymethylmethacrylate plates increased rapidly to maximum peaks, when they were exposed to water vapor, and then gradually decreased to certain constant values.
These phenomena may be interpreted as physical picture of phase changes in the adsorbed water phase from the amorphous state to the crystalline state, as well as the deposit films of evaporated metals on solid surfaces. But the surface conductivity of polycapramide increases as the moisture content increases with time, suggesting a rapid absorption of water molecules into the solid. An analysis of this process of phase change of adsorbed water is outlined.
23(1955); http://dx.doi.org/10.1063/1.1740591View Description Hide Description
The self‐diffusion of liquidsodium in the temperature range, 98° to 226°, has been studied by the capillary reservoir technique. The data fit the empirical equation, D=1.10×10—3 exp (—2430/RT). The Stokes‐Einstein equation gives a good correlation of the self‐diffusion and viscosity data. The difference in the self‐diffusion coefficients of the solid and liquidsodium is explained in terms of the ``relaxation'' theory of diffusion proposed by Nachtrieb and Handler.
23(1955); http://dx.doi.org/10.1063/1.1740592View Description Hide Description
A refined procedure for obtaining the structure of free molecules from electron diffraction data is described which compensates for the interference arising from non‐nuclear scattering. The procedure is applied to CCl4 using somewhat more extensive rotating sector data than has hitherto been published for this molecule. Estimates are made for the first time in electron diffraction results of the effect of anharmonicity of vibration on the measurement of internuclear distance and of the effect of the failure of the Born approximation on the measurement of amplitudes of vibration. A method of estimating the reliability of the results is described.