Volume 38, Issue 4, 15 February 1963
Index of content:
Decomposition of Chemically Activated Ethyl‐d 3 Radicals. Primary Intramolecular Kinetic Isotope Effect in a Nonequilibrium System38(1963); http://dx.doi.org/10.1063/1.1733764View Description Hide Description
The rate of decomposition of ethyl‐d 3 radicals formed by chemical activation was studied at 195° and 300°K over the pressure range from 0.05 to 3.0 mm. The excited radicals decomposed by hydrogen or deuterium atom rupture or were collisionally stabilized. The rate of decomposition was determined relative to the rate of stabilization by complete product analysis. Detailed description is given. The limiting high‐pressure rate for hydrogen rupture from energized ethyl‐d 3 radicals was determined to be 6.5×107 sec—1 at 300°K and 2.5×107 sec—1 at 195°K. The limiting low‐pressure rate for hydrogen rupture was found to be 2.0×107 sec—1 at 300°K and 1.0×107 sec—1 at 195°K. The intramolecular hydrogen to deuterium rupture ratio was determined to be ∼2.0 at 300°K and ∼3.0 at 195°K for this nonequilibrium reaction system, and appreciably less than similar ratios determined earlier for the ethyl‐d 2 system. The disproportionation to recombination ratio for ethyl radicals was found to be 0.14 at 300°K and to be 0.17 at 195°K. The apparent isotopic H/D disproportionation ratio in ethyl‐d 3, measured at both temperatures, was 1.6 in reasonable agreement with the value of 1.4 of Boddy and Steacie.
Theoretical rates were calculated from a quantum statistical harmonic oscillator formulation of the rate constant. Good qualitative and semiquantitative agreement has been found between the various experimental quantities of this study (as well as a previous one dealing with ethyl‐d 2 radicals) and magnitudes calculated from a model which has quite a loose activated complex (150 cm—1, C–C–H bends) with the figure axis rotation active, and in which the energized radical has both an active free internal rotation and figure axis rotation.
Approximate Radial Functions for First‐Row Transition‐Metal Atoms and Ions. II. 4p and 4d Atomic Orbitals38(1963); http://dx.doi.org/10.1063/1.1733765View Description Hide Description
Orthogonalized 4p and 4d radial wavefunctions for first‐row transition‐metal atoms and ions have been computed using a minimum set of Slater‐type functions with integral quantum numbers. Configurations of the type 3dx 4p, 3dx 4p 2, 3dx 4d and 3dx 4d 2 were studied. Free parameters were varied to minimize the energy of these electrons in the (fixed) Coulomb and exchange potential field of the inner shells, considered in a previous paper. Various criteria suggest that these functions are reasonably good. The results were generalized to provide estimates of parameters for related configurations.
38(1963); http://dx.doi.org/10.1063/1.1733766View Description Hide Description
The Padé approximant procedure is used to study the low‐temperature series for the Ising problem. The critical behavior of the spontaneous magnetization of an Ising ferromagnet and of the liquid‐vapor coexistence curve of the corresponding lattice gas is found to be where (in three dimensions) 0.303≤β≤0.318. It is conjectured that β=5/16=0.31250. The low‐temperature initial susceptibility and the compressibility of the lattice gas at condensation are found to diverge as where in two dimensions γ′=1.75±0.01 while in three dimensions γ′=1.25 (+0.07, —0.02). Consideration of a heuristic model partition function suggests the identity α′+2β+γ′=2 where α′ is the index of divergence of the specific heat below Tc. The amplitudes of the singularities are derived and extrapolation formulas are presented for the plane triangular, square, and honeycomb lattices and the three‐dimensional face‐centered, body‐centered, and simple cubic lattices. The results are compared briefly with experimental evidence.
38(1963); http://dx.doi.org/10.1063/1.1733767View Description Hide Description
Calculations on the 2pπ u state of H2 + suggest that d‐type atomic orbitals will make appreciable contributions to the MO's of pi electrons in unsaturated molecules. A symmetry analysis shows that in planar aromatic hydrocarbons only two of the five d orbitals may hybridize with the p orbitals in pi MO systems. The coefficients of the d functions in these MO's were estimated, and their effects on the orbital energies were determined. Resonance energies, charge densities,dipole moments, hyperfine coupling constants, and bond orders were calculated from these modified orbitals, and the results were compared with experiment and with the results of simple Hückel theory. The definitions of charge densities and bond orders must be modified when d orbitals are included. The inclusion of d‐hybridization leads one to expect certain effects which are not predicted by the Hückel theory: (a) The simple Hückel theory predicts equal resonance energies for trans‐ and cis‐butadiene. Inclusion of d orbitals makes trans‐butadiene more stable than cis‐butadiene by about 700 cal. (b) Simple Hückel theory predicts that the square cyclobutadiene molecule will have no resonance stabilization. Inclusion of d orbitals produces a stabilization of about 6 kcal. (c) Simple Hückel theory predicts that phenanthrene has a zero dipole moment. Inclusion of d orbitals leads one to expect a dipole moment of 0.17 D. (d) Simple Hückel theory predicts zero spin densities at certain positions in the pyrene negative ion. Inclusion of d orbitals allows small spin densities to appear at these positions. On the whole, the inclusion of d‐orbitals does not greatly alter the interpretation of resonance energies and bond lengths given by the simple Hückel theory. Nor does it shed any light on the problem of the anamolous length of the central bond of naphthalene. The effect of d‐hybrids may prove to have an importance in the interpretation of some properties at least as great as that of other refinements of MO theories of aromatic hydrocarbons, such as configuration interaction.
38(1963); http://dx.doi.org/10.1063/1.1733768View Description Hide Description
The compressibility of solid argon was measured in the temperature range 78° to 84°K by a new optical method. A value for the coefficient of thermal expansion was also obtained. The results are at 78°K and at 81°K. The experimental method is discussed and the results compared with existing experimental data.
Anharmonic Effects in Unimolecular Rate Theory. Dynamics of a Rotating Anharmonic Triatomic Molecule38(1963); http://dx.doi.org/10.1063/1.1733769View Description Hide Description
The motion of a rotating linear symmetrical triatomic molecule is investigated by numerical integration of the equations of motion. Harmonic‐ and Morse‐function bond potentials are used, and vibrations of large amplitude are studied. Contrary to one of the usual approximations of unimolecular rate theory, the coupling between rotational and vibrational energy in the anharmonic system is quite strong when the vibrational energy is large (of the order of the dissociation energy); rotational energy is roughly 50% effective in inducing dissociation.
38(1963); http://dx.doi.org/10.1063/1.1733770View Description Hide Description
The general relation of fundamental molecular constants between electronic states is investigated in some detail. Formulas stating such relations are found, and the interaction matrix elements, which relate the corresponding electronic states, are examined. Calculations of the quadratic, cubic, and quartic force constants for the hydrogen molecule ion H2 + are carried out, as an example, by utilizing these formulas. The calculated values agree very satisfactorily with those obtained from spectroscopic data.
38(1963); http://dx.doi.org/10.1063/1.1733771View Description Hide Description
Cr++ in solution produces a paramagnetic shift in the NMR absorption of O17 in ClO4 —, as well as the expected paramagnetic shift for O17 in H2O. As the concentration of ClO4 — increases, the shift in the H2O17 absorption is diminished, and eventually changes sign. The effects are ascribed to preferential replacement by ClO4 — of water molecules from the axial positions in the first coordination sphere about Cr++.
38(1963); http://dx.doi.org/10.1063/1.1733772View Description Hide Description
The transformations that occur in ices II, III, and V at atmospheric pressure when they are heated from liquid‐nitrogen temperature have been examined by simple thermal analysis and by x‐ray diffraction. They transform first to cubic ice I (ice Ic). The rate of transformation of ices II and III depends upon the temperature, and that of ice II probably depends upon its thermal history. The temperature dependence of the rate for ice V, and the history dependence of the rate for ices III and V were not examined. Ice Ic has previously been made only in small quantities; it can now be made in as large quantities as required by transformation of the high‐pressure ices. The transformation of ice Ic to ordinary hexagonal ice(ice Ih) has also been examined. The rate depends markedly on the thermal history of the sample and this may help to explain the apparently inconsistent rates that have been reported by various workers.
38(1963); http://dx.doi.org/10.1063/1.1733773View Description Hide Description
General methods are developed for evaluating Mayer cluster diagrams for systems of molecules with orientation‐dependent forces. These methods are particularly useful for obtaining chain and ring contributions. Simplification occurs for ordinary two‐body forces in the absence of external fields because of invariance under rotation of the two‐body complex as a whole. Using these methods we adapt Mayer's rearrangement procedure to calculate the cluster expansion of the potential of the average force between two ionic or dipolar solute molecules that are immersed and fixed in a gas of dipolar molecules. The comparison of this potential with the corresponding macroscopic quantity leads to a cluster expansion for the dielectric constant of the dipolar gas.
38(1963); http://dx.doi.org/10.1063/1.1733774View Description Hide Description
Nuclear magnetic‐resonance studies of the groups IV, V, and VI transition‐metal diborides show that the boron nuclei have a small quadrupole coupling constant, and negative frequency shift of the order of 10—4. The V51resonance in VB2 provides a measure of the quadrupole coupling constant for V51 as 2.35 Mc/sec and a frequency shift of —3.37×10—3. The frequency shifts are enhanced at low temperatures. These data are explained within the framework of a suggested metal—boron donor—acceptor bonds by proposing s—d exchange polarization and diamagnetic``ring current'' contributions to the field at the nucleus.
38(1963); http://dx.doi.org/10.1063/1.1733775View Description Hide Description
The kinetics of adsorbed layers of potassium chloride on tungsten and of chlorine on tungsten have been investigated in the range 300°—1900°K by means of the field electron microscope. Data are interpreted as showing that KCl in the presence of tungsten at room temperature forms a W–KCl complex to which the potassium is weakly bound. Activation at approximately 500°K results in the desorption of potassium leaving a tungsten chloride (WCl x ) layer which is stable to about 1100°K. Work functions, patterns and critical temperatures for KCl on tungsten and chlorine on tungsten are indistinguishable in the range 1100°—1900°K. Limiting processes above 1100°K are believed to be the formation and subsequent desorption of tungsten chloride and atomic chlorine. Temperature‐dependent processes, such as migration, desorption, and structure change, associated with experimentally determined activation energies of ∼10 to 80 kcal, are discussed. The behavior of chlorine on tungsten is shown to be similar to that of oxygen on tungsten in the temperature range studied.
38(1963); http://dx.doi.org/10.1063/1.1733776View Description Hide Description
The addition of HI to i‐butene above 200°C proceeds homogeneously and quantitatively to yield i‐butane+I2 in accordance with the equationIt is shown that the rate‐determining step is the formation of the intermediate t‐BuI which is present in vanishingly small stationary concentrationThe second‐order rate constant k 2 is given by (units of liter/mole‐sec)From the known thermodynamic data the reverse, first‐order rate constant k 1 is given by (units of sec—1)
Comparisons with similar data for EtI and i‐PrI show that the substitution of Me groups for H lowers the E act by about 6 kcal/Me group and also the A factor by about a factor of 5. This can be explained on the basis of a loss of internal rotational entropy in the transition state.
Qualitative observations indicate that C2H3Cl adds HI at a rate intermediate between C2H4 and C3H6. The principle products are C2H5Cl+I2 above 290°C, but sufficient C2H6+HCl appear to vitiate simple kinetic studies. Qualitative observation of the system EtCl+I2 indicate an I‐atom‐catalyzed elimination of HCl with an E act∼43 kcal/mole.
38(1963); http://dx.doi.org/10.1063/1.1733777View Description Hide Description
By modification of a Beckmann DB spectrophotometer for use with high‐temperature gas systems it has been possible to follow the kinetics of reaction of CH3I+HI which goes quantitatively to CH4+I2 in the temperature range, 260° to 316°C. The kinetics fit the mechanism proposed earlier by Benson and O'Neal very well.The rate law for this system is (neglecting 4)Although this equation can be integrated exactly, the integrated forms are not sensitive to the data, and various expansions must be used. Values for k 1 and k 3/k 2 are found to be in excellent agreement with earlier estimates. From the activation energyE 1 and the assumption that E 2≤0.5 kcal, the bond energy of CH3I is found to be about 55±1 kcal/mole, in excellent agreement with other estimates. Values are given, in addition, for the individual rate constants,k 2, k 3 and k 4, as well as their Arrhenius parameters.
The A factors for reactions 1 and 4 are shown to be in excess of collision frequencies, indicating steric factors slightly in excess of unity and thus the formation of very loose transition‐state complexes. This appears to be typical of iodine‐atom or I2‐molecule reactions and thus far quite unique.
38(1963); http://dx.doi.org/10.1063/1.1733778View Description Hide Description
The isotopic fractionations of nitrogen and oxygen in water have been measured in the range 2°—27°C. The extrapolated values at 0°C of k′/k, the ratio of Henry's Law constants, are 1.00085 (±0.00010) for nitrogen and 1.00080 (±0.00015) for oxygen in the sense of the heavier species being more soluble. Several possible sources are recognized for the observed effects which are, however, of the magnitude to be expected from the motion of point masses in ``iceberg'' cavities of reasonable dimensions.
38(1963); http://dx.doi.org/10.1063/1.1733779View Description Hide Description
The optical absorptionspectrum of the molecular crystal metal‐free phthalocyanine has been investigated in the region 25 000 to 3500 Å. The spectrum of the phthalocyanine molecule retains much of its identity in the crystal, as evidenced by the similarity in the regions of main absorption. This is a consequence of the weak intermolecular binding forces. The crystal absorptions in the region 8000 to 5000 Å, and below 4000 Å can be attributed to excitations from the highest filled molecular orbital to the vibrationally broadened and shifted excited states of the molecule which occur in the crystal field. Vibrational structure was observed which was attributed to a symmetrical breathing vibration of the peripheral benzene rings and, quite possibly, a similar vibration of the entire phthalocyanine molecule.
38(1963); http://dx.doi.org/10.1063/1.1733780View Description Hide Description
The spectral response of photoconductivity in metal‐free phthalocyanine crystals was obtained in the region 2500–25 000 Å, and was found to have the same response edges as the optical absorptionspectrum. The correspondence between the valley‐to‐valley separation of the structure found in the strong response regions of the spectral response of photoconductivity and the peak‐to‐peak separation of the infrared optical absorptionspectrum has been used to formulate a model for photoconductivity in metal‐free phthalocyanine crystals which involves the direct creation of carriers by suitable radiation.
An expression for the effective lifetime of a photoexcited carrier in a crystal with a finite surface recombination velocity was derived. This was found experimentally to be approximately 0.9×10—8 sec. Using this lifetime and the mobility determined by Hall‐effect measurements, the diffusion length for electrons was calculated to be 5×10—6 cm. A comparison of this diffusion length with the reciprocal of the extinction coefficient indicates that the free carriers excited by 7300‐Å radiation are produced further from the surface than a diffusion length. Thus, the lifetime of the free carriers should be more nearly characteristic of the bulk. The experimentally determined lifetime is in rough agreement with the theoretical decay time for fluorescence. This emphasizes the importance of the first excited singlet state in the conduction process. The structure of the spectral response of photoconductivity was used in conjunction with previous discussions of the applicability of the band model to infer the nature of the conduction band in metal‐free phthalocyanine crystals.
Vibrational Spectra of Molten Halides of Mercury. I. Mercuric Chloride, Mercuric Bromide, and Mercury Chlorobromide38(1963); http://dx.doi.org/10.1063/1.1733781View Description Hide Description
The Raman spectra for HgCl2, HgBr2, and HgBrCl in the pure molten state are: HgCl2: 313 cm—1 (10, p), 376 (0, dp); HgBr2: 195 cm—1 (10, p), 271 (0, dp); HgBrCl: 111 (v.w.), 203 (v.w.), 236 (m), 319 (v.w.), and 335 (m). The vibrational assignment and force constants are reported in accord with the view that the linear X—Hg—X molecular species are retained in these melts as in the gaseous and crystalline states. The broad‐band shape for the intense Raman line in these melts and the appearance of a Raman forbidden frequency as a very weak line in the spectra of molten HgCl2 and HgBr2 are examined from the viewpoint of the nature of the Hg—X chemical bond and cooperative rotational interactions in these molecular molten salts. The appearance of the two Raman lines of HgCl2 and HgBr2 (319 and 203 cm—1) in the spectrum of HgBrCl is understood if a disproportion reaction is recognized in this mixed halide salt in the molten state.
38(1963); http://dx.doi.org/10.1063/1.1733782View Description Hide Description
An investigation by Raman spectroscopy of solutions of molten mercuric chloride containing KCl and NH4Cl as solutes over the composition range 10%—70% added solute is reported. The observed spectra may be completely assigned if HgX2, HgX3 —, and HgX4 = are recognized as the predominant species in these molten salt mixtures. The vibrational assignment is discussed and the force constants are calculated for these species. From the intensity variations of the strongest Raman lines, 374, 282, and 267 cm—1, the relative concentrations of the above three polyatomic species are deduced as the concentration of the added ligand (Cl—) varies from 0% to 70%. The ionicity of the Hg–Cl bond in HgCl2, and HgCl3 —, and HgCl4 =, as reflected by the bond force constants, is considered.
38(1963); http://dx.doi.org/10.1063/1.1733783View Description Hide Description
The infrared spectra of carbon suboxide and malononitrile isolated in solid argon matrices at low temperatures have been measured in the spectral region 440–4400 cm—1. A detailed comparison with prior spectroscopic data is made. It is shown that the matrix spectra of C3O2 support the linear symmetric model. A comparison of the matrix spectra and vibrational assignments of the three isoelectronic molecules C3O2, CH2(CN)2, and B2O3 is shown to favor a large apex angle in B2O3.