Index of content:
Volume 42, Issue 10, 15 May 1965
Self‐Consistent Group Calculations on Polyatomic Molecules. I. Basic Theory with an Application to Methane42(1965); http://dx.doi.org/10.1063/1.1695733View Description Hide Description
In polyatomic molecules it is usual to recognize physically distinct groups of electrons (e.g., inner shells, σ bonds, π electrons). The π electrons of conjugated molecules have received most attention, other groups of electrons being recognized only as a ``framework'' with empirically determined characteristics. In this series of papers, all groups of electrons are admitted, each group (localized or nonlocalized) being made self‐consistent in the field of the others. In this way bond properties, π‐electron parameters, etc., may be determined from first principles, taking into account the whole molecular environment. Excited states may be determined by admitting ``excitons'' (i.e., localized excitations) within the various groups.
The theory is illustrated by means of a completely nonempirical calculation on the methane molecule. The ground state is somewhat better than that given by approximate SCF theory, the excited states are somewhat worse. One advantage of the approach is that it lends itself admirably to semiempirical development.
42(1965); http://dx.doi.org/10.1063/1.1695734View Description Hide Description
Binary mutual diffusion coefficients have been measured for the systems He—T2 and He–TH by a radioactive tracer method at four temperatures in the range 195° to 374°K. The results, reduced to one atmosphere and normalized to the system He–H2, can be expressed within an average deviation of slightly less than 1% by the empirical relations
The ratio of the normalized coefficients for He—T2 and He–TH show a small departure from unity, starting at 1.02 at the lowest temperature and decreasing smoothly to 0.996 at the highest. On the assumption that deviations from classical mechanics, contributions from internal degrees of freedom, and the effects of asymmetric force fields are the same, or negligibly small, for both systems, different sets of Lennard‐Jones (12–6) potential parameters have been obtained which correlate the experimental results as well as the empirical equations.
42(1965); http://dx.doi.org/10.1063/1.1695735View Description Hide Description
Binary mutual diffusion coefficients have been measured by a radioactive tracer method for the following systems: H2−T2 and D2−T2 at 195°, 273°, and 353°K; H2–TH and D2−TH, at 195° and 273°K.
The ratios of the normalized coefficients for H2−T2 relative to H2–TH and for D2−T2 relative to D2−TH show the same trend as that previously reported for He–T2 relative to He–TH. In the present case both ratios are slightly greater than unity at 195° and slightly less than unity at 273°K. A larger isotope effect, produced by the substitution of D2 for H2, is reflected in the normalized coefficients for D2−T2 relative to H2−T2 and for D2−TH relative to H2–TH. The average values of these ratios are about 2% greater than unity at the lowest temperature and about 5% greater than unity at the higher temperatures.
42(1965); http://dx.doi.org/10.1063/1.1695736View Description Hide Description
Measurements of diffusion in T2−H2 and T2−D2 in three apparatuses of the two‐bulb type are reported at 295.0°K. The ratios of the diffusion cross sections are 1.024±0.014, 1.018±0.011, and 1.015±0.011 in the three apparatuses. This confirms, within mutual experimental error, the observations of Amdur and Beatty (preceding paper). The average diffusion coefficients at 1 atm, corrected to a reduced mass equivalent to H2–H2diffusion, are 1.441 cm2/sec from the T2−H2 measurements and 1.469 cm2/sec from the T2−D2 measurements.
42(1965); http://dx.doi.org/10.1063/1.1695737View Description Hide Description
The effects of uv and x‐ray radiations on sodium metaphosphate glass doped with either CdSO4 or NiO, were studied. The optical and ESRabsorptions of the glass were measured. The formation of Cd+ and Ni+ was demonstrated. A new interpretation is given to the color centers induced by irradiation in the pure base glass.
Adsorption of Inorganic Anions on a Mercury Electrode from Solutions in Formamide. I. Adsorption of Iodide Ions42(1965); http://dx.doi.org/10.1063/1.1695738View Description Hide Description
The adsorption of the iodide ion on a mercuryelectrode from solutions of potassium iodide in formamide has been studied by measuring the double‐layer capacity and the interfacial tension as a function of potential and concentration at 25°C. The adsorption can be described by a modified Langmuir (Frumkin) isotherm with a large lateral repulsive interaction energy, but examination of the inner‐layer capacity suggests that the adsorbed layer behaves more like a two‐dimensional imperfect gas than an array of particles on localized sites implied by the Langmuir model. The amounts adsorbed are calculated and the capacity resolved into its component parts with the aid of the isotherm and diffuse‐layer theory. The capacity of the inner region of the double layer measured at constant amount adsorbed is almost independent of the amount adsorbed and approximates to the inner‐layer capacity for a nonadsorbed electrolyte, i.e., potassium fluoride. The relative distances from the interface of the inner and outer Helmholtz planes are calculated from the components of the capacity and compared with similar values for aqueous potassium iodide. Methods devised by Grahame and Parsons for determining the potential at an anion site and the Stern specific adsorption potential Φ are compared and discussed in relation to the form of the isotherm, and values of Φ are calculated. [The symbol Φ is also used elsewhere to denote surface pressure because of established usage. It is obvious from the context which parameter Φ refers to wherever it occurs.] The results are shown to be consistent with both the ideal (Henry's law) and Langmuir forms of the chemical part of the electrochemicalfree energy of the adsorbed ions. The discreteness of charge effect and the Esin and Markov coefficient are compared for the formamide and aqueous solutions. The absence of any appreciable specific adsorption of potassium ions is demonstrated by comparison of the cation surface excesses with the predictions of diffuse layer theory.
42(1965); http://dx.doi.org/10.1063/1.1695739View Description Hide Description
Electron paramagnetic resonance studies of the tetrahedral CuCl4 = ion in single crystals of Cs2CuCl4 and Cs2ZnCl4 yield the spectroscopic parameters g 1=2.083±0.001, g 2=2.103±0.003, g 3=2.384±0.006 (Cs2CuCl4) or 2.446±0.002 (Cs2ZnCl4), and | A 1 | = (5.1±0.5)×10−3 cm−1, | A 2 | = (4.6±0.5)×10−3 cm−1, and | A 3 | = (2.5±0.5)×10−3 cm−1. The indicated errors are estimated from the slight asymmetries in the line shapes and from the lack of full resolution of the hyperfine components. The resonances show no resolved superhyperfine structure. It is demonstrated that the linewidths of 2.2×10−3 T observed between inflections at low temperatures arise from unresolved superhyperfine interaction and are consistent with the presence of an unpaired electron which spends 1.3% of its time occupying 3s orbitals of the Cl ions of the complex. Comparison with the superhyperfine structure observed in octahedral CuCl6 4— suggests that this electron also spends 16.7% of its time occupying Cl ion 3p orbitals. Insertion of these numbers into an LCAO—MO analysis of the g values in terms of the known energies of the d—d transitions shows that the unpaired electron spends 12% of its time in a 4p(Cu) orbital and 70% of its time in the 3d(Cu) state. These numbers are consistent with the EPRhyperfine splitting and the polarization ratios and extinction coefficients of the d—d bands. Further considerations demonstrate that the wavefunction of the unpaired electron is a nonbonding orbital.
42(1965); http://dx.doi.org/10.1063/1.1695740View Description Hide Description
The 19F high‐resolution spectrum of 1,1‐difluorocyclohexane has been observed at temperatures from −93° to +40°C. The rate of conformational isomerization was determined by a complete line‐shape analysis method for temperatures from −71° to +6°C. Activation parameters ΔH ‡ and ΔGcc ‡ in kilocalories/mole and ΔScc ‡ in entropy units were 9.0, 9.8, −3.3 and 8.6, 9.8, −5.0 for 1:1 vol/vol solutions in CS2 and CFCl3, respectively, at the coalescence temperature of 228°K. In the low‐temperature spectra of the CS2 solution, the resonance of the equatorial fluorine is shifted 15.64 ppm downfield from the axial and J FF is 235.3 cps; also J (Hax–Fax) the axial‐axial vicinal H–F coupling constant is 34.3 cps and J (Heq–Fax) is 11.5 cps. At temperatures above −10°C, neglect of the H–F coupling in the line‐shape analysis produces systematic errors in the apparent exchange rate.
42(1965); http://dx.doi.org/10.1063/1.1695741View Description Hide Description
Relaxation times and collisional de‐excitation probabilities of the vibrational, electronic, and rotational degrees of freedom of the NO molecule were determined by acoustic measurements at 296°K (τ0 pT vib=4.0×10−7 sec, P 10 vib=1/2700; τ0 pTel=1.0×10−8 sec, P 10 el=1/110; τ0 pT rot=1.2×10−10 sec). In fact, these measurements were the first acoustic determination of electronic relaxation in any gas. In comparison to O2 and N2 the vibrational and rotational relaxation times are shorter than expected. This may be attributed to the dipole moment of the NO molecule.
42(1965); http://dx.doi.org/10.1063/1.1695742View Description Hide Description
The absorption and fluorescence spectra of emerald are characteristic of Cr3+ in the slightly distorted octahedral site of beryl [Be3Al2(SiO3)6]. Details of the spectra, such as dichroism and fine structure, are analyzed successfully in terms of a D 3 site symmetry. The large trigonal field parameter values v=−1550 cm−1, v′=+1380 cm−1 arise from polarization of oxygen ligands by next‐nearest neighbors. The Zeeman effect for the red 2 E lines is analyzed on the basis of the D 3 site symmetry, and data are given for the Paschen—Back effect for both emerald and ruby.
42(1965); http://dx.doi.org/10.1063/1.1695743View Description Hide Description
The completeness of the Cole—Cole diagram in the analysis of dielectric relaxation is proved by showing explicitly that a semicircle in the Cole—Cole diagram corresponds uniquely to a Debye relaxation function. A method is established to distinguish a continuous distribution of relaxation times from a single relaxation time.
42(1965); http://dx.doi.org/10.1063/1.1695744View Description Hide Description
The equation of state of a system of light molecules is regarded as the sum of a classical term and a quantum correction term. Experimental data for argon are used as the classical contribution and the quantum term is evaluated both for a 12–6 Lennard‐Jones cell model and for a uniform potential approximation of this model. The former is seen to give a quantum correction term far too small in magnitude, while the latter approximation produces theoretical isotherms in good agreement with experimental data for both hydrogen and deuterium. Experimental hydrogen—deuterium data are then used to construct high‐temperature classical corresponding‐states isotherms.
Generalized Oscillator Strengths and Electronic Collision Cross Sections for Nitrogen at Excitation Energies Above 10 eV42(1965); http://dx.doi.org/10.1063/1.1695745View Description Hide Description
Collision cross sections and generalized oscillator strengths have been determined for each of 13 transitions in nitrogen whose excitation energies lie in the interval 10 to 83 eV. Only the generalized oscillator strengths have been reported since the collision cross sections can be calculated from these. Incident kinetic energy was approximately 500 V in each case.
42(1965); http://dx.doi.org/10.1063/1.1695746View Description Hide Description
An improved monochromator is described which provides an electron beam sufficiently homogeneous in energy so that peak widths range from 0.28 V at 400‐V kinetic energy to 0.13 V at 150‐V kinetic energy. Using this device excitation potentials have been determined for CO2 and N2. The highest peak in the spectrum of N2 occurs at an excitation potential of 12.93 V while the most intense transition in the ultraviolet absorptionspectrum, according to Huffman, Tanaka, and Larrabee, occurs at 12.74 V. This discrepancy exceeds the experimental error in the determination and indicates a failure of the Born approximation.
Oscillator Strengths of Several Peaks in the Electron‐Impact Spectrum of Carbon Dioxide. Spin—Orbit Coupling42(1965); http://dx.doi.org/10.1063/1.1695747View Description Hide Description
Electron‐impact spectra of CO2 have been obtained at incident kinetic energies of 150, 200, 300, and 400 V. Oscillator strengths of four transitions are calculated from the spectra and compared with other deminations. Assignment of term symbols is discussed.
42(1965); http://dx.doi.org/10.1063/1.1695748View Description Hide Description
By use of a classical model, the effect of adsorbed particles on the accommodation coefficients at a gas—solid interface is studied. The interaction between the adsorbed and incident particles is assumed to be impulsive. The results show an important contribution of this effect on the over‐all value of the accommodation coefficients even at the surface coverage as low as 1%.
42(1965); http://dx.doi.org/10.1063/1.1695749View Description Hide Description
A detailed account is given of the kinetic theory for a fluid composed of perfectly rough spheres. When one applies the method of Chapman and Enskog to a dilute gas of these spheres he finds that the nonequilibrium distribution function satisfies a nonself‐adjoint integral equation. The solution of this equation is not an isotropic function of the molecular spin velocity. A study has been made of the bearing of this spin anisotropy upon the calculated values for the gas transport coefficients.
42(1965); http://dx.doi.org/10.1063/1.1695750View Description Hide Description
The fluorescence excited in iodine by the green emission line of mercury, in the presence of foreign gases, has been examined by high‐resolution photoelectric photometry. Cross sections for quenching, vibrational, and rotational energy transfer for the v′ = 25, J′ = 34 level of the B 3Π0u+ state of iodine have been obtained, for collisions with 3He, 4He, Ne, Ar, Kr, Xe, H2, O2, CO2, SO2, CH3Cl, and NH3. Emission bands have been rotationally analyzed to yield partial total cross sections for the inelastic processes. These have been corrected for multiple scattering by a computer simulation procedure.
The correlation of quenching efficiency with the mass and polarizability of the collision partner, found by Brown for the quenching of the v′ = 15 level of iodine, holds for the v′ = 25 level as well. There is no contribution to quenching efficiency from a permanent electric dipole moment. The data suggest that a complex set of interactions, including electrostatic polarization, spin—orbit forces, and specific chemical effects, are responsible for quenching, indicating a multiplicity of repulsive states contributing to the induced predissociation process. The vibrational energy‐transfer efficiency is maximum when the mean collision time equals the period of oscillation of the molecule, which corresponds to a collision reduced mass ≃40 for T = 370°K, v′ = 25 of I2; vibrational transfer is largely independent of the internal structure of the collision partner. The efficiency of pure rotational energy transfer (Δv′ = 0) shows a similar smooth dependence on reduced mass of the collision system, with the exception of the molecules SO2, CO2, and CH3Cl, which are more efficient. Quantitative measurements have been made on partial components of total inelastic cross sections for ΔJ′ up to ±20 angular momentum units, with evidence for a total spread of ΔJ′ up to 30 or 40. The width of the distribution of partial cross section components decreases in the order ; also, the ΔJ′ distribution is broader for collisions with heavier particles.
42(1965); http://dx.doi.org/10.1063/1.1695751View Description Hide Description
Thermal analysis of the glass transformation permits the determination of the temperature at which the transformation occurs at a maximum rate. It is found that this temperature depends on the experiment's rate of warmup. Appropriate handling of kinetic equations and experimental data permits the evaluation of the thermodynamic functions that characterize the activation barrier. Experimental results on glycerol are comparable to results extrapolated from dielectric relaxation studies.
42(1965); http://dx.doi.org/10.1063/1.1695752View Description Hide Description
A new technique has been developed for the direct observation of the decomposition of multiply charged polyatomic ions. Positive ions or ion pairs and ejected electrons, formed in a uniform electrostatic field by a 1‐keV electron beam, are accelerated in opposite directions to multiplier detectors. The masses of the positive ions are determined by measuring the time interval between electron and ion pulses by delayed coincidence. The formation of positive ion pairs is demonstrated and their masses determined by electron—ion—ion delayed coincidence techniques. The effects of initial kinetic energy on mass‐spectrum peak shapes and travel time correlations between members of an ion pair are discussed. Both of these effects are experimentally observed. The technique has been applied to the study of ionization and fragmentation of CO2, CF4, CH4, and C3H6. Numerous decompositions leading to the formation of positive ion pairs are observed. Significant fractions of particular high‐kinetic‐energy fragment ions are formed by these processes.