Volume 44, Issue 2, 15 January 1966

Improvement of Uncoupled Hartree—Fock Expectation Values for Physical Properties
View Description Hide DescriptionIt is shown that if one uses the uncoupled Hartree—Fock method as a zero‐order approximation for calculating atomic and molecular second‐order properties (either static or dynamic), then the first‐order corrections to this approximation are determined solely by quantities already available from the zero‐order calculations. No new equations need be solved.

ESR Spectrum of FOO
View Description Hide DescriptionThe ESR spectrum obtained during the electron irradiation of liquid CF_{4} containing trace amounts of oxygen consists of a 12.83‐G doublet at g=2.0038. Under the conditions of the experiments the radical producing this spectrum has a mean lifetime of ∼20 min. This observed spectrum is similar to the doublet which has been found in various oxides of fluorine. Addition of small amounts of oxygen enriched in ^{17}O shows that the radical contains two nonequivalent oxygen atoms which have appreciable hyperfine constants. The ^{17}O coupling constants, a _{O}′=22.17 and a _{O}″=14.50 G, are similar to those found in RO_{2}·. The simplest radical which can be proposed to explain these results in FO_{2}·. Upon prolonged irradiation the CF_{4} shows a second, transient spectrum which is tentatively assigned to CF_{3}OCF_{2}·.

Resonances in Electron Scattering from H_{2}, HD, and D_{2}
View Description Hide DescriptionResonances in the transmission of electrons through H_{2}, HD, and D_{2} have been studied for electrons of energy 11 to 13 eV. In H_{2} and HD pairs of resonances were observed, indicating that there exist two electronic states of H_{2} ^{−} and HD^{−}, each with well‐developed vibrational structure. In D_{2} only one series of resonances is observed. The single series is attributed to the overlap of two states of D_{2} ^{−} because of a smaller vibrational separation. The absolute energy scale for the resonances has been recalibrated to an estimated accuracy of 0.1 eV.

Inelastic Electron Scattering from H_{2}
View Description Hide DescriptionEnergy‐loss spectra have been measured for 13.7‐ to 50.7‐eV electrons in H_{2}. For incident energies below about 16 eV, energy‐loss peaks are observed due to either or both of the a ^{3}Σ_{ g } ^{+} and c ^{3}Π_{ u } states of H_{2}. The excitation cross section of the v=0 and v=1 vibrational levels of the B ^{1}Σ_{ u } ^{+} state show sharp and large resonances, corresponding in energy with resonances in the total scattering. The absolute electronenergy scale in H_{2} was recalibrated to an estimated accuracy of 0.1 eV.

Energy of Excimer Luminescence. V. Excimer Fluorescence of Naphthalene and Methylnaphthalenes
View Description Hide DescriptionThe interpretation of the energies of excimer luminescence of naphthalene and 12 of its alkyl derivatives is considered, and it is shown (i) that there is considerable configuration interaction between molecular‐exciton and charge‐resonance states and (ii) that the energy of excimer fluorescence may not be interpreted without invoking this configuration interaction. Excimer‐fluorescence energies are calculated for the substituted naphthalenes using a four‐electron MO treatment of the interaction and as a function of Z, the Slater orbital effective charge exponent, and of the interplanar distance D. Agreement with excimer‐luminescence energies is obtained for values of Z=3.18 and values of D between 3.4 and 3.7 Å, with the largest intermolecular distance D being obtained for those compounds in which steric hindrance is expected to be largest.

Ionic Association in Molten AgNO_{3}
View Description Hide DescriptionAn interpretation of the vibrational spectrum of molten silver nitrate based on normal coordinate analysis is presented. The results indicate that ion pairing may be responsible for the observed splitting of one degenerate fundamental and appearance of the infrared‐active band in the Raman spectrum. A force constant of 0.5 mdyn/Å is estimated for the Ag–O interaction.

Quantum Dynamics of Anharmonic Oscillators. I. Simple Examples
View Description Hide DescriptionThe dynamical behavior of two anharmonic oscillators, having a linear and a square‐well potential, respectively, is studied. The expectation values of the coordinate and the mean spread of the oscillating wave packets are calculated as functions of time and presented graphically. Significant departures from the behavior of the corresponding classical systems are observed. These results cast some doubt on the use of classical‐mechanical models in the theory of unimolecular rates.

Isotope Effects on Molar Volume and Surface Tension: Simple Theoretical Model and Experimental Data for Hydrocarbons
View Description Hide DescriptionExperimental measurements of molar volumes and surface tensions of benzene, toluene, cyclohexane, and methylcyclohexane and of their completely deuterated analogs are presented. The lighter species have a greater volume by about 0.3%. Surface tensions of the lighter species are greater, also, and increase from 0.2% to 1% as the number of hydrogens per carbon increases. Results are interpreted on the basis of the bond‐stretching anharmonicity which makes C–H bonds longer and more polarizable than C—D bonds. The ``steric'' and polarizability effects are comparable in magnitude but opposite in sign in their influence on cohesive properties. It is shown by a simple theoretical model that the ``pure‐mass effect'' on molar volume arising from zero‐point translational motions of the molecules as a whole is negligible in comparison with the effects stemming from zero‐point motions of the C–H and C—D bonds.

Vibrational Levels of the ^{2} D—E State of Ce^{3+} in CaF_{2}
View Description Hide DescriptionThe equations for the Jahn—Teller problem of an E electronic state and an E vibrational mode are solved by a numerical technique analogous to the procedure for finding solutions for a lower‐order eigenvalue equation.
The vibrational fine structure in the spectrum of CaF_{2}:Ce^{3+} at 3100 Å is compared with the structure which a first‐order Jahn—Teller effect would predict. A stabilization energy of about 330 cm^{−1} and a E mode vibrational frequency of about 210 cm^{−1} are indicated.

Force Fields in KrF_{2} and XeF_{2}
View Description Hide DescriptionA possible simple explanation is given of the different signs of the bond—bond interaction constants f_{rr} for the vibrations of KrF_{2} and XeF_{2}. The magnitude and sign of f_{rr} are related to the ionization potential of the central rare‐gas atom and the net charge distribution in the molecule. In KrF_{2} the negative sign may be due to the greater weight of a no‐bond structure in a resonance description.

Vibrational Relaxation of Diatomic Molecules
View Description Hide DescriptionA one‐dimensional model is explored and rigorous solutions are obtained to the classical equations of motion yielding transition probabilities between low‐lying vibrational levels of diatomic molecules. Results are listed for four halogens, O_{2}, N_{2}, and CO colliding in pure gases and O_{2} with Ar or He as a collision partner. Selecting a single variable ``a'' (the range term of the Morse potential function), excellent agreement was found with the available experimental data over a 30‐fold temperature range. The validity of the Landau—Teller theory is discussed; in particular, the effect of the consideration of an attractive potential and the simplification involved in its explicit treatment. Transitions involving double quantum jumps are considered. Some preliminary results of a two‐dimensional model are discussed.

Theoretical Estimation of the Conductivity of Different Periodic DNA Models
View Description Hide DescriptionUsing the deformation‐potential approximation, we have estimated the conductivity of some periodic DNA models. The necessary band structures we had determined previously using the tight‐binding approximation. We have obtained separately the contributions to the conductivity of the mobile electrons and the positive holes.
For the total conductivities (σ_{0}) we have obtained values between 10^{3}−10^{5}Ω^{−1}·cm^{−1}. In the cases when the conduction bands are rather narrow we have obtained much larger values for the electronic contribution than for the contribution of the positive holes. This discrepancy can be interpreted within the framework of the deformation potential approximation, but it makes questionable the applicability of this method for narrow bands.

Inelastic Collisions of H_{2} ^{+} and N_{2} ^{+} Ions with Hydrogen Molecules
View Description Hide DescriptionAbsolute total cross sections have been measured for some inelastic processes occurring in collisions of N_{2} ^{+} and H_{2} ^{+} ions with H_{2} molecules. The reactions which were studied are:The cross sections have been determined over the range of kinetic energy of the incident ions, 3–100 eV. The experimental method consists of energy and mass analyzing the products of collisions occurring when a beam of ions of known kinetic energy passes through a scattering chamber containing target gas at low pressure. The energy analysis provides considerable new information regarding the mechanisms of the reactions. The results are in reasonable agreement with previous measurements. Comparisons of the experimental results with existing theories are made. In the case of charge transfer, the symmetric atomic‐resonance theory of Rapp and Francis is found to be a good qualitative description of the H_{2} ^{+}–H_{2}charge‐transfer process.

Photoionization by Argon Resonance Lines
View Description Hide DescriptionThe direct and sensitized photoionization of ammonia and propane by argon resonance lines has been investigated. The ion current of direct photoionization approximately followed Beers law. The ratio of the absorption cross section of propane to that of ammonia was found to be 3.2. The ion current of sensitized photoionization generally increased with argon pressure. When the direct photoionization current was sufficiently large, however, the ion current decreased with increasing argon pressure, because the ionization induced by the energy transferred from the excited argon atoms is a competitive process of that induced by the photons absorbed by the sample molecules. From these results, it was concluded that the most important role of argon as a sensitizer is to increase the apparent absorption cross section of sample.

Dissociation Energy of F_{2}(g) Obtained from the Study of Gas Flow of Intermediate Pressures Through an Orifice
View Description Hide DescriptionA new treatment for gas flows at intermediate pressures through an orifice has been developed and combined with a new experimental technique to obtain a value for the dissociation energy of F_{2}(g). The value determined is 41.8±0.2 kcal/mole.

Approximations to Hartree—Fock Perturbation Theory
View Description Hide DescriptionA detailed examination is made of several approximations to the first‐order Hartree—Fock perturbation equation. Four distinct methods are considered: the coupled (Method a) and the uncoupled (Method c) approximation of Dalgarno, a new alternative uncoupled approximation (Method b), and the simplified uncoupled approximation of Karplus and Kolker (Method d). By a comparison of the pertinent equations, it is shown that Methods a, b, and d correspond to each other in the use of a core potential analogous to that appearing in the zeroth‐order Hartree—Fock equation, while Method c differs due to the inclusion of an extraneous self‐potential term. An alternative analysis based on an orbital basis set expansion of the perturbed function demonstrates that Method c has an energy denominator of the simple Hückel type, while both Methods a and b include important two‐electron correction terms. Also, it is found that of the four approximations, only Method c can be obtained as the first‐order correction with a zeroth‐order many‐electron Hamiltonian that has the Hartree—Fock determinant as its eigenfunction; the other techniques are one electron in character, as is the Hartree—Fock method itself.
The significance of the difference in the core potential is demonstrated by test calculations of dipole and quadrupolepolarizabilities and shielding factors for the two‐, three‐, and four‐electron isoelectronic series. A variational technique is used with a trial function that has the form of a polynomial times the unperturbed orbital. For the polarizabilities, it is found that Method b is an excellent approximation to Method a, indicating that the self‐consistency condition on the Method a solutions has a very small effect. The shielding factors, however, appear to be more sensitive to the self‐consistency requirement. Both Method c and Method d introduce larger errors than Method b, with Method c particularly poor for three‐electron atoms and ions. The constraint introduced by choice of trial function is shown to be unimportant for polarizabilities, but quite severe for the four‐electron atom shielding factors.
A comparison of the complexity of the various techniques shows that the relative computing times for Methods a, b, c, and d are in the ratio of 300 to 60 to 75 to 1. Thus, Method d is simplest by far, although its speed is achieved by some loss of accuracy with respect to Methods a and b.

Reaction between Atomic Oxygen and Nitrous Oxide
View Description Hide DescriptionA shock tube has been employed to study the reaction between atomic oxygen and nitrous oxide in an excess of molecular oxygen. The temperature was varied from 1700° to 2300°K. The total gas concentrations ranged from 0.085 to 1.42×10^{−5} moles/cc. The atomic oxygen was generated by the thermal decomposition of ozone. The rate constant for the reaction between atomic oxygen and nitrous oxide is shown to be k _{2′}+k _{2″} = (2.3±0.4)×10^{13} exp(−25 000±800/RT) cc/mole sec.
It is shown that the best fit to the experimental data is obtained when the extrapolation of the low‐temperature rate constant for the reactionis employed rather than the rate constant obtained through the reverse reaction and the equilibrium constant. The former rate constant is a factor of 6 greater than the latter rate constant.

H_{2}S as a Free‐Radical Interceptor in the Gas‐Phase Radiolysis and Photolysis of Propane
View Description Hide DescriptionThe gas‐phase photolysis (1236 Å) and the γ‐ray radiolysis of C_{3}D_{8} has been investigated in the presence of varying concentrations of H_{2}S. When 10% or more H_{2}S is added to C_{3}D_{8}, the majority of the D, CD_{3}, C_{2}D_{3}, and C_{2}D_{5} radicals abstract an H atom from H_{2}S to form HD, CD_{3}H, C_{2}D_{3}H, and C_{2}D_{5}H, respectively. The fully deuterated molecules formed in these mixtures result from the unimolecular elimination of a stable molecule from C_{3}D_{8} or C_{3}D_{8} ^{+} and from fast bimolecular processes such as ion—molecule reactions
The mechanisms of the radiolysis and the photolysis proposed in earlier studies have been re‐examined in the light of the information derived from the C_{3}D_{8}—H_{2}S experiments and of some additional photolysis experiments on CD_{3}CH_{2}CD_{3}—NO mixtures. The results indicate that the modes of decomposition of the neutral excited propane molecule are as follows:The internally excited C_{2}D_{4}, C_{2}D_{5}, C_{3}D_{6}, and C_{3}D_{7} species formed in these primary processes decompose to form D, CD_{3}, C_{2}D_{2}, C_{2}D_{3}, and C_{2}D_{4} unless they are collisionally stabilized.
In the radiolysis of C_{3}D_{8}—H_{2}S mixtures, yields of the free radicals can be adequately accounted for by taking into account the modes of fragmentation of the parent ion and of the excited propane. The C_{2}D_{5} ^{+} ions are shown to react with H_{2}S in part by the deuteron‐transfer reactionThe effect of pressure and the effectiveness of HI as a free‐radical interceptor in the radiolysis have been examined.

Repulsive Interactions and Molecular Rotation in Inert‐Gas Lattices
View Description Hide DescriptionA model is discussed from which the effect of repulsive interactions on the rotational energy levels of a solute molecule in an inert‐gas lattice may be calculated. The model is based on the assumption that repulsive interactions may be understood in terms of single interatomic‐exchange processes in the solid. Application is made to the case of HCl in argon, krypton, and xenon. The results show that, for this case, repulsive interactions are small compared to long‐range multipole interactions.

Optical Spectra of Thallium in Glasses as Related to Crystals and Solutions
View Description Hide DescriptionThe absorption and emission spectra of thallium in fused silica, aluminoborate, and phosphate glasses are similar to those of thallium‐doped alkali halides and solutions. The absorption and emission bands in the different systems can be attributed to transitions within the central Tl^{+} ion in a center with a (TlX_{ n })^{(n−1)—} configuration, where X stands for the anions neighboring the Tl^{+} ion. There is a shift in the absorption bands with the nature of the anions and cations neighboring the Tl^{+} ion. This shift may be related to the chemical shift observed in NMR studies. The thallium centers in glass are possibly present in ordered regions in the glass structure. The minimum size of such an ordered region is estimated to be about 15 Å. There are indications of dimers being formed in thallium‐doped fused silica.