Volume 62, Issue 2, 15 January 1975
Index of content:

The ground state properties of spin‐aligned atomic hydrogen, deuterium, and tritium
View Description Hide DescriptionThe bulk, ground stateproperties of atomic hydrogen, deuterium, and tritium systems are calculated assuming that all pair interactions occur via the ^{3}Σ^{+} _{ u } atomic triplet potential. The conditions required to obtain this system, including inhibition of recombination through the energetically favorable singlet interaction, are discussed. The internal energy, pressure, and compressibility are calculated over the volume range 40 cm^{3}/mole ? V ⩽200 cm^{3}/mole applying the Monte Carlo technique with a quantum mechanical variational wavefunction. The system studied consisted of 32 atoms in a box with periodic boundary conditions. Results show that atomic triplet hydrogen and deuterium remain gasous at 0 K; i.e., the internal energy is positive at all molar volumes considered. Under the same conditions, tritium forms a liquid with a binding energy of E _{0} ? −0.75 K per atom, at a volume of V ? 130 cm^{3}/mole. The pair distribution function for these systems is also calculated. A brief discussion of the predicted superfluid behavior of ^{3}Σ^{+} _{ u } hydrogen and tritium is presented.

Isotope effect on the hyperfine splittings of the deuteriobenzene anions: An example of the dynamic Jahn–Teller effect
View Description Hide DescriptionThe vibronic wavefunctions and energy levels of the benzene, benzene−1−d, benzene−2,6−d _{2}, benzene−1,4−d _{2}, and benzene−1,3,5−d _{3} anion radicals have been obtained and used to determine the effect of deuterium substitution on the degenerate energy levels and spin densities of the benzene anion. It is shown that a dynamic Jahn−Teller effect treatment is required for these systems to obtain a quantitative interpretation of the consequences of deuterium substitution. The ground vibronic states of benzene^{−} and benzene−1,3,5−d _{3} ^{−} are degenerate. In benzene−2,6−d _{2} ^{−}, the symmetric state (A _{1} under C _{2v }) is 22 cm^{−1} below the antisymmetric state (B _{1} under C _{2v }). In benzene−1−d ^{−} and benzene−1,4−d _{2} ^{−}, the antisymmetric states are lower by 9 and 39 cm^{−1}, respectively. The benzene−2,6−d _{2} ^{−} and benzene−1,4−d _{2} ^{−} hyperfine coupling constants and their temperature dependence calculated using the vibronic wavefunctions and energy splittings are in very good agreement with the experimental values. For benzene−1−d, the experimental splitting is estimated to be 20 cm^{−1}, about twice as large as the calculated value, and agreement between the experimental and calculated hyperfine constants is less satisfactory. The vibronic energy splitting are interpreted in terms of the effect of deuterium substitution on the vibrational potential energies corresponding to the symmetric and antisymmetric electronic states. Calculations of the expectation values of the unpaired electron energy over the neutral molecule and the two anion Born−Oppenheimer state vibrational functions show that changes in the average values of the out−of−plane bending coordinates upon deuteration lead to a splitting of the vibrational potential energies. To a first approximation, the differences among the anions are a function of the unpaired orbital bond orders at the deuterated positions in the two electronic states. If the substituted bond order is large and negative, deuterium substitution increases the vibrational potential energy, but if it is approximately zero, the potential energy is essentially unchanged.

Recomputation of certain functions in the Peterlin–Stuart theory of flow birefringence and directions for the evaluation of experimental data in terms of molecular weights and molecular dimensions
View Description Hide DescriptionDetermination of the physical dimensions of nonspherical rigid macromolecules or particles by means of the flow birefringence technique requires reference to theoretical data derived from the Peterlin−Stuart theory. The data universally used for this purpose are those computed nearly 25 years ago by Scheraga, Edsall, and Gadd. Since simplification and approximations mandatory at that time are no longer necessary with modern computer technique, more precise theoretical data were now obtained by recomputation of the pertinent a _{ h k } and b _{ h k } values. In addition, the considerable number of additional coefficient values that are required for the application of the Peterlin−Stuart theory to the dimensional analysis by means of flow light scattering were computed. The results are followed by a brief survey and discussion of explicit equations useful for the practical application of the flow birefringence technique for dimensional analysis.

Freezing of vibrational degrees of freedom in free‐jet flows with application to jets containing CO_{2}
View Description Hide DescriptionThe primary objective of this study is to advance the development of a procedure for predicting the terminal vibrational temperatures in free−jet flows of either pure gases or gas mixtures. A secondary objective is to apply this procedure to free−jet flows of (a) pure CO_{2} and (b) dilute binary mixtures of CO_{2} in N_{2} and CO_{2} in H_{2}. Predictions are based on the sudden−freeze model described by Knuth [Proceedings of the 1972 Heat Transfer and Fluid Mechanics Institute (Stanford U. P., Stanford, California, 1972)]. The pressure and temperature dependence of the vibrational relaxation time, required for application of Knuth’s freezing−point criterion, are deduced from available experimental data on relative probabilities for collisional de−excitation of a given species by impurity molecules. The predicted terminal vibrational temperatures are correlated to excellent approximation by a dimensionless scaling parameter based on source conditions. Measurements were made using the supersonic−molecular−beam technique suggested by Milne e t a l. [J. Chem. Phys. 56, 3007 (1972)]. This technique takes advantage of the temperature dependence of the fragmentation pattern realized when molecules are ionized by electron impact, which temperature dependence can be established quantitatively using an effusive molecular beam with a variable−temperature source. Good agreement between predicted and measured

Potential energy surface for the model unimolecular reaction HNC → HCN
View Description Hide DescriptionA b i n i t i oelectronic structuretheory has been used to determine the more important features of the potential energy surface for the simple isomerizationreaction HNC → HCN. Extended basis sets were used in conjunction with both self−consistent−field (SCF) and configuration interaction (CI) wavefunctions. For nonlinear or C _{ s } geometrical arrangements of the three atoms, the CI included 11735 configurations, i.e., all single and double excitations. This large scale CI reproduces the HCN ground state geometry quite accurately and has been used to tentatively identify HNC in the interstellar medium. The SCF calculations predict HNC to lie 9.5 kcal/mole above HCN, while CI yields 14.6 kcal/mole. Similarly, barrier heights of 40.2 and 34.9 kcal/mole are predicted by SCF and CI. Thus, the SCF approximation is qualitatively reasonable for HNC → HCN. If HNC is designated by a reaction angle of 180° and HCN by 0°, then the saddle point or transition state is predicted to lie at 73.7°, significantly closer to HCN. A reaction path is determined from the SCF potential surface. The surface will be used in RRKM and classical trajectory studies of the dynamics of this reaction.

Photoelectron and far‐ultraviolet absorption spectra of chlorofluoro derivatives of ethane
View Description Hide DescriptionThe Hei photoelectron and vacuum ultraviolet absorption spectra of the following chlorofluoro derivatives of ethane have been measured: C_{2}F_{5}Cl, CH_{3}CF_{2}Cl, CF_{2}Cl−Cf_{2}Cl, CF_{2}Cl−CFHCL, and CF_{2}CL−CFCl_{2}. The lowest ionization potentials (12−13 eV) and all absorption bands from 50 000−84 000 cm^{−1} are due to transitions from the chlorine lone pair orbitals (Cl). The I.P.’s between 14 and 16 eV are due to ionization from orbitals mainly populated in the C−Cl, C−C, and C−H bonds, while at higher energies, ionization from orbitals of F lone pair (F) and C−F bonding character takes place. The lowest electronic transition is of the valence−shell type; at higher frequencies, Rydberg bands are found due to 4s→Cl and 4p→Cl type transitions.

A method analyzing the dielectric relaxation spectra of mixtures by decomposition into Debye elementary domains. Application to the study of the water spectrum
View Description Hide DescriptionThe authors propose a method of spectral analysis which consists of decomposing the experimental dielectric relaxation spectra of mixtures into a sum of elementary spectra of the Debye type. The technique of this approach of spectral parameters yields a noticeable improvement on the usual methods. After dealing with a great number of theoretical examples, so as to put the computation programs through a test, the study of water was carried out at 20°C. In this case, the experimental spectrum was reconstituted from three Debye constituents.

Photoelectron and far‐ultraviolet spectra of CF_{3}Br, CF_{2}BrCl, and CF_{2}Br_{2}
View Description Hide DescriptionThe Hei photoelectron and vacuum ultraviolet spectra up to about 20 eV of CF_{3}Be, CF_{2}Br_{2}, and CF_{2}BrCl have been measured. In both spectra, we find bands at energies lower than in the corresponding chlorine derivatives. Otherwise, the spectra can be interpreted along similar lines. The lowest ionization potentials and the lowest frequency bands in the ultraviolet spectra are due to transitions from the bromine lone pair orbitals.

An ESR analysis of a heat‐stable radical in γ‐irradiated single crystals of 1‐methylthymine
View Description Hide DescriptionFree radicals formed in γ−irradiated single crystals of 1−methylthymine were studied by ESR spectroscopy. In addition to the known C6−hydrogen adduct radical, a second radical is formed which is very stable for short periods at 200°C, as well as being present in the crystals at room temperature before high temperature annealing.Computer simulation was used as an aid to identifying this radical, which is 1−methyl−5−methyleneuracil−10−y1, formed by net hydrogen abstraction from the methyl group. Certain ESRspectral features suggest molecular packing disorder about an axis constructed along C6 and N3. The principal values for proton hf couplings perpendicular to both the CH bond and the unpaired electron’s p orbital direction, along the C−H bond and along the p orbital direction, respectively, in gauss, are: H_{1}(24.5, 8.1, 15.4); H_{2}(H_{2}−C10∥H−C6)(24.8, 6.9, 15.4); H_{C6}(14.0, 5.2, 10.5); and the gtensor values parallel and perpendicular to the p orbital direction are, respectively, 2.0018 and 2.0027.

Circular dichroism of unordered polymers: Extended time dependent Hartree theory for polypeptides
View Description Hide DescriptionEquations describing circular dichroism (CD) and optical rotatory dispersion (ORD) of a system of unordered polymers in solution are derived via a linear response method in terms of exact states of the system. Origin dependent extrinsic magnetic moment operators are not used. After a multipole expansion of the induced transverse current and a long wavelength expansion of the susceptibilities, the equation of motion of the radiation field’s average vector potential is solved and a definition of the refractive index provides an account of CD−ORD. It is shown that the contribution to the current by the susceptibility characterizing induced electric dipole polarization through intrinsic magnetic dipolar coupling with the curl of the radiation field is identical to the contribution by the susceptibility characterizing induced magnetic dipole polarization through electric dipolar coupling with the radiation field only for isotropic media. Approximate polypeptide susceptibilities are obtained by an extension of the time dependent Hartree scheme. The extension is shown to be necessary when electric and nπ* magnetic dipole transitions are degenerate or near degenerate, for which anomalous dispersion arises and rotational strength is not conserved. The resulting susceptibilities are obtained from the solution to a normal mode problem. The normal modes are determined not only by electric dipolar coupling but also by the coupling of electric quadrupoles with others and with electric dipoles. The time dependent Hartree scheme is then on a comparable level with the matrix scheme, and the two methods are discussed.

Vibrational nonequilibrium in carbon dioxide electric discharge lasers
View Description Hide DescriptionAn experimental and theoretical investigation of vibrational nonequilibrium in the CO_{2} electric discharge laser was performed. The vibrational temperature for each vibrational mode of CO_{2} was measured under a variety of discharge conditions. Measurements indicate nonequilibrium between ν_{1} and ν_{2} can be significant. Possible causes for the apparent nonequilibrium which were theoretically examined included anomalously high gain on certain transitions which has been attributed to overlapping hot band contributions, use of different optical broadening cross sections, use of different electron−vibration excitation cross sections, and the effect of uncertainty in all V−V and V−T transfer rates. The most likely cause of the measured nonequilibrium was found to be a lack of strong coupling between the ν_{1} and ν_{2} modes.

Use of double cosets in constructing integrals over symmetry orbitals
View Description Hide DescriptionDouble cosets are used to reduce the formulas for integrals over symmetry orbitals to unique integrals over atomic orbitals.

Molecular beam kinetics: Angular distributions and chemiluminescence in reactions of alkali dimers with halogen atoms and molecules
View Description Hide DescriptionCrossed−beam studies are presented for several reactions of diatomic alkali molecules with halogen atoms and molecules. The alkali dimers are generated by association of atoms in a supersonic nozzle expansion, the halogen atoms by thermal dissociation of molecules. For both the X + K_{2} and X_{2} + K_{2}reactions (X = Cl, Br), the angular distributions of reactively scattered KX peak forwards (in the center−of−mass system) with respect to the incoming alkali dimer, the final relative translational energy of products is fairly high, ∼10−20 kcal/mole, and the total reaction cross sections are large, ∼50−150 Å^{2}. For the X + A_{2}reactions (X = Cl, Br, I; A_{2} = Na_{2}, K_{2}, Rb_{2}), excited alkali atom emission is observed from nearly all energetically accessible transitions which fall within the spectral range of the experiments (2200−8000 Å). Some of these lines come from states located above the reaction exoergicity and thus indicate that the initial relative translation of the reactants is converted into electronic excitation of the product atom. The chemiluminescence spectra for X + K_{2} correspond to a statistical distribution of excited states, roughly characterized by a temperature of ∼5000°K. The cross sections for chemiluminescence from the lowest excited ^{2} P alkali atom state are ∼10−100 Å^{2}. The X + A_{2} results are interpreted in terms of electron jumps forming X^{−} + A_{2} ^{+} at crossings of potential surfaces. Calculations using a semiempirical pseudopotential method show the orbital degeneracy of the halogen atom has an important role. This is indicated also by a study of the analogous H + A_{2}reaction, where orbital degeneracy is lacking and no chemiluminescence is observed. For the X_{2} + A_{2}reactions, the angular distributions indicate that the dominant reaction path forms A + AX + X. Chemiluminescence is also observed from the two paths which yield A* + AX + X and AX + AX* (for X_{2} = Cl_{2}, Br_{2}, I_{2}, ICl, and IBr; A_{2} = K_{2}, Rb_{2}, and Cs_{2}). For the K_{2}reactions, the cross sections are ∼0.3−3 Å^{2} for A* emission and smaller for the AX* emission; for Rb_{2} and Cs_{2} the AX* emission becomes stronger. No AX* emission is observed for the analogous X_{2} + Na_{2}reactions, although it is energetically allowed. The molecular emission in reactions of ICl and IBr with K_{2} comes from KI*. These observations are consistent with an electron−jump mechanism which allows facile four−center reaction via (A^{‐}) A^{+}⋅⋅⋅X^{−} (X^{‐}), a biradical ion−pair intermediate.

Statistical partitioning of electronic energy: Reactions of alkali dimers with halogen atoms
View Description Hide DescriptionThe phase space theory of chemical kinetics is applied to reactions of alkali dimers with halogen atoms. Predicted populations of excited electronic states of the product alkali atoms are in good agreement with the results of recent chemiluminescence experiments. This agreement suggests that for this system, in contrast to most other thermal energy collision processes, there is relatively free transfer of energy between electronic and other internal degrees of freedom during reaction.

Monte Carlo calculations for pressure dissociation of H_{2}
View Description Hide DescriptionA Monte Carlo method is proposed for the calculation of dissociation of diatomic homonuclear molecules as a function of temperature and density. The procedure is illustrated for hydrogen in the temperature range up to 15000 K. The essentially quantum mechanical processes of dissociation and binding are replaced here by a classical model system of free atoms and molecules whose numbers in the system may vary according to certain probabilistic rules. A choice must be made of the interaction potentials between particles, which are then replaced by equivalent hard−spheres repulsive interactions. The attractive part of the singlet H−H interaction, which is responsible for the bound state of two atoms, is replaced by an intrinsic ’’binding’’ energy attributed to each molecule present in the system. Results show that dissociation starts at densities well below the packing density of molecules.

’’Exactly soluble’’ two‐component lattice solution with upper and lower critical solution temperatures
View Description Hide DescriptionA decorated lattice model of a two−component liquid solution is presented which has closed−loop coexistence curves with both upper and lower critical solution temperatures analogous to the behavior found in the nicotine + water and m−toluidine + glycerol systems. The model can be transformed exactly into the spin−1/2 Ising model for which exact results are known in two dimensions and reliable estimates are available in three dimensions. The model exhibits nonclassical critical exponents at both upper and lower critical solution temperatures and has coexistence curves in qualitative agreement with those for real systems. The coexistence curves exhibit characteristic features found in most systems with closed−loop coexistence curves.

Vibrational energy transfer from the (00°1) level of ^{14}N_{2}O and ^{12}CO_{2} to the (m, n ^{ l }, 1) levels of these molecules and of their isotopic species
View Description Hide DescriptionWe have studied versus temperature the fast vibvrational energy transfers which occur between two nitrous oxide molecules, or two carbon dioxide molecules, initially excited by a laser pulse into the (00°1) level. These transfers occur upon near−resonant collisions of the type M(m, n ^{ l }, 1) + M(m′, n′^{ l }′, 0) ? M(m, n ^{ l }, 0) + M(m′, n′^{ l }′, 1) with M = ^{14}N_{2}O) or ^{12}CO_{2}. The rates of these V−V transfers have been measured from room temperature up to 900 K by the laser−induced fluorescence method. These exchanges can play an important role in the kinetics of the fast V−V transfers which occur in gaseous mixtures involving these molecules. This is particularly the case for the transfers occurring between different isotopic species of CO_{2} and N_{2}O, such as ^{12}CO_{2}−^{13}CO_{2}, and mixtures of ^{14}N_{2}O with ^{14}N^{15}NO, ^{15}N^{14}NO, and ^{15}N_{2}O, also studied in this work. The transfer rates for the isotopic mixtures of nitrous oxide have been measured versus temperature. The experimental results are compared with the values calculated on the basis of the long−range multipolar interactions, according to a first−order perturbation theory.

Condensation of a supersaturated vapor. II. The homogeneous nucleation of the n‐alkyl benzenes
View Description Hide DescriptionThe design of an improved version of the upward thermal diffusion cloud chamber is described. Such a chamber was constructed and used to measure the supersaturations required to observe a rate of homogeneous nucleation of 2−3 drops cm^{−3}⋅sec^{−1}. Measurements were made on benzene, toluene, o r t h o−xylene, and n−butylbenzene over as much as a 150°C range of temperatures. The results obtained are compared to the predictions of the classical theory of homogeneous nucleation (Volmer−Becker−Döring−Zeldovich) and of the Lothe−Pound theory. The classical theory is found to be in excellent agreement with the experimental results.

Vibrational deactivation of O_{3} molecules in gas mixtures. II.
View Description Hide DescriptionExperimental measurements of the rate constants for vibrational deactivation of O_{3} by O_{3}, O_{2}, CO_{2}, H_{2}, D_{2}, CH_{4}, N_{2}, He, Ar, SF_{6}, CH_{3}Cl, CH_{2}Cl_{2}, CCl_{4}, and C_{2}H_{2} are presented. Vibrational relaxation of O_{3} is shown to follow the sequence (1) rapid V → V intermode coupling between the ν_{1} and ν_{3} modes, (2) a slower coupling of the ν_{1}, ν_{3} modes to the ν_{2} mode, and (3) V → T relaxation through the O_{3}(010) level. The results are described in terms of a simple analytic model for vibrational relaxation of O_{3}.

Kinetics of diffusion‐controlled reactions: Transient effects in fluorescence quenching
View Description Hide DescriptionA test of the continuum model for diffusion controlled reactions as applied to fluorescence quenching is presented and discussed. By proper selection of systems, it was possible to observe nonexponential decay which followed the decay law exp(−a t − 2b√t) as predicted by the continuum model. Analysis of these decay curves gave the encounter radius and pair diffusion coefficient. Reasonable values were obtained for both. Steady−state fluorescence quenching measurements were also made and compared with fluorescence decay studies. Evidence was found for ground−state complex formation. When this was taken into account, good agreement between the continuum model and the experimental results was obtained.