Volume 61, Issue 3, 01 August 1974

Assignments in the electronic spectrum of water
View Description Hide DescriptionTo explain the inelastic feature at 4.5 eV in the spectrum of water and to study its spectrum in some detail, we have carried out several calculations on the excited states of water using the equations‐of‐motion method. We conclude that the calculated vertical excitation energy of 6.9 eV for the ^{3} B _{1} state corresponds to the strong feature at 7.2 eV observed in low‐energy electron scattering spectrum. The 4.5 eV inelastic process almost certainly does not correspond to a vertical excitation of water at the ground state geometry. The other excitation energies and oscillator strengths agree well with experiment.

Calculated self‐ and foreign‐gas‐broadened linewidths for CH_{3}D
View Description Hide DescriptionSelf‐, N_{2}−, O_{2}−, and H_{2}− broadened linewidths for CH_{3}D have been calculated using the Anderson‐Tsao‐Curnutte theory. Interactions due to the dipole and octopole moments of CH_{3}D were included. Linewidths have been computed for a wide range of angular momentum quantum numbers J and K, and temperature dependence has been obtained for 100 ≤ T ≤ 300°K.

Low‐energy electron impact study of acetone
View Description Hide DescriptionA low‐energy, high resolution, electron impact spectrometer with a molecular beam target has been constructed and used to study the electronic energy levels of acetone vapor. Similar spectra were also taken with a second electron spectrometer having a static gas target. Both sets of spectra are essentially identical and show the expected singlet states at 4.37, 6.35, and 7.45 eV, the first triplet state at 4.16 eV, and a very broad second triplet process from 5.3 to 6.1 eV with an intensity maximum at 5.88 eV. Attempts to resolve vibrational structure in the latter band were unsuccessful, even though vibrational spacings of 0.14 eV were easily resolved elsewhere in the spectrum.

Quantum ergodicity and vibrational relaxation in isolated molecules. II. λ‐independent effects and relaxation to the asymptotic limit
View Description Hide DescriptionIn this second article on quantum ergodic properties of simple anharmonic molecular models, we present further numerical calculations for the Barbanis and Henon‐Heiles models. For the cases studied herein, the density of energy eigenstates is larger by about a factor of five than that used earlier. We show that the character of the low lying states of the model Hamiltonians is dominated by λ‐independent effects which can be obtained by second order degenerate perturbation theory. Nondegenerate modifications of the above systems are again found to be highly nonergodic. We also discuss estimates of the time scale upon which the dynamics takes place. Two simple estimates are obtained on the basis of the ergodic properties and found to be reasonably accurate for the Barbanis system.

Effect of an external electric field on the yield of free ions. III. Electron scavenging at small concentrations
View Description Hide DescriptionThe method of prescribed diffusion has been applied to obtain the evolution of the neutralization process of an ion pair in the presence of an external electric field. For relatively small external fields the probability of escape calculated by this method agrees exactly with the Onsager formula. The probability of the existence of the ion pair against neutralization has been evaluated in the long‐time limit and its Laplace transform determined to give the scavenging probability in the presence of an external fieldE at small concentrations. Analysis of the results shows that, at small concentrations, the yield of the scavenging reaction should vary with scavenger concentration c as (c + c _{0} E ^{2})^{1/2}, where c _{0} is some constant, rather than simply as c ^{1/2}. Replotting of the experimental data of Rzad and Bakale according to the present procedure removes the discrepancy between their extrapolated yield at zero concentration and the results of the Onsager theory. The maximum and minimum scavenger concentrations within which a square root variation of yield with concentration is to be expected are evaluated as functions of the external field.

Degenerate perturbation theory
View Description Hide DescriptionA number of different perturbation formulations found in the literature are discussed. Although these formulations are derived in quite different ways, simple relations among these derivations are described and, in fact, some are shown to yield identical results. One of these degenerate perturbation theories resulting from different formulations due to Van Vleck, Kemble, and Primas, to des Cloizeaux, and to Buleavski is considered in greater detail. Its linked and cluster expansion properties and some other resummation techniques are briefly discussed.

Study of the structure of molecular complexes. VIII. Small clusters of water molecules surrounding Li^{+}, Na^{+}, K^{+}, F^{−}, and Cl^{−} ions
View Description Hide DescriptionThe two‐body Hartree‐Fock potential for the ion‐water interaction and the two‐body Hartree‐Fock potential for the water‐water interaction have been used in the pairwise additivity approximation to study the Li^{+}(H_{2}O)_{ n }, the Na^{+}(H_{2}O)_{ n }, the K^{+}(H_{2}O)_{ n }, the F^{−}(H_{2}O)_{ n }, and the Cl^{−}(H_{2}O)_{ n } complexes, where n =2,3,4, ⋯ ,10. The complex configurations have been constrained to have either symmetrical geometries around the central ion or to be free to assume the lowest energy configuration. For n smaller than 5 (depending on the specific ion in consideration), the symmetrical configuration is the lowest energy configuration. For higher values of n, some of the water molecules tend to form a second shell of solvated water around the ion. The configurational optimalization was carried out only at T =0°K; but for a small cluster containing only four molecules of water, calculations have been performed at T =298°K. From the study at 298°K we have computed the correlation functionsg _{I–O}, g _{I–H}, g _{O–O}, g _{O–H}, and g _{H–H} (where the subscript I is a shorthand notation for ``ion''). Correlation functions are reported for the cluster F^{−}(H_{2}O)_{ n } at T =298°K with n =27. By comparing the results obtained at T =0°K and with n =10, with those obtained at T =298°K and n =4 and finally with the results obtained at T =298°K and n =27, we feel confident that the conclusions (given below) will remain valid for n >27 and at t ≠0°K. The coordination numbers for the ion‐water clusters are computed (approximatively) to be about 4 for Li^{+}, between 5 and 6 for Na^{+}, between 5 and 7 for K^{+}, between 4 and 6 for F, and between 6 and 7 for Cl^{−}. In the first solvation layer, the average ion oxygen distances are 1.9–2.0 Å for Li^{+}, 2.3–2.4 Å for Na^{+}, 2.8–2.9 Å for K^{+}, 2.7–2.8 Å for F^{−}, and 3.4–3.5 Å for Cl^{−}. The validity of the pairwise additivity approximation has been tested for the small clusters ion (H_{2}O)_{ n } with n =2,3 (and 4 and 5 for Li^{+} and F^{−}).

Spin‐other‐orbit and spin‐spin interactions in the metastable, c ^{3}Π_{ u }(1s,2p) state of H_{2}
View Description Hide DescriptionAn ab initio calculation of the spin‐other‐orbit and spin‐spin interactions in the c ^{3}Π_{ u }(1s,2p) state of molecular hydrogen has been made. This calculation utilized the wavefunction obtained with the optimal double configuration model by Zemke, Lykos, and Wahl. The coupling constants are in good agreement with those calculated by Lombardi using the 45–50 configuration elliptic coordinate wavefunction of Rothenberg and Davidson.

Electron nuclear double resonance of photoexcited phenanthrene‐d _{10} molecules in their lowest triplet state in diphenyl single crystals
View Description Hide DescriptionElectron deuteron double resonancespectra have been obtained for phenanthrene‐d _{10} molecules in their triplet electronic state of lowest energy, when they are dilutely substituted in a diphenyl host crystal. Four discretely different orientations of phenanthrene‐d _{10} molecules at the same set of translationally equivalent substitution sites of the diphenyl host, have been observed. Values of hyperfineinteractiontensor components and of spin densities for these different phenanthrene‐d _{10} molecules have been determined. The distortions of these various molecules from an ideal symmetry and the importance of these different distortions, as well as of the different orientations, for the interpretation of the intensities and polarizations of optical spectra, are discussed in light of the present measurements.

Intramolecular energy transfer in cis‐trans isomerization: A study of fluorescence from single vibronic levels of styrene, trans‐β‐styrene‐d _{1}, styrene‐d _{8}, and ethynlbenzene
View Description Hide DescriptionThe fluorescence lifetimes of, and quantum yields of emission from, individual vibronic levels of isolated molecules of styrene, trans‐β‐styrene‐d _{1}, styrene‐d _{8}, and ethynlbenzene have been measured. These data are subjected to a decomposition, under a plausible hypothesis, into parameters descriptive of an isomerization process and an intersystem crossing process. It is argued that the two processes proceed independently in parallel. The rate of isomerization is found to be independent of the vibrational energy content of the isolated molecule and to have a dependence on isotopic mass consistent with the prediction that the torsional mode is the best ground state acceptor in the reaction channel. A plausible schematic potential energy surface is constructed from a combination of spectroscopic observations and analogies with theoretically derived surfaces for similar molecules. Analysis of the experimental data, and deductions from those data, in terms of the properties of the potential surface, leads to the inference that intramolecular vibrational relaxation is slower than chemical reaction for excess vibrational energy up to ∼2500 cm^{−1}.

ESR study of trapped electrons produced in alkane glasses at 4 °K
View Description Hide DescriptionIn gamma irradiated 3‐MP, MCH, and 3‐MHX glasses, the same yields were obtained between 4 and 71°K, indicating that electrons are stabilized in pre‐existing traps prior to solvation. The linewidths were reduced on warm‐up of the glassesirradiated at 4°K and depended on the annealing time at 71°K, implying that the solvation occurs very slowly around 71°K. A comparative study of power saturation in 3‐MP and MCH suggested that the spurs formed at 4°K were spatially expanded compared to those at 71°K. The structural change of trapping sites caused by solvation was clearly reflected on the power saturation characteristics.

Rotational relaxation in polar gases
View Description Hide DescriptionAn expression for transition probability for rotational‐translational energy transfer for polar molecules has been derived, using the distorted wave approximation. The polar molecules have been assumed as point dipoles imbedded in hard cores. Calculations have been performed for the transition (1 → 0, 1 → 0) for HCl, DCl, HBr, H_{2}O, H_{2}S, and NH_{3} at various temperatures (300–500 °K). The calculated (Z _{rot})_{10} values are in good agreement with experimental (Z _{rot})_{eff} data. Further, the theory predicts decrease of (Z _{rot})_{10} with increase in temperature, dipole moment, and moment of inertia. The temperature dependence is thus opposite to that predicted by the classical theory of Zeleznik, but agrees well with the dependence of (Z _{rot})_{eff} obtained from experimental thermal conductivity data.

An x‐ray, spectroscopic, and magnetic study of the structure of nickel squarate dihydrate, NiC_{4}O_{4} · 2H_{2}O
View Description Hide DescriptionThe structure of nickel squarate dihydrate, NiC_{4}O_{4} · 2H_{2}O, has been investigated by initial susceptibilitymeasurements,infrared spectroscopy, and single crystal x‐ray diffraction techniques. The results indicate that the structure consists of Ni ions situated at the centers of the edges of a cube, with squarate ions in the cube faces. Each nickel is roughly octahedrally coordinated by four squarate oxygens, and by two water oxygens. The lattice constants were found to be a = b = c =8.068_{5} A, with α = β = γ = 90° within experimental accuracy. The structure was found to be noncubic. A spin‐orbit coupling parameter of −280 (30) cm^{−1}, which is 86% of the free ion value, is obtained from the magnetic and spectroscopic results. The structure of this compound, which is isostructural with the Mn(II), Fe(II), and CO(II) squarates, is different than that proposed by two other sets of workers. All crystals investigated were found to be macroscopically twinned, and a reason for such twinning is proposed.

Optical properties of some aromatic liquids in the vacuum ultraviolet
View Description Hide DescriptionThe optical properties of benzene, pyridine, quinoline, and 2‐ethylnaphthalene in the liquid state have been studied for photonenergies from 2 to 10.6 eV. For each liquid the extinction coefficientk has been obtained from transmission measurements, and self‐consistent values of the refractive indexn calculated over the experimental energy range by a Kramers‐Kronig analysis. The calculated absorption cross sections per liquid molecule have been compared with the corresponding absorption cross sections per vapor molecule, where the vapor data have been obtained from the literature. The absorption cross section spectra for liquid and vapor are very similar in the energy region studied, such that the observed absorption can be attributed to the same electronic excitations in both phases. In addition, evidence of collective excitations of electrons, not seen in the vapor state, is seen in all four liquids.

Macroscopic viscosity and the dielectric relaxation of aliphatic chain compounds
View Description Hide DescriptionDielectric constants and losses have been measured at up to eight frequencies between 1 and 35 GHz for six 1‐bromoalkanes in three nonpolar solvents of different viscosity (η). The data have been analyzed for mean relaxation times (τ) which are compared with those previously obtained for liquid 1‐alkenes, n‐alkanones in several solvents, liquid 1‐bromoalkanes and 1‐bromoalkanes in cyclohexane solution. Relaxation times for 1‐alkenes calculated from the viscosity dependence of the relaxation times for corresponding 1‐bromoalkanes compare quite well with the experimental values. It would appear that the mechanisms of dipole reorientation for 1‐bromoalkanes and 1‐alkenes are similar. Plots of log τ against log η for several n‐alkanones and 1‐bromoalkanes are linear and the slopes for all the systems are similar.

Use of rotation operators in the general description of polymer properties
View Description Hide DescriptionIn this paper we are concerned with the formulation of a general mathematical scheme which may be used to describe many polymer properties of interest. The responses of polymers to the following experimental techniques have been analysed: infrared absorption, x‐ray diffraction, nuclear magnetic resonance absorption, fluorescencepolarization, and elasticity measurements. A principal feature of the analysis is the use of matrix elements of the three‐dimensional rotation operator. This approach greatly facilitates the treatment of the various types of symmetry, both statistical and crystallographic, which are often an inherent feature of polymer structure. It is clearly demonstrated how measurements from different experiments can complement each other and lead to a more complete description of the polymer.

Dielectric constant of ice
View Description Hide DescriptionA series expansion for the dielectric constant of the Bernal‐Fowler‐Pauling model of ice relaxed to allow Bjerrum faults is developed using a renormalization technique which eliminates large numbers of subgraphs. In the no fault limit the dielectric constant has the form ε_{0} = ε_{∞} + (4πG/3)(N/V)(μ^{2}/kT) where the Bethe type approximation yields G = 3 and the exact result in two dimensions is G = 9/π. In two dimensions the series for G exhibits reasonable convergence to the exact result. For cubic ice the series of Gobush and Hoeve are confirmed and slightly extended. These cases lend support to the series results for the Bernal‐Fowler‐Pauling model of hexagonal ice; namely, that there is very little anisotropy in ε_{0} and G is very close to 3. These results are used in discussing whether more refined models of ice are needed. Also, the discussion comparing G with the Kirkwood correlation functiong _{ K }, begun by Stillinger and Cotter, is continued.

On the reduction of many‐body dielectric theories to the Onsager equation
View Description Hide DescriptionAn approximate theory for the dielectric constant ε of a dense polar fluid was derived by Ramshaw, Schaefer, Waugh, and Deutch (RSWD). In the present article, the RSWD theory is generalized and made rigorous by another method of derivation. The result is a rigorous expression for ε which differs from the RSWD expression by the presence of a fluctuation term. Both the rigorous expression and the RSWD expression are then specialized to the Onsager model. It is found that the rigorous expression for ε reduces to the Onsager equation, but that the RSWD expression does not because the fluctuation term is nonzero (and nonnegligible) for the Onsager model. The well‐known discrepancy between the Onsager equation and the theory of Harris and Alder is found to have the same origin.

Analysis of rotational barriers in molecules on the basis of exchange perturbation theory
View Description Hide DescriptionExchange perturbation theory of the Rayleigh‐Schrödinger type in first and second orders is applied to a calculation of barriers of internal rotation about single bonds in molecules. The barrier is assumed to arise as a result of exchange interactions between nonbonded atoms; the electrons of these atoms are replaced by one effective electron per atom, with a Gaussian charge distribution. Spins of effective electrons on different atoms are taken to be parallel. The method is applied to a large variety of molecules; calculated results for the barriers are in substantial agreement with experiment. A decomposition of the interaction energy for different conformers and for the barrier itself is given in terms of two‐ and many‐atom exchange interactions.

Interactions of hyperthermal atomic beams with solid surfaces
View Description Hide DescriptionInteractions of high‐energy supersonic atomic beams with solid surfaces and surfacecontaminants have been studied experimentally. In situAuger electron spectroscopy indicates that hydrocarbons from the oil diffusion pump are the major contaminants. The hypothesis that a threshold energy exists for sputtering of these surfacecontaminants by an incident beam has been further tested. The dependence of the threshold energy on the incident‐beam angle has been examined for three different incident‐beam angles, namely 50°, 60°, and 70° from the surface normal. A simple correlating expression for E _{th}(μ,Θ_{ i }) has been derived.