Index of content:
Volume 62, Issue 1, 01 January 1975

A b i n i t i o study of the electronic structure and hyperfine coupling in simple hydrocarbon radicals. I. Test of the calculation method on methyl and vinyl
View Description Hide DescriptionNonempirical calculations of the energy, proton, and carbon−13 hyperfine splittings for methyl (ĊH_{3}) and vinyl radicals (H_{2}C=ĊH) in their equilibrium geometry are presented. The spin−restricted SCF method and first−order double−perturbation theory including all spin−adapted monoexcited states with three unpaired electrons have been used. The basis set consists of Gaussian−type orbitals contracted in a double−zeta form. The orbital exponents of the hydrogen functions have been simultaneously varied using a scaling procedure in order to simulate a minimum Slater hydrogenoid orbital. The sensitivity of SCF energies and hyperfine splittings to variations in values of the orbital exponent ζ_{H} have been investigated. The lowest total energy is obtained for ζ_{H}=1.15. Although calculated hydrogen hyperfine splittings increase with ζ_{H}, neither the zeroth−order nor the first−order spin density, computed from canonical MO’s or quasilocalized equivalent MO’s can be correlated to ζ^{3} _{H}. A structural analysis of the contributions of the various excited states reveals that the intrabond CH→CH* excitation yields about 90% of the first−order spin density at the proton in each case. This quantity depends most critically on the nuclear effective charge of the hydrogen atom through the value of the CH* antibonding MO at the nucleus. For vinyl, the splittings computed using the unoptimized exponents (ζ_{H}=1.0) are a _{H} _{ α }=+7.52 G; a _{H} c i s =+37.56 G; a _{H} t r a n s=+23.20 G, and a _{Ċ}=+123.52 G; a _{C} _{α}=−4.53 G.

A b i n i t i o study of the electronic structure and hyperfine coupling properties in simple hydrocarbon radicals. II. Short‐range and long‐range interactions in alkyl free radicals
View Description Hide DescriptionNonempirical calculations of the ground−state energy, proton and carbon−13 coupling constants of methyl, ethyl, n−propyl, and cyclopropyl radicals have been performed in the frame of spin−restricted LCAO−SCF open−shell and first−order double−perturbation theories. The rotation barrier is negligible for the ethyl radical. The two barriers of the n−propyl radical are, respectively, 0.3 kcal/mole (0.4 exptl) and 4.7 kcal/mole for the rotations about the Ċ−C_{α} and C_{α}−C_{β}bonds. The cyclopropyl radical is found to be nonplanar with an out−of−plane angle of 41° and an inversion barrier of 3.80 kcal/mole. For the equilibrium conformations, the computed carbon−13 splittings of the radical carbon of methyl (1), ethyl (2), n−propyl (3), and cyclopropyl (4) are +31.04, +37.90, +37.72, and +138.83 G, respectively; the theoretical α −carbon−13 splittings are −18.14 (2), −17.15 (3), and −8.35 G (4); the β −carbon−13 splitting is +11.8 G for the stable conformation of the n−propyl radical. The calculated coupling constants are negative for α hydrogens, namely −31.03 (1), −33.82 (2), −34.34 (3), and −9.20 G (4); they are found positive for β hydrogens, i.e., +16.8 (2), +23.58 (3), and 12.12 G (4); the γ couplings of the freely rotating hydrogens of the n−propyl radical are negative −0.21 G. The variation of these couplings with conformational and torsional effects has also been investigated. The radical carbon−13 splitting is quite insensitive to rotations of substituents but increases markedly with out−of−plane deviations at the radical site. The coupling constants of α nuclei a _{H} _{ α }, a _{C} _{α} are also insensitive to conformational modifications. For β atoms, the contact hyperfine splittings are found to follow the relation a _{β}=B _{0}+B _{2} cos^{2}ϑ independently of the chemical nature of the nuclei, B _{0} being negative if vibronic effects are neglected. Long−range couplings in γ position are generally negative, except in the region depicted by the so−called W−plan arrangement. The role of delocalization and spin polarization is discussed for each kind of coupling. It is shown that intrabond excitations of the CH→CH* type dominate the spin polarization at the proton in all positions, while inner−shell excitations are found to be essential in the case of the radical carbon.

In–out decomposition for inelastic collisions as subdynamics. III. Perturbation theory and the semiclassical limit
View Description Hide DescriptionA new representation for the subdynamics is given such that the resultant coupling matrix becomes identical with the semiclassical expression away from turning points. A perturbation theory is developed which also reduces to semiclassical theory away from the turning points. The subdynamic perturbation expression is therefore capable of making up for the deficiencies of the semiclassical theory at the turning points. A numerical illustration is given.

Deuterium spin–lattice relaxation in ferroelectric triglycine sulfate
View Description Hide DescriptionThe ND_{3} deuteron spin−lattice relaxation time has been studied near the ferroelectric phase transition in single crystal triglycine sulfate. The results confirm proton−discorder motion in the hydrogen bond between glycine II and glycine III ions but they cast doubt upon the hypothesis concerning critical flipping of the glycinium I ion. Evidence is presented indicating faster hindered rotation of the glycinium I ND_{3} group compared to that of such groups at the other glycine ions.

Resonance Raman spectra of Cu‐etioporphyrins I, I‐m e s o‐d _{4}, and IV
View Description Hide DescriptionResonance Raman spectra obtained using the Ar^{+} and tunable Rhodamine 6G dye lasers are presented for the position isomers Cu−etioporphyrin I and IV in dilute (10^{−4} M) solution. The spectra show significant differences in several vibrations enabling the molecules to be distinguished. Several anomalously polarized (ρ_{ l } ≳ 3/4) vibrations are observed which show dispersion of the depolarization ratios. The dispersion of ρ_{l} is interpreted as arising from reduction of chromophore symmetry from its idealized D _{4h }. The solution data for Cu−etioporphyrin I and Cu−etioporphyrin IV are consistent with C _{4h } symmetry and C _{2v } symmetry, respectively, thereby demonstrating the sensitivity of resonant Raman scattering to slight perturbations of the chromophore due to peripheral substituents. Resonance Raman data are also presented for the deuterated analog Cu−etioporphyrin I (m e s o−d _{4}). Several shifts in the vibrational modes are observed and possible vibrational assignments are discussed.

ICR studies of some hydrogen atom abstraction reactions: X^{+} + H_{2} → XH^{+} + H
View Description Hide DescriptionIon cyclotron resonance methods are used to identify and to measure the rate constants for the abstraction of a hydrogen atom from H_{2} by CH^{+}, CH_{2} ^{+}, CH_{4} ^{+}, N^{+}, NH^{+}, NH_{2} ^{+}, NH_{3} ^{+}, O^{+}, OH^{+}, H_{2}O^{+}, CO^{+}, N_{2} ^{+}, C_{2} ^{+}, and C_{2}H^{+} ions. Although in most cases hydrogen atom abstraction is the only available exothermic pathway for these reactions at thermal energies, the rate constants measured show that except for O^{+}, CO^{+}, and N_{2} ^{+}, a large fraction of collisions between these ions and H_{2} are not reactive. The rate constants measured range from a low of (3±1) × 10^{−13} cm^{3}/sec for the NH_{3} ^{+}−H_{2}reaction to (1.73±0.04) × 10^{−9} cm^{3}/sec for the N_{2} ^{+}−H_{2}reaction. These values compare to the Langevin value of about 1.5 × 10^{−9} cm^{3}/sec for collisions between these ions and H_{2}. An examination was also made for possible thermoneutral hydrogen atom exchange reactions for those ions which do not react with H_{2} (CH_{5} ^{+}, CH_{3} ^{+}, NH_{4} ^{+}, H_{3}O^{+}, H_{2}S^{+}, H_{3}S^{+}). The only exchange reaction observed was for collisions between CD_{3} ^{+} ions and H_{2}, for which a rate constant of (5.1±0.5) × 10^{−10} cm^{3}/sec was measured.

Two‐photon dissociation of water: A new OH source for spectroscopic studies
View Description Hide DescriptionWe have observed the phenomenon of two−photon dissociation of water using a tunable uv laser beam and the generation of hydroxyl radicals (OH) as a dissociation product. This phenomenon affords a new way for measuring the quenching rates of electronically excited OH due to nitrogen, water, and other molecules under atmospheric conditions.

Study of electric field gradient parameters and quadrupole splitting of rozenit
View Description Hide DescriptionLow symmetry effects of the Fe^{2+} ion sites in FeSO_{4}⋅4H_{2}O (rozenit) on the electronic level splitting and the electric field gradient have been considered. Direct lattice sum calculations were performed to obtain the EFG and the multipole moments due to charges associated with all lattice points. The calculated temperature dependence of quadrupole splitting is in good agreement with the experimental values taken from 77 to 300°K. The direction of the maximum field gradient at various temperature is calculated to be nearly in the crystallographic axis b. The ground orbital state is a mixture from the first excited state.

Far infrared collision‐induced spectrum in gaseous methane. I. Band shape and temperature dependence
View Description Hide DescriptionThe far infrared collision−induced spectrum in CH_{4} is observed in the region 20−600 cm^{−1} at temperatures between 163 and 296 K. These results are compared with a synthetic spectrum computed from the theory of Ozier and Fox giving the integrated intensity of the absorption resulting from rotational transitions of the octupole−induced dipole in colliding pairs of molecules. Although such a calculated spectrum accounts for the gross features of the experimental bands, they predict too little absorption in the low and high parts of the band.

Molecular beam investigation of the effect of inner‐shell electrons in molecular collisions
View Description Hide DescriptionDifferential elasticscattering cross sections were obtained at thermal energies using crossed molecular beams for metastable Kr*, Ar*, Ne*, and He* scattered by ground−state krypton. Potential well depths are calculated from the location of the observed rainbow maxima and are compared to those for the analogous alkali atoms Rb, K, Na, and Li scattered by krypton. The effect of the inner−shell electrons on molecular collisions is deduced. At high electron shell levels, the (n−1) electron decreases the strength of the interaction during a collision whereas at low shell levels, the interaction strength is increased by the (n−1) electron.s and pelectrons are shown to affect the interaction strength differently at the lowest shell level.

Dipole properties of atoms and molecules in the random phase approximation
View Description Hide DescriptionA random phase approximation (RPA) calculation and a direct sum over states is used to calculate second−order optical properties and van der Waals coefficients. A basis set expansion technique is used and no continuumlike functions are included in the basis. However, unlike other methods we do not force the basis functions to satisfy any sum−rule constraints but rather the formalism (RPA) is such that the Thomas−Reiche−Kuhn sum rule is satisfied exactly. Central attention is paid to the dynamic polarizability from which most of the other properties are derived. Application is made to helium and molecular hydrogen. In addition to the polarizability and van der Waals coefficients, results are given for the molecular anisotropy of H_{2}, Rayleigh scattering cross sections, and Verdet constants as a function of frequency. Agreement with experiment and other theories is good. Other energy weighted sum rules are calculated and compare very well with previous estimates. The practicality of our method suggests its applications to larger molecular systems and other properties.

Isotope chemistry and molecular structure. Total deuterium isotope effects
View Description Hide DescriptionA qualitative discussion is given on the relationship between the magnitude of isotope effects in polyatomic systems and bending and stretching force constants. This is followed by a general method for the calculation of the isotope effect which can be ascribed to each force constant in the general quadratic potential energy for the vibration of a polyatomic molecule. The method is applied to deuterium isotope effects in the molecules H_{2}O, CH_{2}O, CH_{4}, C_{2}H_{4}, C_{2}H_{6}, and C_{6}H_{6} at and above 300°K. It is found that deuterium isotope effects associated with individual internal valence force constants are nearly additive at room temperature. Strict additivity holds in the high temperature limit. Bond stretching force constants account for at least 65% of the total deuterium−to−protium reduced partition function ratio at 300°K and become even more dominant at higher temperatures. The origin of the relative importance of stretching and bending forces as a function of temperature is found in the first two terms of the finite orthogonal polynomial method of Bigeleisen and Ishida. Correlations are established between the magnitude of deuterium isotope effects in different molecules as a function of temperature with stretching and bending force constants.

Interaction between penetration sites in diffusion through thin membranes
View Description Hide DescriptionTwo models of permeation through thin membranes are proposed: In the first, the membrane is represented as a plate with randomly distributed perforations, and the permeation rate is controlled by the rate at which penetrant diffuses through an external medium; in the second, the penetrant is considered to be adsorbed on one face of the membrane, and the rate controlling process is lateral diffusion across that face to a set of randomly distributed penetration sites. These models are treated by a self−consistent field procedure, and it appears that interaction between penetration sites influences the permeability significantly even when the number of penetration sites per unit area is quite low.

Temperature dependence of the ^{14}N nuclear quadrupole resonance and the observation of the phase transition in cubic tetracyanoethylene
View Description Hide DescriptionThe ^{14}N nuclear quadrupole resonance spectrum of cubic tetracyanoethylene was found. The temperature dependence was determined between 77.3 K and room temperature. The transition temperature between the cubic and the monoclinic phase was found to be 292.0±0.5 K. The values of e q Q and η for both phases are discussed considering the contributions of the crystalline electric field and the existence of specific intermolecular interactions.

Compression and bonding of ice VII and an empirical linear expression for the isothermal compression of solids
View Description Hide DescriptionThe volume of ice VII was measured between 3.0 and 8.0 GPa at 298 K using a high−pressure x−ray diffraction technique. The specific volume (0.708, +0.023, −0.012 cm^{3}/g), the isothermal bulk modulus (12.54±0.27 GPa), and the modulus’ pressure derivative (5.56±0.14) for ice VII at 298 K and zero pressure were determined using an empirical equation for isothermal compression. That equation is [P V _{0} ^{2}/(V _{0} − V)]^{1/2} = C _{ T } + S _{ T } [P (V _{0} − V)]^{1/2}, where C T and S _{ T } are constants, V _{0} is the ambient volume, and V is the volume at pressure P. This linear relation, which describes the state of nonporous materials along their Hugoniots, is shown to characterize the isothermal compression of solids as well as does the Murnaghan equation. The zero pressure, 298 K oxygen−oxygen distance in ice VII extrapolated from the present data and a simple bonding model for the hydrogen−bonded oxygen atoms strongly support Kamb’s description of the ice VII structure as two interpenetrating ice Ic frameworks.

Electrical conductivity in biological semiconductors
View Description Hide DescriptionWe propose and study a simple quantum−mechanical model Hamiltonian which describes the physical picture of the ’’conformon’’ recently discussed by Kemeny and Goklany. We find an activation entropy which is consistent with the proper Arrhenius behavior only in certain temperature ranges; this entropy may also give the enormous enhancement observed in the prefactor of the conductivity. Our model leads naturally to a possibitlity for overcoming the expected d e c r e a s e in mobility due to the very mechanism (large conformational change) for obtaining the large entropic enhancement. Namely, the conformational change may be associated with localized holes, whereas an appreciable mobility may result from electrons which are rather delocalized. A simple mechanism leading to compensation is also briefly discussed.

Thermodynamic properties of NpO(g)
View Description Hide DescriptionThe thermodynamic properties of NpO(g) were determined by mass−spectrometric studies of two isomolecular exchange reactions of the type M(g) + M′O(g) = M′ (g) + MO(g) involving the gaseous atoms and monoxides of lanthanum and yttrium. In one series of determinations, both reactions were studied simultaneously. The standard free energy of formation of NpO(g) is given by ΔG _{ f }° (NpO,g) = −12890 −13.73T (cal mol^{−1}) over the temperature range 1660−1980 K. An uncertainty of ±1 kcal mol^{−1} is estimated. The derived thermodynamic properties of NpO(g) suggest the existence of low−lying electronic states in the gaseous molecule. The total volatility of neptunium−bearing species over the univariant system, NpO_{2}(s) + Np(l) + vapor, was measured by the mass−effusion method, and the partial pressures of NpO(g) obtained therefrom were used to confirm the accuracy of the isomolecular results and to derive the standard free energy of formation of NpO_{2}(s): ΔG _{ f }° (NpO_{2},s) ? −256000 + 40.4 T (cal mol^{−1}).

Extension of Koopmans’ theorem. I. Derivation
View Description Hide DescriptionIt is shown that the spin orbitals that diagonalize the generalized Hartree−Fock potentials [Int. J. Quantum Chem. Symp., 8, 501 (1974)] for a correlated wavefunction, together with the corresponding orbital energies, give a natural extension of Koopmans’ theorem to correlated reference states.

Extension of Koopmans’ theorem. II. Accurate ionization energies from correlated wavefunctions for closed‐shell atoms
View Description Hide DescriptionExtended Koopmans’ theorem ionization energies are presented for MC−SCF wavefunctions of the 1s ^{2} 2s ^{2} (^{1} S) ground state isoelectronic series, Li^{−} through O^{4+}, and also for some larger CI wavefunctions of Be and B^{+}. Correlation in these reference states reduces the error in the Koopmans’ ionization energy for the 2s electron to approximately 0.01−0.08 eV (1/100−1/20 the SCF Koopmans’ error) in all states except the negative ion, for which the MC−SCF extended Koopmans’ error of 0.25 eV was of the same magnitude but of opposite sign to the SCF error. Our extended Koopmans’ energies for 1sionization were only slightly better than the corresponding SCF values. Koopmans’ theorem does not yield a 2pionization energy (1s ^{2} 2s ^{2} → 1s ^{2} 2p), but the extended Koopmans’ theorem yields an ionization energy whose error is about one−third the SCF 2s error.

Brillouin, Rayleigh, and depolarized Rayleigh scattering studies of polypropylene glycol. I
View Description Hide DescriptionA comprehensive light scattering study of an important polymer—polypropylene glycol, HO−[CH(CH_{3}) −CH_{2}O]_{ n }−H—having an average molecular weight of about 425 (PPG 425) was carried out. From the polarized spectra, the velocity and attenuation coefficient of the longitudinal hypersound as a function of temperature were determined. Measurements of the velocity and attenuation coefficient indicate the presence of molecular relaxations between 250−390°K. A maximum in the sound attenuation vs temperature curve was observed. The Landau−Placzek ratio over a wide range of temperatures was also measured and compared with the theory of Litovitz and co−workers on the relaxing molecular liquid over a wide temperature range. Depolarized scattering studies were also carried out. The molecular reorientation time and activation energy are determined from the spectral linewidthmeasurement as a function of temperature. Depolarization ratios (ρ_{ v } and ρ_{ h }) were determined. The Krishnan effect was observed at temperatures below 296°K.