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Volume 60, Issue 1, 01 January 1974

Self‐consistent charge and configuration molecular orbital calculations on PF_{3}
View Description Hide DescriptionWe present the results of a self‐consistent charge and configuration molecular orbital (SCCC‐MO) calculation undertaken for the PF_{3} molecule using a basis set of 3s, 3p, and 3d phosphorus and the fluorine 2s and 2p atomic orbitals. The positions of the predicted occupied MO energies agree well with the observed vertical ionization potentials for PF_{3}. The predicted charge distribution and dipole moment are also in fair agreement with experimental observations. It is shown that the predicted orbital energy scheme can lead to a plausible explanation of the observed absorptionspectrum. In addition the predicted virtual orbitals agree well with other chemical and spectroscopic evidence available for PF_{3}.

Statistical mechanics of random‐flight chains. V Excluded volume expansion and second virial coefficient for linear chains of varying shape
View Description Hide DescriptionThe excluded‐volume expansion factor of a flexible chain is calculated with a smooth‐density model providing for a distribution of both sizes and shapes of the segment cloud. From the known average moments of the inertial tensor found previously by Monte Carlo methods, an approximate empirical function is constructed to describe the distribution of ellipsoidal dimensions. With a suitably related pseudopotential representing the excluded‐volume forces, an expansion factor for the mean square radius is obtained which requires very little scale adjustment to match first‐order perturbation theory and which also gives a good representation at higher values of the interaction parameter. The empirical function approach is supplemented with a Monte Carlo study to remove bias inherent in the choice of the functional form. Because of the small increase in asymmetry with increasing excluded volume, the direct effect of shape variation on the expansion factor is less important than that of size variation. A calculation of the interaction of two chains and the resulting second virial coefficient is carried out, and in this case both shape and size variations are important.

Nuclear corrections to molecular properties. IV. Theory for low‐lying vibrational states of polyatomic molecules with application to the water molecule near the Hartree‐Fock limit
View Description Hide DescriptionPerturbation theory is used in conjunction with ab initio electronic structure calculations to obtain information about the effects of pure vibration on properties of polyatomic molecules. It is shown that any property can be developed in the form , where , and {B_{ij} } are certain constants and (ν_{1}, ν_{2}, ⋯ ν_{ N }) are the quantum numbers for N modes of vibration. Several isotopic variants of the water molecule with Σ_{ i }ν_{ i } ≤ 3 are used to illustrate the utility of the method at the Hartree‐Fock level of approximation. The properties examined include the energy, the dipole moment, and the nuclear quadrupole coupling constants.

Quantum efficiency of diffusion limited energy transfer in La_{1−x−y }Ce_{ x }Tb_{ y }PO_{4}
View Description Hide DescriptionIn this paper, we present a detailed study of the concentration and temperature dependences of the quantum efficiency of energy transfer between Ce^{3+} and Tb^{3+} in La_{1−x−y }Ce_{ x }Tb_{ y }PO_{4}. The determination of the transfer quantum efficiency in terms of the donor luminescence lifetimes is critically compared with that in terms of the donor luminescence intensities. It is shown that for the latter determination it is important to take into account any overlap in the donor and acceptor absorption spectra in the excitation wavelength region. From the exponential behavior, the concentration, and thermal dependences of the donor luminescence decay, it is shown that the diffusion of donor excitation plays an important role in the energy transfer process.

EPR of mixed valence complexes: Frequency and concentration dependent linewidths in hexaminechromium (III) chlorocuprates (I, II)
View Description Hide DescriptionNine compounds in the mixed valence series of hexaminechromium (III) chlorocuprate (I,III), which may be formulated as [Cr(NH_{3})_{6}] [CuCl_{4}]_{1−x } [CuCl_{5}]_{ x } over a substantial range of x, have been investigated by a room temperature EPR study employing four microwave frequencies. The data indicate a variation of linewidth with concentration and frequency for each compound. The linewidth variation with concentration is largely associated with a concentration dependence of the internal dipolar and exchange fields while the frequency dependence is mainly associated with the ``10/3 effect.'' A simple model is employed to account for these variations and to evaluate the appropriate exchange fields. This is the first example of EPR study incorporating two different paramagnetic ions in which the concentration of one of the ions can be variated over a large range with little variation in other parameters.

Intramolecular kinetic isotope effect in the reaction of fluorine atoms with methane‐d _{2} (CH_{2}D_{2})
View Description Hide DescriptionThe relative rates of the two competing isotopic reactions: F + CH_{2}D_{2} → HF + CHD_{2} and F + CH_{2}D_{2} → DF + CH_{2}D, were measured in a fast flow system by direct mass spectrometric analysis of the reaction products in the temperature range of 159° to 298°K. The ratio of rates can be expressed as an Arrhenius type equation: k _{F+HCHD2 }/k _{F+DCH2D} = (0.81 ± 0.03) exp[(275 ± 15)/R T]. The relation between the intramolecular isotope effectk _{F+HCHD2 }/k _{F+DCH2D} and the intermolecular isotope effectk _{F+CH4 }/k _{F+CD4 } is discussed with regard to secondary isotope effects in the fluorine atom + methanereaction.

Molecular Zeeman spectra of ^{6,7}Li ^{79,81}Br
View Description Hide DescriptionThe molecular Zeemanspectra of the four isotopes of lithium bromide have been investigated using a molecular beam electric resonance apparatus augmented with a magnet in the resonance region. Values for the rotational magnetic moment, nuclear shielding anisotropies, diamagnetic susceptibilities, bromine nuclear magnetic moment, and quadrupole moment of the electron distribution for each isotope in the ν = 0 vibrational level and J = 1 rotation level were obtained from these data. For ^{7}Li^{79}Br, g_{J} = 0.112056(64), σ_{Br T } = − 0.000321(82), σ_{Li T } = − 0.0000480(42), ξ_{ T } = 2.35(50) × 10^{−30} erg G^{−2} · molecule^{−1}, μ_{Br} = 2.1049(8) nuclear magnetons, and _{0}<Q_{e} >_{1} = 1.00(10) × 10^{15} cm^{2}. Values of these parameters for ^{6}Li^{79}Br, ^{6}Li^{81}Br, and ^{7}Li^{81}Br are also reported. Unlike most previous experiments of this type, no static electric field is applied to the resonance region. The motional electric field which the molecules see as they travel through the magnetic field serves as the parity mixing electric field which is necessary for the transition process. The linear velocity dependence of this field tends to cancel the inverse velocity dependence in the interaction time. The theoretical line shape has been investigated by computer.

Approach to the description of atoms using hyperspherical coordinates
View Description Hide DescriptionWe formulate and develop an expansion of N‐electron atomic wavefunctions in hyperspherical coordinates. The expansion basis is a complete set of functions of 3N − 1 angle variables which describe the relative configuration of the electrons. The system is scaled in size by one extensive variable, the hyperradius r. All angular momentum and Pauli antisymmetry properties of the system are contained in the hyperspherical basis. A new, total angular momentum, antisymmetry‐adapted basis is derived and used to construct an expansion of the total electronic wavefunction which has all of these properties term by term. These basis functions are called configurational normal modes and provide a new element of atomic structure to replace the electron orbital. Several methods of implementing calculations with this expansion are discussed.

Argon matrix infrared spectra and vibrational analysis of the hydroperoxyl and deuteroperoxyl free radicals
View Description Hide DescriptionMatrix reactions of H and D atoms from a microwavedischargesource with oxygen molecules diluted in argon have produced significantly higher yields of HO_{2} and DO_{2} than the previous photolysis methods. Oxygen isotopic enrichment confirmed the previous vibrational assignments to HO_{2}; significantly greater concentrations of DO_{2} allowed observation of the weak 0–0 mode at 1123 cm^{−1}. Normal coordinate calculations using HO_{2} and DO_{2} oxygen isotopic frequencies gave excellent agreement with the observed data. The bonding in HO_{2} is suggested to be largely covalent, in contrast to the ionic species .

Critical behavior of cross‐transport coefficients
View Description Hide DescriptionWe show that, near the consolute critical point of a binary mixture, thermodiffusion (k_{T} ), as well as baro‐ and electrodiffusion, should diverge like the isothermal osmotic compressibility. This is a stronger divergence than expected according to earlier predictions, and seems to be borne out by experiment. A few hydrodynamical consequences are discussed.

Application of matrix isolation spectroscopy to quantitative sputtering studies. I. Energies and oscillator strengths of the resonance transitions of gold atoms isolated in noble gas matrices
View Description Hide DescriptionMatrix isolation spectroscopy has been applied to quantitative sputtering studies by developing techniques for the codeposition of backsputtered metal atoms with a large excess of noble gas atoms. The electronic spectra of Au atoms, produced by bombardment of an Au target with 50 keV Ar^{+} ions, were studied in Ar, Kr, and Xe matrices. Energy level shifts of the Auresonance doublet due to matrix perturbations have been interpreted in terms of changes in the spin‐orbit coupling interaction of the Au 6p electron. The values in the various matrices were found to be ζ_{Xe} = 2570 cm^{−1}; ζ_{Kr} = 2943 cm^{−1}; ζ_{Ar} = 3215 cm^{−1} (ζ_{gas} = 2543 cm^{−1}). The [inverted lazy s] 650 cm^{−1} splitting of the ^{2} P _{3/2} state in the various matrices was interpreted in terms of an axial distortion of a dodecahedral substitutional site. Simultaneous diagonalization of spin‐orbit and ``crystal'' field interactions was employed to obtain ζ and A _{2} splitting parameters. Oscillator strengths for the resonance transitions were determined by developing an equation which relates the sputtering yield, integrated current, and a geometric factor based on a cosine law distribution of sputtered atoms to the integrated absorbance over an absorption band and the area sampled by the spectrometer beam.Oscillator strengths for the ^{2} P _{1/2} and ^{2} P _{3/2} transitions were found to be 0.132, 0.293 in Ar; 0.090, 0.200 in Kr; and 0.061, 0.145 in Xe. By comparison the gaseous atom values (``hook'' method) are 0.19, 0.41. It is pointed out that the matrix isolation method can determine Au atom concentrations equivalent to 0.1 monolayer and is therefore among the more sensitive and rapid techniques for measuring sputtering yields.

Deuterium quadrupole coupling in formic acid
View Description Hide DescriptionThe 1_{01} → 0_{00} and 3_{13} → 3_{12} transitions of HCOOD were measured using a beam maser spectrometer with 4 kHz resolution. The measurements of three completely resolved components for each of these transitions allowed an unambiguous assignment of the spectrum. The quadrupole coupling strength in the O–D bond direction is eq_{zz}Q = 272 ± 3 kHz with an asymmetry η = −0.075 ± 0.010. Analysis of previous data on DCOOH yields a deuterium quadrupole coupling strength along the D–C bond direction of eq_{zz}Q = 166 kHz.

Bethe surface, elastic and inelastic differential cross sections, Compton profile, and binding effects for H_{2} obtained by electron scattering with 25 keV incident electrons
View Description Hide DescriptionElectron impact spectra for H_{2} have been obtained at scattering angles of 1°, 1.5°, 2°, 3°, 4°, 5°, 7°, and 10° using 25 keV incident electrons. The measured intensities were converted to generalized oscillator strengths and placed on an absolute scale at each scattering angle by the use of the Bethe sum rule for the generalized oscillator strength distribution. The cross section differential with respect to both solid angle and energy loss of the scattered electron was corrected for relativistic and exchange effects and integrated over energy loss to obtain the inelastic differential cross sections. In addition the elastic cross section differential with respect to solid angle was measured. The results are all in excellent agreement with theoretical calculations. The total elastic cross section was determined using additional data from another source. The Compton profile was determined from the 7° scattering data and was found to agree well with the previous x‐ray results. Consistent generalized optical sums (2,1, − 1, − 2) and optical sum inequalities for the generalized oscillator strength were also obtained. In addition inelastic scattering factors were computed from the (−1) optical sum and were found to agree well with available theory. Chemical binding effects were explored using electron density difference functions obtained from the differential cross sections. For the first time the intensity difference functions for the elastic and inelastic scattering were determined separately. It is argued that the experimental method used in this study to obtain the intensity difference functions represents the best approach so far developed for obtaining direct information about molecular real space charge densities.

Thermodynamic properties for a simple model of solid carbon dioxide: Monte Carlo, cell model, and quasiharmonic calculations
View Description Hide DescriptionMonte Carlo, cell model, and quasiharmonic calculations are employed to investigate a molecular crystal model consisting of rigid linear molecules disposed in the cubic P a 3 structure and interacting with pair potentials between the ends. The errors involved in employing the cell model and quasiharmonic approximations are established. The thermodynamic properties for a model of solid CO_{2} are calculated as functions of temperature for a variety of 6—n potentials, including those obtained from previous lattice dynamical calculations in which fits were made to observed phonon frequencies. The results are compared with experimental measurements of the sublimation energy, heat capacity,bulk modulus, Grüneisen function, and thermal expansion. The best over‐all fit was obtained with a 6–9 potential. However, a consistent inadequacy of this interaction model is that it exhibits too much thermal expansion for any reasonable fit to the other properties.

Hydrogen‐deuterium isotope effect in the decay of radical pairs in x‐ray irradiated hydroxyurea
View Description Hide DescriptionThe rate constants for the transformation of radical pairs to single radicals in x‐ray irradiated hydroxyurea have been determined from the decay of ESR spectra at temperatures from 253–268°K. The ratio of decay rates for a protonated to a deuterated sample changes from approximately 13 in the initial stage to 5 in the later stage. The decay curves are explained by assuming that the decay is associated with a diffusion of H (D) vacancies from one radical of a pair to a neighboring molecule, dissociating the radical pair. The decay rates in the initial stage of decay for a protonated sample, k _{11}(H), and for a deuterated sample, k _{11}(D), may be presented as k _{11}(H) = 1 × 10^{7} exp[(−0.50 eV)/k T], k _{11}(D) = 6 × 10^{11} exp[(−0.82 eV)/k T].

Exact quantum mechanical study of kinetic isotope effects in the collinear reaction Cl + H_{2} → HCl + H. The H_{2}/D_{2} and the H_{2}/T_{2} isotope effects
View Description Hide DescriptionExact quantum mechanical probabilities for the collinear reaction of chlorine atoms with H_{2}, D_{2}, and T_{2} in their ground and first vibrational excites states, were calculated for a semiempirical LEPS potential energy surface. These probabilities were used to calculate the kinetic isotope effectsk _{Cl+H2 }/k _{Cl+D2 } and k _{Cl+H2 }/k _{Cl+T2 } which are compared with experimental data and with results of transition state theory calculations. The effect of the vibrational excitation of the hydrogen molecules on the rate of their reaction with chlorine atoms was also studied.

Proton spin‐lattice relaxation studies of reorienting methyl groups in solids
View Description Hide DescriptionSpin‐lattice relaxation times (T _{1}) have been measured at 30 MHz as a function of temperature for the methyl protons in a series of compounds, each of which contains a single methyl group. In all cases except one, the measurements were carried out above 77°K, where thermally activated motion predominates. The purpose was to determine activation energies for methyl rotation and to detect phase transitions. The following activation energies were found for polycrystalline samples from the slopes of plots of ln T _{1} vs T ^{−1} on the low‐temperature side of the T _{1} minimum: CH_{3}PCl_{2} (2.25 kcal/mole), CH_{3}PSCl_{2} (2.35), CH_{3}SCN (2.4), CH_{3}CD_{2}I (3.2), and CH_{3}CD_{2}Br (3.6). For CH_{3}COCl and CH_{3}NCS, which apparently form glasses, only the high‐temperature side of the T _{1} minimum could be observed. The apparent activation energies were 1.45 and 0.57 kcal/mole, respectively. Significantly nonexponential behavior was observed near and to the high‐temperature side of the T _{1} minima. The relationship of these activation energies to internal rotation barriers obtained from ir, microwave, and cw NMR absorption studies is discussed.

Some theorems satisfied, and some theorems not satisfied by Born‐Oppenheimer type wavefunctions
View Description Hide DescriptionIt is shown that within Born‐Oppenheimer type approximations, hypervirial theorems and generalized Hellman‐Feynman theorems are often not satisfied, the discrepancies between them and the theorems actually satisfied being of the order of the ``adiabatic correction.''

Green's function approach to the direct perturbation calculation of the excitation energies of closed shell fermion systems
View Description Hide DescriptionGeneral expressions to the third order of perturbation theory for a direct calculation of the excitation energies of closed shell atomic and molecular systems are presented. The Hartree‐Fock ground state orbitals are used as single particle states, but the method may be easily generalized for an arbitrary one‐electron basis. The derivation is based on the Green function and diagrammatic approaches. A ``double projection'' scheme is developed which enables not only a very effective reduction of the number of Feynman diagrams which must be explicitly considered but also yields very compact formulas for the excitation energies, which may be easily implemented on a computer. The method is illustrated and checked on a simple six‐electronic model system for which the exact solutions are available.

Effect of high energy radiation on sodium methylarsonate and n‐propylarsonic acid studied by electron spin resonance spectroscopy
View Description Hide DescriptionExposure of Na_{2}MeAsO_{3} and n‐PrAsO(OH)_{2} to γ rays at 77°K gave radical species whose ESR spectra comprised sets of four lines assigned to hyperfine coupling to ^{75}As nuclei. All centers had magnetic axial symmetry. Evidence is presented in favor of the identification of the trapped species as , , , (two equivalent protons also detected) in Na_{2}MeAsO_{3}, and the species AsO(OH)_{2}, PrAsO(OH)_{2}, and, less certainly, HAsPrO(OH)_{2} and in n‐PrAsO(OH)_{2}. Structural aspects of the results are considered, and possible mechanisms for the formation of these radicals are proposed.