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Volume 62, Issue 11, 01 June 1975

Ornstein–Zernike equation for the direct correlation function with a Yukawa tail
View Description Hide DescriptionThe Ornstein–Zernike (OZ) equation with a core condition h (x) = −1 for x<1 and a direct correlation function of Yukawa form c (x) = K exp[−z (x−1)]/x for x≳1 was solved analytically by one of us recently [E. W., Mol. Phys. 25, 45 (1973)]. The equation is of interest (i) as the mean‐spherical approximation for a potential that is the sum of hard‐sphere and Yukawa terms; (ii) as a generalized mean‐spherical approximation for a hard‐sphere system; and (iii) as the key ingredient in the generalized mean‐sphrerical approximations for ionic and polar fluids of Ho/ye, Lebowitz, and Stell, J. Chem. Phys. 61, 3253 (1974). Here we analyze the solution of the above equation to give a quantitatively useful picture of its character. A rapidly convergent expansion in K is obtained. In addition, a general cluster expansion for the solution of the OZ equation with arbitrary c (x) previously derived by one of us (G.S.) is applied to the equation to yield a complementary representation of its solution. Detailed numerical results are given.

Surface and bulk exciton transitions in the reflection spectrum of tetracene crystals
View Description Hide DescriptionThe reflection spectrum of the 0–0 component of the first singlet transition of tetracene crystal has been measured for temperatures ranging from 300 to 1.7 °K. A discontinuous change in the Davydov splitting occurs near 186 °K signifying the occurrence of a phase transition. At the lowest temperatures two anomalous reflectivity minima are observed inside the b‐polarized stopping band that are very similar to structure in the corresponding reflection band of anthracene crystal. The reflectivity minima are tentatively assigned to transitions to surfaceexciton states lying approximately 5 cm^{−1} and 160 cm^{−1} above the b‐polarized excitontransition at 5349 Å. The other structure within the reflection band is interpreted as a coupling of the polariton to vibrational modes of intra‐ and intermolecular origins.

Quantum yields for the production of O(^{1} S), N(^{2} D), and N_{2}(A ^{3}Σ^{+} _{ u }) from the vacuum uv photolysis of N_{2}O
View Description Hide DescriptionRelative quantum yields have been measured for O(^{1} S), N(^{2} D), and N_{2}(A ^{3}Σ^{+} _{ u }) production from N_{2}O over the wavelength range 1100–1500 Å. The measurements of O(^{1} S) were made by observing the ^{1} S _{0} → ^{1} D _{2} emission at 5577 Å. N(^{2} D) was measured via the intensity of NO β bands generated by N(^{2} D)+N_{2}O → N_{2}+NO(B ^{2}Π_{ r }) followed by NO(B ^{2}Π_{ r }) → NO(X ^{2}Π_{ r }) % +hν (NO β bands). The N_{2}(A ^{3}Σ^{+} _{ u }) was measured by the intensity of NO γ bands generated by N_{2}(A ^{3}Σ^{+} _{ u })+NO → N_{2}+NO(A ^{2}Σ^{+}) followed by NO(A ^{2}Σ^{+}) → NO+hν (NO γ bands). The O(^{1} S) quantum yield is close to unity over the 1280–1380 Å wavelength range. N(^{2} D) exhibits a large yield for λ?1200 Å. The quantum yield of N_{2}(A ^{3}Σ^{+} _{ u }) is ? 0.2 over the entire 1100–1500 Å region.

Quantum yields for the production of S(^{1} S) from OCS (1100–1700 Å)
View Description Hide DescriptionThe 4589 Å emission of S(^{1} S _{0}) has been used to measure the quantum yields of S(^{1} S _{0}) production from OCS over the wavelength interval 1100–1700 Å. A large yield is found from 1420 to 1600 Å with smaller yields being observed at both shorter and longer wavelengths.

Coexistence curve for polystyrene–cyclohexane near the critical point
View Description Hide DescriptionThe coexistence curves for the system polystyrene–cyclohexane have been determined with a specially designed differential refractometer, which determines concentrations of the two coexisting phases with a precision of ± 0.01%. The plots of the coexistence curve data represented by log(X ^{+}−X _{ c }) and log(X _{ c }−X ^{−}) versus the reduced temperature ε = (T _{ c }−T)/T _{ c } yield largely curved lines. The shape of the coexistence curve very near the critical point, however, is asymptotically symmetric. The coexistence curve obtained with an over‐all concentration at the critical concentration is represented by the relation X ^{+}−X ^{−} = Bε^{β} with β=0.348 and B=0.97 in the temperature region of T _{ c } −T<2.0 °C. The critical point exponent β and the coefficient B vary only slightly depending on the over‐all concentration. Although the data give a curved diameter, a precision of the present experiment is not sufficient to determine the asymptotic behavior of the diameter.

A quasiclassical trajectory study of the H_{2}+F_{2} reactions
View Description Hide DescriptionA theoretical investigation of the reactiondynamics of the reactions H_{2}(v=0,2,4, or 6) + F_{2}(v=0 or 6) → H+HF+F, 2HF, F_{2}H+H, H_{2}F+F, F_{2}+2H, and H_{2}+2F has been accomplished using Monte Carlo averaging over quasiclassical trajectories on a reasonable semiempirical potential‐energy surface. The details of the dynamical mechanism of the reaction processes were investigated by examining geometrically restricted reaction paths and selected restricted initial states. Reaction cross sections have been computed and estimates of rate coefficients have been made. The computed thermal rates are many orders of magnitude lower than thermal collision frequencies. Reaction thresholds are lowered significantly for vibrationally excited hydrogen.

The interaction of rare gas atoms with graphite surfaces. II. Adatom–adatom potentials
View Description Hide DescriptionThe Gordon–Kim local density method is applied to the calculation of the interaction energy of pairs of neon, argon, and krypton atoms adsorbed on the basal plane of graphite. At the adatom–surface equilibrium separation, the adatom–adatom interaction potentials are found to be from 12% to 20% more repulsive than the gas phase counterparts. At much smaller adatom–surface separations, the adatom–adatom effective potential well depth is only 3% of the gas phase well depth. It is found that the nonadditive contributions to the interaction energy are more important for the smaller rare gas adatoms than for the larger ones. This trend is observed experimentally. It is concluded that rare gas films on graphite are too mobile to be in registry with the substrate.

New type of cluster theory for molecular fluids: Interaction site cluster expansion
View Description Hide DescriptionA new cluster series, called the interaction site cluster expansion, is derived for classical molecular fluids. For a general class of molecular models, the series provides an exact formula for the equilibrium pair correlations between interaction sites on different molecules. In the models considered, each molecule contains m of these interaction sites. The total intermolecular potential between two molecules is the sum of m ^{2} site–site potentials. A site–site potential depends on the separation between the sites only. However, because the sites are not necessarily located at the centers of molecules, the total molecular pair interaction can depend strongly on molecular orientations. Even though the interaction site cluster expansion is exact, the cluster integrals in the series involve the translational coordinates of the interaction sites only. The molecular orientational coordinates are removed by a transformation which introduces i n t r amolecular correlation functions into the series. Thus, the new cluster series expresses the intermolecular site–site correlation functions in terms of diagrams involving site–site cluster bonds and i n t r amolecular correlation bonds. The interaction site cluster expansions are used to derive several important results. It is shown that when the site–site interactions are hard core potentials, the pair correlation functions rigorously contain not only discontinuities but also cusps. The locations for these singularities are derived. A method is presented which shows how these singularities are smoothed when the hard core potentials are softened. The singularities as well as special limiting results derived herein are used to provide a justification for the reference interaction site model (RISM) equation.

Configuration interaction studies of the excited states of water
View Description Hide DescriptionWe report the results of extensive configuration interaction studies on 16 excited states of water. These states can be accurately described as corresponding to excitation from one of the highest two molecular orbitals (1b _{1} or 3a _{1}) of the ground state into either the 3s or one of the three 3pRydberg orbitals. The results provide the most accurate and consistent treatment of these states to date (within 0.1 eV for all known transitions) and form a reliable basis for the assignment of the photon and electron impact spectra of H_{2}O.

Molecular and applied modulation effects in electron electron double resonance. V. Passage effects in high resolution frequency and field swept ELDOR
View Description Hide DescriptionThe observation of electron electron double resonance(ELDOR)linewidths for nitroxide radicals which are significantly less than the hyperfine envelope widths is reported. For a 1.5×10^{−3} M solution of 2,2,6,6‐tetramethyl‐4‐piperidinol‐1‐oxyl (TANOL) in s e c‐butylbenzene (SBB) between the temperatures of −40 °C and −70 °C, the ELDORlinewidths correspond to single spin packet widths determined by the effective electron spin–spin relaxation rates. An analysis of the precise dependence of frequency swept absorption and dispersionELDOR signals upon microwave radiation field intensities and upon the details of the applied Zeeman modulation and accompanying phase‐sensitive detection is also presented. Quantitative prediction of molecular and applied modulation effects is accomplished employing a modified density matrix treatment. Best fit parameters for TANOL in SBB at −63 °C include w _{ e }(0) = 1.75×10^{5} Hz, T ^{ e } _{1e }(0) = 1.3×10^{−6} sec, T ^{ e } _{2e }(0) = 2.7×10^{−7} sec, w _{ n }(^{14}N) = 2.6×10^{5} Hz, w _{ n }(all ^{1}H) = 0 Hz, τ_{2} = 2×10^{−10} sec, ? = 2.00587, g _{∥} = g _{ z z } = 2.00210, g _{⊥} = (1/2)(g _{ x x } + g _{ y y }) = 2.00775, ? (^{14}N) = 43.235 MHz, A _{∥}(^{14}N) = A _{ z z } = 92.65 MHz, A _{⊥}(^{14}N) = (1/2)(A _{ x x } + A _{ y y }) = 18.53 MHz, ? (^{1}H,axial CH_{3}) = 1.28 MHz, ? (^{1}H,axial CH_{2}) = 1.57 MHz, ? (^{1}H,equatorial CH_{2}) = 0.84 MHz, ? (^{1}H,all other) = 0. The theoretical and experimental results afford crucial insight into the design and performance of ELDORexperiments for optimum sensitivity in the determination of spectroscopic parameters and molecular relaxation rates.

^{129}I Mössbauer studies of iodine in the +1 and +3 oxidation states
View Description Hide DescriptionThe ^{129}I Mössbauer spectra of I(pyridine)_{2}ClO_{4} and ‐NO_{3}, I(thiourea)_{2}I, I(acetate)_{3}, a possible phosphate derivative I^{I}‐phosphate, and I_{2}O_{4} are reported. Comparisons of the results of these experiments with those of previous workers raise questions concerning the use of simple models in interpreting ^{129}I Mössbauer data.

Theory of exchange splitting of core levels in x‐ray photoemission spectroscopy of hemin
View Description Hide DescriptionESCA experiments provide information on ionizationenergy differences between core electrons of different spins in a magnetic system, which is related to the exchange interaction between core and the unpaired valence electrons. Using self‐consistent charge extended Hückel wavefunctions for hemin, we obtain 7.1 eV for the exchange energy difference between up and down spin 3selectrons of iron. On allowing for the correction by a factor of about 2 from correlation and relaxation effects in the ionized state, the theoretical splitting compares well with the experimental value, 2.4±0.07 eV. The latter is substantially less than in Fe^{+3} ionic compounds, in agreement with the smaller unpaired spin population on the iron atom in hemin. Comments are made on the relative values of the energies of ionization from iron atom 3s and 3p core states in hemin, relative to ferric and ferrous compounds, the trend of which is in keeping with the charge on the iron in hemin.

Contribution to the theory of dielectric relaxation in polar media
View Description Hide DescriptionA discussion of the connection between the frequency dependent dielectric constant ε and the short range orientational correlation functiond is given for a simple model of polar media. The introduction of separate spatial regions with the attendent difficulties in determining the connection between their (time dependent) correlation functions is avoided by noting that ε must satisfy two relations. The use of these relations allows the long range orientational correlations to be eliminated from the expression for ε, the resulting ε being given as a function of d. The result is a generalization of that given by Nee and Zwanzig [J. Chem. Phys. 52, 6353 (1970)]. A short discussion of the results is given, including a physical picture of the connection between the long and short range orientational correlations.

Energy and lifetime of O^{2−} from analytic continuation of isoelectronic bound states
View Description Hide DescriptionWe offer a method for determining the stability of dinegative ions for isoelectronic series exhibiting a bound singly charged anion. Nonlinear variational ground state energies obtained with bound, multiconfigurational wavefunctions are followed above the first ionization threshold as the nuclear charge (1/λ) is decreased. Resonance energies and widths for physical states are constructed by analytically continuing the energy around a singularity at a nonphysical λ=λ*. Results for the Ne isoelectronic series predict an O^{2−} resonance state at 5.38 eV (width = 1.3 eV) above the O^{−} + e ^{−} continuum theshold. The marked O^{2−} instability suggests that estimates of the O^{−}electron affinity, arising from thermochemical Born–Haber cycles, may require quantum corrections. We also discuss several chemical systems for which the method will be useful and which may lead to predictions of bound states existing in the continuum.

EPR of low spin d ^{7} Fe^{+}, Co^{2+}, and Ni^{3+} cyanide complexes in NaCl and KCl
View Description Hide DescriptionLow spin d ^{7} complexes of type [M(CN)_{4}⋅XY]n−, where M is Fe^{+}, Co^{2+}, or Ni^{3+}, the axial ligands X, Y being Cl^{−}, CN^{−}, or NC^{−}, have been produced and stabilized in NaCl and/or KCl crystals doped with diamagnetic Fe(CN)_{6} ^{4−} (d ^{6}), Co(CN)_{6} ^{3−} (d ^{6}) or Ni(CN)_{4} ^{2−} (d ^{8}), by a suitable combination of irradiation and heat treatment. These complexes were identified by EPR on the basis of the g factors which are characteristic of unpaired electrons in the d _{ z } _{ 2 } orbital pointing towards the ligands X and Y, and the super hyperfine structure from the nuclei of these ligands observed in the EPR spectra. Systematic variations are noted in the EPR parameters, which are discussed in terms of changes in the nature of binding in these complexes in relation to the charge state of the metal ion, the host lattice spacings, and the nature of the axial ligands. In addition to showing that CN^{−} and NC^{−} are much stronger ligands than Cl^{−}, the study pointed out the importance of back bonding in CN^{−}‐ and NC^{−}‐type ligands.

Dissociation of H_{2} ^{+} ion by collision‐induced vibrational excitation
View Description Hide DescriptionCollision‐induced dissociation of hydrogen molecular ion due to the vibrational excitation from ground vibrational state to the continuum of electronic ground state (1sσ_{ g }) has been studied, using sudden approximation. In close encounters, the interaction between the nucleus of projectile and the two nuclei of molecular ion has been taken as the sum of two screened Coulomb‐type interactions. Exact values for the ground vibrational state and quasiclassical wavefunctions for the continuum have been used. The angular distribution,energy distribution, and total vibrational dissociation cross section for fragments in a given excess energy range have been calculated with He, Ar, and Xe as projectiles. Cross sections for dissociation by Ar impact have been calculated for collision energies ranging from 3 to 50 keV, and for He and Xe at 10 keV. It is concluded that the electronic dissociation plays a dominant role even in the small excess energy region of dissociated fragments.

A π, τ, π/2 type pulse sequence method for the determination of T _{1} in rotational transitions
View Description Hide DescriptionWe report a pulse sequence measurement of T _{1} in the J=0 → J=1 rotational transition in OCS in the pure gas, OCS–He mixtures, and OCS–CH_{3}F mixtures at low pressures. This pulse sequence method is similar to the π, τ, π/2 pulse sequence used in nuclear magnetic resonance to measureT _{1}. The pulse method of measuringT _{1} in rotational systems has several advantages over the analysis of transient absorption (transient nutation) results or the analysis of power broadened steady state absorption lines. We find T _{1}=T _{2} for the J=0 → J=1 OCS transitions in pure OCS, OCS–He mixtures, and OCS–CH_{3}F mixtures.

Pyroelectric α‐Cu(IO_{3})_{2}. Crystal structure of the transition metal iodates. III
View Description Hide DescriptionAlpha‐cupric iodate, α‐Cu(IO_{3})_{2}, is pyroelectric and piezoelectric at room temperature and crystallizes in the monoclinic space group P2_{1} with two formulas in the unit cell. The lattice constants at 298 °K are a =5.56902 ± 0.00010, b=5.11098 ± 0.00009, c=9.26976 ± 0.00036 Å and β=95.82 ± 0.02 ° (λCuKα_{1} − 1.540562 Å). The integrated intensities of most reflections within a hemisphere of reciprocal space with radius (sinϑ)/λ?1.02 Å^{−1} were measured on two different crystals using two different diffractometers, resulting in 1814 F m e a s for one set and 4272 F m e a s for the second set of independent structure factors. The crystal structure was solved using Patterson and Fourier series and refined by the method of least squares, the final agreement factor R becoming 0.063 for the first set, and 0.035 for the second set of F m e a s. The iodate ions form a nearly‐regular hexagonal closest‐packed array, with Cu^{2+} in the resulting octahedral interstices. The two independent iodate groups, each with three short I–O distances averaging 1.82 Å, share oxygen atoms to form a three‐dimensional framework of corner‐sharing polyhedra. One iodate ion forms three additional I–O distances averaging 2.66 Å, the other has four that average 2.95 Å. The CuO_{6} octahedron is tetragonally distorted, with four bonds averaging 1.97 Å and two apical Cu–O bonds averaging 2.39 Å. The two sets of F m e a s, and the resulting derived structural parameters, are compared using normal probability plot analysis.

Resonances in the collinear inelastic scattering of He by H^{+} _{2} below the reaction threshold
View Description Hide DescriptionCollinear quantum mechanical calculations are reported for the inelastic scattering of He by H^{+} _{2} below the reaction threshold. The inelastic transition probability curves show a severe oscillatory behavior similar to that recently observed in reaction probability curves for this same system. Perturbation calculations and considerations of the channel phase shifts indicate that the resonance structure is caused by the existence of quasibound (resonance) states of HeH^{+} _{2}. A simple picture is presented which accounts for these quasibound states.

EPR studies of x‐ray irradiated KH_{2}AsO_{4} and KH_{2}PO_{4}‐type ferroelectrics and antiferroelectrics
View Description Hide DescriptionEPR has been used to characterize the hyperfine couplings and electronic structure of a new paramagnetic center (H_{2}AsO_{4})^{2−} in x‐irradiated ferroelectric crystals of pure KH_{2}AsO_{4} and mixed KH_{2}PO_{4}–KH_{2}AsO_{4}, and antiferroelectric mixed crystals of NH_{4}H_{2}PO_{4}–NH_{4}H_{2}AsO_{4}, NH_{4}H_{2}PO_{4}–KH_{2}AsO_{4}, and ND_{4}D_{2}PO_{4}–KD_{2}AsO_{4}. This center is formed by the capture of an electron by proton deficient AsO^{3−} _{4} units in these crystals. The assignment of the center is supported by EPR studies on the temperature dependence of the proton superhyperfine structure of these crystals. The present study also corrects an earlier identification of this center in NH_{4}H_{2}PO_{4}–KH_{2}AsO_{4} as a hole‐type ionic defect center AsO^{2−} _{4}. Our results also provide a direct experimental basis for the currently accepted model of electrical (protonic) conduction in these crystals and help to resolve an earlier controversy regarding conductivity measurements on sulfate‐doped ammonium and potassium salts. In conjunction with x‐ray photoelectron spectroscopic studies, the EPR results on doped crystals also provide interesting results on electron‐capture processes in single crystals. The present work also provides an explanation of some anomalous trends of the hyperfine coupling variation in other XO_{4}‐type radicals.