# Showing papers in "Journal of Chemical Physics in 1965"

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TL;DR: In this article, a derivation of the effect of a time-dependent magnetic field gradient on the spin-echo experiment, particularly in the presence of spin diffusion, is given.

Abstract: A derivation is given of the effect of a time‐dependent magnetic field gradient on the spin‐echo experiment, particularly in the presence of spin diffusion. There are several reasons for preferring certain kinds of time‐dependent magnetic field gradients to the more usual steady gradient. If the gradient is reduced during the rf pulses, H1 need not be particularly large; if the gradient is small at the time of the echo, the echo will be broad and its amplitude easy to measure. Both of these relaxations of restrictions on the measurement of diffusion coefficients by the spin‐echo technique serve to extend its range of applicability. Furthermore, a pulsed gradient can be recommended when it is critical to define the precise time period over which diffusion is being measured.The theoretical expression derived has been verified experimentally for several choices of time dependent magnetic field gradient. An apparatus is described suitable for the production of pulsed gradients with amplitudes as large as 100 ...

7,409 citations

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TL;DR: In this paper, a molecularkinetic theory was proposed to explain the temperature dependence of relaxation behavior in glass-forming liquids in terms of the temperature variation of the size of the cooperatively rearranging region.

Abstract: A molecular‐kinetic theory, which explains the temperature dependence of relaxation behavior in glass‐forming liquids in terms of the temperature variation of the size of the cooperatively rearranging region, is presented. The size of this cooperatively rearranging region is shown to be determined by configuration restrictions in these glass‐forming liquids and is expressed in terms of their configurational entropy. The result of the theory is a relation practically coinciding with the empirical WLF equation. Application of the theory to viscosimetric experiments permits evaluation of the ratio of the kinetic glass temperature Tg (derived from usual ``quasistatic'' experiments) to the equilibrium second‐order transition temperature T2 (indicated by either statistical‐mechanical theory or extrapolations of experimental data) as well as the hindrance‐free energy per molecule. These parameters have been evaluated for fifteen substances, the experimental data for which were available. Hindrance‐free energies ...

4,770 citations

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TL;DR: In this paper, the x-ray form factors for a bonded hydrogen in the hydrogen molecule have been calculated for a spherical approximation to the bonded atom, and the corresponding complex scattering factors have also been calculated.

Abstract: The x‐ray form factors for a bonded hydrogen in the hydrogen molecule have been calculated for a spherical approximation to the bonded atom. These factors may be better suited for the least‐squares refinement of x‐ray diffraction data from organic molecular crystals than those for the isolated hydrogen atom. It has been shown that within the spherical approximation for the bonded hydrogens in H2, a least‐squares refinement of the atomic positions will result in a bond length (Re value) short of neutron diffraction or spectroscopic values. The spherical atoms are optimally positioned 0.07 A off each proton into the bond. A nonspherical density for the bonded hydrogen atom in the hydrogen molecule has also been defined and the corresponding complex scattering factors have been calculated. The electronic density for the hydrogen molecule in these calculations was based on a modified form of the Kolos—Roothaan wavefunction for H2. Scattering calculations were made tractable by expansion of a plane wave in spheroidal wavefunctions.

2,394 citations

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TL;DR: A unified theory of homogeneous and electrochemical electron transfer rates using statistical mechanics is developed in this article, where the atomic motions inside the inner coordination shell of each reactant are treated as vibrations and the motions outside are treated by the particle description.

Abstract: A unified theory of homogeneous and electrochemical electron‐transfer rates is developed using statistical mechanics. The treatment is a generalization of earlier papers of this series and is concerned with seeking a fairly broad basis for the quantitative correlations among chemical and electrochemical rate constants predicted in these earlier papers. The atomic motions inside the inner coordination shell of each reactant are treated as vibrations. The motions outside are treated by the "particle description," which emphasizes the functional dependence of potential energy and free energy on molecular properties and which avoids, thereby, some unnecessary assumptions about the molecular interactions.

2,281 citations

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TL;DR: In this paper, the decay of donor luminescence in a rigid solution when modified by electronic energy transfer by the exchange mechanism is treated theoretically, and the rate constant for the elementary process of energy transfer is taken to be of the Dexter form, const exp(−2R/L), where R is the donor-acceptor distance and L is a positive constant.

Abstract: The decay of donor luminescence in a rigid solution when modified by electronic energy transfer by the exchange mechanism is treated theoretically. The rate constant for the elementary process of energy transfer is taken to be of the Dexter form, const exp(−2R/L), where R is the donor—acceptor distance and L is a positive constant. Calculations are made of the yield and decay time of the donor luminescence as functions of the acceptor concentration. The resulting relationship among the above quantities enables one to analyze experimental data in a quantitative manner, and thereby to obtain information about an intermolecular exchange interaction. As an example of such an analysis, Ermolaev's data on triplet—triplet transfer between some aromatic molecules are compared with our results, and very good agreement is found with a choice of the single parameter L.

1,988 citations

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TL;DR: In this paper, a new method was devised for obtaining absolute cross sections of gases relative to H2, and a McLeod gauge was used to obtain the absolute cross section in H2.

Abstract: The total ionization cross sections of He, Ne, Ar, Kr, Xe, H2, D2, N2, O2, CO, NO, CO2, N2O, and CH4 have been measured from threshold to 1000 eV in a total ionization tube. More limited measurements were performed in C2H4 and SF6. Great care was taken to assure complete collection of electron and ion currents, and the absence of spurious instrumental errors. A new method was devised for obtaining absolute cross sections of gases relative to H2, and a McLeod gauge was used to obtain the absolute cross section in H2. The cross sections in NO and O2 could not be obtained by this method, and an approximate correction to direct McLeod‐gauge readings was used for these gases. It is believed that the results are as accurate as is possible with the present method. It is difficult to explain the differences found between cross sections measured by various investigators. McLeod‐gauge errors appear to account for most of the difference in absolute magnitude.

1,720 citations

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TL;DR: The theory of phase separation from a single phase fluid by a spinodal mechanism is given in this paper, where the predicted structure may be described in terms of a superpositioning of sinusoidal composition modulations of a fixed wavelength, but random in amplitude, orientation, and phase.

Abstract: The theory of phase separation from a single phase fluid by a spinodal mechanism is given. The predicted structure may be described in terms of a superpositioning of sinusoidal composition modulations of a fixed wavelength, but random in amplitude, orientation, and phase. Sections through a calculated structure are shown. These show that the structure has many of the geometrical features found in phase separable glasses, in particular the high degree of connectivity among particles of each phase.

1,486 citations

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TL;DR: In this paper, a general discussion of approximate methods for obtaining selfconsistent molecular orbitals for all valence electrons of large molecules is presented, and two schemes are found which are invariant to transformations among atomic orbitals on a given atom.

Abstract: A general discussion of approximate methods for obtaining self‐consistent molecular orbitals for all valence electrons of large molecules is presented. It is shown that the procedure of neglecting differential overlap in electron‐interaction integrals (familiar in π‐electron theory) without further adjustment may lead to results which are not invariant to simple transformations of the atomic orbital basis set such as rotation of axes or replacement of s, p orbitals by hybrids. The behavior of approximate methods in this context is examined in detail and two schemes are found which are invariant to transformations among atomic orbitals on a given atom. One of these (the simpler but more approximate) involves the complete neglect of differential overlap (CNDO) in all basis sets connected by such transformations. The other involves the neglect of diatomic differential overlap (NDDO) only, that is only products of orbitals on different atoms being neglected in the electron‐repulsion integrals.

1,283 citations

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TL;DR: In this article, the ground-state energy of H2 has been extended to include large internuclear distances and accurate potential energy curve for 0.4≤R≤4.0 a.u.

Abstract: Previous calculation of the ground‐state energy of H2 has been extended to include large internuclear distances and accurate potential‐energy curve for 0.4≤R≤10.0 a.u. is presented. For 0.4≤R≤4.0 a.u. expectation values of several operators have also been calculated. The calculation was made using a wavefunction in the form of an expansion in elliptic coordinates. The wavefunction depends on the interelectronic distance but, in contrast to the James—Coolidge expansion, is flexible enough to describe properly the dissociation of the molecule. Extensive calculations have also been made for the repulsive 3Σu+ state (1.0≤R≤10.0) and for the 1Πu state (1.0≤R≤10.0). In the former case a van der Waals minimum has been found at R=7.85 a.u. and 4.3 cm−1 below the dissociation limit. For the 1Πu state the computed binding energy De=20 490.0 cm−1 and the equilibrium internuclear distance Re=1.0330 A are in a satisfactory agreement with the experimental values De=20 488.5 cm−1 and Re=1.0327 A. In this case a van der ...

1,064 citations

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TL;DR: In this paper, a specific form for the equation of state of a fluid near its critical point is proposed, where a function Φ(x, y) is introduced, with x a measure of the temperature and y of the density.

Abstract: A specific form is proposed for the equation of state of a fluid near its critical point. A function Φ(x, y) is introduced, with x a measure of the temperature and y of the density. Fluids obeying an equation of state of van der Waals type (``classical'' fluids) are characterized by Φ being a constant. It is suggested that in a real fluid Φ(x, y) is a homogeneous function of x and y, with a positive degree of homogeneity (Sec. 2). This leads to a nonclassical compressibility, the behavior of which is determined by the degree of homogeneity of Φ (Sec. 3). A previously derived relation connecting the degree of the critical isotherm, the degree of the coexistence curve, and the compressibility index, again follows, this time without the restrictive assumption of effective isochore linearity (Sec. 4). The locus in the temperature—density plane of the points of inflection in the pressure—density isotherms, as determined experimentally by Habgood and Schneider, is accounted for (Sec. 5). It is shown that if a certain combination of the compressibility and coexistence curve indices is an integer, then the constant‐volume specific heat on the critical isochore has a logarithmic singularity at the critical temperature with, in general, a superimposed finite discontinuity (Sec. 6).

920 citations

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TL;DR: In this article, the Bloch-Torrey equations are modified to include the case of anisotropic, restricted diffusion and flow, and the problem of solving these modified equations for the amplitude of a spin echo in a time-dependent magnetic field gradient subject to restricting boundary conditions is discussed.

Abstract: The Bloch—Torrey equations are modified to include the case of anisotropic, restricted diffusion and flow. The problem of solving these modified equations for the amplitude of a spin echo in a time‐dependent magnetic‐field gradient subject to restricting boundary conditions is discussed. This problem is solved for a number of selected cases. In particular, it is found that a magnetic‐field gradient applied in short, intense pulses is effective in defining the time during which nuclear displacements take place. A simplified equation, suitable for the pulsed‐gradient experiment, is presented and solved for two different examples of systems showing restricted diffusion. A procedure for analyzing the data from pulsed‐gradient measurements is suggested, and its merits are discussed. Suggestions are made of systems which may well be expected to show restricted, anisotropic diffusion or interesting flow properties.

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TL;DR: In this article, a quasiclassical procedure for the examination of the collision dynamics of atom-diatomic-molecule reactions with activation energy is introduced, which is applied to the exchange reaction resulting from a hydrogen atom and a hydrogen molecule moving on a simple barrier potential of the London-Eyring-Polanyi-Sato type.

Abstract: A quasiclassical procedure for the examination of the collision dynamics of atom—diatomic‐molecule reactions with activation energy is introduced. By means of Monte Carlo averages over a large number of appropriately chosen three‐dimensional classical trajectories, the total reaction cross section (Sr) and other reaction attributes can be determined as a function of the initial relative velocity (Vr) and the initial molecular rotation‐vibration state (J, ν).The method is applied to the exchange reaction resulting from a hydrogen atom and a hydrogen molecule moving on a simple barrier potential of the London—Eyring—Polanyi—Sato type. It is found that Sr is a monotonically increasing function of relative velocity that rises smoothly from a threshold at ∼0.9×106 cm/sec to its asymptotic value of ∼4.5a02 at ∼1.8×106 cm/sec. The zero‐point vibrational energy of the molecule contributes to the energy required for reaction, but the rotational energy does not. The reaction probability, which depends on VR, ν, and...

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TL;DR: In this paper, the authors used the self-consistent molecular orbital method with complete neglect of differential overlap (CNDO) to calculate molecular orbitals for the valence electrons of diatomic and small polyatomic molecules.

Abstract: The approximate self‐consistent molecular orbital method with complete neglect of differential overlap (CNDO), described in Paper I, is used to calculate molecular orbitals for the valence electrons of diatomic and small polyatomic molecules. A small number of bonding parameters (β‐resonance integrals) are chosen semiempirically so that the results are comparable to previous accurate LCAO—SCF wavefunctions for diatomic hydrides using a similar basis set. With this calibration, it is found that calculations on other diatomics and polyatomics lead to molecular orbitals and electron distributions in reasonable agreement with the full calculations where available. Although the new method is not yet successful in predicting bond lengths and dissociation energies, it does lead to the correct geometry, reasonable bond angles and bending force constants for the polyatomic molecules considered. It also gives calculated barriers to internal rotation for ethane, methylamine, and methanol which are in fair agreement with experiment.

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TL;DR: In this paper, the experimentally measured intensities of the solution absorption spectra of Pr3+, Nd3+, Er3+, Tm3+, and Yb3+ in three different solvents were correlated with a theoretical expression derived by Judd.

Abstract: We have correlated the experimentally measured intensities of the solution absorption spectra of Pr3+, Nd3+, Er3+, Tm3+, and Yb3+ in three different solvents with a theoretical expression derived by Judd. The expression, P=Σ lim λTλσ(fNψJ‖∪(λ)‖fNψJ′′)2λ=2,4,6 is derived from a theory in which the ligand‐field interactions with the central 3+ ion cause a mixing of higher configurations of opposite parity into the fN configuration and gives rise to induced electric‐dipole transitions. A prerequisite for the intensity calculations is the computation of complete intermediate coupling eigenvectors for the energy levels investigated. Other possible mechanisms such as magnetic‐dipole and electric‐quadrupole transitions are considered. The oscillator strengths of important magnetic‐dipole transitions are tabulated.The results give the first experimental verification of the ability of the theory to account for large changes in certain bands of the same lanthanide observed in different solvents. Conclusions are dra...

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TL;DR: In this article, a method for the calculation of dipole polarizabilities of closed-shell atomic systems is presented, which involves the direct calculation of the Hartree-Fock wavefunction of the atom in the presence of the perturbing field.

Abstract: A method for the calculation of the dipole polarizabilities of closed‐shell atomic systems is presented. This method involves the direct calculation of the Hartree—Fock wavefunction of the atom in the presence of the perturbing field. The orbitals are expressed as linear combinations of Slater‐type functions. A large number of carefully chosen and optimized basis functions are used so as to assure a good fit to the true Hartree—Fock wavefunction. The polarizability is then calculated from the limiting value of α=p/F for F=0, where F is the electric field strength, and p is the induced dipole moment.

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TL;DR: The van der Waals, Cahn-Hilliard theory of interfacial tension is reformulated for a fluid in the neighborhood of its critical point in this article, and the reformulated theory becomes equivalent to the Ornstein-Zernike, Debye theory of molecular correlations when the interface thickness is identified with the correlation length.

Abstract: The van der Waals, Cahn—Hilliard theory of interfacial tension is reformulated for a fluid in the neighborhood of its critical point. The reformulated theory becomes equivalent to the Ornstein—Zernike, Debye theory of molecular correlations when the interface thickness is identified with the correlation length. When account is taken of the nonclassical behavior of the compressibility and coexistence curve, the theory is found to be in good agreement with independently known facts in three‐dimensional systems, yet slightly but unambiguously wrong in two dimensions. When one of the hypotheses of the original theory is replaced by an alternative hypothesis, the resulting theory is found to be correct in both two and three dimensions.

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TL;DR: In this paper, a simple method using the techniques of transformation theory for the generation of the matrix elements of unusual potential functions for one-dimensional quantum-mechanical problems is described.

Abstract: A simple method using the techniques of transformation theory for the generation of the matrix elements of unusual potential functions for one‐dimensional quantum‐mechanical problems is described. It is applicable both to functions which exist as a set of points, for example, a curve or table, as well as to those in explicit form. Some representative calculations have been made for anharmonic oscillators.

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TL;DR: In this paper, a recent statistical theory of rearrangement collisions was modified to bring it into accord with the detailed balance theorem, and the energy dependence of the cross sections near threshold and approximate formulas for the cross section at arbitrary energies were derived.

Abstract: This paper amends a recent statistical theory of rearrangement collisions to bring it into accord with the detailed‐balance theorem. Both classical and quantum formulations are discussed. The energy dependence of the cross sections near threshold and approximate formulas for the cross sections at arbitrary energies are derived.

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TL;DR: An extension of a previous one component theory of hard-sphere systems and the surface tension of real systems is made to mixtures in this article, based on consideration of an approximate expression for the work of adding an additional hard sphere to a mixture.

Abstract: An extension of a previous one‐component theory of hard‐sphere systems (in three, two, and one dimensions) and the surface tension of real systems is made to mixtures. The theory is based on consideration of an approximate expression for the work of adding an additional hard sphere to a mixture. Comparison between theory and molecular‐dynamics calculations of the various contributions to the virial pressure (related to contact distribution functions) of such hard‐sphere mixtures is excellent. Comparison of the theory with experimental surface tensions of mixtures of simple liquids is satisfactory.

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TL;DR: In this article, the Fourier transformation of infrared and Raman band shapes reveals the meaning of the spectrum in terms of molecular rotation much more clearly than does the usual frequency shape.

Abstract: It is suggested that Fourier transformation of infrared and Raman band shapes reveals the meaning of the spectrum in terms of molecular rotation much more clearly than does the usual frequency shape. By looking at the time dependence directly, one may separately examine the molecular motion at short and long times The motion at short times may be analyzed directly in terms of the molecular dynamics, by the use of a power series in the time, whereas the behavior at long times is best examined by statistical arguments. This kind of analysis is illustrated by several examples, including the spectra of liquid CO and CH4.

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TL;DR: In this article, the rate theory has been reformulated using the Cohen and Turnbull expression for the probability of finding a vacant site and yields an equation of the form η=A0exp[Ev*/RT+γV0/Vf].

Abstract: The rate‐theory approach of Eyring and the free‐volume theory of Cohen and Turnbull for liquid viscosities have been reconsidered. The rate theory has been reformulated using the Cohen and Turnbull expression for the probability of finding a vacant site and yields an equation of the form η=A0exp[Ev*/RT+γV0/Vf]. This result has been applied to many liquids ranging from fused silica to liquid argon and including polyatomic van der Waals as well as hydrogen‐bonded liquids.Consistent fits to both temperature and pressure dependence of viscosity were obtained. A significant conclusion is that the free volume of liquids is considerably higher than that suggested by the WLF and Cohen and Turnbull equations.

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TL;DR: In this article, an identity is derived relating the shear and bulk moduli of any isotropic material in which particles interact by means of two-body central forces; this is a generalization of the familiar Cauchy identity occurring in the theory of elasticity of solids.

Abstract: This article presents a calculation of the infinite‐frequency elastic moduli of monatomic fluids. When the intermolecular potential has the standard Lennard‐Jones form, the elastic moduli are shown to be related to the pressure and internal energy of the fluid. Numerical values of the elastic moduli at various densities and temperatures are presented in tabular and graphical form. An identity is derived relating the shear and bulk moduli of any isotropic material in which particles interact by means of two‐body central forces; this is a generalization of the familiar Cauchy identity occurring in the theory of elasticity of solids. The approach is based on analysis of the high‐frequency limit of exact time‐correlation function expressions for shear and bulk viscosity.

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TL;DR: In this article, the symmetry properties of the third-rank tensor β, which comprises the set of coefficients of quadratic terms in the expansion of the induced dipole moment in the electric field, are investigated, and various linear combinations belonging to the irreducible representations are tabulated for the important molecular symmetry groups.

Abstract: The symmetry properties of the third‐rank tensor β which comprises the set of coefficients of quadratic terms in the expansion of the induced‐dipole moment in the electric field are investigated, and the various linear combinations belonging to the irreducible representations are tabulated for the important molecular symmetry groups. Depolarization ratios are calculated for a sample composed of randomly oriented molecules (liquid phase). Examples of the selection rules in both liquid and crystalline phases are discussed, and these selection rules are contrasted with the ones appropriate for infrared absorption and the ordinary Raman effect.Molecular modes allowed in the infrared are always allowed in the hyper‐Raman effect and have a depolarization ratio (for linearly polarized incident radiation) ≤⅔, while allowed hyper‐Raman transitions forbidden in the infrared have a depolarization ratio of ⅔.

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TL;DR: In this paper, a detailed single-crystal structure analysis was performed for ethylene oxide hydrate and the results confirmed the polyhedral host lattice formed by 46 hydrogen-bonded water molecules in a cubic unit cell of 12.03 A with space-group symmetry Pm3n.

Abstract: A detailed single‐crystal structure analysis is reported for ethylene oxide hydrate. This confirms the polyhedral host lattice formed by 46 hydrogen‐bonded water molecules in a cubic unit cell of 12.03 A with space‐group symmetry Pm3n. Disordered ethylene oxide molecules occupy the six equivalent tetrakaidecahedral cavities, and their electron‐density distribution suggests that they are hindered axial rotors. Additional guest molecules, either ethylene oxide, oxygen, or nitrogen molecules occupy the two dodecahedral cavities with high disorder and low statistical weight. The compound is therefore nonstoichiometric having the limiting formula 2M·6C2H4O·46H2O, in which the percentage of M is variable. If M is assumed to be entirely ethylene oxide, as is likely from the method of preparation, the composition of the crystals obtained from an equilibrated aqueous solution of 8 mole % ethylene oxide at 9°C is 6.4C2H4O·46H2O.

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TL;DR: In this article, a class of compounds which are so structured that the phenyl groups along a main alkane chain are separated by exactly three carbon atoms, e.g., 1,3-diphenylpropane, 1, 3,5-triphenylpentane, has been found to possess unique fluorescence characteristics.

Abstract: Fluorescence spectra have been measured for a variety of diphenyl and triphenyl alkanes in cyclohexane and in p‐dioxane. A class of compounds which are so structured that the phenyl groups along a main alkane chain are separated by exactly three carbon atoms, e.g., 1,3‐diphenylpropane, 1,3,5‐triphenylpentane, has been found to possess unique fluorescence characteristics. These are the appearance of a long‐wavelength band in the region of 330 mμ and a marked decrease in the fluorescence yield. The long‐wavelength band is attributed to an emission from an excimer (a transient dimer) formed intramolecularly by the association of excited and unexcited phenyl groups. Formation of excimers in the specific class of compounds is discussed in relation to molecular configuration. Efficiency of excimer formation, solvent effects, and quenching by dissolved oxygen are some of the topics discussed through kinetic considerations.

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TL;DR: The structure of the tetrahydrofuran/hydrogen sulfide double hydrate has been determined from three-dimensional single-crystal data as discussed by the authors, and the analysis confirmed the clathrate host lattice characteristic of 17 cubic (Type II) gas hydrates.

Abstract: The structure of the tetrahydrofuran/hydrogen sulfide double hydrate has been determined from three‐dimensional single‐crystal data. The analysis confirmed the clathrate host lattice characteristic of 17‐A cubic (Type II) gas hydrates. The hexakaidecahedral voids enclose tetrahydrofuran molecules which appear to undergo free rotation. Statistically, 46% of the pentagonal dodecahedra are occupied by hydrogen sulfide molecules.

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TL;DR: In this article, a simple method for measurement of quantum yields for the singlet→triplet crossing process in solution has been developed, where the compound to be tested is used as a sensitizer for one or more cis-trans isomerization reactions and the quantum yield of the induced process is measured.

Abstract: A simple method for measurement of quantum yields for the singlet→triplet crossing process in solution has been developed. The compound to be tested is used as a sensitizer for one or more cis—trans isomerization reactions and the quantum yield of the induced process is measured. The results are discussed briefly

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TL;DR: In this article, the authors studied the time dependence of the fluorescence intensity as a function of laser intensity, crystal temperature and excitation wavelength, and concluded that the triplet state at 14 750 cm−1 can be populated (i) by direct absorption of laser photons involving an activation energy of 350 cm− 1; (ii) via two-photon absorption, presumably leading to a vibrationally excited state of the 1B2u exciton, followed by intersystem crossing; (iii) via one−photon (second-harmonic) excitation from levels�

Abstract: Experimental and theoretical studies are reported of the short‐lived and delayed fluorescence of anthracene single crystals, excited by single‐ and double‐photon absorption. A giant‐pulse ruby laser provides the primary source of radiation of 14 400 cm−1 (up to 1027 photons/cm2·sec) and is also used to generate second‐harmonic radiation from ADP, as well as stimulated Raman radiation of 12 800 and 17 500 cm−1 from liquid oxygen. The time dependence of the fluorescence intensity is studied as a function of laser intensity, crystal temperature and excitation wavelength. The very intense fast fluorescence with a half‐life of 30 nsec at 300°K, characteristic of singlet exciton decay, and the relatively weak delayed fluorescence which involves intermediate triplet states, are separated using sectored disks. It is concluded that the triplet state at 14 750 cm−1 can be populated (i) by direct absorption of laser photons involving an activation energy of 350 cm−1; (ii) via two‐photon absorption, presumably leading to a vibrationally excited state of the 1B2u exciton, followed by intersystem crossing; (iii) via one‐photon (second‐harmonic) excitation from levels≥700 cm−1 into the singlet absorption band, followed by conversion of the singlet exciton into a triplet pair. The latter process is suggested by the observed activation energy of 700 cm−1. In agreement with these interpretations, the delayed fluorescence intensity is found to vary with the second to fourth power of the laser intensity depending on the experimental conditions. Also, light of 17 500 cm−1 leads exclusively to Process (i), light of 12 800 cm−1 exclusively to (ii). Triplet lifetimes from 2–17 msec are obtained, depending on crystal purity, which indicates that unimolecular triplet decay is an extrinsic, radiationless process. A singlet—triplet intersystem crossing rate constant of about 3×10−5 sec−1 is estimated. The triplet—triplet annihilation rate constant is found to be about 5×10−11 cm3 sec−1. This value considered together with the triplet‐pair creation process suggests a triplet exchange rate ≳ 1013 sec−1 and a triplet diffusion constant ≳o5×10−4cm2/sec.

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TL;DR: In this article, the relativistic wavefunctions employed were solutions of the Dirac equations and the radii corresponding to the principal maxima in the radial distribution functions r2ψi2(r) have been obtained for all the atoms in the periodic table.

Abstract: Radii corresponding to the principal maxima in the radial distribution functions r2ψi2(r) have been obtained for the ground states of all the atoms in the periodic table. The relativistic wavefunctions employed were solutions of the Dirac equations. Slater's ρ⅓ method for including exchange and Latter's method for the self‐interaction correction were used in ``creating'' the potential.The radii corresponding to these maxima are used as measures of the size of each orbital. The relation between the orbital radii of the valence electrons is shown as plots for the first, second, and third series of transition elements.In the elements below nobelium, only four maxima occur in the total charge‐density function. The relation of these maxima to the shell structure of the atom and the effect of shielding by outer electrons are discussed. The effect of the relativistic contraction on orbitals of low angular momentum is shown.

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TL;DR: A series of strontium ferrate compositions ranging from SrFeO2.7 to Stochastic Ferrate 3.0 have been produced by equilibration at oxygen pressures ranging from 0.2 to 855 atm.

Abstract: A series of strontium ferrate compositions ranging from SrFeO2.7 to SrFeO3.0 have been produced by equilibration at oxygen pressures ranging from 0.2 to 855 atm. The stoichiometric composition SrFeO3.0 exhibits a simple cubic perovskite structure (a=3.850 A). Ceramic disks of this material are conductive (ρ≈10−3 Ω·cm) and their temperature dependence is characteristic of metallic conduction. Magnetic measurements indicate that SrFeO3.0 is antiferromagnetic below 130°K. With increasing oxygen deficiency, specimens show increased cell constants and eventually tetragonal distortion. Decrease in the Neel temperature and increased resistivity accompany these changes.