Volume 50, Issue 1, 01 January 1969

Variational Corrections to Decoupling Approximations in Molecular Collision Theory
View Description Hide DescriptionA simple correction to the decoupling approximation is introduced in order to account for the possible occurrence of energy‐conserving transitions. The correction, derived from a variational principle for effective potentials, uses only matrix elements and wavefunctions available from decoupling procedure computations to introduce a nonlocal, imaginary part, for the effective potential. The imaginary part is used to compute transition rates for energetically allowed transitions, which are neglected in the decoupling approximation. Explicit results (and error terms) are obtained in the two‐state approximation.

Intensity Perturbations Due to Configuration Interaction Observed in the Electron Energy‐Loss Spectrum of N_{2}
View Description Hide DescriptionThe electron energy‐loss spectrum of 25‐keV electrons in molecular nitrogen has been re‐investigated in the 12.5–14.9 eV energy‐loss range with improved energy resolution of 10 meV. The band intensities of the and progressions, which consist of the bands , and as recently turned out, exhibit strong perturbations due to configuration interaction with the and state, respectively. The disturbed intensity in the progressions is quite analogous to the one in the two‐electron excitation region of helium. Intensity perturbations in the series, if any, should be very weak.

Interatomic Potentials for HeNe, HeAr, and NeAr
View Description Hide DescriptionSemiempirical potentials for HeNe, HeAr, and NeAr are determined according to Nesbet's scheme from Hartree–Fock (H–F) repulsions and the experimental Boyle temperature in terms of the (exp‐6) and Morse models. For the Morse model, the agreement with potentials determined entirely from experimental data is within about 10%; it is poorer for the (exp‐6) model. However, both models afford poor agreement with the theoretical dispersion attraction. Hybrid model potentials, constructed by equating the H–F repulsion with the repulsive term of the model potential and requiring a first‐order contact with the theoretical dispersion, have much too shallow a well. Possible means for obtaining improved hybrids are explored.

Light Scattering from Multicomponent Fluids
View Description Hide DescriptionThe spectrum of the light scattered by a multicomponent fluid is discussed using the thermodynamic approach originally suggested by Landau and Placzek. The structure of the central Rayleigh line is discussed for two particular cases; the infinitely dilute solution of rigid polymers and a binary mixture.

Vibrational Analysis of Copper Chloride Dihydrate
View Description Hide DescriptionRoom‐ and low‐temperature infrared spectra of copper chloride dihydrate and its deutero modifications have been obtained, as well as polarized spectra of oriented polycrystalline films of the hydrate. Bands due to vibrations of H_{2}O, D_{2}O and HOD molecules in the hydrate, as well as their polarization, are considered in terms of the crystal structure and previous interpretations of the vibrational bands of the solid.

Kinetics of Triplet–Triplet Annihilation in the Vapor Phase of Naphthalene, Anthracene, and Phenanthrene
View Description Hide DescriptionThe triplet–triplet annihilation process has been investigated in naphthalene, anthracene, and phenanthrene vapor. The observation of spontaneous and delayed fluorescence produced by flash excitation when combined with steady‐state fluorescence measurements permits the determination of the temperature and pressure dependence of (absolute) and (in arbitrary units) ( intersystem‐crossing yield; , triplet–triplet annihilation rate constant;, probability of a triplet–triplet annihilation reaction leading to an excited singlet ). An attempt is made to separate the observed temperature and pressure dependence of and into the individual contributions of , and . The behavior of with respect to temperature is interpreted in terms of the Stevens–Parker mechanism, where excimers are involved as an intermediate product in the annihilation process of two triplets: in molecules where is smaller than the excimer binding energy is temperature dependent (anthracene). In molecules where has a constant “saturation value” near unity (napthalene, phenanthrene). In anthracene the temperature dependence of shows a marked parallelism to that of fluorescence self‐quenching. Napthalene is found to exhibit a temperature‐dependent in contrast to phenanthrene and anthracene.

Rotatory‐Diffusion Broadening of Rayleigh Lines Scattered from Optically Anisotropic Macromolecules in Solution
View Description Hide DescriptionA technique for the spectroscopic detection of pure rotatory Brownian movement of anisotropicmacromolecules in solution are developed in combination with a high‐resolution optical heterodyne spectrometer. The line broadening originating in the translational diffusion of the solutemacromolecule, which is a dominant factor in intensity in the Rayleigh component, is suppressed by taking the forward scattering. Then, only the depolarized light whose amplitude is fully modulated by the rotation of solute molecules is filtered off by the polarizer and received by a photomultiplier tube. The time‐dependent component of the output from the phototube is analyzed by a wave analyzer to give a spectrum of the scattered light. From the spectral linewidth thus obtained, the rotatory diffusion coefficient of Tobacco Mosaic Virus in aqueous solution has been obtained and found to be 350 ± 20 sec^{−1}. On the other hand, the optically isotropic polystyrene latex sphere has shown no broadening in this system. From these results and from the evidence of sharpening of the linewidth with increasing solvent viscosity, it is concluded that the observed broadening originates in the amplitude modulation of the scattered light by the rotatory diffusion of TMV. This “depolarized light mixing” technique is quite general and able to cover a frequency range from 10^{1} to 10^{7} Hz. And it is believed to be useful especially in the studies of rotatory diffusion and transconformation of anisotropicmacromolecules, and in studies of chemical kinetics accompanying an anisotropic change of polarizabilities.

Spin Relaxation: The Multiple‐Time‐Scale Point of View
View Description Hide DescriptionThe linear (Redfield) form of the equation of motion for the density matrix of a spin system immersed in a heat bath is derived. The usual derivations employ perturbation theory which suffers from the presence of secular terms familiar from nonlinear mechanics. We employ the multiple‐time‐scale technique as developed by Frieman and Sandri to eliminate the secular terms and render the expansions valid for all time. The method introduces explicit time variables to exploit the multiplicity of time scales inherent to the problem.

Fine Structure of the X‐Ray K‐Absorption Spectrum of Yttrium
View Description Hide DescriptionThe x‐ray K‐absorption spectrum of metallic yttrium has been investigated using a 400‐mm bent crystal (mica) spectrograph. The extended fine structure has been explained in the light of Hayasi's theory. The bond lengths have been computed for the yttrium metal and five of its compounds using Lytle's analysis. Plasma oscillation theory seems to explain satisfactorily the first two absorption maxima close to the absorption edge.

Magnetic Resonance Lineshape and Chemical Shift of Molecules in Clathrates
View Description Hide DescriptionProtonmagnetic resonancespectra of small molecules in hydroquinone clathrate cages have been observed. Despite the fact that diffusion is a very slow process in these systems, lines were sufficiently narrow (< 100 Hz) to observe separate resonances corresponding to chemically shifted protons. The observed line shape, which is not Lorentzian, has been related to anisotropic orientational probability of the enclathrated molecule within the crystalline potential. The degree of alignment found for H_{2}S at room temperature is ∼ 6 × 10^{−4}.

Nuclear Spin–Lattice Relaxation in Phenylacetylene
View Description Hide DescriptionThe temperature dependence of the proton and deuteron spin–lattice relaxation times in phenylacetylene and phenylacetylene‐d_{1} has been measured by the adiabatic fast‐passage method. The intramolecular and intermolecular contributions to relaxation have been separated by the measurement of ring protons at different concentrations of phenylacetylene in CS_{2} and C_{6}D_{6}. The deuteron electric field gradients in the R–C ≡ C–D compounds are relatively insensitive to the nature of the substituent R, and therefore the –C ≡ C–D grouping can be employed as a probe to study rotational motions in molecular liquids of the R–C ≡ C–D type. The reorientational correlation time, in neat phenylacetylene‐d_{1} , and at infinite dilution in CS_{2} at 26°C, has been calculated from the deuteron and found in good agreement with those calculated from viscosity using both the microviscosity model and the Hill model. Analogous comparison of the experimental translational correlation time for neat phenylacetylene at 26°C, and the calculated values has also been carried out.

Simple Bond‐Charge Model for Potential‐Energy Curves of Heteronuclear Diatomic Molecules
View Description Hide DescriptionA model for the vibrational potential‐energy functions of diatomic molecules, previously applied to homonuclear molecules only, is extended to 54 heteronuclear diatomic molecules in 93 different electronic states. Experimental and values are used to determine for each species the empirical bond‐charge and bond‐length parameters, and , in the homopolar model potential This potential is known to be reasonably accurate for near . The molecular virial theorem requires that the term proportional to represent electronic potential energy; this is modeled by supposing that an electronic charge is at the bond center, and a net charge of is at each nucleus, with for neutral molecules. The virial theorem also requires that the term proportional to represent electronic kinetic energy; this is modeled by supposing that the electrons move free‐electron‐like in a one‐dimensional box of length . As in the homonuclear case, the parameters are found to vary little from state to state in a given molecule, or through a given row in the periodic table. It is shown that heteronuclear values can be estimated from homonuclear values using formulas like , and it is shown further that values are measures of the core (ionic) radii of atoms A and B in a molecule. Values of the parameters correlate nicely with other, more conventional measures of bond population or bond order. Alternative, more complicated, heteropolar models for a heteronuclear diatomic molecule are examined. These models involve different charge parameters and on the two nuclei, and location of the bond charge elsewhere than at the bond center. Predicted and values, and hence the vibrational force constants, are shown to be insensitive to choice of the model. Values for the molecular electric dipole and quadrupole moments are more sensitive to the model, however. Arguments are presented for preferring the homopolar model, with and at the bond center, as the zero‐order model for describing molecular vibrations.

Experimental Measurements of the Diffusion Coefficients of H Atoms in H_{2} and in H_{2}–He and H_{2}–Ar Mixtures
View Description Hide DescriptionThe catalytic sink technique previously described was used to measure the diffusion coefficients of H atoms in H_{2} over the temperature range 202°–364°K and in H_{2}–He and H_{2}–Ar mixtures at 275°K. The rigid‐sphere collision diameters of H atoms in H_{2}, He, and Ar were 1.89, 1.94, and 1.84, respectively. However, the temperature dependence of the H–H_{2}diffusion coefficients does not fit the rigid‐sphere equation but can be represented by the use of the Lennard‐Jones parameters and . Comparisons are made with values derived from viscosity data and with theoretical calculations.

Structure of the Alkali Hydroxides. III. Microwave Spectra of RbOH and RbOD
View Description Hide DescriptionThe microwave spectra of gaseous RbOH and RbOD have been measured with a high‐temperature spectrometer. The spectra are generally similar to those observed in CsOH and indicate an essentially linear structure for rubidium hydroxide. The variation of rotational constant with excitation of the bending mode shows anomalies similar to those found in CsOH. The Rb–O bond length is found to be 2.30_{5} Å, while the O–H distance is 0.96_{5} Å. Analysis of the nuclear quadrupolehyperfine structure gives values of − 67.9 Mc/sec in ^{85}RbOH and − 35 Mc/sec in ^{87}RbOH.

Dielectric Behavior of NaOH‐Doped Ice
View Description Hide DescriptionThe dielectric behavior of icedoped with different NaOH concentrations was investigated in the 0° to − 25°C temperature range. In the lower concentration range of 1–4 × 10^{−6} M NaOH, the conductivity behavior was similar to pure ice. At higher concentrations in the range of 7 × 10^{−6} M NaOH, significantly higher conductivities were observed with the low‐frequency conductivity being about 5 × 10^{−8} (Ω·cm)^{−1} and exhibiting only a slight temperature dependence. At lower temperatures the static dielectric constant was found to decrease with increasing NaOH concentration. The dielectric relaxation times and corresponding activation energies were about the same as for pure ice. The over‐all behavior is distinctly different from that of HF, HCl, and NH_{3}‐doped ice. The model postulated to explain the observed results involves the interstitial incorporation of Na bonded to an (OH) site in its normal lattice position. It is postulated that this mode of incorporation causes lattice distortion that increases either the concentration or mobility of the OH‐ionic defects which in turn accounts for the increased conductivity.

Calculation of Lower Bounds to Energies of Molecular Systems. I. Mathematical Methods and Energy Variances for Simple Systems
View Description Hide DescriptionThe energy variance, which provides a sensitive test for any proposed wavefunction, has been calculated for a series of Gaussian‐type wavefunctions for the systems H_{2} ^{+}, H_{2}, HeH^{+}, He_{2} ^{++}, and H_{3} ^{+}. The integrals that arise over the square of the Hamiltonian can be expressed either in closed form, or involving a single numerical integration. The magnitude of the values obtained for the energy variance, which should be zero for an exact solution, are consistent with other suggestions that the operator magnifies the poor features of trial functions. Moreover, for the two‐electron systems, an evaluation of the three components of , , , and , shows by their lack of convergence that they all contribute to this result. A further examination of these wavefunctions is made by a calculation of the net forces acting on the nuclei.

Crystal Structure of the Transition‐Metal Molybdates and Tungstates. V. Paramagnetic Alpha‐Nh_{2}(MoO_{4})_{3}
View Description Hide DescriptionParamagneticα‐Nd_{2}(MoO_{4})_{3}, prepared below the transition temperature of 960°C, crystallizes in a subtle variant of the scheelite structure. The lattice constants of the basic tetragonal unit cell are and , with space group and of a Nd_{2}(MoO_{4})_{3} formula per unit cell. The ordered distribution of two Nd atoms over every three available sites results in additional weak scattering corresponding to a monoclinic unit cell with , , and , with , space group . The integrated intensities of 2490 scheelitelike reflections within a reciprocal hemisphere of radius were measured with PEXRAD, of which 198 were independent and above background. Refinement of the atomic positions, assuming a statistical distribution of Nd on each scheelite 4b site, resulted in an agreement factor between measured and calculated structure factors of 0.0375. Each Nd atom is dodecahedrally coordinated to eight oxygen atoms, with four Nd–O distances of 2.492 ± 0.010 Å and four others of 2.509 ± 0.011 Å. Each Mo atom occupies a tetrahedron of oxygen atoms, with four identical Mo−O distances of 1.800 ± 0.011 Å. An arrangement of Nd atoms and vacancies in the monoclinic cell giving a predicted scattering pattern in satisfactory agreement with observation is presented.

Inter‐ and Intramolecular Processes in Organic Solutions under Excitation in the Vacuum Ultraviolet
View Description Hide DescriptionThe efficiency of energy transfer from solvent to solute is investigated as a function of solute concentration and excitation wavelength for solutions of diphenyloxazole in benzene, toluene, cyclohexane, and hexane. The results for benzene and toluene are similar but different from those for cyclohexane and hexane. For the first pair of solventsenergy transfer takes place almost exclusively from the first excited level for all wavelengths of excitation; only for higher acceptor concentrations does the direct transfer from higher levels become noticeable. The transfer efficiency from the first excited level depends, however, strongly on the electronic level which has been initially excited. The effect of dilution of the transferring solvent is studied. For cyclohexane and hexane two or more transfer mechanisms or transferring species seem to be significantly involved even for low acceptor concentrations. The quenching effect of carbon tetrachloride and of chloroform is investigated for benzene and toluene and that of oxygen for all four solvents. While quenching of benzene and toluene by oxygen is primarily “dynamic” the quenching effect in cyclohexane and hexane is “static.” The results are compared with available results for excitation with high‐energy radiation.

Molecular Theory of Flow Alignment of Nematic Liquid Crystals
View Description Hide DescriptionA mechanism to explain flow alignment of nematic liquid crystals is proposed. It is based on the rodlike shape of the molecules of these substances. A model calculation is performed in which the molecules are assumed to be equally and rigidly oriented ellipsoids of revolution, colliding with each other like the molecules of a gas. The two coefficients governing the linear relationship between torque per unit volume and shear rate are derived. The theory is used to predict the degree of flow alignment (which is found to be incomplete and to be independent of the shear rate) and to establish a relationship between the viscosity and one of the shear–torque coefficients. Theory and experiment are compared for p‐azoxyanisole, and good agreement is found.

Vibrational Spectra and Structure of Organophosphorus Compounds. VI. Infrared and Raman Spectra of CH_{3}OPSF_{2} and CD_{3}OPSF_{2}
View Description Hide DescriptionThe infrared spectra of both CH_{3}OPSF_{2} and CD_{3}OPSF_{2} in the vapor phase have been recorded from 4000 to 33 cm^{−1}. Carbon disulfide solution spectra were also investigated to 200 cm^{−1}. The Raman spectra of the liquids and solids have been recorded and depolarization values measured. At least two isomeric configurations are indicated from the low‐temperature Raman spectra, and from the lack of the variation of band intensity, it is concluded they have nearly equal energy. Only one torsional vibration was observed at 192 cm^{−1}, and it is concluded that it is composed of the CH_{3} and P–O–C torsional vibrations and possibly mixed with other low‐frequency skeletal modes. The doublet due to the P=S stretching vibration has a separation of only 31 cm^{−1}, whereas 100–150 cm^{−1} has been proposed as the separation for this normal mode in this type of compound. The other fundamental vibrations are assigned based on band positions, depolarization values, and isotopic shifts. The assignments are also compared to those previously given for the CH_{3}OPCl_{2} and CH_{3}OPSCl_{2} molecules.