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15 Dec 1967

Volume 47, Issue 12, pp. 4873-5462

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Use of Computer Experiments to Locate the Melting Transition and Calculate the Entropy in the Solid Phase

William G. Hoover and Francis H. Ree

J. Chem. Phys. 47, 4873 (1967); http://dx.doi.org/10.1063/1.1701730 (6 pages) | Cited 99 times

Online Publication Date: 3 May 2004

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Modern computers can accurately simulate the behavior of idealized systems of several hundred particles, but they have trouble in studying the melting process in which small‐system surface effects make the transition irreversible. It is here suggested that a thermodynamically reversible path linking the solid and fluid phases can be obtained by using a periodic ``external field'' to stabilize the solid phase at low density. The properties of the artificially stabilized solid at low density are studied theoretically, and two practical schemes are outlined for determining the melting parameters by using computer‐calculated entropies.

Time‐Dependent Reorientation Probabilities and Molecular Relaxation

J. E. Anderson

J. Chem. Phys. 47, 4879 (1967); http://dx.doi.org/10.1063/1.1701731 (5 pages) | Cited 30 times

Online Publication Date: 3 May 2004

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This article considers situations in which the probability of molecular reorientation is governed by a secondary, time‐dependent process. A ``projection technique'' for computing reorientational correlation functions in these situations is described, together with a ``simple defect'' model of molecular relaxation. The effects of different types of secondary time‐dependent processes on the observable correlation time distribution are discussed.

F☒F Spin—Spin Coupling in Perfluoro‐o‐Xylene

J. Jonas

J. Chem. Phys. 47, 4884 (1967); http://dx.doi.org/10.1063/1.1701732 (5 pages) | Cited 5 times

Online Publication Date: 3 May 2004

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The F☒F coupling constants between the ortho‐ring fluorines and the fluorines of the CF3 group were measured at different temperatures in perfluoro‐o‐xylene and some related compounds. The rotationally averaged coupling constants calculated by using the approximate dependence of the JFF upon the dihedral angle between the C☒F bond of the CFX2 group and that of the 2‐fluorine atom are in good agreement with the observed values. Qualitative conclusions about the conformational behavior of two adjacent CF3 groups were supported by calculations of repulsion energies between the fluorine atoms in these groups using a simple van der Waals repulsive potential. It is proposed that the small temperature dependence of the JFF in the compounds studied is due to intermolecular interactions.

Optical Birefringence in Alkali Halides

C. F. Squire and E. R. Zamecki

J. Chem. Phys. 47, 4888 (1967); http://dx.doi.org/10.1063/1.1701733 (3 pages) | Cited 4 times

Online Publication Date: 3 May 2004

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Experiments on a number of alkali halide single crystals of high purity and optical quality have shown evidence of small birefringence properties. These crystals have been found to have a small paramagnetic uniaxial anisotropy when studied with a delicate torsion pendulum technique and the magnetic centers were assigned to dislocations oriented in great number along the 〈100〉 direction. The present optical study suggests that the optical‐anisotropy‐producing defects also may be aligned with the 〈100〉 direction.

Determining Hydrogen Diffusion in Doped Fused Silica from the Fluorescence

E. A. Weaver, R. W. Heckman, and E. L. Williams

J. Chem. Phys. 47, 4891 (1967); http://dx.doi.org/10.1063/1.1701734 (5 pages)

Online Publication Date: 3 May 2004

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Fused silica doped with both Tb and Eu exhibits a visible fluorescent green band under ultraviolet light after a heat treatment above 700°C in a hydrogen atmosphere. The growth kinetics of this band have been studied as a function of time, temperature, and hydrogen pressure in the temperature range of 700°—1050°C, and have been found to be a hydrogen diffusion‐controlled reaction. From these measurements and using tritium, diffusion coefficients have been evaluated, and in the temperature range of 850°—1040°C can be represented by the relation: D=6.5×10−5 exp(−12.5 kcal mole−1/RT)cm2sec.−1 The mechanism of the fluorescent scheme is believed to be a reduction of the Eu3+ ion to Eu2+ ion by the diffusing hydrogen, with the reduced ion being able to absorb light. This is followed by an energy transfer to the trivalent terbium ion, and then a terbium fluorescence.

Perturbed Orbital Energies in the Radiolysis of Saturated Hydrocarbons

Moon‐Tak So and Suei‐Rong Huang

J. Chem. Phys. 47, 4896 (1967); http://dx.doi.org/10.1063/1.1701735 (6 pages)

Online Publication Date: 3 May 2004

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In the combination of two saturated hydrocarbon radicals forming a new bond, a perturbed orbital energy will arise. This energy is equivalent to the energy necessary to decompose the product molecule into the two original radicals. By comparing perturbed orbital energies, it is possible to predict the decomposition products of irradiated molecules. The secular equations derived are solved using the LCBO molecular‐orbital approximations. Theoretical predictions of radiolytic decomposition products, based on the calculated perturbed orbital energies, are then compared with experimental G values. The agreement between theory and experiment is satisfactory.

Electronic Structure of Hexaquometal Ions. III. Magnetic Measurements

Richard L. Carlin and Emanuel G. Terezakis

J. Chem. Phys. 47, 4901 (1967); http://dx.doi.org/10.1063/1.1701736 (6 pages) | Cited 4 times

Online Publication Date: 3 May 2004

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Magnetic measurements obtained by the Gouy method are reported over a temperature range (77°—300°K) for hexahydrated trivalent ions of titanium and vanadium, and estimates of trigonal field parameters are presented. Measurements on C(NH2)3V(SO4)2⋅6H2O to 1.96°K on a pendulum magnetometer confirm the ground state in this compound as 3A (3T1g). The correlation of these studies with earlier spectral results is discussed. It is also shown that V(urea)6Br3 exhibits magnetic behavior similar to that of the hydrates, and that C(NH2)3Cr(SO4)2⋅6H2O is magnetically normal.

Coalescence Conditions as Constraints in Open‐Shell SCF Theory

D. P. Chong

J. Chem. Phys. 47, 4907 (1967); http://dx.doi.org/10.1063/1.1701737 (3 pages) | Cited 16 times

Online Publication Date: 3 May 2004

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The general coalescence conditions of Pack and Byers Brown are applied to the special case of electron—nucleus coalescence for SCF orbitals in atoms and molecules. Integral coalescence conditions are derived and then used to construct constraints for the variation of the orbitals. The constrained variation leads to new pseudo‐eigenvalue equations, which may be solved by combining the methods of parametrization and perturbation.

Ground‐State Reduced Potential Curve (RPC) and the Anomaly of Cl2

F. Jenč

J. Chem. Phys. 47, 4910 (1967); http://dx.doi.org/10.1063/1.1701739 (7 pages) | Cited 8 times

Online Publication Date: 3 May 2004

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The study of ground‐state reduced potential curves indicates that either there is some error in the analysis of the spectrum and/or in the values of molecular constants of the Cl2 molecule or a nonnegligible perturbation of the ground state of Cl2 exists. In case the analysis of the spectrum and the values of the molecular constants are correct, the RPC method then leads to the following conclusion: The perturbation of the electronic states of halogens, predicted in order to explain the remarkably anomalous intensities of the band spectra, is, in I2, of the type proposed by Van Vleck whereas, for Cl2, the interpretation suggested by Mulliken holds.

Deviations from Pairwise Additivity in Intermolecular Potentials

D. R. Williams, L. J. Schaad, and J. N. Murrell

J. Chem. Phys. 47, 4916 (1967); http://dx.doi.org/10.1063/1.1701740 (7 pages) | Cited 44 times

Online Publication Date: 3 May 2004

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The various contributions to the interaction energy as defined in the theory of intermolecular forces in the region of small orbital overlap [J. N. Murrell, M. Randic, and D. R. Williams, Proc. Roy. Soc. (London) A284, 566 (1965)] are generalized to many‐body systems. Each contribution is examined in a qualitative manner for deviations from pairwise additivity. Numerical calculations of the exchange energy for three helium atoms in triangular and linear arrays are made utilizing the available expansions of Slater‐type orbitals in terms of a Gaussian set. The nonadditive terms for these energies are then calculated over a range of interacting distances. It is concluded that for weakly interacting nonpolar molecules nonpairwise additive terms in the intermolecular potential are likely to be small.

Quantum Statistics and Slow Neutron Scattering by Gases

J. P. Plummer, G. C. Summerfield, and P. F. Zweifel

J. Chem. Phys. 47, 4923 (1967); http://dx.doi.org/10.1063/1.1701741 (7 pages)

Online Publication Date: 3 May 2004

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A surprisingly simple expression in ``closed form'' for the cross section d2σ/dΩdϵ for the scattering of thermal neutrons (including polarized neutrons) from an ideal quantum gas is derived. This result extends the work of Van Hove on the quantum gas. An expansion is obtained for dσ/dϵ. The case of elastic scattering is treated separately. From these expressions is obtained a criterion for ignoring the statistics of the scatterer in favor of classical (Boltzmann) statistics. This criterion should have some validity for weakly interacting systems. It is shown that the effects of statistics on the neutron cross section for a helium‐4 gas range from 5% or less for the noninteracting gas up to as much as 40% for the interacting system.

Strengths, Widths, and Shapes of the Lines of the 3ν CO Band

Darrell E. Burch and David A. Gryvnak

J. Chem. Phys. 47, 4930 (1967); http://dx.doi.org/10.1063/1.1701742 (11 pages) | Cited 12 times

Online Publication Date: 3 May 2004

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Spectral curves of several CO samples have been used to investigate the 3ν band whose center is near 6350 cm−1. The strength of the band for the common 12C16O isotope has been found to be 0.0130±0.0005 atm−1⋅cm−1STP⋅cm−1. An empirical equation, Fm=1+0.011m, has been derived to account for the influence of vibration—rotation on line strengths. The half‐widths of the self‐broadened lines at 1 atm pressure vary from approximately 0.090 cm−1 at ∣ m ∣ = 1 to 0.062 cm−1 at ∣ m ∣ = 20. The widths of self‐broadened lines are 1.08±0.005 times as great as N2‐broadened lines at the same pressure. The Lorentz line shape appears to be appropriate for the collision‐broadened lines within a few cm−1 of their centers; but the extreme wings of the lines are sub‐Lorentzian.

Far‐Infrared Spectra of Ring Compounds. II. The Spectrum and Ring‐Puckering Potential Function of Cyclopentene

Jaan Laane and R. C. Lord

J. Chem. Phys. 47, 4941 (1967); http://dx.doi.org/10.1063/1.1701743 (5 pages) | Cited 84 times

Online Publication Date: 3 May 2004

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The infrared spectrum of cyclopentene has been recorded in the range 18–300 cm−1. Two series of thirteen and nine Q branches, respectively, were observed, both of which arise from the strongly anharmonic energy levels of the B1 ring‐puckering vibration. The longer, more intense series is assigned to molecules in the ground vibrational state of all the other vibrations, and the shorter, weaker series to molecules in the first excited state of the A2 ring‐twisting vibration. Each set of Q branches can be fitted to transitions between the energy levels of a double‐minimum potential function of the form V=a(x4—bx2), where x is the B1 ring‐puckering coordinate. The height of the barrier opposing planarity is calculated to be 232±5 cm−1, and the equilibrium angle between the two dihedral planes of the puckered ring to be 23.3°±1°.

F‐Aggregate Centers in Sodium Fluoride. I

Karl Konrad and Theodore J. Neubert

J. Chem. Phys. 47, 4946 (1967); http://dx.doi.org/10.1063/1.1701744 (5 pages) | Cited 23 times

Online Publication Date: 3 May 2004

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Thermal aggregation of color centers in a sample of NaF, x irradiated 67 h at 200°K, was studied by observation of the optical‐absorption spectrum during warming. At 200°K, a very intense F′ band (470 mμ) is formed and obscures the M1 band of any M centers which may be present. During warming the F′ band decreases to half‐intensity at 280°K but some remains even at 320°K. M centers begin to appear at ∼270°K, preceded by the appearance of a band at 725 mμ which forms and then thermally bleaches. The 725‐mμ band is assigned to M+ centers resulting from capture of α centers by F centers. R+ centers (λ=max520 mμ) are also observed to form during warming. Thermal aggregation to yield M centers is not nearly as extensive in NaF as in KCl, nor does the M1 band grow on standing in the dark at room temperature. Bleaching the sample with F‐band light at room temperature produced large R1, R2, R+, and M1 bands as well as six smaller bands (576, 604, 630, 736, 870, and 1040 mμ), measured at 65°K. Zero‐phonon lines are associated with the R2, R+, 604‐, 870‐, and 1040‐mμ bands. Additional experiments on samples containing M+ centers indicate that the M+ band exhibits a dichroism parallel to that of the M1 band and may be bleached at low temperature by x‐ray‐released electrons. The M+‐band maximum shifts from 726 mμ (273°K) to 736 mμ (80°K) as temperature is decreased, while the half‐width (0.18 eV at 80°K) behaves in the usual way.

Proton Magnetic Resonance Coordination‐Number Study of AlCl3 in Aqueous Mixtures of Acetone, N,N‐Dimethylformamide, Dimethylsulfoxide, Dioxane, Tetrahydrofuran, and Tetramethylurea

Anthony Fratiello, Robert E. Lee, Vone M. Nishida, and Ronald E. Schuster

J. Chem. Phys. 47, 4951 (1967); http://dx.doi.org/10.1063/1.1701745 (5 pages) | Cited 22 times

Online Publication Date: 3 May 2004

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The coordination number of Al(III) in aqueous mixtures of acetone, dimethylformamide, dimethylsulfoxide, dioxane, tetrahydrofuran, and tetramethylurea was measured over a range of solvent concentrations by a proton magnetic resonance technique. At low temperatures, proton exchange is slowed to such an extent in these mixtures that separate resonance signals are observed for bulk water and water molecules in the Al(III) solvation shell. Coordination numbers were measured by direct integration of the two water signals. The measurements show that in aqueous mixtures of acetone and tetramethylurea, and over a small solvent concentration range, dioxane and tetrahydrofuran, only water solvates Al(III). This was indicated by the value of six molecules obtained for the contribution of water to the Al(III) solvation shell in these mixtures. In aqueous mixtures of dimethylformamide and dimethylsulfoxide, wherein separate signals were also observed for the nonaqueous components, both solvents contribute to the Al(III) solvation shell. No evidence for ion pairing was found in any of the mixtures.

Magnetic‐Field Deflection of XeF6

R. F. Code, W. E. Falconer, W. Klemperer, and I. Ozier

J. Chem. Phys. 47, 4955 (1967); http://dx.doi.org/10.1063/1.1701746 (4 pages) | Cited 12 times

Online Publication Date: 3 May 2004

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The deflection of a molecular beam of XeF6 has been measured in an inhomogeneous magnetic field. From the similarity of the deflection of XeF6 and SF6 and the difference with the deflection of O2 it is concluded that gaseous XeF6 at room temperature does not contain a paramagnetic component greater than ∼1% in abundance. This conclusion is not consistent with Goodman's hypothesis that a low‐lying 3Tu state of XeF6 is appreciably populated at room temperature.

Statistical‐Mechanical Derivation of the Partial Molecular Stress Tensors in Isothermal Multicomponent Systems

Fred M. Snell, Ruth Aranow, and Robert A. Spangler

J. Chem. Phys. 47, 4959 (1967); http://dx.doi.org/10.1063/1.1701747 (13 pages) | Cited 15 times

Online Publication Date: 3 May 2004

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Commencing with the general equations of molecular dynamics as used by Bearman and Kirkwood, the hydrodynamic equations of motion are derived for each component in an isothermal multicomponent system consisting of sensibly spherical nonreacting molecules. It was the primary purpose of the investigation of which this is a report to attempt to obtain a microscopic statistical basis for the macroscopic phenomenologic development of Snell and Spangler, especially in regard to their new formulation for the partial molecular stress tensors. An expansion of the number densities in pair space of perturbed nonequilibrium states alternate to that used by Bearman and Kirkwood is employed. Our expansion esplicitly recognizes the position vector arguments of both the number densities in singlet space and the local mean velocities of the individual components, as well as for the equilibrium pair correlation function. The quantities are then expanded about the central position vector in a Taylor's series. The results are not only corroborative of the previous phenomenologic development when the flows of the individual components are solenoidal and attention is confined to systems in which the kinetic contribution to the stress tensor is negligible in comparison to the contribution arising from intermolecular interaction, but they also provide a new microscopic theory of hydrodynamical flow in multicomponent systems.

Theoretical Calculation of the Potential Curves of the Be2 Molecule

Charles F. Bender and Ernest R. Davidson

J. Chem. Phys. 47, 4972 (1967); http://dx.doi.org/10.1063/1.1701748 (7 pages) | Cited 82 times

Online Publication Date: 3 May 2004

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The low‐lying electronic states of the Be2 molecule have been examined using MO SCF CI with a basis set of elliptical orbitals. The ground state of the molecule was found to be repulsive in the best calculation. The excited states all seem to be bound with potential curves similar to that predicted for Be2+. Two new techniques for improving the convergence of configuration interaction are introduced and applied to the ground‐state calculation.

Kinetic Theory of Polyatomic Gases

Richard S. C. She and Norman F. Sather

J. Chem. Phys. 47, 4978 (1967); http://dx.doi.org/10.1063/1.1701749 (16 pages) | Cited 4 times

Online Publication Date: 3 May 2004

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A classical‐mechanical kinetic theory of dilute gases is developed for molecules with arbitrary degrees of freedom and interacting according to an arbitrary potential. The Boltzmann equation for the truncated singlet distribution function is derived by application of a general form of the divergence theorem, and the equilibrium solution is obtained from an H theorem for the fluid. The solution of the Boltzmann equation by a procedure of the Chapman—Enskog type is described for the case of molecules having translational and rotational degrees of freedom. Formulas for the transport properties of the gas are obtained in the form of multidimensional integral functionals of the intermolecular potential function.

Vapor Pressure of Holmium

G. F. Wakefield, A. H. Daane, and F. H. Spedding

J. Chem. Phys. 47, 4994 (1967); http://dx.doi.org/10.1063/1.1701750 (6 pages) | Cited 2 times

Online Publication Date: 3 May 2004

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The vapor pressure of holmium was measured from 10−8 to 101 torr using modifications of the Langmuir and Knudsen methods. A tube‐type orifice permitted use of the Knudsen method at the higher pressures, with suitable corrections. Lowest pressures were measured using a graphite condenser surrounding a large area Langmuir sample, with the vaporized metal being trapped as the nonvolatile carbide. The vapor pressure of the solid α‐holmium is given by logPtorr=(−15 137/T°K)+8.426, and the vapor pressure of the liquid by logPtorr=(−14 122/T°K)+7.849. The heat of vaporization and heat of sublimation (298°K) were 64.7±0.5 and 70.6±0.7 kcal/mole, respectively. The enthalpy change from α‐solid to liquid holmium, corresponding to heats of fusion and transformation, was 4.6±0.7 kcal/mole.

Paramagnetic Relaxation of Trapped Hydrogen Atoms in Irradiated Frozen Aqueous Solutions

John Zimbrick and Larry Kevan

J. Chem. Phys. 47, 5000 (1967); http://dx.doi.org/10.1063/1.1701751 (9 pages) | Cited 16 times

Online Publication Date: 3 May 2004

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The paramagnetic relaxation characteristics of trapped hydrogen atoms in γ‐irradiated acidic and oxyanion ices were studied by power‐saturation techniques. Relaxation times were measured as a function of radiation dose, deuteration, phase, and solute. The EPR linewidth of the trapped hydrogen atom was measured under various conditions. The EPR lineshape and power‐saturation response indicate that the linewidth is due to contributions from both homogeneous and inhomogeneous interactions. The changes in relaxation time with radiation dose indicate that hydrogen atoms are trapped with a uniform distribution near oxyanions in the ice and are not trapped within radiation‐produced spurs. The presence of phase effects on relaxation times supports an interstitial‐defect model for the hydrogen‐atom trapping site and suggests that the trap potential energy well is shallower in the polycrystalline phase than in the glassy phase. In polycrystalline ices the coupling between trapped hydrogen atoms and lattice phonons is modified by the type of oxyanion.

Polymer Relaxation Times from Birefringence Relaxation Measurements

Douglas S. Thompson and Stanley J. Gill

J. Chem. Phys. 47, 5008 (1967); http://dx.doi.org/10.1063/1.1701752 (10 pages) | Cited 17 times

Online Publication Date: 3 May 2004

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A theoretical description of the time dependence of induced birefringence in polymers, based on the ``pearl‐necklace'' model, is presented, and relations between relaxation and frequency dependence methods are discussed. The relaxation theory is applied to the results of measurements of the longest relaxation time for the DNA from bacteriophage T2. The measured relaxation time, in the limit of infinite dilution, is τ1=0.45 sec. The molecular weight calculated from this value using the theoretical expression for a nondraining coil with excluded volume is in good agreement with the value of the molecular weight obtained from low‐shear intrinsic viscosity measurements.

Near‐Infrared Band Progressions of Ring Molecules and Ring‐Puckering Motion

Toyotoshi Ueda and Takehiko Shimanouchi

J. Chem. Phys. 47, 5018 (1967); http://dx.doi.org/10.1063/1.1701753 (13 pages) | Cited 55 times

Online Publication Date: 3 May 2004

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A series of bands found in the 2900–2600‐cm−1 region of infrared spectra of 2,5‐dihydrofuran, trimethylene oxide, cyclopentene, 2,5‐dihydrothiophene, 2,3‐dihydrofuran and 2,3‐dihydrothiophene are assigned to the ring‐puckering difference spectra, of which the reference band is the CH2 symmetrical stretching vibration.
The assignments were confirmed for 2,5‐dihydrofuran and trimethylene oxide, for which the pure ring‐puckering bands had already been analyzed in detail. From the difference spectra the puckering potential of cyclopentene was determined as V(Z) = 0.551×104Z2+0.533×106Z4+0.554×103exp(−100Z2) with the central barrier of 244.6 cm−1, and that of 2,5‐dihydrothiophene was V(Z) = 0.1396×105Z2+0.6637×106Z4, where V is in cm−1 and Z is in angstroms.
The spectrum showed that 2,3‐dihydrofuran has the nonplanar structure with the potential barrier height of about 86.8 cm−1. For 2,3‐dihydrothiophene tentative assignments were given and the puckering potential was calculated.

Infrared Spectrum, Force Constants, and Thermodynamic Functions of SiF2

V. M. Khanna, R. Hauge, R. F. Curl, and J. L. Margrave

J. Chem. Phys. 47, 5031 (1967); http://dx.doi.org/10.1063/1.1701755 (7 pages) | Cited 13 times

Online Publication Date: 3 May 2004

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The infrared spectrum of gaseous SiF2 has been recorded from 1050 to 400 cm−1. Two bands centered at 872 and 855 cm−1 are, respectively, assigned to the antisymmetric stretching (ν3) and symmetric stretching (ν1) frequencies of the molecule. The symmetric bending frequency (ν2) as determined from the earlier ultraviolet absorption studies lies at 345 cm−1 and could not be observed because this was well below the low‐frequency limit of the spectrometer used. The observed vibrational frequencies are combined with the available microwave data to obtain the following values of the quadratic force constants:fr=5.019 mdyn/Å, frr=0.310 mdyn/Å, fα/r2=0.440 mdyn/Å, fαr/r=0.123 mdyn/Å. Two cubic potential constants have been evaluated, K222=−9.5 cm−1 and K122=9.9 cm−1. The average structure of SiF2 in its ground state is computed and found to be 〈r〉=1.5947 Å, 〈α〉=100°53′, where r is the Si☒F bond distance and α the F☒Si☒F angle. A table of thermodynamic functions of SiF2 is presented.

Signs of Spin—Spin Coupling Constants between Methyl Protons and Ring Fluorine Nuclei in Fluorotoluene Derivatives. Further Evidence for a Positive Hyperfine Interaction in the C☒F Bond

D. J. Blears, S. S. Danyluk, and T. Schaefer

J. Chem. Phys. 47, 5037 (1967); http://dx.doi.org/10.1063/1.1701756 (6 pages) | Cited 8 times

Online Publication Date: 3 May 2004

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The signs of spin—spin coupling constants between the methyl protons and fluorine nuclei in ortho, meta, and para fluorotoluene derivatives have been determined by double‐resonance techniques. J0F,CH3 and JpF,CH3 are positive, while JmF,CH3 is negative. This sign sequence is opposite to that of the corresponding methyl proton‐ring proton couplings and is the consequence of a positive hyperfine coupling constant in the C☒F bond. This result implies that double‐bond character in the C☒F bond entails an additional σ—π interaction overshadowing that expected by analogy with the C☒H bond. Sizeable negative π contributions to J0HF and JpHF are indicated by the experimental results.
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