Showing papers in "Journal of Chemical Physics in 1956"
TL;DR: In this paper, a mechanism for electron transfer reactions is described, in which there is very little spatial overlap of the electronic orbitals of the two reacting molecules in the activated complex, and a quantitative theory of the rates of oxidation reduction reactions involving electron transfer in solution is presented.
Abstract: A mechanism for electron transfer reactions is described, in which there is very little spatial overlap of the electronic orbitals of the two reacting molecules in the activated complex. Assuming such a mechanism, a quantitative theory of the rates of oxidation‐reduction reactions involving electron transfer in solution is presented. The assumption of "slight‐overlap" is shown to lead to a reaction path which involves an intermediate state X* in which the electrical polarization of the solvent does not have the usual value appropriate for the given ionic charges (i.e., it does not have an equilibrium value). Using an equation developed elsewhere for the electrostatic free energy of nonequilibrium states, the free energy of all possible intermediate states is calculated. The characteristics of the most probable state are then determined with the aid of the calculus of variations by minimizing its free energy subject to certain restraints. A simple expression for the electrostatic contribution to the free energy of formation of the intermediate state from the reactants, ΔF*, is thereby obtained in terms of known quantities, such as ionic radii, charges, and the standard free energy of reaction.
This intermediate state X* can either disappear to reform the reactants, or by an electronic jump mechanism to form a state X in which the ions are characteristic of the products. When the latter process is more probable than the former, the over‐all reaction rate is shown to be simply the rate of formation of the intermediate state, namely the collision number in solution multiplied by exp(—ΔF*/kT). Evidence in favor of this is cited. In a detailed quantitative comparison, given elsewhere, with the kinetic data, no arbitrary parameters are needed to obtain reasonable agreement of calculated and experimental results.
5,265 citations
TL;DR: In this paper, the authors considered the problem of diffusing a chain molecule diffusing in a viscous fluid under the influence of external forces or currents, and calculated the viscosity, birefringence of flow, and dielectric and tensile relaxation behavior explicitly.
Abstract: The problem of the motions of a chain molecule diffusing in a viscous fluid under the influence of external forces or currents is considered for a particular model. This model is a chain of beads connected by ideal springs. Hydrodynamic interaction between the beads is introduced in the approximate form due to Kirkwood and Riseman. It is possible to solve this problem exactly with the use of a transformation to a set of normal coordinates. The viscosity, birefringence of flow, and dielectric and tensile relaxation behavior are calculated explicitly. The intrinsic viscosity in steady flow is somewhat different from the Kirkwood‐Riseman result, and there is no change of viscosity with shear rate. The spectrum of relaxation times is similar to that found by Rouse and by F. Bueche, but has its maximum at a lower frequency than those obtained by Kuhn and Kuhn and by Kirkwood and Fuoss in other ways.
2,110 citations
TL;DR: In this paper, spectra of heavy water have been obtained under high resolution between 1.25-4.1μ (2400-8000 cm-1) and approximately 4500 lines have been measured, and the majority of them analyzed into ten bands of D2O and nine bands of HDO.
Abstract: Spectra of heavy water have been obtained under high resolution between 1.25—4.1μ (2400—8000 cm—1). Approximately 4500 lines have been measured, and the majority of them analyzed into ten bands of D2O and nine bands of HDO. The analysis is described in some detail, spectra of all bands are shown and a partial table of lines and a complete table of energy levels are presented. The vibration‐rotation constants are derived and compared with those of H2O.
1,234 citations
TL;DR: In this paper, a model for calculating rate constants of processes which narrow nuclear magnetic resonance absorption lines having discrete components is presented for calculating the free energy of activation required for reorientations about the C-N amide bond.
Abstract: Mathematical methods are presented for calculating rate constants of processes which narrow nuclear magnetic resonance absorption lines having discrete components. High resolution proton spectra show that the R1CO‐NR2R3 skeletons of N,N‐dimethylformamide (DMF) and N,N‐dimethylacetamide (DMA) are planar and suggest that N‐methylformamide, N‐methylacetamide, N‐methylformanilide and N‐methylacetanilide exist predominantly in one configuration. The presence of a significant amount of double bond character in the C–N amide bond is proved by the temperature dependent coalescence observed for the chemically shifted proton doublet of the N(CH3)2 groups in DMF and DMA, which gives values of about 22 and 19 kcal respectively for the free energy of activation required for reorientations about the bond.
1,040 citations
TL;DR: In this paper, a previously given theory of the electronic spectra and structure of complex unsaturated molecules is further elucidated by listing specific formulas for the charge density, bond order, transition moment, and configuration interaction matrix elements.
Abstract: A previously given theory of the electronic spectra and structure of complex unsaturated molecules is further elucidated by listing specific formulas for the charge density, bond order, transition moment, and configuration interaction matrix elements.The theory is then applied to give a number of simple rules for alternant hydrocarbons. These refer to the energies of the singly excited states and the effects of configuration interaction, the degeneracy between certain singlet and triplet states, the prohibition of certain electronic transitions which would be allowed from a group theoretical point of view, and the charge density distribution of the ground and singly excited states. A mechanism is proposed to explain some of the anomalously rapid singlet‐triplet radiationless transitions which are observed in connection with studies of the lower triplet states of complex molecules.Quantitative application of the theory is made to the spectra of the polyacenes, benzene through pentacene, and to the bond ord...
964 citations
TL;DR: In this paper, the free energy, energy, and entropy of a nonequilibrium system were derived for various properties of systems having such electrostatic configurations, including the spacial dependence of the electrostatic potential.
Abstract: Various processes such as electron transferreactions, redox reactions at electrodes, and electronic excitation of dissolved ions may proceed by way of intermediate states whose electrical polarization is not in equilibrium with the field arising from the charges present. The usual expressions for the electrostatic-free energy and for the differential equation satisfied by the potential assume that the polarization and the field are in equilibrium. Accordingly, these equations are of but limited applicability to these processes. In the present paper equations are derived for various properties of systems having such nonequilibrium electrostatic configurations. These properties include the free energy, energy, and entropy of the nonequilibrium system, and the spacial dependence of the electrostatic potential. The free energy, for example, will be used to calculate the probability of formation of nonequilibrium states in certain problems of physical interest.
921 citations
TL;DR: In this article, a scalar term AI·S resulting from the indirect electron-coupled interaction between the two nuclei removes all the discrepancies between the calculated and observed decay times.
Abstract: Magnetic relaxation times of hydrogen and fluorine in anhydrous hydrofluoric acid cannot be accounted for on the assumption of a pure dipole‐dipole interaction between the hydrogen and the fluorine nuclei in the same molecule. However, the introduction, in the Hamiltonian, of a scalar term AI·S resulting from the indirect electron‐coupled interaction between the two nuclei removes all the discrepancies between the calculated and observed decay times. Although the splitting due to this scalar term is smeared out by the rapid chemical exchange of the protons with the traces of water present in the acid, the nuclear Overhauser effect provides the extra parameter required to separate the dipole‐dipole interaction from the scalar interaction and to calculate separately the scalar splitting and the exchange rate of the protons. The value obtained for the splitting is A/h=615 cps.The same method has been applied to investigate the structure of the HF molecule in solutions. The experimental results can be explain...
617 citations
TL;DR: In this article, it was shown that an electron spin polarization associated with an odd electron in a molecular orbital in an aromatic free radical can, through an atomic exchange coupling mechanism, produce an appreciable resultant electron spin polarisation in s−atomic orbitals at the aromatic protons.
Abstract: It is shown that an electron spin polarization associated with an odd electron in a π‐molecular orbital in an aromatic free radical can, through an atomic exchange coupling mechanism, produce an appreciable resultant electron spin polarization in s‐atomic orbitals at the aromatic protons. This resultant spin polarization gives rise to hyperfine interactions with aromatic protons which are of the same order of magnitude as those observed in the paramagnetic resonance spectra of aromatic free radicals. An equation is developed which relates (proton‐spin)‐(electron‐spin) hyperfine coupling constants to the π distribution of the odd electron in the aromatic free radicals.
601 citations
TL;DR: In this paper, a chart is given which shows a systematic relation of electronegativity to the periodic system of the elements, and a linear relationship is found between electrone gativity and the work function of metals.
Abstract: Electronegativity values derived from various methods are compared, and a complete electronegativity scale is arranged for all the elements. A chart is given which shows a systematic relation of electronegativity to the periodic system of the elements. A linear relationship is found between electronegativity and the work function of metals.
584 citations
TL;DR: In this paper, the potential energy of graphite lattice summations of importance in the graphite system have been computed by direct summation assuming a Lennard-Jones 6-12 potential between carbon atoms.
Abstract: The lattice summations of the potential energy of importance in the graphite system have been computed by direct summation assuming a Lennard‐Jones 6–12 potential between carbon atoms. From these summations, potential energy curves were constructed for interactions between a carbon atom and a graphite monolayer, between a carbon atom and a graphite surface, between a graphite monolayer and a semi‐infinite graphite crystal and between two graphite semi‐infinite crystals. Using these curves, the equilibrium distance between two isolated physically interacting carbon atoms was found to be 2.70 a, where a is the carbon‐carbon distance in a graphite sheet. The distance between a surface plane and the rest of the crystal was found to be 1.7% greater than the interlayer spacing. Theoretical values of the energy of cohesion and the compressibility were calculated from the potential curve for the interaction between two semi‐infinite crystals. They were ΔEc = —330 ergs/cm2 and β = 3.18×10—12 cm2/dyne, respectively...
524 citations
TL;DR: In this paper, it was shown that for every transition in its individual residues, a helix has two transitions whose moments are respectively parallel and perpendicular to the screw axis, and that the largest contributions to the rotational strengths of these bands are equal and opposite in the two cases.
Abstract: It is shown that for every transition in its individual residues, a helix has two transitions whose moments are respectively parallel and perpendicular to the screw axis. The largest contributions to the rotational strengths of these bands are equal and opposite in the two cases. As a result, their net effect on the optical activity contains a term proportional to the interval between the two upper states. This term shows abnormal dispersion and its magnitude and sign are more easily interpreted than any other component of the rotatory power.
TL;DR: In this article, a method is proposed whereby an expression for the kinetics of an electrode reaction containing any number of intermediate steps may be obtained, and the method is applied to five paths for the electrolytic evolution of oxygen at anodes and yields limiting expressions for the dependence of the current density (or rate) of the reaction upon electrode potential which are diagnostic of the various rate controlling steps assumed.
Abstract: The kinetics of activation controlled electrode reactions differ from those of chemical kinetics by the potential dependence of the rate constant of a step involving charge transfer and the constancy of concentration of reactants in the initial state. A method is proposed whereby an expression for the kinetics of an electrode reaction containing any number of intermediate steps may be obtained.The method is applied to five paths for the electrolytic evolution of oxygen at anodes and yields limiting expressions for the dependence of the current density (or rate) of the reaction upon electrode potential which are diagnostic of the various rate controlling steps assumed. If discharge of OH′ or H2O molecules is rate determining, the Tafel slope is 2RT/F at overpotentials > 50 mv. If some other reaction involving charge transfer is rate determining, two possible Tafel slopes, each independent of potential in its range of applicability, occur, depending upon degree of coverage of the electrode with intermediate...
TL;DR: In this article, the spectral properties of monosubstituted amides and their corresponding deuterated compounds have been determined from the experimental results, and from the comparison with the spectra of related substances, the assignments of these characteristic bands have been made.
Abstract: Infrared spectra of various monosubstituted amides and the corresponding deuterated compounds have been measured in the gaseous, liquid, and crystalline states and in solutions. From the experimental results, the bands characteristic of the amide structure have been determined. Furthermore, from the comparison with the spectra of related substances and by the application of the product rule, the assignments of these characteristic bands have been made. The observed change of frequencies of these characteristic bands with change of state confirms this assignment.
TL;DR: In this paper, the assignment of the controversial CH2 wagging mode is discussed in detail and especially in terms of new evidence from the spectra of n-paraffins, both as single crystals and as polycrystalline aggregates.
Abstract: The infrared spectrum of polyethylene has been obtained between about 3000 cm—1 and 70 cm—1, polarization measurements on oriented specimens having been obtained to about 350 cm—1. Assignments of the fundamentals are made with the help of a group theory analysis. The assignment of the controversial CH2 wagging mode is discussed in detail and especially in terms of new evidence from the spectra of n‐paraffins, both as single crystals and as polycrystalline aggregates. It is shown that this mode is to be assigned to a weak band at 1369 cm—1. A satisfactory determination of the bands which arise from CH3 groups is also made possible by a study of the paraffin spectra. The splitting of bands in the spectrum is conclusively shown to arise from interactions between molecules in the crystalline phase. The nature of this interaction is discussed in terms of recent theories.
TL;DR: The crystal structure of gadolinium orthoferrite, GdFeO3, has been determined from single-crystal x-ray data as discussed by the authors, and the structure is solved on the basis that the most probable space group is D2h(16)-Pbnm.
Abstract: The crystal structure of gadolinium orthoferrite, GdFeO3, has been determined from single‐crystal x‐ray data. There are four GdFeO3 distorted perovskite units in the orthorhombic cell with lattice constants a=5.346, b=5.616, c=7.668, all ±0.004 A. The structure is solved on the basis that the most probable space group is D2h(16)— Pbnm. However, although the atomic coordinates lead to very good agreement between calculated and observed reflection amplitudes, there are at least very slight deviations from the centrosymmetric space group because the iron sublattices are imperfectly antiferromagnetic.
TL;DR: In this paper, a simple microcrystalline model was developed to discuss the effect of molecular motion in the liquid state on the paramagnetic relaxation of ions or molecules with spin S = ½.
Abstract: A simple ``microcrystalline model'' is developed to discuss the effect of molecular motion in the liquid state on the paramagnetic relaxation of ions or molecules with spin S = ½. This theory relates the paramagnetic relaxation times T1 and T2′ to the anisotropy in g, Δg = gII — g⊥, to the anisotropy in the nuclear hyperfine interaction, A–B, and to the correlation time τc which describes the Brownian tumbling motion of the microcrystal in the liquid state. The contribution of the anisotropic hyperfine interaction to the paramagnetic relaxation turns out to depend on the nuclear spin quantum number Iz, so that different hyperfine multiplets in a paramagnetic resonance spectrum can show different line widths.
TL;DR: In this article, it is found that hydrogen is found to diffuse into and increase the conductivity of single ZnO crystals, and diffusion rates have been obtained, as well as the temperature and pressure dependencies of the quantity of hydrogen in the crystal.
Abstract: Hydrogen is found to diffuse into and increase the conductivity of single ZnO crystals. The diffusion rates have been obtained, as well as the temperature and pressure dependencies of the quantity of hydrogen in the crystal. This quantity is found to be influenced by the electrons already in the crystal. It is thought likely that hydroxyl groups are formed from the hydrogen and oxide ions. The donor center has an ionization energy of 0.04 ev.
TL;DR: In this paper, the authors make a quantitative distinction between the classical proton transfer, quantum-mechanical tunneling transfer, and water rotation as rate determining stages and show that if resonance in H3O· is set up sufficiently quickly after arrival of a given proton at a water molecule, rotation of H 3O· cannot be a rate determining step.
Abstract: Measurements of the conductance of HCl in water, methanol, ethanol, n‐propanol, ethylene glycol, glycerol, 1:4 dioxane, acetone, formic, and acetic acids and the respective aqueous‐nonaqueous systems have been made as a function of concentration of water and HCl. The degree of anomalous proton conductance decreases with increasing n in CnH2n+1OH, and conductance minima occur in aqueous alcoholic HCl solutions of low H2O content.Former theories of proton conductance have permitted no quantitative distinction to be made between the rates of classical proton transfer, quantum‐mechanical tunneling transfer, and water rotation as rate determining stages. If resonance in H3O· is set up sufficiently quickly after arrival of a given proton at a water molecule, rotation of H3O· cannot be a rate determining step.Detailed calculations of the rates of classical proton transfer, tunnel transfer, and the rate of rotation of water are made. Classical transfer is much slower and tunnel transfer much faster than correspon...
TL;DR: In this article, the Schwartz, Slawsky and Herzfeld method for the calculation of vibrational relaxation times of gases has been extended in its application to polyatomic molecules, and a general method is developed for calculating the effective relaxation times and the associated constants of the sound velocity relaxation equation.
Abstract: The Schwartz, Slawsky, and Herzfeld method for the calculation of vibrational relaxation times of gases has been extended in its application to polyatomic molecules. A general method is developed for the calculation of the effective relaxation times and the associated constants of the sound velocity relaxation equation. Calculations have been made for the bimolecular collisions of methane and the chloromethanes involving changes of one, two, and three quanta. A normal coordinate treatment is used to obtain the atomic vibrational amplitudes. The effect of an intermolecular potential function, embodying a dipole interaction term, is included for the polar molecules of this investigation.Calculated results are compared with experimental data. For CH4 and CH3Cl the calculations agree well with experimental results. For CH2Cl2, CHCl3, and CCl4 the calculated relaxation times are higher than selected experimental values by factors of 8–9. For CH2Cl2, CHCl3, and CCl4 two major relaxation times are calculated. In the case of CH2Cl2 the two relaxation areas have been observed. The experimental data on CHCl3 and CCl4 remain inconclusive in respect to the two predicted relaxation areas. Collisions involving three quanta are shown to be important for CH2Cl2, CHCl3, and CCl4.
TL;DR: In this article, the general formulas obtained by Ramsey for the indirect second-order magnetic coupling of nuclear spins by electron spin and orbital magnetic moments in 1Σ molecules are used together with an antisymmetrized product of molecular spin orbitals to obtain a set of general equations for nuclear spin couplings which only involve (a) the individual molecular orbitals, and (b) rotationally invariant one and two electron space operators.
Abstract: The general formulas obtained by Ramsey for the indirect second‐order magnetic coupling of nuclear spins by electron spin and orbital magnetic moments in 1Σ molecules are used together with an antisymmetrized product of molecular spin orbitals to obtain a set of general equations for nuclear spin couplings which only involve (a) the individual molecular orbitals, and (b) rotationally invariant one and two electron space operators. By approximating the molecular orbitals with linear combinations of atomic orbitals quite tractable formulas are obtained for ``long‐range'' nuclear spin‐spin couplings, i.e., couplings between nuclei separated by two, three, or more bond lengths. The application of these formulas are illustrated by the development of an approximate formula for proton‐proton coupling constants in terms of interproton bond orders, the application of this formula to methane, as well as some qualitative considerations of F19—F19 coupling constants in tetrafluoroethylene. In general nuclear spin cou...
TL;DR: In this paper, some properties of the zeta matrices which simplify the analytical treatment of vibration-rotation interaction are given, as well as methods of obtaining relationships among zeta elements which depend only on the atomic masses and geometry of the molecule.
Abstract: Some properties of the zeta matrices which simplify the analytical treatment of vibration‐rotation interaction are given. Methods of obtaining relationships among the zeta elements which depend only on the atomic masses and geometry of the molecule are outlined and some examples are discussed. Symmetry arguments are introduced to simplify the results further.
TL;DR: In this article, a linear correlation between X−H≡Y distance R and frequency shift of the X-H stretching motion Δv is presented for O−H−O, N−H ≥ O, and N−N≡N hydrogen bonds.
Abstract: Empirical correlations between X–H≡Y distance R and frequency shift of the X–H stretching motion Δv are presented for O–H≡O, N–H≡O, and N–H≡N hydrogen bonds. A linear correlation is possible provided a distinct straight line is assumed for each hydrogen bond type. The equations of the best straight lines and standard deviations are: O−H···O Δν(cm−1)=4.43·103(2.84−R) σ(Δν)=199cm−1N−H···O Δν(cm−1)=0.548·103(3.21−R)σ(Δν)=24cm−1N−H···N Δν(cm−1)=1.05·103(3.38−R) ?
TL;DR: In this article, a factor group analysis of the one-dimensional space group, selection rules and approximate vibrational patterns of the infrared active fundamentals have been derived from a calculated planar zigzag chain model of (CF2)n, resulting in a satisfactory assignment of the bands in the infrared spectra of both polymers.
Abstract: The infrared spectra of polytetrafluoroethylene and polychlorotrifluoroethylene have been obtained between 4000 cm—1 and 70 cm—1. Polarization measurements on oriented samples were obtained in the region of 4000 cm—1 to 300 cm—1. It is known from x‐ray diffraction studies that both polymers have helical chain configurations. From a factor group analysis of the one‐dimensional space group, selection rules and approximate vibrational patterns of the infrared active fundamentals have been derived. A calculation of the normal frequencies of an assumed planar zig‐zag chain model of (CF2)n has been made, resulting in a satisfactory assignment of the bands in the infrared spectra of both polymers.
TL;DR: The pi-electron approximation as discussed by the authors is defined to be the approximation in which the following two restrictions are imposed upon the total approximate electronic wave functions for some group of molecular states: (i) the wave function for each state satisfies the sigma-pi separability conditions: (ii) each of (Σ), (II), and Ψ is normalized to unity; (iii) each state is well behaved.
Abstract: The pi‐electron approximation is defined to be the approximation in which the following two restrictions are imposed upon the total approximate electronic wave functions for some group of molecular states:(I) The wave function for each state satisfies the sigma‐pi separability conditions: (A) the wave function has the form Ψ = [(Σ) (II)], where (Σ) and (II) are antisymmetrized functions describing the so‐called sigma and pi electrons, respectively, and the outer brackets connote antisymmetrization with respect to sigma‐pi exchange; (B) each of (Σ), (II), and Ψ is normalized to unity; (C) each of (Σ), (II), and Ψ is well‐behaved.(II) The sigma description is the same for all states.Imposition of these restrictions is shown to be sufficient to validate the customary procedure in which the pi electrons in a molecule are treated apart from the rest.A formula is given for the pi‐electron Hamiltonian to be used when the pi‐electron approximation is invoked. Present day pi‐electron theories are examined, and lin...
TL;DR: In this article, a general method for the analytical treatment of vibration-rotation interaction in polyatomic molecules is presented, especially adapted to carry out the calculation of the Coriolis coupling coefficients along with the normal coordinate treatment in terms of any chosen set of internal coordinates.
Abstract: A general method for the analytical treatment of vibration‐rotation interaction in polyatomic molecules is presented. The method is especially adapted to carry out the calculation of the Coriolis coupling coefficients along with the normal coordinate treatment in terms of any chosen set of internal coordinates. The relations existing among the ζ elements and the potential constants are established in a general and convenient form. Particular attention is given to symmetric top molecules, and the effect of vibration‐rotation interaction on band structure is discussed. Approximate methods for the calculation of zeta values are considered also.
TL;DR: In this article, the scintillation counting behavior of a group of fifty-five pure crystalline organic compounds has been extensively studied with the goal of developing a better understanding of the Scintillation process and of scintillator behavior.
Abstract: The scintillation counting behavior of a group of fifty‐five pure crystalline organic compounds has been extensively studied. The data obtained have been analyzed with the goal of developing a better understanding of the scintillation process and of scintillator behavior.The materials were carefully purified, and massive crystals were grown. Relative scintillation average‐pulse‐height efficiencies at 30°C and —70°C for cobalt‐60 gamma‐ray excitation, gamma‐ray excited scintillation decay times, and 2537 A ultraviolet‐excited reflection and transmission photofluorescence spectra have been determined. A few solutions were also studied for comparison purposes. The purification and properties of the different materials are discussed in detail.The experimental data have been analyzed on the basis of Birks' photon cascade theory of the scintillation process. The ratio of the scintillation efficiency to the integrated photofluorescence intensity is shown to be a measure of Birks' primary photon production effici...
TL;DR: The best values of the rotational constants B and C were found to be 10 542.7 and 5876.7 Mc/sec for CH3NO2 and 8697.1 and 5254.3 MC/sec respectively as discussed by the authors.
Abstract: The J = 1 to J = 2 and J = 2 to J = 3 transitions for CH3NO2 and CD3NO2 have been assigned for several internal rotational states. The best values of the rotational constants B and C were found to be 10 542.7 and 5876.7 Mc/sec for CH3NO2 and 8697.1 and 5254.3 Mc/sec for CD3NO2. The rotational constant for the NO2 group about the symmetry axis is 13 277.5 Mc/sec. These constants are determined assuming no inertial defect, slightly different values are calculated if other assumptions are made. Some of the assigned lines are a very sensitive function of the low barrier to internal rotation. The barrier term V6 was determined to be 6.03±0.03 calories/mole for CH3NO2 and 5.19±0.03 calories/mole for CD3NO2. The term V12 is less than 0.05 calorie/mole. The dipole moment of CH3NO2 is 3.46±0.02 Debye units.