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Showing papers in "Journal of Chemical Physics in 1952"


Journal ArticleDOI
TL;DR: In this paper, an expression for the viscosity of solutions and suspensions of finite concentration is derived by considering the effect of the addition of one solute-molecule to an existing solution, which is considered as a continuous medium.
Abstract: An expression for the viscosity of solutions and suspensions of finite concentration is derived by considering the effect of the addition of one solute‐molecule to an existing solution, which is considered as a continuous medium.

3,724 citations


Journal ArticleDOI
TL;DR: In this paper, the electron density at each carbon atom, of the highest occupied π−orbital in the ground state of the molecule is calculated by means of the LCAO method.
Abstract: In the search for a quantitative correlation between reactivity and electronic configuration of aromatic hydrocarbons, the electron density, at each carbon atom, of the highest occupied π‐orbital in the ground state of the molecule is calculated by means of the LCAO method. Comparing the result of such a calculation on fifteen condensed aromatic hydrocarbons with their chemical reactivities, we find that the position at which the electron density is largest is most readily attacked by electrophilic or oxidizing reagents.It is, therefore, concluded that distinct from other π‐electrons the pair of π‐electrons occupying the highest orbital, which is referred to as frontier electrons, plays a decisive role in chemical activation of these hydrocarbon molecules. The theoretical significance of this discrimination of the frontier electrons in relation to the chemical activation is discussed.

1,791 citations


Journal ArticleDOI
TL;DR: In this paper, a semi-empirical approach was used to calculate the energy of the ground state and the first few excited states of permanganate, chromate, and perchlorate ions.
Abstract: We have made use of a semiempirical treatment to calculate the energies of the molecular orbitals for the ground state and the first few excited states of permanganate, chromate, and perchlorate ions. The calculation of the excitation energies is in agreement with the qualitative features of the observed spectra, i.e., absorption in the far ultraviolet for ClO4−, two strong maxima in the visible or near ultraviolet for MnO4− and CrO4= with the chromate spectrum displaced toward higher energies. An approximate calculation of the relative f‐values for the first transitions in CrO4= and MnO4− is also in agreement with experiment.The data on the absorption spectra of permanganate ion in different crystalline fields is interpreted in terms of the symmetries of the excited states predicted by our calculations.

1,344 citations


Journal ArticleDOI
TL;DR: In this article, the semiclassical Franck-Condon principle is related to the more rigorous (exact) quantum-mechanical perturbation formula in the following ways: (1) the FranckCondon formula can be derived from the ''exact'' formula by using a mean value approximation or by neglecting certain commutators.
Abstract: The semiclassical Franck‐Condon principle is shown to be related to the more rigorous (``exact'') quantum‐mechanical perturbation formula in the following ways: (1) the Franck‐Condon formula can be derived from the ``exact'' formula by using a mean value approximation or by neglecting certain commutators; (2) if the electric dipole moments are treated as approximately independent of position, the Franck‐Condon and the ``exact'' absorption (or emission) spectrum have the same zeroth, first, and second moments, i.e., the same integrated spectrum, mean absorption frequency, and breadth; (3) the errors in higher moments than the second become relatively unimportant at high temperatures. If the electron‐nuclear interaction is sufficiently strong the errors are unimportant even at absolute zero.The use of a quasi‐molecular description in a many particle problem is found to be possible only if the masses or stiffnesses are allowed to be temperature dependent.A detailed analysis is made of the case in which the e...

1,092 citations


Journal ArticleDOI
TL;DR: In this article, the authors calculated the vibrational relaxation times in gases using an exponential repulsion in a one-dimensional model and derived the constants of the interaction potential by fitting it to the data of Hirschfelder, et al. The theoretical values for the relaxation times are 10 to 30 times shorter than the experimental ones, which difference may be accounted for by the use of the onedimensional model.
Abstract: Vibrational relaxation times in gases are calculated with the method of Zener using an exponential repulsion in a one‐dimensional model. The constants of the interaction potential are determined by fitting it to the data of Hirschfelder, et al. The great effect which some impurities have is accounted for either by their low mass and resultant high velocity or by ``near resonance'' transfers in which the vibrational quantum of the substratum is used partly to excite the vibration of the impurity, only the difference being transferred to translation. However, there are other impurities, the action of which cannot be explained in this manner. The theoretical values for the relaxation times are 10 to 30 times shorter than the experimental ones, which difference may be accounted for by the use of the one‐dimensional model. Macroscopic equations governing the more complex relaxation processes in polyatomic gases and gas mixtures are developed.

987 citations


Journal ArticleDOI
TL;DR: In this paper, the steric and pressure effects associated with the recombination of free radicals both depend on the nature of the activated complex, and are therefore intimately related, from a consideration of the reverse process of unimolecular dissociation, some equations are derived for these properties using an extension of earlier transition state and quasi-unimolecular theories.
Abstract: The steric and pressure effects associated with the recombination of free radicals both depend on the nature of the activated complex, and are therefore intimately related. From a consideration of the reverse process of unimolecular dissociation, some equations are derived for these properties using an extension of earlier transition state and quasi‐unimolecular theories. The present formalism differs from previous formulations of the latter in a number of ways, particularly in the expression used for the density of quantum states of the high energy molecules. Subsequent applications of the theory tentatively suggest that essentially all vibrational degrees of freedom of these molecules can contribute their energy to the vibrationally excited molecules. Consequently, vibrational anharmonicity would appear to be an important factor in intramolecular energy transfer. The present paper is an extension of a previously developed theory for the recombination of methyl radicals and iodine atoms.

773 citations


Journal ArticleDOI
TL;DR: In this paper, two principles of a statistical mechanics of time-dependent phenomena are proposed and argued for, namely, the proper mathematical object to describe the physical situation is the stationary random process specified by the ensemble of time series ai(Xt)i=1−s and the distribution ρ(X).
Abstract: Two principles of a statistical mechanics of time‐dependent phenomena are proposed and argued for. The first states that the proper mathematical object to describe the physical situation is the stationary random process specified by the ensemble of time series ai(Xt)i=1···s and the distribution ρ(X). The set phase functions ai(X)i=1···s represent the set of grossly observable features of the system. Xt is the image of the phase X after time t. ρ(X) is a stationary distribution. The second principle is concerned with the very common case in which the phenomenological equations are of the first order in time and states that in this case the random process in question is a Markoff process. A Fokker‐Planck equation is derived for the process, and an entropy is defined and is shown always to increase. Phenomenological equations are derived as a first approximation to the Markoff process. These involve a certain matrix ξij which is shown to satisfy symmetry relations which are a generalization of Onsager's. The...

659 citations


Journal ArticleDOI
TL;DR: In this paper, it was shown that Hg2I2−coated liquid mercury droplets (2-8 microns diameter) solidify at rates that are proportional to droplet volume and satisfactorily described by the theory of homogeneous nucleation of crystals.
Abstract: The solidification rate of supercooled liquid mercury droplets is strongly dependent upon the nature of foreign substances on their surface or suspended in them. Droplets (2–8 microns diameter) coated with mercury laurate solidify at rates that are proportional to droplet volume and satisfactorily described by the theory of homogeneous nucleation of crystals. Droplets coated with mercury acetate solidify with frequencies that are proportional to droplet area and in good agreement with the theory of heterogeneous nucleation.The results on Hg2I2‐coated droplets are interpreted on the hypothesis that nucleation is effected by suspended crystallites of one kind. For some droplet dispersions the kinetic results are apparently best described by a multiplicity of solidification frequencies/area or volume. Various hypotheses for this multiplicity are considered.

658 citations


Journal ArticleDOI
TL;DR: In this paper, the matrix elements of spin-orbit interaction were obtained for polyatomic molecules using M.O. wave functions, taking account of configurational interaction, and the results were then applied to the calculation of singlet-triplet transition probabilities in aromatic compounds.
Abstract: The matrix elements of spin‐orbit interaction are obtained for polyatomic molecules using M.O. wave functions, taking account of configurational interaction. These results are then applied to the calculation of singlet‐triplet transition probabilities in aromatic compounds. It is shown without evaluation of integrals that intercombination transitions in these compounds should be much weaker than in most other classes of organic compounds. This is in agreement with experimental results on the phosphorescence lifetimes of these compounds.

490 citations


Journal ArticleDOI
TL;DR: In this article, a method of measuring the ionic and electronic conductivities independently, as functions of the chemical potential ζ of the silver component, has been proposed, and the electronic conductivity is found to vary as expBζ both above and below the transition at 177°C.
Abstract: Mixed electronic and ionic conduction in silver sulfide is examined. The importance of terminal conditions which may affect the ratio of ionic to electronic currents in experimental measurements is emphasized. In particular, either the electronic or ionic components can be completely suppressed. This is the basis of a new method of measuring the ionic and electronic conductivities independently, as functions of the chemical potential ζ of the silver component. The electronic conductivity is found to vary as expBζ both above and below the transition at 177°C. However, the coefficient B changes abruptly from e/kT below the transition to e/2kT above. This result can be understood theoretically in terms of the following picture: Excess silver is present mainly as dissolved atoms below the transition and as dissociated ions and electrons above. In the former case, only the electrons contribute to ζ, whereas in the latter there is a contribution both from the electrons and the ions.

475 citations


Journal ArticleDOI
TL;DR: In this article, a collisional perturbation of spin-orbital coupling in the π-electron orbitals of naphthalene is interpreted in terms of a collision.
Abstract: A yellow color is produced when two colorless pure liquids, α‐chloronaphthalene and ethyl iodide, are mixed, although no chemical reaction occurs. Spectroscopic examination reveals that the lowest singlet→triplet absorption band of the naphthalene molecule is greatly enhanced in intensity in the presence of the iodide, and that the development of this absorption band is responsible for the color effect. The process is interpreted in terms of a collisional perturbation of spin‐orbital coupling in the π‐electron orbitals of the naphthalene. The significance of this phenomenon in several topics in spectroscopy and chemistry is discussed. In particular, the molecular mechanism of heavy atom quenching of fluorescence by foreign species is resolved. A novel Beer's law anomaly is predicted for intercombinations.

Journal ArticleDOI
TL;DR: In this article, complex dielectric constants have been measured for ice from the melting point to −65°C and for solid D2O to −35°C, by a combination of bridge and transient methods.
Abstract: Complex dielectric constants have been measured for ice from the melting point to −65°C, and for solid D2O to −35°C, by a combination of bridge and transient methods. For both, the dispersion is described by the simple Debye formula, and the relaxation times τ by the simple rate expression τ = A exp(B/RT). For ice, A = 5.3×10−16 sec, B = 13.2 kcal/mole; and for solid D2O, A = 7.7×10−16 sec, B = 13.4 kcal/mole. The equilibrium dielectric constant for ice is 91.5 at 0°C and increases at lower temperatures; the values for solid D2O are only slightly smaller. Measures taken to minimize errors from voids in the sample and direct current conductance are discussed.

Journal ArticleDOI
TL;DR: In this article, the authors developed a selfconsistent theory of rubber-like materials consisting of networks of non-Gaussian chain molecules and derived three kinds of series developments for the distribution function of perfectly flexible single chains from the Fourier integral solution of Rayleigh.
Abstract: The aim of this paper is to develop a selfconsistent theory of rubber‐like materials consisting of networks of non‐Gaussian chain molecules. Three kinds of series developments are derived for the distribution function of perfectly flexible single chains from the Fourier integral solution of Rayleigh; namely, (1) long chains with actual extension much less than the maximum extension, (2) long chains with actual extension comparable to the maximum extension, and (3) short chains. In the non‐Gaussian network theory, the leading term of the series (2) is used as the starting point for the individual chains of the network. Calculations are made for the case where the free junctions are moving with no restriction, and for the case where the free junctions are assumed to be at their most probable positions. The final expressions of the elastic energy for the two cases are compared, and it is shown that the percentage difference of the two expressions is of the order 1/n (n being the average number of links per chain), which is negligible for sufficiently large n. Finally an expression of the elastic energy is obtained with the assumption that all junctions are fixed and is shown to be, in general, a function of three strain invariants. The interdependence of the coefficients of the invariants is shown. Comparison of theory and experiment is given. Because of the interdependence of the coefficients only part of the observed deviations from Gaussian theory can be explained by our molecular theory. The remaining discrepancies must be ascribed to van der Waals forces. This should show up in the (not yet investigated) temperature dependence of these discrepancies.

Journal ArticleDOI
TL;DR: In this paper, the properties of water are treated by a statistical method in which the numbers of molecules in four, three, two, one, and zero-bonded states are estimated from dielectric and latent heat data.
Abstract: Results of dielectric constant and loss measurements at λ=9.22, 3.175, and 1.264 cm are given for a wide variety of aqueous solutions of ions and organic molecules. The water relaxation time is shortened by positive ions and lengthened by hydrogen bond‐forming molecules. The properties of water are treated by a statistical method in which the numbers of molecules in four, three, two, one, and zero‐bonded states are estimated from dielectric and latent heat data. Fair agreement with experiment is obtained in calculating the static dielectric constant of ice at 0° and water from 0–370°C, using Kirkwood's dielectric theory and Verwey's calculation of the dipole moment of a four‐bonded water molecule. The effects of temperature and solutes on the water relaxation time are discussed in terms of this statistical method. The effective number of water molecules ``irrotationally bound,'' i.e., prevented from turning in the electric field by the ion or the organic molecule, is estimated from the depression of the l...

Journal ArticleDOI
TL;DR: In this paper, the rotational energy of a nonrigid asymmetric rotor was derived for the first order treatment of a first-order treatment and the relation W = W0+A1W02+A2W0J(J+1)+A3J2(J + 1)2+A4J(j+1)
Abstract: A first‐order treatment yields the relation W=W0+A1W02+A2W0J(J+1)+A3J2(J+1)2+A4J(J+1)〈Pz2〉+A5〈Pz4〉+A6W0〈Pz2〉 for the rotational energy W of a nonrigid asymmetric rotor. The A's are constants independent of the rotational quantum numbers (J, K−1, K+1) while W0 is the rigid‐rotor energy. Pz is the operator for the component of angular momentum along the axis of quantization. Formulas are given for 〈Pz2〉 and 〈Pz4〉, based on continued fractions, as well as expansions useful for nearly symmetric cases. As a special case, the corrections are derived for transitions between the components of asymmetry doublets.

Journal ArticleDOI
TL;DR: In this paper, it was shown that the segmental jumping frequency is about 0.3 sec−1 at the transition temperature in polystyrene and a simple relation was found between bulk viscosity and diffusion constant.
Abstract: An attempt has been made to explain the observed viscous behavior of bulk polymers. It is found that the viscosity and diffusion may be represented by a theory which takes into account the coupling together of the molecules. Two equivalent treatments are given. One makes use of a segmental friction factor in the same manner as the common formulation of dilute solution viscosity of polymers. The second method uses the concept of segmental jumping. Since both are equivalent, an expression for the friction factor is found in terms of the segmental jumping frequency. Using this fact it is possible to calculate the segmental jumping frequency from bulk viscosity data. A simple application leads to the result that the jumping frequency is about 0.3 sec−1 at the transition temperature in polystyrene.In addition a simple relation is found to hold between bulk viscosity and diffusion constant. The proportionality constant is easily evaluated and so one is now able to obtain self‐diffusion constants directly from v...

Journal ArticleDOI
TL;DR: In this paper, the individual absorption coefficient curves of NO2 and N2O4, separated by means of a mechanical analog differential analyzer, are presented and a discussion of the apparently continuous nature of the N 2O4 absorption is included.
Abstract: The individual absorption coefficient curves of NO2 and N2O4, separated by means of a mechanical analog differential analyzer are presented. Beer's law is assumed to be applicable to the system. The range 2400–5000A is covered. A discussion of the apparently continuous nature of the N2O4 absorption is included.

Journal ArticleDOI
TL;DR: In this article, a solution is presented to the general problem of the transient behavior of a linear fixed bed system where the rate of adsorption is determined by the combined effect of a liquid film and solid diffusion into spherical particles.
Abstract: A solution is presented to the general problem of the transient behavior of a linear fixed bed system where the rate of adsorption is determined by the combined effect of a liquid film and solid diffusion into spherical particles The result obtained is an expression for the effluent following a sudden change in the influent concentration It is given in two forms: (a) An exact solution to the problem in the form of an infinite integral suitable for numerical integration (b) An approximation to the exact solution together with an expression for the leading error term in this approximation The approximate solution and the error term are given as closed trigonometric expressions which can be easily evaluated


Journal ArticleDOI
TL;DR: In this paper, two rules are presented which relate the intensities of vibrational fundamentals of different isotopic species, analogous to the Teller-Redlich product rule which relates frequencies.
Abstract: Two rules are presented which relate the intensities of vibrational fundamentals of different isotopic species. They are thus analogous to the Teller‐Redlich product rule which relates frequencies. They apply to either infrared or Raman intensities. One rule permits the calculation of dipole‐moment derivatives without the determination of normal coordinates. The application of the rules is illustrated.

Journal ArticleDOI
TL;DR: In this article, the frictional coefficient, f0, of a polymer molecule in dilute solution is assumed to vary directly as an average linear dimension of the chain, from this assumption equations are developed, as follows, which are analogous to those used successfully in the interpretation of intrinsic viscosity measurements; f0/η0 =KfM½α and Kf=P(〈r02〉/M)½ where α represents the factor by which the actual root-mean-square end-to-end distance exceeds the unperturbed distance (�
Abstract: The frictional coefficient, f0, of a polymer molecule in dilute solution is assumed to vary directly as an average linear dimension of the chain. From this assumption equations are developed, as follows, which are analogous to those used successfully in the interpretation of intrinsic viscosity measurements; f0/η0 =KfM½α and Kf=P(〈r02〉/M)½ where α represents the factor by which the actual root‐mean‐square end‐to‐end distance exceeds the unperturbed distance (〈r02〉)½, M is the molecular weight, η0 the viscosity of the medium, and P should be a universal constant.Data in the literature on the dependence on molecular weight of sedimentation constants and diffusion coefficients, extrapolated to infinite dilution confirm the conclusions drawn from these equations.

Journal ArticleDOI
TL;DR: In this paper, it is shown that the critical condition of inflammability requires the solution of the nonlinear Poisson Boltzmann differential equation for a reaction vessel of cylindrical or spherical shape.
Abstract: The theory of thermal explosions originally proposed by Frank‐Kamenetzky has been the subject of a number of investigations. The critical condition of inflammability requires the solution of the nonlinear Poisson‐Boltzmann differential equation. For the case of a reaction vessel of cylindrical or spherical shape the solution was obtained by previous investigators by numerical integration of the equation. It is shown, however, in the following that the solutions can be obtained in terms of known functions.

Journal ArticleDOI
TL;DR: In this paper, the theory of conductance in polarizable media was modified in such a way as to be applicable to electrolytic solutions by the introduction of a new set of boundary conditions.
Abstract: The theory of ``Conductance in Polarizable Media'' developed by one of the authors is modified in such a way as to be applicable to electrolytic solutions. This is achieved by the introduction of a new set of boundary conditions. In their original form they expressed the fact that the polarizing ions could not carry any current through the boundary. Now it is assumed that the discharge at the electrodes is a rate process of the first order, characterized by a rate constant ξ. In Sec. II the case of an applied ac voltage is treated. The expressions for the equivalent parallel conductance and capacitance of the polarization layer 1/Rp and Cp are derived by the same method, and to the same extent, as in the older theory. If ξ tends to zero, the previous results are obtained (``completely blocked electrode''). If ξ increases, the ``polarization capacitance'' and the ``excess resistance'' both decrease until they vanish for ξ=∞ (``open electrode''). The dependence on frequency remains similar for all finite va...


Journal ArticleDOI
TL;DR: In this article, a variety of spectroscopic data shows that the absorption frequencies of n→π electronic transitions progressively increase in the series of solvents, paraffin, alcohol, and water.
Abstract: A variety of spectroscopic data shows that the absorption frequencies of n→π electronic transitions progressively increase in the series of solvents, paraffin, alcohol, and water. This general effect of polar solvents on the frequency of n→π transitions is related to the characteristic change in the molecular charge distribution accompanying this type of transition. In certain cases solvation effects can be of considerable value in distinguishing between n→π and π→π electronic transitions.Evidence is presented which indicates that the absorption bands of the ions, NO3− (32,000 cm−1), CO3= (46,000 cm−1) and CS3= (20,000 cm−1) are n→π transitions.

Journal ArticleDOI
TL;DR: In this article, a general theoretical method for evaluating the effect on thermodynamic properties of cooperative orientation in solutions is developed, applied to the systems methanol+benzene, methanhol carbon tetrachloride, and chloroform+ethanol.
Abstract: A general theoretical method for evaluating the effect on thermodynamic properties of cooperative orientation in solutions is developed. The theory is applied to the systems methanol+benzene, methanol carbon tetrachloride, and chloroform+ethanol. Theoretical curves for excess free energy of mixing, heat of mixing, and excess entropy of mixing as functions of composition are presented and are in reasonable quantitative agreement with experimental values for the first two systems and qualitatively similar to the experimental curves for the third. It is concluded that the method provides a useful approach to the theory of solutions of associated liquids in general.

Journal ArticleDOI
TL;DR: In this paper, the number of resonance forms of any specified number of unpaired electrons of aromatic hydrocarbons is reduced to combinatorial problems, many of which can be solved on the basis of five simple lemmas.
Abstract: The computation of resonance forms of any specified number of unpaired electrons (``radicality'') of aromatic hydrocarbons is reduced to combinatorial problems, many of which can be solved on the basis of five simple lemmas. In this first of two papers, only unexcited (Kekule) forms are computed. Algorithms are deduced for deriving the number N of such forms for classes covering practically all nonreticulate aromatic hydrocarbons and a number of singly, doubly, or triply infinite series of reticulate ones. One lemma leads to a simplification of the combinatorial problems from the hexagonal to the square lattice (``dot diagrams''). Points of purely mathematical interest arise and may merit further study.

Journal ArticleDOI
TL;DR: In this article, a comparison of quantum yields of fluorescence and phosphorescence in solid solution with quantum yields in other phases suggests that the mechanism of radiationless transitions, in the absence of concentration quenching and specific solvent and quencher action, is intramolecular potential surface crossing, followed by the transfer of excess vibrational energy to the solvent.
Abstract: Absolute quantum yield measurements of fluorescence and phosphorescence have been made for a number of organic molecules dissolved in a transparent solid solution (E.P.A.) at 77°K. The quantum efficiencies range from nearly zero for bromobenzene to 0.6 for benzophenone. The measurements are believed to be accurate to about 10 percent. The nonradiative processes, which account for the quanta not re‐emitted, are discussed. If the radiationless processes all originate in the triplet state, the triplet state lifetimes measured in solid solution can be corrected to give the natural lifetime of the triplet (phosphorescent) state. Since one cannot tell a priori that this assumption is justified, other experiments are necessary. If the singlet‐triplet absorption strength is known, one can tell whether this correction should be applied or not, and infer the origin of the radiationless transition. Finally, a comparison of quantum yields in solid solution with quantum yields in other phases suggests that the mechanism of radiationless transitions, in the absence of concentration quenching and specific solvent and quencher action, is intramolecular potential surface crossing, followed by the transfer of excess vibrational energy to the solvent.

Journal ArticleDOI
TL;DR: In this article, the infrared and Raman data of light and heavy ethane (C2H6 and C2D6) have been reexamined for the purpose of determining as accurately as possible the potential constants of the ethane molecule.
Abstract: The infrared and Raman data of light and heavy ethane (C2H6 and C2D6) have been reexamined for the purpose of determining as accurately as possible the potential constants of the ethane molecule. In order to fill in some of the gaps in the spectroscopic data, additional high resolution measurements have been made on the infrared spectrum of heavy ethane which have given more precise values for the active fundamental frequencies and zeta‐values. Resolution of the fine structure associated with the parallel band ν5* has given the value of the large moment of inertia of C2D6, thus completing the information required for the spectroscopic determination of the dimensions of ethane. The data yield, C–C distance=1.543A, C–H distance=1.102A, H–C–C angle=109°37′, and H–C–H angle=109°19′. The twenty‐two distinct potential constants compatible with the D3d symmetry of ethane have been determined through their relationships to the normal frequencies and zeta‐values of C2H6 and C2D6. The normal frequencies have been o...