Showing papers in "Journal of Chemical Physics in 1935"

The Activated Complex in Chemical Reactions

Abstract: The calculation of absolute reaction rates is formulated in terms of quantities which are available from the potential surfaces which can be constructed at the present time. The probability of the activated state is calculated using ordinary statistical mechanics. This probability multiplied by the rate of decomposition gives the specific rate of reaction. The occurrence of quantized vibrations in the activated complex, in degrees of freedom which are unquantized in the original molecules, leads to relative reaction rates for isotopes quite different from the rates predicted using simple kinetic theory. The necessary conditions for the general statistical treatment to reduce to the usual kinetic treatment are given.

Statistical Mechanics of Fluid Mixtures

Abstract: Expressions for the chemical potentials of the components of gas mixtures and liquid solutions are obtained in terms of relatively simple integrals in the configuration spaces of molecular pairs. The molecular pair distribution functions appearing in these integrals are investigated in some detail, in their dependence upon the composition and density of the fluid. The equation of state of a real gas mixture is discussed, and an approximate molecular pair distribution function, typical of dense fluids, is calculated. Applications of the method to the theory of solutions will be the subject of a later article.

On the Possibility of a Metallic Modification of Hydrogen

Abstract: Any lattice in which the hydrogen atoms would be translationally identical (Bravais lattice) would have metallic properties. In the present paper the energy of a body‐centered lattice of hydrogen is calculated as a function of the lattice constant. This energy is shown to assume its minimum value for a lattice constant which corresponds to a density many times higher than that of the ordinary, molecular lattice of solid hydrogen. This minimum—though negative—is much higher than that of the molecular form. The body‐centered modification of hydrogen cannot be obtained with the present pressures, nor can the other simple metallic lattices. The chances are better, perhaps, for intermediate, layer‐like lattices.

The Relation Between the Internuclear Distances and Force Constants of Molecules and Its Application to Polyatomic Molecules

Abstract: The relation between the internuclear distances and force constants found for diatomic molecules is discussed, and is shown to carry over to polyatomic molecules. It is shown that internuclear distances of polyatomic molecules can be predicted from vibrational data alone, with considerable accuracy.

The Absolute Rate of Reactions in Condensed Phases

Abstract: The theory of absolute reaction rates is developed for condensed phases. The equation for the rate of a reaction of any order in any phase where the slow process is the passage over an energy barrier consists of the product of a transmission coefficient κ, a frequency kT/h, an equilibrium constant between an activated complex and the reactants and an activity coefficient factor. Previous theories of reaction rates such as Bronsted's, the collision theory of Mc C. Lewis, etc., are seen to be special cases of the general theory. A variety of examples are considered.

Electronic Structures of Molecules XI. Electroaffinity, Molecular Orbitals and Dipole Moments

Abstract: A convenient criterion for defining equal electronegativity of two atoms is stated in terms of coefficients in LCAO approximate molecular orbitals. Connections between relative electronegativities, coefficients in LCAO orbitals, effective charges on atoms in partially polar molecules, and dipole moments, are then analyzed, and various equations are obtained expressing these connections. The discussion is largely applicable to polyatomic as well as to diatomic molecules. A theoretical derivation is given for an empirical equation, found by Pauling, which forms a basis for the latter's approximate scale of relative electronegativities. Pauling's and other possible approximate scales are discussed, and it is shown how an approximate ``absolute electroaffinity'' can conveniently be defined on each scale. A very rough theoretical justification is given for the empirically observed proportionality between relative electronegativities obtained from Pauling's and from the writer's scale. The necessary existence of a ``homopolar dipole'' contribution to the electric moment of any bond is shown, provided the atoms forming the bond are of unequal size. By ``homopolar dipole'' is meant a contribution which would not vanish, for atoms of unequal size, even if they are of equal electroaffinity. Dipole moments of H2O, NH3 and HX are briefly discussed. It is concluded that the dipole moment scale of electronegativity is probably not well founded. An important object of the paper is to show how electroaffinity and other data can be used in the approximate determination of the polarities of molecular orbitals and so of bonds, the results being expressed both in terms of coefficients in LCAO molecular orbitals and in terms of effective charges transferred. Applications are made to the electronic structures of various diatomic molecules, especially HI, HI+, HO—, ClO—.

The Atomic Distribution in Red and Black Phosphorus and the Crystal Structure of Black Phosphorus

Abstract: No satisfactory crystal structure determination has been made of any of the forms of phosphorus. Five samples of black phosphorus gave identical powder patterns different from those reported by Linck and Jung, whose rhombohedral structure gives improbable interatomic distances and coordination. A sample which had been prepared at room temperature and 35,000 atmospheres gave the diffuse rings of an ``amorphous'' x‐ray pattern. Another sample, prepared at 300°C and 8000 atmospheres, is a new form of phosphorus, having the same density as black. Atomic distribution curves of crystalline and ``amorphous'' black and red phosphorus were obtained by the method of Fourier analysis. All four gave practically the same curve, showing three neighbors at 2.28A and about twelve at 3.6A. With the aid of the atomic distribution curves and the fact that certain lines showed a preferred orientation, it was possible to determine the structure of black phosphorus. It consists of double layers; the cell is side‐centered ortho...

Precision Determination of Lattice Constants

Abstract: In Part I the theoretical and experimental conditions which must be satisfied in order to determine lattice constants with a precision of a few parts per hundred thousand are discussed with particular application to the symmetrical focusing type of camera. Cohen's method of calculation of lattice constants for the elimination of ``drift'' and experimental errors is applied. Methods are developed for the evaluation of standard errors and fiduciary limits of results from a single film and from a set of films. The usefulness of x‐ray targets made of alloys rather than pure elements for the purpose of securing a larger number and better distribution of lines is indicated. The influence of the number and Miller indices of diffraction lines on the values of lattice constants in noncubic systems is shown. The importance of the methods of sample preparation for precision work is emphasized. In Part II, precision measurements on Al,Ni, Ag, Au, Si, Fe, Mo, W, Mg, Zn, Cd, Sb, Bi and Sn are reported for materials of a high degree of purity. The fiduciary limits of these lattice constants vary between 2 and 7 parts per hundred thousand and are so chosen that the probability of the correct value lying between the stated limits is 19 out of 20.

The Statistical Weights of the Rotational Levels of Polyatomic Molecules, Including Methane, Ammonia, Benzene, Cyclopropane and Ethylene

Abstract: A general method is described for calculating the statistical weights (degeneracies) of the energy levels of polyatomic molecules. Wave functions for a molecule are assumed to be expressible as linear combinations of products of the electronic, vibrational, rotational and nuclear spin functions. By using standard methods of group theory, the number of linear combinations of these products are found having the correct symmetry with respect to those permutations of identical atoms which are equivalent to rotations of the molecule. It is not necessary to find the combinations themselves. The molecules CH4, CD4, CH3D, CHD3, CH2D2, CH3X, CD3X, NH3, ND3, C6H6, C3H6 and C2H2 are treated. In addition noncombining species in polyatomic molecules and the splitting of energy levels due to the multiplicity of equilibrium configurations are discussed. Tables of statistical weights are given for the above molecules which could be used to interpret alternating intensities in rotation‐vibration spectra or for more exact calculations of thermodynamic quantities than are usually made.

The Pressure‐Volume‐Temperature Relations of the Liquid, and the Phase Diagram of Heavy Water

Abstract: The pressure‐volume‐temperature relations of both liquid D2O and H2O are measured between —20° and 95°C and up to 12,000 kg/cm2, and the transition parameters of the liquid and solid modifications of D2O in the range between —60° and +20°C and up to about 9000 kg/cm2. An unstable modification of solid D2O, for which the designation IV is proposed, is found in the field of stability of V. Reference to the original work on H2O shows that the corresponding modification of H2O also exists. In general the properties of H2O and D2O covered by these measurements are very much alike, and differ in the direction suggested by the greater zero‐point energy of H2O: the molar volume of D2O is always greater than that of H2O at the same pressure and temperature, and the transition lines of D2O always run at higher temperatures. In finer detail, however, the differences between the two waters do not vary regularly, and probably other considerations than of zero‐point energy alone are necessary for a complete explanation.

Electron Diffraction by Gases

Abstract: The method of electron diffraction is used for determining the C–O–C valence angle (α) in 4,4′ diiododiphenyl ether [(C6H4I)2O] and the molecular structures of phosphorus (P4) and arsenic (As4). The electron diffraction photographs were analyzed by four different methods as follows: (1) Visual measurements, (2) measurements of densitometer records, (3) conversion of densitometer records into relative intensity curves, (4) comparison of transformed intensity curves obtained by multiplying the intensity of scattering by [(1/λ) sin θ/2]2 which produces prominent maxima for measurement. The valence angle α was found to be 118±3° for 4,4′ diiododiphenyl ether, definitely greater than the oxygen valence angle found for simpler types of molecules. Phosphorus and arsenic molecules were found to have a regular tetrahedral structure within the limits of experimental error, the atomic separations being 2.21A and 2.44A, respectively, [methods (1) and (2) were used for the case of arsenic]. The minimum atomic distances as found by crystal structure analysis for phosphorus and arsenic are approximately the same as the atomic separations obtained for the gas molecules, showing in addition that these distances do not change greatly when the bond angle decreases from 100° to 60°.

Valence Strength and the Magnetism of Complex Salts

Abstract: Certain complex salts, notably ferro‐ and ferricyanides, have susceptibilities much lower than those predicted by the Bose‐Stoner ``spin only'' formula. The first interpretation was that given by Pauling on the basis of (I) directed wave functions. In the present paper it is shown that alternative explanations are possible with (II) the crystalline potential model of Schlapp and Penney, or with (III) Mulliken's method of molecular orbitals. In any of the theories, the interatomic forces, if sufficiently large, will disrupt the Russell‐Saunders coupling, and make the deepest state have a smaller spin, and hence smaller susceptibility, than that given by the Hund rule. This situation is not to be confused with that in normal paramagnetic salts, such as sulphates or fluorides, where only the spin‐orbit coupling is destroyed. The similarity of the predictions with all three theories is comforting, since any one method in valence usually involves rather questionable approximations. Because of this similarity, a preference between the theories cannot be established merely from ability to interpret the anomalously low magnetism of the cyanides. Covalent bonds, as in cyanides, seem to be more effective in suppressing magnetism than are ionic ones, as in fluorides, but so far the evidence to this effect is empirical rather than theoretical.

Electronic Structures of Polyatomic Molecules. VII. Ammonia and Water Type Molecules and Their Derivatives

Abstract: Spectroscopic and ionization potential data are used in obtaining electron configurations in terms of molecular orbitals for NH3, PH3, H2O, H2S and their derivatives, e.g., CH3NH2, (CH3)2NH, N2H4, H2O2, CH3OH, NH2Cl, ClOH, Cl2O. These electron configurations hold for molecules in their normal states, but can be used in predicting the energy of ``vertically'' excited states, i.e., energies corresponding to nuclear dimensions the same as for the normal state. Frequent close similarities between the spectra of parent molecules and their derivatives are explained (also the similarities between alkyl halides such as CH3I, C2H5I, etc.). Estimates of vertical ionization potentials for the various orbitals used are given. Various points (types of orbitals used, Rydberg series, predissociation) are touched on. The longest wavelength ultraviolet spectra and minimum ionization potential are attributed in the NH3 derivatives to excitation of a nearly nonbonding electron of the N atom, in the H2O and H2S derivatives to excitation of a nonbonding O or S atom electron. (Exception: compounds containing I, Br, and perhaps Cl, where the halogen atom supplies the most easily excited and ionized electron.)

Energy Levels of a Symmetrical Double Minima Problem with Applications to the NH3 and ND3 Molecules

Abstract: The energy levels for a potential energy V = — C sech2 r/2ρ+D sech4 r/2ρ have been obtained by numerical solution of continued fractions. Values of the constants have been found such that the computed energy levels agree satisfactorily with the experimental values for the NH3 and ND3 molecules. The height of the ammonia pyramid is found to be 0.37A, the height of the potential hill is found to be 2076 cm—1, and the dissociation energy is about five volts.

The Crystal Structure of Lepidocrocite

Abstract: The unit of structure, space group symmetry and detailed atomic arrangement of lepidocrocite are determined from x‐ray data, and the existence and location of hydrogen bonds in the structure are established from considerations of interatomic distances. The orthorhombic lattice is end centered on (100), and has the axes a0 = 3.87A, b0 12.51A, and c0 = 3.06A. The space group is Vh17—Amam. The parameters are determined as uFe = —0.332, uO = +0.282, and uOH = +0.075. The structure is described as consisting of iron‐centered oxygen octahedra joined by the sharing of edges into two‐dimensionally infinite layers, with the successive layers held together by hydrogen bonds. The relationship between the diaspore‐goethite structure and the bohmite‐lepidocrocite structure is discussed from the standpoint of the coordination theory, and found to depend on two alternative ways of satisfying the electrostatic valence rule.

The Vitreous State

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The Structure of Rhombic Sulphur

Abstract: From rotation and oscillation photographs with Mo Kα, rhombic sulphur is found to have the following cell and space group; a = 10.48A, b = 12.92A, c = 24.55A, Z = 128, space group Vh24(Fddd). The structure contains S8 molecules which are symmetrical puckered rings with S–S distance 2.12A and bond angle α = 105°. The atomic coordinates are determined by comparison of calculated amplitudes with visual intensity estimates from oscillation photographs. The relation of rhombic sulphur to the high temperature forms is discussed briefly.

Electronic Structures of Molecules X. Aldehydes, Ketones and Related Molecules

Abstract: Electron configurations for the normal states of H2CO, CH3HCO, Cl2CO are explicitly given, also for the low excited states of H2CO. The structures, ionization potentials, and longest wavelength electronic band spectra of these and other related or analogous molecules (saturated aldehydes, ketones, thioaldehydes, thioketones, etc.) are interpreted in relation to these configurations. In particular is it shown that the minimum ionization potential of =C=O or =C=S corresponds to removal of a nonbonding 2p electron from the O atom or a nonbonding 3p from the S atom, unless the groups attached to the C contain other unusually easily ionized electrons. Similarly, the longest wavelength band system, commonly attributed to the C=O (or C=S) double bond, corresponds to excitation of the nonbonding 2po or 3ps to an excited orbital which is largely but probably not quite wholly localized in the C=O or C=S bond, and which has C↔O or C↔S antibonding power, i.e., loosens the bond somewhat. This excitation process is res...

The Electronic Structure of Diamond

Abstract: The method of Wigner, Seitz and Slater has been applied to the determination of the electronic structure of diamond. It is found that the energy levels of the carbon atom are broadened into bands similar to the energy bands in metals. The 2s level of the atom splits into two bands, and the 2p level into six bands. The two 2s bands are completely filled by electrons and the two lowest of the 2p bands. The lowest unfilled band has a much higher energy than the highest filled band. The lack of electrical conductivity is explained and other properties of the diamond are discussed.

Electronic Structures of Polyatomic Molecules and Valence VI. On the Method of Molecular Orbitals

Abstract: The use of the method of nonlocalized molecular orbitals in building up a conceptual scheme or qualitative theoretical framework into which empirical data (chemical and spectroscopic) can be fitted, is emphasized. This should be distinguished from the use of the method, often with rough ``LCAO'' approximations (linear combinations of atomic orbitals), in semiquantitative calculations.

The Group Relation Between the Mulliken and Slater‐Pauling Theories of Valence

Abstract: By means of the group theory of characters, it is shown that there is an intimate relation between Mulliken's molecular orbitals and the Slater‐Pauling directed wave functions. One can pass from the former to the latter by making a simple transformation from an irreducible to a reducible representation. Consequently the same formal valence rules are usually given by either method, and one can understand generally why wave functions of the central atom which are nonbonding in Mulliken's procedure are likewise never employed in constructing Pauling's ``hybridized'' linear combinations.

The Liquid ``Structure'' of Methyl Alcohol

Abstract: Fourier integral analyses of the x‐ray diffraction patterns of liquid nonyl and methyl alcohol are made. From these the radial distribution of atoms around any one atom is obtained. On the basis of the radial distribution curves, conclusions are drawn concerning the molecular configuration in the liquid. For nonyl alcohol this analysis confirms the results of Warren. In the case of methyl alcohol the analysis gives strong indication of hydrogen binding (dipole binding) between oxygen atoms of neighboring molecules. The short ``life'' of a given intermolecular bond in the liquid is emphasized. It is pointed out that the application of the ordinary Bragg equation to the peaks in the diffraction pattern of a liquid has no justification.

Electronic Structures of Polyatomic Molecules. IX. Methane, Ethane, Ethylene, Acetylene

Abstract: Electron configurations for the normal states of C2H6, C2H4, and C2H2 are given, and are used in interpreting observed ionization potentials. Excited orbitals of CH4 and the others are also discussed and tentative interpretations given for the ultraviolet spectra. ``Reduced'' interatomic distances are studied as a measure of overlapping and resonance of orbitals of different atoms or radicals.

Wave Mechanical Treatment of the Molecule Li2

Abstract: The Li2+ molecule has been treated by methods previously applied to the study of Li2 by the writer. It appears that the dissociation energy of Li2+ must be greater than that of Li2, and is probably 1.30±0.05 e.v. The ratio of one‐ to two‐electron bond strengths appears to be greater with Li2 than with H2 because the bonding wave functions are more diffuse. The inner shells play a deterring role in the binding in Li2+ similar to that found in Li2. The Heitler‐London wave function has been compared with the much more accurate series function, and the general character of the satisfactory molecular orbital is noted. The form of the variational process used here appears to be particularly suitable for the treatment of one‐electron bonds, and simple functions may be used to give highly satisfactory results, as illustrated by the cases of Li2+ and H2+.

The Far Ultraviolet Absorption Spectra and Ionization Potentials of C6H6 and C6D6

Abstract: The absorption spectra of C6H6 and C6D6 have been photographed under high dispersion in the region 2000–1000A. The spectra of both substances are very similar. A strong continuous absorption starts fairly sharply around 1840A and gradually weakens out to zero at 1600A. It is followed by a region extending down to about 1360A which contains very strong sharp bands. The strongest of these bands only suffer small shifts to the violet in going from C6H6 to C6D6. This shift which is due to the change in the difference of zero‐point energy between the normal and the excited states reveals the bands to be vibrationless electronic transitions. It was found that these bands could be arranged into two Rydberg series which had approximately the same limit corresponding to an ionization potential of 9.190±.005 volts for C6H6. The ionization potential of C6D6 is only about 3 × 10—4 volts greater than that for C6H6. All the electronic states are split up into patterns which are believed to be caused by true electronic multiplicity. The excitation is apparently from a nonbonding electron more strongly attached to the carbon atom. The vibrations which accompany the bands are comparatively weak. However for C6H6 the following vibration frequencies associated with the excited states were observed. ω1 = 677 cm—1, ω2 = 968 cm—1. These become 630 and 926 cm—1 for C6D6. Tentative assignments of their modes of vibration are made. The bands below 1360A are considerably more diffuse than those previously mentioned and the isotopic shifts to the violet are much larger for these bands. However they are still believed to be vibrationless electronic transitions though they are due to the excitation of an electron which is considerably more bonding than that corresponding to the first ionization potential. A consideration of them enables the approximate value 11.7±.3 volts to be predicted for the second ionization potential of benzene.

The Far Ultraviolet Absorption Spectra of Formaldehyde and the Alkyl Derivatives of H2O and H2S

Abstract: The absorption spectra of formaldehyde and of compounds of the type HOH, ROH, ROR and HSH, RSH, RSR have been observed in the region 2300–1000A. An analysis of the spectrum of formaldehyde yields a value of 10.83±0.01 volts for the first ionization potential of the C=O bond and about 164 Cal./mole for the strength of this bond. The spectra of the alkyl derivatives of H2S are all shown to be shifted to the long wavelength region relative to those of H2O. Rough estimates of their ionization potentials are given and the influence of dipole moment on the ultraviolet absorption spectra and ionization potentials of polyatomic molecules is discussed.

The Absolute Rate of Homogeneous Atomic Reactions

Abstract: The absolute rate of the recombination of three hydrogen atoms is calculated entirely theoretically. The manner in which rotation determines the dimensions of the activated complex in cases having little or no activation energy is discussed. The theoretical data are in good agreement with the experimental rates of Steiner and of Amdur. An immediate consequence of the theory is that energy transfer occurs most effectively among particles which can react with each other, free atoms being more efficient than molecules. A qualitative application of potential surfaces to the problem of energy transfer as met in velocity of sound experiments and in experiments on maintenance of high pressure rates of unimolecular reactions is made.

The Vitreous State

Abstract: The tendency of glass forming substances to supercooling is discussed in connection with the existence of large or irregular groups in the melts of such substances. If the size of these groups makes their direct addition to the crystal lattice difficult, and if the forces within them are so strong as to prevent a rapid disintegration of the groups, the melt will tend to supercooling and glass formation. In the inorganic glasses consisting of oxides of metalloids or the corresponding acids or salts, the formation of large or irregular groups is caused by the strong tendency of these metalloids to coordinate oxygen in a definite way. If the number of available oxygen atoms is smaller than necessary for the formation of discrete polyhedral groups with the required coordination, the polyhedra will be linked together sharing oxygen atoms. The resulting groups will delay crystallization and thus cause the formation of glass.