Showing papers in "Journal of Chemical Physics in 1961"
TL;DR: In this paper, the in-plane π bonding may be as important in determining the properties of a Cu complex as is the inplane σ bonding, and the relationship between π and σ has been investigated.
Abstract: ESR spectra of copper complexes have been interpreted by means of molecular orbital theory, and the ``covalent'' character of both σ and π bonds have been discussed for a variety of compounds. Overlap integrals have been considered in a consistent manner in treating σ bonds. Particular attention has been given to Cu phthalocyanine and several of its derivatives. The in‐plane π bonding may be as important in determining the properties of a Cu complex as is the in‐plane σ bonding.
1,415 citations
TL;DR: In this article, it was shown that the distortion of the hydrated complex by collisions with other water molecules is responsible for the decrease in T2 in Mn++ (and other) solutions in very high magnetic fields.
Abstract: The proton relaxation time in solutions of paramagnetic ions depends, among other factors, on the relaxation time of the electron spins, τs. It is shown that the latter, for ions of the iron group, is determined mostly by the distortion of the hydrated complex by collisions with other water molecules. The theory provides a quantitative explanation for the decrease in T2 in Mn++ (and other) solutions in very high magnetic fields. The experimentally observed field and temperature dependence of the proton relaxation times, T1 and T2, for ions of the iron group is compared with theory and the features which depend on τs are stressed.
1,192 citations
TL;DR: In this article, the Herzberg-Teller development for vibronic transition moments is introduced into the Kramers-Heisenberg dispersion equation and an equation for the polarizability components is obtained which leads directly to the Raman selection rules.
Abstract: The Herzberg‐Teller development for vibronic transition moments is introduced into the Kramers‐Heisenberg dispersion equation. It is shown how ``forbidden'' character (vibrationally induced intensity) in allowed electronic transitions is responsible for the Raman intensities of fundamentals. This suggests a direct link between certain vibronic spectroscopic observations and Raman intensities. The development is carried to the first order in nuclear displacements only—the higher terms give rise to Raman intensities of combinations and overtones. An equation for the polarizability components is obtained which leads directly to the Raman selection rules and in addition provides interesting predictions concerning the Raman and the resonance Raman effect in relation to excited electronic states. Rules are worked out governing the participation of excited electronic states in the Raman effect and these are employed to demonstrate a separability of σ and π contributions to the scattering of totally symmetric modes. The polarizability expression obtained here is compared with that of the semiclassical theory of Shorygin and an interesting resemblance is found. Finally it is shown how, depending on details of the electronic structure, the predicted form of the frequency dependence of scattered intensity ranges between the two expressions that have been commonly used to interpret observations.
1,063 citations
TL;DR: In this article, it was shown that at small Δv considerable energy is required to redistribute the excess volume; however, at Δv considerably greater than some value δvg (corresponding to potentials within the linear region), most of the volume added can be redistributed freely.
Abstract: Free volume vf is defined as that part of the thermal expansion, or excess volume Δv which can be redistributed without energy change. Assuming a Lennard‐Jones potential function for a molecule within its cage in the condensed phase, it can be shown that at small Δv considerable energy is required to redistribute the excess volume; however, at Δv considerably greater than some value δvg (corresponding to potentials within the linear region), most of the volume added can be redistributed freely. The transition from glass to liquid may be associated with the introduction of appreciable free volume into the system. Free volume will be distributed at random within the amorphous phase and there is a contribution to the entropy from this randomness which is not present in the entropy of the crystalline phase. According to our model all liquids would become glasses at sufficiently low temperature if crystallization did not intervene. Therefore whether or not a glass forms is determined by the crystallization kinetic constants and the cooling rate of the liquid. The experience on the glass formation is consistent with the generalization: at a given level of cohesive energy the glass‐forming tendency of a substance in a particular class is greater the less is the ratio of the energy to the entropy of crystallization.
1,062 citations
TL;DR: In this article, a theoretical analysis is made of the rate of intramolecular transfer of the odd electron between the two phenyl groups in the mononegative ions of the α,ω-diphenyalkanes, φ-(CH2)n-φ.
Abstract: A theoretical analysis is made of the rate of intramolecular transfer of the odd electron between the two phenyl groups in the mononegative ions of the α,ω‐diphenyalkanes, φ—(CH2)n—φ. The essential features of the calculations are: (a) It is shown that the polymethylene chain can be replaced by a pseudopotential corresponding to an effective direct transfer between the rings. (b) There is a strong tendency for self‐trapping of the odd electron on one phenyl ring, or the other, due to solvent polarization and bond distortions in the rings. This self‐trapping greatly reduces the rate of intramolecular charge transfer. (c) The intramolecular charge transfer occurs as an electronic resonance effect when a short‐lived thermally activated molecular state is formed in which the two rings appear to the odd electron to be equivalent to one another. The activation energy is estimated to be of the order of 1000 cm—1. (d) It is found that the rate of intramolecular charge transfer decreases exponentially with the length of the polymethylene chain, the decrease being as much or more than a factor of ten for each added methylene group.
921 citations
TL;DR: In this paper, the conditional probabilities of occurrence of helical and coiled states of the peptide units were obtained in the form of a 3×3 matrix and the order of this matrix is the lowest possible for the model employed, and is derived by a logical procedure which serves to eliminate redundancies in the enumeration of states.
Abstract: The evaluation of the configurational partition function of a polypeptide molecule, with the internal rotation angles as variables, leads to an improved treatment of the phenomenon of helix‐coil transition in polypeptide molecules. The conditional probabilities of occurrence of helical and coiled states of the peptide units are obtained in the form of a 3×3 matrix. The order of this matrix is the lowest possible for the model employed, and is derived by a logical procedure which serves to eliminate redundancies in the enumeration of states. The eigenvalues of this matrix yield the various molecular averages as functions of the degree of polymerization, temperature, and molecular constants. Explicit formulas are given for the degree of intramolecular hydrogen bonding, average number of helical sequences, and the distribution of their lengths, as well as the number average and the weight average of these lengths.
750 citations
TL;DR: In this paper, it is shown that the intramolecular energy transfer efficiency is a sensitive function of the relative positions of the resonance energy levels of the ions and the metastable triplet states of the complexes.
Abstract: Results of luminescence studies on chelates of La3+, Sm3+, Eu3+, Gd3+, Tb3+, Dy3+, Tm3+, Yb3+, and Lu3+ are reported It is shown that the intramolecular energy transfer efficiency is a sensitive function of the relative positions of the resonance energy levels of the ions and the metastable triplet states of the complexes In the case of Eu3+ it is demonstrated that, by a proper choice of ligands, it is possible to selectively excite only the lowest resonance level of the two existing resonance levels of this ion Coupling of the rare earth ions to the ligands is discussed, and a comparison is made between the optical properties of rare earth ions in chelates and in inorganic salts
687 citations
TL;DR: In this paper, a model for the calculation of viscosity, diffusion, thermal diffusion, and the translational part of the heat conductivity of dilute polar gases is proposed.
Abstract: A model is proposed for the calculation of viscosity, diffusion, thermal diffusion, and the translational part of the heat conductivity of dilute polar gases. It is assumed that the molecular‐collision trajectories are negligibly distorted by transfer of internal rotational energy, and that the relative orientation of two colliding dipoles remains fixed throughout the significant portion of the collision trajectory around the distance of closest approach. For this model, the Chapman‐Enskog theory retains its usual form, but the collision integrals which appear must be averaged over all possible relative orientations occurring in collisions. Collision integrals have been calculated for the Stockmayer (12–6–3) potential, [open phi](r)=4e0[(σ0/r)12−(σ0/r)6+δ(σ0/r)3], for kT/e0 from zero to 100 and for δ from —2.5 to +2.5, and averaged over all orientations (assumed equally probable). Sufficient collision integrals are tabulated that the convergence error of the Chapman‐Enskog theoretical expressions is not a...
575 citations
TL;DR: In this paper, a quantitative theory of the isotropic electron−nuclear spin interactions of carbon 13 in pi-electron radicals is presented and applied to the hyperfine splittings observed in the electron spin resonance spectra of these substances.
Abstract: A quantitative theory of the isotropic electron‐nuclear spin interactions of carbon 13 in pi‐electron radicals is presented and applied to the hyperfine splittings observed in the electron spin resonance spectra of these substances. The splittings arise from sigma‐pi interactions which polarize both the 1s and 2s electrons. The 1s‐orbital spin polarization is shown to contribute a term of negative sign with a magnitude comparable to that from the 2s electrons. For an sp2 hybridized carbon atom that is bonded to three atoms, Xi (i=1, 2, 3), the hyperfine constant aC has the form aC=(SC+ ∑ i=13QCXiC)ρπ+ ∑ i=13QXiCCρiπ, where ρπ and ρiπ(i=1,2,3) are the pi‐electron spin densities on atoms C and Xi, respectively. The contribution of the 1s electrons is determined by SC and that of the 2s electrons by the Q's, where QBCA is the sigma‐pi parameter for the nucleus of atom A resulting from the interaction between the bond BC and the pi‐electron spin density on atom B. Calculations for a planar CHC2 fragment model...
506 citations
TL;DR: In this paper, the authors measured the nuclear relaxation in water and showed that the increase of relaxation rate is observable in natural water (0.037% O17), and becomes very appreciable in water enriched in O17.
Abstract: Measurements of the nuclear relaxation in water are reported. The transverse relaxation rate (1/T2) of the proton resonance is pH dependent. The effect is shown to be due to a spin‐spin splitting of the proton resonance by O17 (spin 5/2), which is only partially averaged out by proton exchange. The increase of relaxation rate is observable in natural water (0.037% O17), and becomes very appreciable in water enriched in O17. Additional information can be obtained by measuring relaxation rates in the presence of an rf field H1, using a method due to Solomon. A study of the width of the O17 resonance as a function of pH is in quantitative agreement with the results of the proton resonance. The observations provide a direct determination of the rate constants of the exchange reactions: H2O+H3O+→ lim k1H3O++H2O and H2O+HO−→ lim k2HO−+H2O. It is found that k1=(10.6±4)×109 liter mole−1 sec−1 and k2=(3.8±1.5)×109 liter mole−1 sec−1. The spin‐spin interaction between H and O17 in water is determined as 92±15 cps. In the Appendices, theoretical equations for the exchange contribution to the relaxation rate are derived.
475 citations
TL;DR: In this paper, a general mathematical treatment of vibronic coupling of two electronic states in molecules and dimers is presented, and the 2×2 matrix Hamiltonian which is derived is shown to reduce to two one-dimensional Hamiltonians provided a certain minimum amount of symmetry is present.
Abstract: A general mathematical treatment of vibronic coupling of two electronic states in molecules and dimers is presented. The 2×2 matrix Hamiltonian which is derived is shown to reduce to two one‐dimensional Hamiltonians provided a certain minimum amount of symmetry is present. Some general selection rules governing electronic transitions to these states from the ground state are obtained, showing that the spectral distribution in hot bands may differ considerably from that in normal bands when vibronic coupling occurs. A special model which considers the coupling to arise from a single mode of vibration is presented. Two limiting cases which can be treated approximately by perturbation theory are considered in detail. These are shown to give rise to a ``pseudo Jahn‐Teller effect'' and to vibrational borrowing in the two different limits.
TL;DR: In this paper, a model for solid-solid or solid-gas reactions between spherical particles and a fine powder or gas has been developed, and the oxidation of uniformly sized nickel spheres has been shown to fit this model to 100% reaction.
Abstract: A model for solid‐solid or solid‐gas reactions between spherical particles and a fine powder or gas has been developed. The oxidation of uniformly sized nickel spheres has been shown to fit this model to 100% reaction. Previously reported models are inadequate because they do not meet the boundary conditions set down and because the volume of the product was assumed to equal that of one of the reactants. The inadequacy of earlier experimental results has been explained by the failure to experimentally meet the boundary conditions imposed.
TL;DR: The origin of the relative nuclear resonance shifts in monosubstituted benzenes has been investigated in this article, where the largest resonance shifts were observed for the carbon atom directly bonded to X.
Abstract: The origin of the relative nuclear resonance shifts in monosubstituted benzenes has been investigated. In order to obtain more complete experimental information both C13 and H1 resonance shifts in a variety of aryl‐X compounds were measured. The H1 resonances were measured on 5 mole % solutions in cyclohexane to minimize solvent effects; the carbon shifts were obtained from natural abundance C13 resonance measurements in the neat liquid. Unambiguous assignments of both H1 and C13 resonance spectra were made possible with the aid of deuterated compounds. The largest resonance shifts were observed for the carbon atom directly bonded to X. As in the corresponding CH3X compounds, these shifts arise primarily from the inductive and magnetic anisotropy effects of X. Magnetic anisotropy effects of X are also observable in both the C13 and H1 resonances at the ortho position. A very close correspondence between C13 and H1 resonances is observed at the para position, where the primary contribution to the relative shifts arises from resonance effects of X. This implies that the proton resonance responds to the π‐electron density on the carbon to which it is bonded, and that under favorable conditions, both H1 and C13 resonance shifts might be employed to obtain information about the π‐electron density distribution in aromatic systems. At the meta position the C13 resonance shifts are surprisingly small and uniform, indicating small or negligible inductive effects due to X, and there is no evident correlation with the meta‐proton shifts. Both the C13 and H1 shifts at the para position show an approximate correlation with chemical reactivity parameters (Hammett σ constants) but no such correlation exists for the meta‐carbon or meta‐hydrogen shifts.
TL;DR: In this paper, a family of curves is obtained, determined by the location of the bonded atoms in rows of the periodic table, which correspond closely to those in Badger's rule for quadratic force constants.
Abstract: Empirical study of cubic and quartic vibrational force constants for diatomic molecules shows them to be approximately exponential functions of internuclear distance. A family of curves is obtained, determined by the location of the bonded atoms in rows of the periodic table. Displacements between successive curves correspond closely to those in Badger's rule for quadratic force constants (for which the parameters are redetermined to accord with all data now available). Constants for excited electronic and ionic states appear on practically the same curves as those for the ground states. Predictions based on the diatomic correlations agree with the available cubic constants for bond stretching in polyatomic molecules, regardless of the type of bonding involved. Some implications of these regularities are discussed.
TL;DR: In this paper, a series of uranyl complexes KxUO2Ly(NO3)2, where L is the variable ligand (or ligands), has been prepared; it has been shown that a ligand series may be defined using the antisymmetric stretching frequency of the uranyl entity, and this series exhibits a remarkable parallelism with the spectrochemical series defined by Δ in octahedral complexes of transition metals of the first and 2nd series.
Abstract: A series of uranyl complexes KxUO2Ly(NO3)2, where L is the variable ligand (or ligands), has been prepared; it has been shown that a ligand series may be defined using the antisymmetric stretching frequency of the uranyl entity, and this series exhibits a remarkable parallelism with the spectrochemical series defined by Δ in octahedral complexes of transition metals of the 1st and 2nd series. This parallelism has been rationalized using a mixed ligand field theory in which the uranyl ion is considered subject to bonding with ligands which are arranged hexagonally in a plane equatorial to the O–U–O axis. It is shown that the large changes of ν3 and ν1 are due primarily to electron population of the φu and δu atomic orbitals of uranium. Such population is physically equivalent to the reductions AmO2+ +→AmO2+ and NpO2+ +→NpO2+, which cause a decrease of approximately 100 cm—1 in ν3. It is further shown that Δν3 = — electrostatic effect — σ(L→M) — π(L→M) ± π(M→L), where in the last term the plus sign is the ...
TL;DR: The infrared spectra of CH3OH, CH3OD, CD3O, and CD3OD in the five phases gas, liquid, vitreous solid, α-crystal, and (except perhaps for CD3OH and β−crystal for which the solid-solid transitions have not been studied) β•crystal have been recorded in the range 4000 to 300 cm−1 as discussed by the authors.
Abstract: The infrared spectra of CH3OH, CH3OD, CD3OH, and CD3OD in the five phases gas, liquid, vitreous solid, α‐crystal, and (except perhaps for CD3OH and CD3OD for which the solid‐solid transitions have not been studied) β‐crystal have been recorded in the range 4000 to 300 cm−1. The Raman spectrum of liquid CD3OH has been recorded. A complete assignment of the internal modes is given, which differs somewhat from previous assignments for the CH3 bending and rocking vibrations. No significant difference in spectrum occurred between the α‐crystal and β‐crystal phases. Under the full symmetry of the β‐phase determined by x‐ray diffraction only one OH out‐of‐plane bending band should occur. Two bands are observed, and it is concluded that the carbon and oxygen atoms in one chain are not coplanar, as is required by the symmetry determined by x‐ray diffraction [K. J. Tauer and W. N. Lipscomb, Acta Cryst. 5, 606 (1952)], but that the chains are puckered and the x‐ray symmetry arises because the puckered chains are irr...
TL;DR: In this paper, a general description of an application of the Wilson's GF-matrix method to the treatment of optically active lattice vibrations is given, and formulas are derived for the calculation of the frequencies of the lattice vibration of a one-dimensional, the diamond, and CaF2 lattices.
Abstract: A general description has been given of an application of the Wilson's GF‐matrix method to the treatment of optically active lattice vibrations. As examples, formulas are derived for the calculation of the frequencies of the lattice vibrations of a one‐dimensional, the diamond, and CaF2 lattices.
TL;DR: In this paper, it was shown that the same equation of state of hard sphere fluid is obtained when one used the integral condition as when the infinity condition is used, and that the results of the two-dimensional rigid sphere fluid were in good agreement with machine Monte Carlo calculations by Jacobson and Wood and dynamical machine calculations of Wainwright and Alder.
Abstract: The approximate theory of the three‐dimensional hard sphere fluid developed by Reiss, Frisch, and Lebowitz has given astonishingly good predictions with little labor. In an attempt to investigate the reason for this result we adduce, in this paper, further evidence for the internal consistency of the approximations of this theory. Thus it is noted that the same equation of state of hard sphere fluid is obtained when one used the ``integral condition'' as when the ``infinity condition'' is used. We have then applied the theory to study the thermodynamic properties, in particular the equation of state, of the rigid sphere fluid in two and one dimensions. The approximate equation of state of the two‐dimensional rigid sphere fluid is in good agreement over the range of fluid densities with the results of the machine Monte Carlo calculations by Jacobson and Wood and dynamical machine calculations of Wainwright and Alder. The exact Tonks' equation of state of the one‐dimensional rigid sphere fluid is derived in a particularly simple manner.
TL;DR: In this article, a model for the diffusion of gases in porous media in the absence of pressure gradients is presented, in which the porous medium is visualized as a collection of uniformly distributed ''dust'' particles which are constrained to be stationary.
Abstract: A model is presented for the diffusion of gases in porous media in the absence of pressure gradients, in which the porous medium is visualized as a collection of uniformly distributed ``dust'' particles which are constrained to be stationary. By formally considering the dust particles as giant molecules, it is possible to derive all the desired results very simply from rigorous kinetic theory as special cases of multicomponent mixtures. By formally varying the mole fractions of the real gas molecules, the entire pressure range from the Knudsen region to the normal diffusion region can be covered. This model permits the first satisfactory theoretical derivation of the experimentally discovered fact that the flux ratio for binary mixtures is equal to (m2/m1)½ at all pressures (not just in the Knudsen region). It also permits a rigorous theoretical treatment of the entire transition region for the first time, from which is obtained the usual Bosanquet interpolation formula and a differential equation for diffusion which covers the entire range (and appears to be new). The model gives no quantitative a priori characterization of the porous medium itself, but if one gas mixture is measured in a given medium, then the behavior of other gas mixtures in the same medium can be predicted.
TL;DR: In this article, an investigation of the major contributions which make up the relative chemical shifts in CH3X and CH3CH2X compounds was made, revealing surprisingly large contributions to both C13 and H1 shifts arising from magnetic anisotropy effects of the X substituent.
Abstract: An investigation has been made of the major contributions which make up the relative chemical shifts in CH3X and CH3CH2X compounds. In order to obtain more detailed information, both the carbon and hydrogen chemical shifts were measured. The carbon shifts were obtained by measuring natural abundance C13 resonances in the pure liquids; the H1 resonances were measured on gaseous samples to avoid solvent effects. The results reveal surprisingly large contributions to both C13 and H1 shifts arising from magnetic anisotropy effects of the X substituent. In CH3X compounds, the contribution to the proton shifts is negative while that to the C13 shifts is positive. In CH3CH2X compounds, these effects contribute to the resonance shifts of carbon and hydrogen nuclei in both the methylene and methyl group. When such contributions are allowed for, an approximate correlation with the electronegativity of X can be obtained, indicating that inductive effects, together with anisotropy effects, account for the major part ...
TL;DR: In this paper, the zones of pressure and temperature in which diamond growth occurs have been determined for a number of metals, and the experimentally determined equilibrium line agrees very closely with the theoretical extrapolation of the thermodynamically calculated line proposed by Berman and Simon.
Abstract: Diamond growth occurs at high temperatures and pressures in the presence of certain molten metals which serve as solvent catalysts. The zones of pressure and temperature in which diamond growth occurs have been determined for a number of metals. These zones are bounded on the low‐temperature side by the melting point of the metal‐carbon eutectic at pressure. They are bounded on the high‐temperature side by the diamond‐graphite equilibrium line. This experimentally determined equilibrium line agrees very closely with the theoretical extrapolation of the thermodynamically calculated line proposed by Berman and Simon, viz., P(kbar)=7.1+0.027T(∘K).
TL;DR: In this paper, a study of the formation of cubic boron nitride showed that the alkali and alkaline earth metals and their nitrides are effective catalysts for converting hexagonal BN into cubic, and a minimum of about 45 000 atm and 1500°C has been found to be optimum up to the present time.
Abstract: A study of the formation of cubic boron nitride shows that the alkali and alkaline earth metals and their nitrides are effective catalysts for converting hexagonal boron nitride into cubic. The pressure and temperature required varies with the catalyst, and a minimum of about 45 000 atm and 1500°C has been found to be optimum up to the present time.
TL;DR: In this article, a priori account of the van der Waals minimum and the repulsion region with a wave function of sufficient flexibility to deal with both is given, in terms of atomic and overlap populations.
Abstract: Single‐configuration LCAO MO SCF wave functions and corresponding total energies were calculated for two ground‐state He atoms interacting over an extensive range (0.4 to 12.0 A). Comparison with available experimental data is made; remarkably good agreement is obtained for distances greater than 1.5 A. For the first time, it is believed, an a priori account is given of both the van der Waals minimum and the repulsion region with a wave function of sufficient flexibility to deal with both. The details of repulsion and of bonding in the van der Waals region are analyzed in terms of atomic and overlap populations.
TL;DR: Theoretical considerations suggest that the absorption and emission spectra of certain dyes may be shifted by hundreds of angstroms upon the application of a strong electric field.
Abstract: Theoretical considerations suggest that the absorption and emission spectra of certain dyes may be shifted by hundreds of angstroms upon application of a strong electric field. The effect could be called ``electrochromism,'' in analogy to ``thermochromism'' and ``photochromism.'' The theory of the effect is outlined and is discussed in terms of compounds which might be expected to show it most strongly.
TL;DR: In this paper, the authors adapted Howard Reiss' ''Vector model'' to calculate the self-nucleation rate for the sulfuric acid water system and similar systems and concluded that rapid self-Nucleation would take place at sulfur acid partial pressures in the range 10−8−10−10 mm Hg.
Abstract: Howard Reiss' ``Vector model'' was adapted to calculate the self‐nucleation rate for the sulfuric acid‐water system and similar systems.A numerical calculation was carried out for the typical case of 50% relative humidity at 25°C. It was concluded that rapid self‐nucleation would take place at sulfuric acid partial pressures in the range 10‐8‐10‐10 mm Hg. The considerable uncertainty is principally due to lack of data on the partial pressure of sulfuric acid above its aqueous solutions and on the dominant sulfuric acid‐bearing species in humid atmospheres.
TL;DR: In this paper, double and triple ionization by electron impact in molecules is examined and the data support the view that the threshold law for the probability of double ionization is a square-law function of the excess electron energy.
Abstract: Double and triple ionization by electron impact in molecules is examined and, as was found for the monatomic gases, the data support the view that the threshold law for the probability of double ionization is a square‐law function of the excess electron energy. Some excited states have been detected, and autoionization does not seem to be important. The vertical potentials for all the processes of multiple ionization observed have been measured. The relative electronic‐transition probabilities for single, double, and triple ionization are compared. The factors affecting the stability of multiply charged molecular ions are discussed, and an attempt is made to correlate the electron impact data with the molecular structures. It is shown that Coulomb repulsion between the separated charges causes the potential energy functions describing these ions to be of unusual form.
TL;DR: The triplet states of the (φ3PCH3)+(TCNQ)2− and (π3AsCH)+(Tetracyanoquinodimethane)2+ salts are further manifested by an anisotropic splitting of the resonance into a doublet (zero-field splitting) and the appearance of half-field Δm=±2 transitions.
Abstract: Electron spin resonance studies have been carried out on a number of ion‐radical salts based on the strong π‐acceptor tetracyanoquinodimethane (TCNQ). These studies have established that spin correlation exists between the magnetic electrons in these salts, giving rise to a ground singlet state and a thermally accessible triplet state. Typical singlet‐triplet separations (J) derived from observed temperature dependences of EPR signal intensities are 0.034 ev for the [(C2H5)3NH]+(TCNQ)2− salt, 0.062 ev for the (φ3PCH3)+(TCNQ)2− and (φ3AsCH3)+(TCNQ)2− salts, and 0.41 ev for the (morpholinium)+(TCNQ)− salt.The triplet states of the (φ3PCH3)+(TCNQ)2− and (φ3AsCH)+(TCNQ)2− salts are further manifested by an anisotropic splitting of the resonance into a doublet (zero‐field splitting) and the appearance of half‐field Δm=±2 transitions. Detailed analysis reveals that both salts may be represented by the spin Hamiltonian H=βH·g·S+DSz2+E(Sx2−Sy2), with | D/hc |=0.0062 cm−1, | E/hc |=0.00098 cm−1, and gx, gy, and gz...
TL;DR: In this article, a perturbation solution of an assumed Boltzmann-type equation for bimolecular chemical reactions in a homogeneous gas phase consisting of molecules with or without internal degrees of freedom, leads to the conclusion that the law of mass action as well as the usually assumed phenomenological rate expressions for chemical reactions, is strictly valid only in lowest order of the perturbations.
Abstract: A perturbation solution of an assumed Boltzmann‐type equation for bimolecular chemical reactions in a homogeneous gas phase consisting of molecules with or without internal degrees of freedom, leads to the conclusion that the law of mass action as well as the usually assumed phenomenological rate expressions for chemical reactions, is strictly valid only in lowest order of the perturbation. Higher order perturbations introduce an affinity and time dependence in the rate coefficient and the law of mass action becomes inadequate to the extent of the contribution of the effects of the perturbations.A transition state formation of rate coefficients for bimolecular gas‐phase reactions is presented under less restrictive sufficient conditions than reported previously.
TL;DR: In this paper, the role of molecular structure on the difference in the thermodynamic properties of isotopic molecules in the liquid and solid states is summarized, and the results are extended to higher-order quantum corrections for a harmonic potential.
Abstract: Evidence for the role of molecular structure on the difference in the thermodynamic properties of isotopic molecules in the liquid and solid states is summarized. The properties considered are vapor pressure, heats of vaporization, molal volume, and transition temperatures. It is shown that the molecular structure must be taken into consideration even for small quantum effects. In the approximation of the first quantum correction the difference in thermodynamic properties of isotopic molecules in the condensed state depends upon the atomic masses and an energy parameter associated with each atom in the molecule. The results are extended to higher‐order quantum corrections for a harmonic potential. The rules of the mean are obtained directly. Various frequency distributions for the lattice modes are considered. For the case where the internal frequencies in the condensed phase are similar to the free molecule, the ordered quantum corrections can be used for T>(hvmax/12(2)½k)mol; T>(hvlattice/2πk). The role...
TL;DR: In this paper, the effects of orientation on the combinatorial term g for the number of ways to pack together Nx linear polymers (x mers) were evaluated as a function of the molecules in each permitted direction for the case of straight rigid rods.
Abstract: This paper is concerned with the effects of orientation on the combinatorial term g for the number of ways to pack together Nx linear polymers (x mers). Accordingly g is evaluated as a function of the number of molecules in each permitted direction for the case of straight rigid rods. The permitted directions can be continuous so that g is derived as a function of the continuous function f(r) which gives the density of rods lying in the solid angle Δr, or the permitted directions can be discrete so that g is the number of ways to pack molecules onto a lattice. To illustrate the usefulness of the orientation dependent combinatorial terms, liquid crystals are discussed. Another phase is found to exist in addition to the previously predicted nematic phase. This phase is tentatively identified with the cholesteric phase.A procedure is developed for the calculation of the orientation dependent combinatorial term associated with the packing together of molecules of arbitrary shape. A very approximate applicatio...