Volume 36, Issue 12, 15 June 1962

NMR Study of the Protolysis Kinetics in Simple Amino Acids. I. Sarcosine Hydrochloride and its Ester
View Description Hide DescriptionThe mean lifetime of the amino group τ of acidic aqueous solutions of sarcosine hydrochloride and sarcosine methylester hydrochloride were measured using the NMR technique at 21±1°C. The experimental results show:
(1) 1/τ is first order in respect to both sarcosine and its ester concentration.
(2) 1/τ depends strongly on 1/a _{H} ^{+} in very acidic solutions and becomes almost independent in dilute acid solution. The interpretation is given in terms of an exchange of protons between the amino acid or its ester with a water molecule which is hydrogen bonded to the amino group. The exchange mechanism involves two steps:[Complex chemical formula][Complex chemical formula]Values of the rate constants for sarcosine hydrochloride are:and for sarcosine methyl ester are:

Calculation of Atomic Valence State Energies of B^{—}, C, and N^{+} in BH_{ n } ^{—}, CH_{ n }, and NH_{ n } ^{+}, n = 1 to 4
View Description Hide DescriptionA general procedure described previously for calculating atomic valence state energies is simplified and extended to calculation of the intra‐atomic portion of resonance energies of two or more valence bond structures. The revised method is illustrated by its detailed application to the ^{1} A _{1} state of CH_{2} (in which, however, the nuclei are displaced to a linear configuration). The atomic valence state and intra‐atomic resonance energies of B^{—}, C, and N^{+} in various electronic states of BH_{ n } ^{—}, CH_{ n }, and NH_{ n } ^{+}, respectively, are then given as a function of hybridization.

Semiempirical Valence Bond Calculations of Electronic Energies of CH, CH_{2}, CH_{3}, and CH_{4}
View Description Hide DescriptionA new energy formula based upon valence bond theory is derived for the ground and some low‐lying excited states of CH_{ n } molecules. The formula essentially partitions the molecular energy into the following parts: promotional energy, Coulomb energy, bond exchange energy, exchange energy from nonbonded interactions (homogeneous and heterogeneous separately), and resonance energy (involving covalent structures only). Dependencies of all parts on hybridization are taken into account. Experimental energies of atomization of the ^{2}Π and ^{2}Δ states of CH, and of CH_{4}, are used to calibrate the method, and a C–H distance of 1.12 Å is used throughout. The unobserved ^{4}Σ^{—} state of CH is predicted to be 10.4 kcal (0–0 difference) above the ground state. A linear ^{3} B _{1}ground state of CH_{2} is obtained; 0–0 transitions to strongly bent (100°) ^{1} A _{1} and linear ^{1} B _{1} states are predicted at 12.4 and 25.0 kcal, respectively. The energy of CH_{3} is minimum when planar. C–H bonddissociation energies (in kcal) are predicted as follows: CH_{3}–H, 89; CH_{2}–H, 106; CH–H, 119. Arguments are presented to show that these values are quite consistent with available spectroscopicionization potentials and electron impact appearance potentials, although the first predicted value may be some 5 to 10 kcal too low, and the last predicted value correspondingly too high.

Radius of Gyration of Polymer Chains. II. Segment Density and Excluded Volume Effects
View Description Hide DescriptionThe segment density ρ(r) at a distance r from the center of mass is evaluated for chains constrained to have a large specified radius of gyration R. It is found thatwhere N is the number of segments and H( ) is the step function. It is argued that this conditional distribution takes better account of large excluded volume effects than a simple scaling of the random flight ρ(r).

Calculation of p‐Band Positions of Aromatic Polycyclic Hydrocarbons by Limited Configuration Interaction Method
View Description Hide DescriptionThe positions of p‐bands of 20 aromatic polycyclic hydrocarbons have been calculated by the semiempirical limited configuration interaction method in a π‐electron approximation using Hückel's molecular orbitals. The agreement with experimental values is very good. The effect of the extent of configuration interaction has been studied. It has been demonstrated that the contribution of electron repulsion integrals is nearly constant within this class of hydrocarbons. The failure of the approximation of Hückel in the studies of spectra of compounds with conjugated double bonds belonging to different classes of hydrocarbons, has been explained by the fact that the contribution of electron repulsion integrals is larger with polyenes and considerably smaller with tropylium and its benzoderivatives. The usefulness of the approximation of Hückel within one class of compounds is demonstrated by a comparison of the experimental and theoretical (according to Hückel) positions of the lowest energy absorption maximum of the aromatic hydrocarbon derivatives.

Infrared Absorption Spectrum of CD_{4} at 4500 cm^{—1}
View Description Hide DescriptionA high‐resolution infrared absorptionspectrum is presented for the region of the first overtone of the triply degenerate vibrational fundamental ν_{3} of CD_{4}. The measured lines between 4430 and 4550 cm^{—1} are reproduced and tabulated. Comparisons are made between the tetrahedral splittings in this spectrum and those in the spectra ν_{3} and ν_{1}+ν_{4} of CH_{4}.

Spectroscopy in Liquid‐Rare‐Gas Solvents. Infrared Spectra of CH_{4} in Argon and of HCl in Xenon
View Description Hide DescriptionA low‐temperature cell employing barium fluoride windows and indiummetal gaskets has been built and is being used for the study of rotational, vibrational, and electronic motions of molecules in liquid rare gases. The ν_{3} fundamental of CH_{4} in liquidargon shows a single, relatively sharp Q branch. The P and R branches are probably present but apparently are lost in the wings of the Q branch. The infrared spectrum near 3.5 μ of HCl in liquidxenon shows well‐resolved P, Q, and R branches, but the individual rotational lines are not resolved. The O branch is not resolved from the tail of the P branch, but there is some indication of the S branch on the high‐frequency side of the spectrum. The Q branch is shifted 36 cm^{—1} to the low‐frequency side of its gas‐phase position. The appearance of O, Q, and S branches is expected because of the presence of an induced dipole moment through the polarizability of the solvent. The agreement between the observed spectrum and that anticipated on the basis of nearly free rotation gives good evidence for the existence of quantized rotational motions of HCl in liquidxenon.

Sixth and Seventh Virial Coefficients for the Parallel Hard‐Cube Model
View Description Hide DescriptionA procedure for calculating virial coefficients for parallel hard lines, squares, and cubes is outlined, and the sixth and seventh virial coefficients are computed for these models. The essential step in the evaluation of the star integrals lies in the recognition of the fact that only a few ``subintegrals'' contribute to each virial coefficient, relative to the total number of labeled star integrals. Both the sixth and seventh virial coefficients are negative for hard cubes, a fact interesting from the point of view of phase transitions. Approximations to the excess entropy are given for squares and cubes.
The procedure for the star integrals is extended to the calculation of approximations to the pair distribution function and the potential of the mean force. These functions are calculated through the fourth approximation for hard lines, squares, and cubes.
The topological graphs needed for the above investigations, together with the values of the related integrals in one dimension, are displayed.

Gas‐Phase Radiolysis of Propane
View Description Hide DescriptionThe radiolysis of CH_{3}CD_{2}CH_{3} and of equimolar C_{3}H_{3}—C_{3}D_{8} mixtures in the presence of radical scavengers has been investigated as a function of pressure from 0.35 to 6000 mm and as a function of temperature from 40° to 220°C.
In the presence of scavengers, hydrogen and methane are mainly produced by molecular elimination. Values for the ratio CH_{3}D/CH_{4} were found to increase with pressure and with surface to volume ratio of the irradiation vessel. Ethane is mostly formed by a hydrogen transfer reaction such asFrom the distribution of the isotopic ethanes formed in the radiolysis of CH_{3}CD_{2}CH_{3}, it can be concluded that the hydrogen atoms in the CH_{3}CD_{2} ^{+} ion undergo a rapid randomization prior to reaction with propane.
Ethylene can be accounted for by the occurrence of the following processes: (a) decomposition: C_{3}H_{8} ^{*}→CH_{4}+C_{2}H_{4}, (b) ion molecule reactions, (c) decomposition of vibrationally excited propyl and/or ethyl radicals.
From a comparison of the radiolysis results with the mass spectral cracking pattern of propane and recent photochemical studies, it can be deduced that the decomposition of propane ion and of neutral excited propane molecules are responsible for the products. The relative importance of these two modes of decomposition depends on the pressure and the size of the reaction vessel.

Photosensitized Reaction between Hydrogen (^{2} P) Atoms and Molecular Nitrogen
View Description Hide DescriptionThe reaction between H(^{2} P) atoms and molecular nitrogen has been studied. H(^{2} P) atoms were produced by irradiating ground‐state H(^{2} S) atoms, generated in a microwavedischarge, with Lyman‐alpha radiation at 1216 Å (∼10^{14}—10^{15} quanta sec^{—1}). The interaction of H(^{2} P) atoms with N_{2} produces ammonia but not hydrazine. Two alternative mechanisms of the primary reaction are proposed. The first involves transfer of electronic energy.The second possibility is a chemical mechanism involving atom transfer.Ammonia is formed either by reaction of N with H or by reaction of NH with H or H_{2}.

Effect of Adsorbed Phases on the Electrical Conductivity of Synthetic Crystalline Zeolites
View Description Hide DescriptionThe electrical conductivity of Linde synthetic crystalline zeolites type X and type A has been measured as a function of various adsorbed phases in the crystals. The potential energy barrier for the conduction process is decreased by the interaction of the adsorbed molecules with the electrostatic field or the field gradient in the lattice. Polar molecules, such as water and ammonia, exhibit a strong association through ion‐dipole interactions with the most mobile cations.
The mechanism of adsorption of various molecules and the self‐diffusion of sodium ions in these phases at discussed in terms of changes in the activation energy,free energy, and entropy of the conduction process. The relative importance of the electrostatic, dispersion, and quadrupole contributions to the interaction energy of the adsorbate with the zeolite is described.

Thermodynamics of Small Systems
View Description Hide DescriptionIt is shown in this paper that the differential equations of macroscopic thermodynamics can be generalized in such a way that they apply as well to small (i.e., nonmacroscopic) systems. Conventional thermodynamic relations then follow from the present treatment as a limiting case (large system). As with macroscopic thermodynamics, there are two main classes of applications: (1) as an aid in analyzing, classifying, and correlating equilibrium experimental data on ``small systems'' such as (non‐interacting) colloid particles, liquid droplets, crystallites, macromolecules, polymers, polyelectrolytes, nucleic acids, proteins, etc.; and (2) to verify, stimulate, and provide a framework for statistical mechanical analysis of models of finite (i.e., ``small'') systems. A well‐known experimental and theoretical example (in which there are sizable effects of chain length) is the helix‐coil transition in synthetic polypeptides and polynucleotides. Unlike macroscopic thermodynamics,thermodynamic functions are different for different environments (open, closed, isothermal, siobaric, etc.). Although it is possible to derive a single set of thermodynamic equations applicable to all environments, it proves useful to give a separate analysis for each environment. Several cases are discussed, and a few simple statistical mechanical models are used for purposes of illustration. The partition function for a ``completely open'' small system can be used without any special technique such as is required when this partition function is applied to a macroscopic system. Solvent effects are discussed and details are given in one case. The present method provides an invariant treatment of the spherical interface of a drop or bubble, independent of any choice of dividing surface. Usually, only mean values of fluctuating extensive variables appear in thermodynamic equations. This is justified in macroscopic thermodynamics because fluctuations are generally unimportant. The situation is different for small systems and we derive, in one case, a hierarchy of thermodynamic equations involving higher moments of the probability distribution of fluctuating extensive properties.

Many‐Electron Theory of Atoms and Molecules. II
View Description Hide DescriptionIt was shown in Paper I that to calculate the correlation energy of an N‐electron system only the unique pairs of Hartree—Fock electrons need be considered. Methods for obtaining these pair correlations are developed. Each pair satisfies a Schrödinger equation similar to that of, say, He or H_{2}. For π electrons the corresponding equation turns out to be just the ``π‐electron Hamiltonian.'' In a closed‐shell system, to obtain any of the pair functions one minimizes the energy of just that pair. There is no ``nightmare of inner shells.'' With the procedure given, any well‐known two‐electron method such as Hylleraas' r _{12}‐coordinate, ``open shell'' or even Heitler—London can be used for an Hartree—Fock pair depending on the nature of the pair. This ``exact pair'' theory leads to ``first‐order'' pairs and to a Brueckner‐type theory for finite systems upon further approximation.

Molecular Chaos and the Boltzmann Equation
View Description Hide DescriptionThe form of the Boltzmann equation implied by a general form of the molecular chaos assumption is derived. It is shown that the Bogolyubov hypothesis is a form of molecular chaos, which is compared with other forms of molecular chaos that have been used in derivations of the Boltzmann equation. The determination of the Boltzmann equation for an infinite system of rigid spheres is reduced to the evaluation of integrals that require only two‐body collision dynamics; the determination is carried explicitly only to the ternary‐correlation approximation.

Electron Paramagnetic Resonance Spectra of Copper Complexes
View Description Hide DescriptionThe electron paramagnetic resonance spectra of a number of copper complexes and of vanadyl acetylacetonate were measured in solution and in the vitreous state. By a judicious choice of various mixtures of solvents, good glasses could be obtained at low temperature, which exhibited spectra with very sharp lines. In a number of cases a complete analysis of the spectrum was possible. We were then able to calculate the magnetic parameters and some properties of the wave functions by assuming either D _{4h } or D _{2h } symmetry. It appears that the vitreous state is well suited for a study of ligand interaction. A hyperfine splitting due to the magnetic moment of nitrogen ligand atoms could often be observed in the vitreous state when it could not be observed in the liquid state. Relaxation of ligands is qualitatively discussed.

Direct Observation of Individual Adatoms: Nitrogen on Tungsten
View Description Hide DescriptionThe utility of the field ion microscope for adsorption studies has been explored by examining the interaction of nitrogen with an atomically smooth tungstensurface. Individual nitrogen adatoms are shown to be visible, and it is demonstrated that adsorption fails to perturb the lattice permanently. In probing the room‐temperature distribution of adsorbed material, the closely packed (110) is found to remain bare, even when exposed to nitrogen at p=2×10^{—6} mm for 2 hr. All the other planes, with the possible exception of the {100} and {130}, are irreversibly covered. Nitrogen, presumably in the form of atoms, is bound on the (110) only at T<190°K. Adsorption on this plane at higher temperatures is limited not by an activation barrier but rather by thermodynamics: the binding energy on the (110) is only 5.1 ev, compared with 6.7 ev elsewhere on the surface.

Second Virial Coefficient of Polyelectrolytes. I
View Description Hide DescriptionThe second virial coefficient of polyelectrolytes at the limit of zero polymer concentration was studied using an interionic interaction theory based on a spherical model for macro‐ions. A formulation of the polyelectrolyte—polyelectrolyte interaction parameter β_{22} is presented. A simple relation for the Donnan equilibrium, which was originally found with a rod‐like model, and which is related to the simple electrolyte—polyelectrolyte interaction parameter β_{23} is discussed. It is shown, for poly(sodium phosphate)—sodium bromide—water system, that the second virial coefficient, which is given as a function of β_{23} and β_{22}, can be described satisfactorily with two adjustable parameters, the dimension of macro‐ions R and its polymer concentration dependence ∂R/∂n _{2}. From the observed value of second virial coefficient, ∂R/∂n _{2} is found to be positive at the limit of zero polymer concentration, in contrast to the negative values of the derivative at higher concentrations. The polymer concentration dependence of the osmotic effect is shown to be consistent with a positive value for ∂R/∂n _{2}.

General Potential‐Energy Function for Exchange Reactions
View Description Hide DescriptionA general potential‐energy function for linear triatomic systems has been developed for use in connection with reaction kinetics calculations. The function is a generalization of the Morse function with a sufficient number of adjustable parameters to permit arbitrary fixing of the location and curvatures of the saddle point of the potential energy surface. The function reduces, of course, to the Morse function when one of the atoms is infinitely distant from the other two. Since the characteristics of the saddle region are adjustable, the function is particularly useful in connection with computations designed to test the effect of different shapes of potential energy surfaces upon reaction probabilities. The function is most readily used for symmetric reactions, but it can be further generalized to cover unsymmetric cases.

Inelastic Scattering from Atoms at Medium Energies. I. Bound States
View Description Hide DescriptionThe problem of computing differential scattering cross sections for the inelastic scattering of 10–80 kv electrons from atoms is treated. Expressions for the electron scattering factor for the excitation of bound states of atoms for small excitation energies are presented using the first Born approximation. The scattering factor and differential cross section for argon at 40 kv have been calculated neglecting spin and polarization effects. Both Hartree—Fock and Slater central‐field wave functions were used in these calculations. Selection rules for electron excitation of bound states of atoms and the behavior of the total inelastic scattering intensity at small scattering angles are discussed. Approximate formulas for the first Born approximation total cross sections have also been derived.

Interpair Nuclear Magnetic Relaxation in Hydrated Crystals
View Description Hide DescriptionA set of pulsed rf spin‐lattice relaxation timemeasurements has been made on the proton system in CaSO_{4}·2H_{2}O. The measurements were performed at several crystal orientations, and over a temperature range from 160° to 365°K. A more limited set of measurements was performed on the proton and Li^{7} systems in Li_{2}SO_{4}·H_{2}O powder. In both systems there is a strong relaxation mechanism arising from dipolar motion. It appears that this relaxation arises from 180° flips of the water molecules. The T _{1} data gives a motional activation energy of 6.2±0.5 kcal/mole in CaSO_{4}·2H_{2}O, a reasonable energy for the two hydrogen bonds which must be broken in the postulated motion. Steady‐power absorption line measurements show essentially no narrowing of the proton resonance, in spite of the fact that the characteristic motional frequency reaches the Larmor frequency, 9.0 Mc/sec, at about 230°K. Interpair, rather than intrapair, interactions are responsible for the relaxation. A simplified calculation using only two interacting pairs in CaSO_{4}·2H_{2}O indicates that the observed minimum value of T _{1} and the lack of appreciable motional narrowing is reasonably accounted for by the proposed mechanism. A similar calculation for the Li^{7} system in Li_{2}SO_{4}·H_{2}O also yields satisfactory agreement with experiment. The results presented demonstrate the importance of an examination of details of internuclear interactions in a particular crystal in the interpretation of motional effects in magnetic resonance experiments.