Showing papers in "Journal of Chemical Physics in 1959"

Molecular Transport in Liquids and Glasses

Abstract: We have derived, by using simple considerations, a relation between the diffusion constant D in a liquid of hard spheres and the ``free volume'' vf. This derivation is based on the concept that statistical redistribution of the free volume occasionally opens up voids large enough for diffusive displacement. The relation is D=A exp[−γv*/vf], where v* is the minimum required volume of the void and A and γ are constants. This equation is of the same form as Doolittle's [J. Appl. Phys. 22, 1471 (1951)] empirical relation between the fluidity φ of simple hydrocarbons and their free volume. It has been shown [Williams, Landel, and Ferry, J. Am. Chem. Soc. 77, 3701 (1955)] that the Doolittle equation also can be adapted to describe the abrupt decrease in molecular kinetic constants with decreasing temperature that accompanies the glass transition in certain liquids. Our result predicts that even the simplest liquids would go through this glass transition if sufficiently undercooled and crystallization did not oc...

Contact Electron‐Spin Coupling of Nuclear Magnetic Moments

Abstract: The valence‐bond theory for the contact electron‐spin coupling of nuclear magnetic moments is used to calculate the proton‐proton, proton‐fluorine, and fluorine‐fluorine coupling constants in ethanic and ethylenic molecules. A considerable simplification is introduced into the theory by approximations which reduce the problem to one involving only a small number of electrons and canonical structures. The agreement between calculated and experimental values is such as to demonstrate that the mechanism considered is the one of primary importance for the nuclear coupling in the compounds studied. Of particular interest is the theoretical confirmation of the observation that in ethylenic compounds the trans coupling between nuclei (HH, HF, FF) is considerably larger than cis coupling.

Studies in Molecular Dynamics. I. General Method

Abstract: A method is outlined by which it is possible to calculate exactly the behavior of several hundred interacting classical particles. The study of this many‐body problem is carried out by an electronic computer which solves numerically the simultaneous equations of motion. The limitations of this numerical scheme are enumerated and the important steps in making the program efficient on the computers are indicated. The applicability of this method to the solution of many problems in both equilibrium and nonequilibrium statistical mechanics is discussed.

Theory of the Phase Transition between Helix and Random Coil in Polypeptide Chains

Abstract: The transition between the helical and randomly coiled forms of a polypeptide chain is discussed by reference to a simple model that allows bonding only between each group and the third preceding Two principal parameters are introduced, a statistical parameter that is essentially an equilibrium constant for the bonding of segments to a portion of the chain that is already in helical form, and a special correction factor for the initiation of a helix A third parameter which specifies the minimum number of segments in a random section between two helical portions has only a minor effect on the results The partition function for this model is handled in two alternative ways, either as a summation suitable for short chains, or in terms of the eigenvalues and eigenvectors of a characteristic matrix; the latter is more suitable for long chains A transition from the random to the helical form is encountered as either the bonding parameter or the chain length is increased The critical value of the bonding pa

Free Energy of a Nonuniform System. III. Nucleation in a Two‐Component Incompressible Fluid

Abstract: By finding the saddle point in the expression derived in Paper I (see reference 8) for the free energy of a nonuniform system, we have derived the properties of a critical nucleus in a two‐component metastable fluid.At very low supersaturations, we find that the properties of the nucleus approach those predicted by the classical theory that assumes the nucleus to be homogeneous with an interfacial energy that does not vary with curvature. However, with increasing supersaturation, the following changes occur in the properties of the critical nucleus. (a) The work required for its formation becomes progressively less than that given by the classical theory, and approaches continuously to zero at the spinodal. (b) The interface with the exterior phase becomes more diffuse until eventually no part of the nucleus is even approximately homogeneous. (c) The composition at the center of the nucleus approaches that of the exterior phase. (d) The radius and excess concentration in the nucleus at first decrease, the...

Statistical Mechanics of Rigid Spheres

Abstract: An equilibrium theory of rigid sphere fluids is developed based on the properties of a new distribution function G(r) which measures the density of rigid sphere molecules in contact with a rigid sphere solute of arbitrary size. A number of exact relations which describe rather fully the functional form of G(r) are derived. These are based on both geometrical considerations and the virial theorem. A knowledge of G(a) where a is the diameter of a rigid sphere enables one to arrive at the equation of state. The resulting analytical expression which is exact up to the third virial coefficient gives the fourth virial coefficient within 3% and the fifth, insofar as it is known, within 5%. Furthermore over the entire range of fluid density, the equation of state derived from theory agrees with that computed using machine methods. Theory also gives an expression for the surface tension of a hard sphere fluid in contact with a perfectly repelling wall. The dependence of surface tension on curvature is also given. ...

Study of the Effects of Substitution on the Absorption Spectra of Porphin

Abstract: A model is presented for the excited states of porphin, which are viewed as arising from two configurations which can be mixed to varying degrees. The effects of substituents are then discussed, first the limitations imposed by symmetry requirements and then the requirements imposed if they act as one electron perturbations. The theory is applied to certain experimental problems. First it is shown how the metal porphins can be viewed as a series showing increasing mixing of the two fundamental configurations. Next the effect of free base formation is explained as a cyclic polyene perturbation. This theory predicts that the lowest porphin transition is polarized parallel to the H–H axis. Formulas are derived for intensity changes caused by various external substituents; their effect on transition energies are also discussed. Finally formulas are developed to account for the effects of aza substitution on the methine bridges.

Structure and Adsorption Characteristics of Clean Surfaces of Germanium and Silicon

Abstract: Diffraction patterns obtained from atomically clean germanium surfaces contained half‐integral order beams in (110) azimuths for both (100) and (110) surfaces and in all azimuths for the (111) surface. These results are considered to be due to displacements of surface atoms from their normal bulk lattice positions in the surface plane. Adsorption of oxygen on all of these surfaces extinguished all of the diffraction beams which were not integral order.In addition to the normal surface lattice spacings of clean (111) and (100) surfaces of silicon, there were surface structures with larger spacings, most of which depended on the conditions of ion bombardment and/or subsequent heat treatment. Two such structures have been observed for the (100) surface of silicon; one is a double‐spaced lattice in the (110) azimuth, similar to that for germanium, and the other has a spacing about 8% greater than that of normal silicon and was obtained only after radiation quenching of the crystal from 1000°C. Two large‐spaced structures were observed for the (111) surface. All of these structures were extinguished by exposure to oxygen. Evidence is presented which indicates that these structures were not due to contamination but to the silicon itself.The method of determining the kinetics of gas adsorption from the low‐energy electron diffraction beams is outlined and the calculations of the fractional coverage and sticking probability are presented for oxygen. For silicon crystals, the calculations of surface coverages and sticking coefficients for oxygen were found to depend on the preceding treatments of the crystals. The rate of adsorption of oxygen was proportional to the pressure, at least for pressures below 10‐6 mm Hg, and depended on the preceding treatments of the crystals. After oxygen adsorption, the clean germanium surface could be regenerated by heating at 500°C for 30 min and for silicon it was regenerated by heating at 900°C for a few minutes. A comparison with results of other observers is given.

Calculation of Energy Levels for Internal Torsion and Over-All Rotation. III

Abstract: A general treatment of hindered internal rotation is given for molecules that can be regarded as a rigid symmetric top attached to a rigid frame which may be completely asymmetric. The perturbation approach developed in previous papers is simplified and extended by use of a method which relates the perturbation coefficients to the exact energy levels obtainable for the limiting case of two coaxial symmetric tops. Tables are given which provide the torsional energy levels and the perturbation coefficients through fourth order in the coupling between internal and over‐all rotation. The tables apply to the lowest three groups of torsional states for a potential barrier of the form V(α)=12VN(1−cosNα)+12V2N(1−cos2Nα), where the periodicity N is arbitrary and O

Free Energy of a Nonuniform System. II. Thermodynamic Basis

Abstract: The thermodynamic treatment of nonuniform systems of Cahn and Hilliard is shown to be equivalent to the self‐consistent thermodynamic formalism of Hart All parameters of the two treatments have been rigorously related and key equations have been shown to be equivalent

C13 Splittings in Proton Magnetic Resonance Spectra. I. Hydrocarbons

Abstract: Indirect spin‐spin couplings between protons and C13 nuclei have been measured for a number of hydrocarbons. The results are interpreted on the basis of a simple semiempirical equation relating the coupling constants with the amounts of s character of the carbon‐atomic orbitals involved in the bonds. No evidence is found for a dependence of the coupling constants on supposed changes in ionic character of the bonds.An equation is also presented relating the coupling constants and the C–H internuclear distances. This provides a new indirect means of evaluating C–H distances, with a reliability apparently at least comparable with that of methods in current use.

Effect of Unimolecular Decay Kinetics on the Interpretation of Appearance Potentials

Abstract: The interpretation of appearance potential data on diatomic molecules should take account of possible effects caused by predissociation, emission of light and autoionization In the case of complex polyatomic molecules, the kinetics of predissociation and the internal thermal energy of the molecules become especially important The intensities of the parent, fragment, and metastable ions produced by photoionization of n‐propylamine, n‐propanol, and methyl ethyl ketone are studied as a function of photon energy The excess kinetic energies of the fragment ions are found to be negligibly small The data are interpreted in terms of Rosenstock's quasi‐equilibrium theory of unimolecular decomposition and indicate that the theory is qualitatively correct for the dissociative processes investigated However, the theory is shown to be quantitatively inadequate at least in the energy range near threshold In this region the rate constant for dissociation varies much more rapidly with energy than the theory predict

Contribution of Bound, Metastable, and Free Molecules to the Second Virial Coefficient and Some Properties of Double Molecules

Abstract: The second virial coefficient for molecules interacting with a spherically symmetric potential is divided into three parts: (1) a contribution Bb, related to the equilibrium constant for the formation of bound double molecules; (2) a contribution Bm, related to the equilibrium constant for the formation of metastably‐bound double molecules; and (3) a contribution Bf, due to molecules which interact but are free to separate after the interaction. Equations are given for determining each of the three parts of the second virial coefficient. A detailed treatment of these three contributions together with numerical tables on a reduced temperature basis is given for the square‐well, Sutherland, and Lennard‐Jones (6–12) potentials.The mean lifetimes of metastably bound double molecules are discussed, and numerical values are given for the special case of argon. Tables for computing mean lifetimes in other Lennard‐Jones gases are given. It is found that most metastably bound double molecules have mean lifetimes c...

Solubility of Carbon in Silicon and Germanium

Abstract: The solubility of carbon in silicon has been measured over the temperature range 1560 to 2900°C. The enthalpy of solution is 59±3 kcal/mole. A phase diagram for the system Si–C is presented, embodying these solubility data as well as the results of other high‐temperature experiments with silicon carbide. It is found that SiC possesses a peritectic point at 2830±40°C. These studies were carried out in argon at pressures as high as 35 atmos. Solubilities of carbon in germanium were measured in the temperature range 2780 to 3170°C, at argon pressures up to 55 atmos, and a tentative phase diagram is given.

General Collision Theory Treatment for the Rate of Bimolecular, Gas Phase Reactions

Abstract: A collisional approach, somewhat similar to the Wang‐Chang and Uhlenbeck treatment for the transport properties of polyatomic molecules, is used to obtain a general expression for the rate of a bimolecular chemical reaction in terms of reaction cross sections. Specialization is then made to the case where a Maxwell‐Boltzmann velocity distribution may be assumed for the reactants. This leads to a Laplace transform relation between the rate constants for reaction of molecules in definite internal quantum states and the reaction cross sections. The further assumption of a Boltzmann distribution among the internal energy states of the reactant molecules then leads to a rate equation of the usual form and to an explicit expression for the single over‐all rate constant. This expression is used to rederive the results of the old ``simple'' collision theories. Finally, a collisional approach is used to rederive the usual rate expression of the Eyring theory of absolute reaction rates. The rather drastic approximations which seem to be necessary for such a derivation are pointed out and discussed.

Internal Rotation in Molecules with Two Internal Rotors: Microwave Spectrum of Acetone

Abstract: The theory of internal rotation in molecules is extended to the case of two internal symmetric rotors attached to a molecule with C2v symmetry. The calculation of the internal rotational energy levels and of the interaction with the over‐all rotational energy levels is discussed both for the high barrier and the low barrier approximation. The symmetry of the Hamiltonian for a molecule with the acetone structure is considered and the selection rules and relative intensities of the various fine structure components are derived.The microwave spectra of acetone and of completely deuterated acetone have been measured and assigned. From the rotational constants, the molecular structure has been partially determined. The most probable values of the structural parameters are r0(C=O) = 1.215 A (assumed), r0(C–C) = 1.515±0.005 A, r0(C–H) = 1.086±0.010 A, ∠CCC = 116°14′±1°, and ∠HCC = 110°16′±1°. The angle between the axes of the methyl groups is approximately 3° larger than the ∠CCC.The dipole moment has been deter...

Microwave Spectrum, Barrier to Internal Rotation, and Structure of Methyl Formate

Abstract: Rotational constants have been assigned to the following isotopic species of methyl formate by investigation of their microwave spectra: HCOOCH3, DCOOCH3, HCOOCH2D, HCOOCD3, HC13OOCH3, HCOOC13H3, HCO18OCH3, and HCOO18CH3. The following structural parameters were obtained from these rotational constants: r (C=O) = 1.200±0.01 A, r (C–O carboxyl) = 1.334±0.01 A, r (C–O methoxyl) = 1.437±0.01 A, r (C–H carboxyl) = 1.101±0.01 A, r (C–H methyl) = 1.086±0.015 A, ∠O=C–O=125°52′±1°, ∠H–C–O (carboxyl) = 109°18′±1°, ∠C–O–C = 114°47′±1°, and ∠H–C–H = 110°40′±1.5°. The carbon‐oxygen skeleton is planar with the methyl group cis to the carboxyl oxygen. The methyl group axis has been assumed to be along the C–O (methoxyl) bond, although some evidence suggests that it may be tilted.The barrier to internal rotation of the methyl group was calculated from the splittings observed in the rotational transitions of the ground torsional state for several isotopic species and found to be 1190±40 cal/mole.The dipole moment was calculated from the observed Stark effect and found to be 1.77±0.03D. The dipole moment lies at an angle of 39.4±2° from the C=O bond and roughly on the line between the ester oxygen and the carboxyl oxygen.

Angular Dissymmetry of the Critical Opalescence in Liquid Mixtures

Abstract: Visible light scattered by a one‐component homogeneous liquid in the vicinity of its critical point or by a homogeneous mixture of two liquids in the vicinity of their critical mixing temperature shows angular dissymmetry which becomes the more pronounced the nearer the temperature comes to the critical temperature. It is shown how this dissymmetry can be used as a measure for the range of molecular forces in the case of ordinary molecules. In the case of polymer molecules, observation of the dissymmetry provides a method for measuring the size of polymer coils in a size range too small to be measured by the usual dissymmetry method applied to diluted solutions.

Theory of Phase Transitions in Solid Heavy Methane

Abstract: It is the purpose of this paper to explain the existence of three solid phases in CD4, and to predict the molecular ordering in each phase, by straightforward deduction from a reasonable assumption concerning the orientational coupling of the molecules. Molecular and lattice vibrations are neglected, the crystal being treated as an f.c.c. array of spherical rotators carrying distributions of charge with tetrahedral symmetry. It is assumed that the dominant term in the orientational coupling of the molecules is their electrostatic interaction, of which only the octopole‐octopole interaction of next neighbors is retained in the calculation. The magnitude of the effective octopole moment is the only disposable constant in the theory. The statistical calculation is based on a classical version of the self‐consistent field idea; neglect of quantum effects makes the results inapplicable to CH4, which shows large isotope differences from CD4. The conditions for self‐consistency in the theory appear as a family of integro‐functional equations, one for each molecule in the crystal. These are brought into convenient form by introduction of tetrahedral harmonics and associated tetrahedral rotator functions. The consistency equations are first solved for the cases in which the orientational distribution function is the same for all molecules in the crystal. There exist three distinct solutions of this type, in which all molecules are subject to identical orienting fields with symmetries T, C2, or D3, respectively. More general solutions are then found, for which the molecules are not all equivalent, but may be freely rotating, or in orienting fields of symmetry T, C2, or D3. The consistency relations state restrictions on the distribution of such molecules in the crystal lattice, and fix the strengths of the orienting fields; they can be satisfied only for small numbers of molecules in a crystal cell. An apparently exhaustive tabulation is made of all solutions with low free energy. Three of these minimize F in some temperature range, and describe stable phases. At the lowest temperatures the stable phase has tetragonal symmetry Vd, with all molecules oscillating about equivalent equilibrium orientations. As T rises this undergoes a first‐order transformation to a phase with octahedral symmetry O, in which one molecule in four rotates freely, surrounded by a shell of oscillating next neighbors. At higher temperatures this undergoes a transformation (described by the theory as of second order) to an orientationally disordered phase. If the molecular octopole moment is assigned the magnitude 0.504×10—24 electron cm3 needed to make the predicted upper transition temperature agree with the 27.1°K observed in CD4, the predicted lower transition temperature is 24.4°K, as against the observed 22.2°K. Predictions of the theory are also in satisfactory agreement with observations on integrated heats of transition, zero‐point entropy, and the optical properties of the phases.

Optical Activity in Absorbing Media

Abstract: Certain dispersion formulas, relating the ellipticity and molecular rotation of optically active solutions, are derived. These are analogous to the Kramers‐Kronig transform relations between the absorption and refractive indices. Some discussion is offered of the factors influencing the respective shapes of absorption and ellipticity curves.

Superposition of Configurations and Natural Spin Orbitals. Applications to the He Problem

Abstract: The method of superposition of configurations is examined in its application to the helium atom in two cases: a 21×21 matrix including all configurations up to 〈6s〉2, and a 20×20 matrix with all configurations up to the 4‐quantum level, including angular terms. A new radial limit is established at −2.87900±0.00003, and this is used to discuss the convergence of such expansions in Legendie functions. The variation with scale factor is discussed in detail. The wave functions are analyzed in terms of natural spin orbitals (NSO's), which seem to have many advantages. The first NSO bears a striking resemblance to the Hartree‐Fock function, and the first two together provide a close approximation to the solution of the extended Hartree‐Fock equations with different orbitals for different electrons. An energy of −2.877924 is obtained for the best (u, v) function found. An analysis of the results suggests that inner orbitals may be better represented by pure exponentials than by Hartree‐Fock orbitals whenever additional correlational degrees of freedom are permitted. Expressed in approximate NSO form, the wave function is almost invariant to choice of basis set, provided that the latter is reasonably chosen. In particular, the necessity of including continuum terms along with the discrete hydrogen‐like set is demonstrated.

Method for the Analysis of Multicomponent Exponential Decay Curves

Abstract: A frequently encountered problem in many branches of science involves the resolution of experimental data into a sum of independent exponential curves of the form f(t)= ∑ i=1nNiexp(−λit), in order to estimate the physically significant parameters Ni and λi. Such problems arise, for example, in the analysis of multicomponent radioactive decay curves, and in the study of the dielectric properties of certain compounds. This paper is concerned with the numerical evaluation of a mathematical approach to the problem. The approach is based on the inversion of the Laplace integral equation by a method of Fourier transforms. The results of the analysis appear in the form of a frequency spectrum. Each true peak in the spectrum indicates a component, the abscissa value at the center of the peak is the decay constant λi, while the height of the peak is directly proportional to Ni/λi. Results obtained on an IBM 650 computer indicate that the method may possess certain advantages over previous methods of analysis.

New Method for the Statistical Computation of Polymer Dimensions

Abstract: A new method is described for the generation of excluded volume random walks of contour lengths comparable to those of real polymer molecules. This work was carried out with a high‐speed electronic digital computer. An essential feature of the method is an unbiased sample enrichment process used to counteract the attrition resulting from chain intersections. Using the new method, samples were generated for chains of 800 links, a limit imposed by machine storage capacity. In principle the method could be carried even further if more storage were available.Mean‐square end‐to‐end lengths of the chains are expressed by the equation 〈rn2〉=anb, where n equals the number of links and a and b are constants.

Infrared Spectra of the Frozen Oxides of Nitrogen

Abstract: Infrared studies have been made of several oxides of nitrogen trapped at liquid‐helium temperatures in matrices of argon, N2, O2, CO2, H2, and N2O. The novel techniques permitting these studies are described. NO is found as the monomer and two forms of dimer, ``cis'' and ``trans''; the cis is more stable. NO2 is found as the monomer, the known stable dimer of planar structure, and two new dimers; one of these has the ONO–NO2 structure, and the other may be the twisted Vd form of the stable dimer. N2O3 is found in its stable form ON–NO2 and in a second form whose spectrum is consistent with the structure ONONO. Observations on covalent N2O5 are also reported.

Total Collision Cross Sections for the Interaction of Atomic Beams of Alkali Metals with Gases

Abstract: Total collision cross sections (Q) for the interaction of atomic beams of K and Cs with a number of molecules were measured with an apparatus of 30″ angular resolution. Although absolute determinations of Q are difficult, relative values are readily obtained (±3%). Results are reported as the ratio (Q*) of the cross section for a given molecule to that of argon for the same beam atom. Seventy‐seven molecules (of varied complexity and reactivity) were studied with K and 16 with Cs beams. Q* ranged from 0.29 to 2.8.The data were correlated using the Massey‐Mohr theory, assuming an attractive intermolecular potential V(r) = —C/r6. For this case Q=b(C/vr)2/5, where vr is the relative velocity and b a known constant. C was estimated from standard formulas for the London dispersion and dipole‐induced dipole forces, using known refraction and dipole moment data. The theoretical values of Q differ by a nearly constant factor from the experimental results; thus values of Q* are predicted with good accuracy. The de...

Direct Method of Measuring Molecular Quadrupole Moments

Abstract: An experiment whose object is the determination of permanent molecular quadrupole moments is suggested. It is analogous to those used in measurements of electro‐optical Kerr constants, but the uniform electric field proportional to the applied voltage V is replaced by the field gradient of a square four‐wire condenser. If the wires at x=±a are at a potential V relative to those at y=±a, then the field gradient on the z axis will tend to orient quadrupolar molecules so that a fluid in the condenser will become doubly refracting. The induced anisotropy in the refractive index of a gas is shown to be first order in the applied voltage and of the form nx—ny=[B+(A/T)]V, while in the Kerr effect it is second order in V, and is given by nx—ny=[C+(D/T)+(E/T 2)]V2. The constant A is proportional to the molecular quadrupole moment and to the anisotropy in the polarizability, while B is proportional to the quadrupole moment induced in a molecule by a uniform field. In spherical molecules A, D, and E are zero. Calcul...

Hydrates of the Tetra n‐butyl and Tetra i‐amyl Quaternary Ammonium Salts

Abstract: The compounds [(n−C4H9)4N+]nXn−·nyH2O have been prepared where X is F‐, Cl‐, Br‐, CH3CO2‐, CrO42‐, WO42‐, C2O42‐, HCO3‐, HPO42‐, and y is approximately 32. They form an isomorphous crystal series which is tetragonal with a=23.65±0.15 A, c=12.40±0.15 A.A similar series of the type [(i−C5H11)4N+]nXn−⋅ny′H2O has been prepared where X is F‐, Cl‐, CrO42‐, WO42‐, and y′ is approximately 40. They also form an isomorphous group which is orthorhombic with a=12.10±0.10 A, b=21.50±0.15 A, c=12.65±0.15 A.These compounds are believed to be of the clathrate type, similar in general character to the gas hydrates.

Angular Dependence of Electron‐Coupled Proton Interactions in CH2 Groups

Abstract: Experimental and theoretical studies have been made of the dependence upon HCH angle of the electron‐coupled proton‐proton interactions in CH2 groups. A valence‐bond approximation is used in the theoretical treatment which predicts that the coupling constant AgemHH decreases from 32 cps to 0 cps for HCH angles of 100° to 125°. For angles greater than 125°, AgemHH is predicted to be negative. Experimental values of AgemHH have been obtained from analyses of the proton magnetic‐resonance spectra of a number of compounds, including several partially deuterated species. Insofar as the HCH angles are known in these compounds, there is good agreement between the theoretical and experimental coupling constants, especially for angles smaller than 120°, for which AgemHH changes more rapidly with angle. Moreover, a negative value is found experimentally for AgemHH in vinyl bromide at an HCH angle which is approximately that at which the theory predicts the coupling to become negative. The substituted ethylenes cons...

Calculation of Line Widths in H2O‐N2 Collisions

Abstract: Anderson’s general theory of collision line broadening has been applied to H2O‐N2 encounters. The only attractive force was assumed to be that between the H2O dipole, μ = 1.87×10−18 esu, and the N2 quadrupole, qN2, an adjustable parameter. A second adjustable parameter, bm, the distance of closest approach, includes the effects of all other forces. The IBM 704 was used in the calculation. Effects of varying the parameters were noted for a number of lines, and in the final calculation, which yielded the widths of all significant type B transitions up to J″ = 13, parameters qN2 = 2.62×10−26 esu and bm = 3.2 A which give an exact fit of the observed width of the microwave line 6−5−5−1, were adopted. The temperature dependence of the line width over the range 220–2400 °K, and the effects of vibration‐rotation interactions were also calculated. At 300 °K widths vary from 0.11115 cm−1 atmos for 11−1−1 to 0.03200 cm−1 atmos−1 for 14−13−13−13, there being a general decrease in width with increasing J, and at a gi...