Volume 40, Issue 8, 15 April 1964

Crystal Structure of 9‐Methyladenine
View Description Hide DescriptionThe crystal structure of 9‐methyladenine has been determined with limited x‐ray diffraction data. The final R factor is 0.091 with atomic standard deviations of about 0.006 Å. The x‐ray determination confirms the proposed structure based on polarized absorption measurements. We conclude that the first ultraviolet transition for 9‐methyladenine is short axis (C _{4}–C _{5}) polarized.

Spectroscopic Studies of Vibrational Nonequilibrium in Supersonic Nozzle Flows
View Description Hide DescriptionStudies have been made of the extent of vibrational nonequilibrium produced in supersonic expansions of undissociated N_{2} from known initial equilibrium conditions attained behind reflected shock waves. The N_{2} was shock heated and compressed to reservoir temperatures and pressures in the ranges 2800° to 4600°K, and 24 to 82 atm. It was then allowed to expand through a 15° axisymmetric nozzle coupled to the end of the shock tube. The extent of vibrational nonequilibrium was determined by measurements of local vibrational temperatures using the spectrum‐line reversal method. The measurements showed the vibrational temperatures in the expansion flows to be much closer to equilibrium than the Landau—Teller relaxation theory predicts. Observations at two area ratios showed that the flow was not completely frozen in the vibrational sense. The probability of N_{2} vibrational de‐excitation inferred from these measurements is about 15 times greater than that inferred from measurements of vibrational relaxation made behind normal shock waves. Reasons for this apparent difference are discussed in terms of the basic environmental and kinetic differences between shock‐wave and nozzle‐expansion flows. The validity of the application of Landau—Teller relaxation assumptions and shock‐tube measured rates to predict nonequilibrium in expansion flows is thus questioned.

Nuclear Magnetic Resonance Fluorine—Fluorine Coupling Constants
View Description Hide DescriptionThe pattern of fluorine—fluorine coupling constants is explained on the basis of two mechanisms for nuclear spin—spin coupling: the ``through‐bond'' and the ``through‐space'' mechanisms. In the former, the interaction proceeds via the electronic structure in the intervening bonds. It is highly dependent on the electron withdrawing power of the substituents on the carbon skeleton. This contribution to the coupling constant goes to zero when the sum of the electronegativities of the substituents becomes sufficiently high. The latter mechanism is operative when two fluorine atoms are sufficiently close in space for there to be appreciable overlap of their electronic clouds. This ``through‐space'' interaction proceeds via an electronic structure where there is no bondper se. Experimental evidence for the existence of both mechanisms is given.

Coriolis Perturbations in the Infrared Spectrum of Ethylene
View Description Hide DescriptionRotational structure has been resolved and analyzed in two of the infrared‐active perpendicular bands of C_{2}H_{4} vapor: the Type b fundamental band, ν_{10}, at 826 cm^{—1}, and the Type c fundamental band, ν_{7}, at 949 cm^{—1}. Many of the individual ^{ PP} and ^{ RR} branch lines have been observed. The analysis has been confined to values of the quantum number K≥3, for which energy levels ethylene shows no detectable deviations from a symmetric‐top rotational structure. The analysis reveals a Coriolis interaction between ν_{7} and ν_{10}, and between ν_{4} and ν_{10}, and values of the Coriolis constants ζ_{7,10} ^{ z } and ζ_{4,10} ^{ y } are obtained; these are related to normal coordinate calculations for the appropriate symmetry species, and force constants are derived to fit the observed zeta constants. The band center of ν_{10} has been revised from the original figure of 810 cm^{—1} to the new value, 826 cm^{—1}, and the inactive frequency ν_{4} is estimated to lie at 1023±3 cm^{—1}, in good agreement with the previous estimate of 1027 cm^{—1}.
The change in the value of ν_{10} leads to a suggested change in the value of the Raman‐active fundamental ν_{6} from 1236 to 1222 cm^{—1}. New combination bands have been observed at 2174 cm^{—1}, assigned as ν_{3}+ν_{10}; and at 2252 cm^{—1}, assigned as ν_{4}+ν_{6}; also rotational structure has been resolved and analyzed in the ν_{6}+ν_{10} band at 2048 cm^{—1}.
The new data obtained for the C_{2}H_{4} molecule are summarized in Table XII, with all of the other data presently available on the vibrational and rotational constants.

Microwave Spectrum of Methyl Hypochlorite
View Description Hide DescriptionThe microwave spectra of the normal species and some isotopically substituted species of methyl hypochlorite (CH_{3}OCl) have been investigated in the frequency region 9 000–38 000 Mc/sec. Analysis of the results indicates the following structural parameters: d(CH)_{av}=1.099 Å, <HCH_{av}=109.4°, d(OCl) = 1.674 Å, d(OC) = 1.389 Å, and <COCl=112.8°. The quadrupole coupling constants for CH_{3}O^{35}Cl are eQq=—84.34 Mc/sec and η=0.408. The coupling constants for CD_{3}OCl and the structural data indicate that the quadrupoletensor is probably cylindrically symmetric. The barrier to internal rotation calculated from splittings in the v _{torsion} = 1 state for CH_{3}O^{35}Cl is 3060±150 cal/mole.

Excess‐Kinetic‐Energy Ions in Organic Mass Spectra
View Description Hide DescriptionThe characteristics of excess‐kinetic‐energy ions in mass spectra have been studied with a Dempster‐type mass spectrometer. A method was devised whereby the total initial kinetic energies possessed by such ions could be measured more accurately than has been done previously, and the kinetic energies of methyl ions, both near‐thermal and excess‐kinetic‐energy, from a wide variety of different organic compounds, are presented. Appearance potential curves were obtained for several excess‐kinetic‐energy methyl ions; these show a second‐power dependence of cross section on electron energy in the threshold region with threshold values of the order of 30 eV. Finally, a method of estimating the discrimination factor of the mass spectrometer toward ions possessing excess kinetic energy was utilized to obtain values for the actual abundances of excess‐kinetic‐energy methyl ions in the fragmentations of several organic compounds. Actual abundances of from 2% to 10% of the total ions in the mass spectrum were found from many compounds.
The values of appearance potentials, kinetic energies, and abundances that have been measured for the complementary excess‐kinetic‐energy ion pairs from methyl amine (masses 15 and 16) and propane (masses 15 and 27) are consistent with a mechanism for formation in which both ions arise from the same initial state in each respective case. The data support the suggestion that excess‐kinetic‐energy fragment ions from the organic compounds are formed by breakdown of doubly charged parent ions.

Microwave Absorption and Molecular Structure in Liquids. LVI. Dielectric Behavior of Water and Heavy Water in Dioxane
View Description Hide DescriptionThe dielectric constants and losses of seven water—dioxane mixtures and six heavy‐water—dioxane mixtures ranging in concentration from 5 to 58 mole % of water have been measured at wavelengths from 0.44 to 10.0 cm. The results are interpreted in terms of two partly superimposed noninteracting Debye dispersions. The high‐frequency dispersion region for the water—dioxane mixtures corresponds to a relaxation time 4×10^{—12} sec, which is concentration independent, while the low‐frequency dispersion region corresponds to a relaxation time which is concentration dependent and rises to a maximum at about 70 to 80 mole % water. The relaxation time 5.6×10^{—12} sec associated with the high‐frequency dispersion region of the heavy‐water—dioxane mixtures differs from the corresponding relaxation time for water—dioxane mixtures by a factor of (½)^{½}. The low‐frequency concentration‐dependent relaxation time was found to be about 1.2 to 1.5 times greater than the corresponding relaxation time of the water—dioxane system. The high‐frequency dispersion region is attributed either to the rotation of the OH (or OD) group about its hydrogen (or deuterium) bond or to over‐all molecular relaxation. The low‐frequency dispersion is attributed to the partial breaking and reforming of the hydrogen (or deuterium) bond. The rotational mechanism becomes a molecular libration in the extrapolating to pure water and contributes to the large atomic polarization observed.

Absolute Correlation of Nuclear Spin—Spin Coupling Constants with Atomic Number. II. Couplings J _{X–C–H} and J _{X—H}
View Description Hide DescriptionA precise correlation of nuclear spin—spin coupling constants J _{X—Y} is presented for molecules where X and Y are bonded or separated by a common atom in a series. If X is a central atom surrounded by equivalent Y atoms with no lone pair electrons and X varies down a group of the periodic table a relationshipis obeyed where Z _{X} is the atomic number of the element X. A and B are experimental constants to be determined. The constants A and B have been determined from literature values of coupling constants for the series J _{X—H} and J _{X–C–H} where X is a Group IV atom. In future work further series will be investigated. Unknown coupling constants in a symmetrical series can be predicted accurately by use of the equation.
Deviations from the correlation are expressed in terms of a deviation parameter ``D.'' The series (CH_{3})_{4}Sn, (CH_{3})_{3}SnH, (CH_{3})_{2}SnH_{2}, (CH_{3})SnH_{3}, and SnH_{4} is investigated in terms of a defined deviation parameter. Positive deviations are shown to be regular in the series for J _{Sn–C–H} indicating increased ``s'' character in the Sn–C bond and corresponding negative deviations are noted for J _{Sn–H} in this series with decreasing s character in the Sn–H bond. A relative deviation parameter is suggested for a given set of molecules with slightly distorted symmetry which has not yet been investigated fully for a series of molecules.
The correlation fails when J _{X—H} and J _{X–C–H} are considered and X has a low atomic number. The interpretation on the basis of hyperfine splitting constants of the single s electron in the alkali metals suggests that such deviations are expected.

Absolute Correlations of Nuclear Spin—Spin Coupling Constants with Atomic Number. III. J _{X—H} in Isoelectronic Series and the Lighter Elements
View Description Hide DescriptionThe equation (J _{X—H/γXγH})^{½} = AZ_{X}+B is obeyed for the isoelectronic series BH_{4} ^{‐}, CH_{4}, and NH_{4} ^{+}. The molecular hydrides of the first period can be considered in terms of the deviation parameters from this as suggested previously. The slope of the equation, ``A'', for an isoelectronic series is considerably greater than the line obtained from a similar correlation of the Group IV molecular hydrides. Terminal and bridge hydrogen coupling with boron in the molecule diborane is considered in terms of deviation parameters from the point for the tetrahedral species BH_{4} ^{‐}. All ions and molecules considered show consistently positive deviation parameters with the s character of the X—H bond exceeding the tetrahedral value and negative deviation parameters for less s character than true tetrahedral.

Multiple Equilibria in Macromolecular Systems
View Description Hide DescriptionThe theory of multiple equilibria for binding of adsorbable molecules to macromolecules is extended to the case of polymerizing systems. The general result reduces to a simple form if no binding sites are excluded on polymerization. It is shown that nonlinear results may be obtained in a binding experiment, depending on the choice of variables, and a method of measuring macromolecular polymerization from a binding experiment is suggested.

Anharmonic Effects in Unimolecular Rate Theory. Vibrations and Collisions of Simple Polyatomic Systems
View Description Hide DescriptionThe equations of motion for the following systems were integrated numerically: (1) a four‐atom linear molecule with Morse function bond stretching potentials; (2) a pair of Morse function diatomic molecules undergoing collisional interaction via a Lennard‐Jones 6–12 potential; (3) a Morse function linear triatomic molecule interacting with an atom via a 6–12 potential; and (4) a Morse function diatomic molecule colliding with an atom via a 6–12 potential. A commonly used approximate method of solution is also used to analyze Case 4. In all cases the systems are constrained to colinear motion. Results are presented graphically. Our conclusions are as follows:
(1) The behavior of the four‐atom anharmonic molecule shows features quite different from those shown by its harmonic counterpart.
(2) Collisional interaction via 6–12 potentials does not lead to efficient transfer of vibrational energy from one molecule to another or to efficient interconversion of translational and vibrational energies.
(3) A commonly used assumption in the calculation of the efficiency of collisional vibrational activation of diatomic molecules breaks down badly at high energies.

An Expansion of Binary Collision Phase Shifts in Powers of h
View Description Hide DescriptionThe phase shifts in binary collisions are expressed as series in increasing powers of Planck's constant,h. The series begins with a term in h ^{—1} and contains all odd powers. Recursion relations are developed which lead to an expression for an arbitrary term in the series. The results apply to an arbitrary interaction potential function, for which any odd number of classical turning points may arise.

On the Semiclassical Expansion of Scattering Phase Shifts
View Description Hide DescriptionA relation between the canonical density matrix and scattering phase shifts is obtained and applied to the derivation of the semiclassical expansion of scattering phase shifts. The method differs from that used by Curtiss and Powers, but the results are shown to be identical.

Quantum Effects in Small‐Angle Molecular‐Beam Scattering
View Description Hide DescriptionQuantum‐mechanical calculations of the differential cross section for the small‐angle elasticscattering of heavy particles are carried out to establish more definitely the region of validity of the classical approximation. Four results are discussed: (1) The Massey—Mohr phase‐shift formula corresponds to the Kennard small‐angle scattering formula in the semiclassical limit. (2) The Schiff approximation for the cross section is exactly the same as the semiclassical approximation at small angles, for any central potential. (3) At very small angles the semiclassical limit for the differential cross section varies as exp (—cθ^{2}), where c is a function of velocity for which explicit expressions are given. (4) The first quantum deviation from the classical limit, which is proportional to ℏ ^{2}, can be combined with the preceding result to give a reasonable representation of the differential cross section over the entire range of small angles for which quantum deviations are appreciable. Detailed calculations for some specific systems are made, and it is shown that Wu's misgivings over the classical interpretation of the experimental results of Amdur and co‐workers are unjustified.

One‐Center Basis Set SCF MO's. I. HF, CH_{4}, and SiH_{4}
View Description Hide DescriptionOne‐center SCF MO ground‐state wavefunctions are reported for HF, CH_{4}, and SiH_{4}. The molecular orbitals are expressed in terms of Slater‐like functions all centered at a common origin. The basis sets employed contain more than 25 functions including, for the spherical harmonics, values of l up to 3. The results of the calculations here reported, performed by the use of a large electronic computer, refer to the geometrical configurations which, among many others considered, gave the minimum of the total energy.
The equilibrium bond length thus determined for HF is 1.728 a.u. with a corresponding value of the energy of — 100.0053 a.u. and of the electric dipole moment of 2.104 D. For CH_{4} and SiH_{4} the equilibrium configurations were found to possess tetrahedral symmetry with bond lengths of 2.08 and 2.787 a.u. and energies of — 39.86597 and — 290.1024 a.u., respectively.
The general features and capabilities of the one‐center expansion approach to molecular systems are discussed.

One‐Center Basis Set SCF MO's. II. NH_{3}, NH_{4} ^{+}, PH_{3}, PH_{4} ^{+}
View Description Hide DescriptionOne‐center‐expanded SCF MOwavefunctions are reported for the ground states of NH_{3} and PH_{3} in their planar and in their calculated equilibrium configurations and of NH_{4} ^{+} and PH_{4} ^{+} in their calculated equilibrium configurations. The calculated molecular energies and the geometrical parameters of the determined equilibrium configurations agree well with the experimental values.
Good agreement is also obtained for the electric dipole moment and the proton affinity of NH_{3} while the calculated value of the height of the potential barrier for inversion appears to be too small. For PH_{3} a good value for the height of the potential barrier is obtained while the calculated electric dipole moment is too large. The calculated proton affinity of PH_{3} seems to be reasonable. A critical examination of the wavefunctions gives an account of the quality of the several results obtained.

One‐Center Basis Set SCF MO's. III. H_{2}O, H_{2}S, and HCl
View Description Hide DescriptionOne‐center expanded SCF MOwavefunctions are reported for H_{2}O, H_{2}S, and HCl in their ground states. The wavefunctions refer to the calculated equilibrium configurations which agree well with the experimental data. The corresponding computed molecular energies are —75.922436, —397.58906, and —458.83776 a.u., respectively, which are reasonably close to the experimental values. The energy obtained for H_{2}O is found to be near the estimated Hartree—Fock value.
The computed electric dipole moment of H_{2}O agrees well with the experimental value, while for H_{2}S and HCl larger discrepancies are found.

Intrinsic Viscosity of Coiling Macromolecules
View Description Hide DescriptionThe intrinsic viscosity of coiling molecules has been calculated using the Kirkwood—Riseman adaptation of the Oseen approximation. Four different models of chain segment distribution were treated: (a) a Gaussian coil, (b) an excluded volume model of Kurata and Yamakawa, (c) a coil expansion model suggested by Peterlin and (d) an excluded volume model deduced from the machine computation of Wall and Erpenbeck. In all cases the partially free draining coil was treated. The mathematical solution of the problem has been carried out on an IBM 704 computer.

Helium Afterglow. I. Atomic Spectrum
View Description Hide DescriptionSpectroscopic investigation of a flowing helium afterglow revealed the presence of strong lines of neutral helium. An examination of the population distribution of the excited atomic states revealed the presence of a Saha equilibrium between the upper states and the free electrons indicating that the primary process of populating these states was the collisional—radiative recombination of He^{+}. A comparison of the axial variation and pressure dependence of the intensity of the emission with the He_{2} ^{+} and He^{+} concentrations strengthened this conclusion.
Observations were made at times from 50–250 μsec into the afterglow (flow velocity ≈6×10^{4} cm/sec) in a system having a diffusion half‐life for He^{+} of the order of 100 μ sec, an ion density of 5×10^{12}/cc and a maximum electron temperature corresponding to ≈0.15 eV.

Helium Afterglow. II. Molecular Spectrum
View Description Hide DescriptionSpectroscopic investigation of a flowing helium afterglow revealed the presence of strong bands of He_{2}. An examination of the axial variation and pressure dependence of the intensity of the emission and He_{2} ^{+} concentration, as evidenced by titration, served to identify the dominant reaction populating the excited molecular states as being the collisional—radiative recombination of He_{2} ^{+}.