Volume 47, Issue 4, 15 August 1967

Electronic States of the Amide Group
View Description Hide DescriptionThe presence of a moderately strong band falling between the n→π^{*} and π→π^{*} (N→V _{1}) transitions of the amide group has been observed for the first time. All‐electron SCF calculations in Gaussian bases aimed at assigning the bands of formamide suggest that the new band is an n→σ^{*} excitation in which the σ^{*} orbital is Rydberg‐like. A second π→σ^{*} big‐orbit transition follows the π→π^{*} (N→V _{1}) excitation. In a basis containing expanded orbitals, the usual virtual orbital—configuration interaction calculations predict that every upper state will be of Rydberg‐orbital dimensions. However, this obvious error can be avoided by indirect SCF calculations on the upper states, which show that in formamide, all states below 13 eV terminating at π^{*} are valence‐shell transitions, whereas all states terminating at σ^{*} are big‐orbit Rydberg states.

Atomic Z Expansions and Electronic Structure of Molecules: Second‐Order One‐Center Calculation of the Hydrogen‐Molecule Ground State
View Description Hide DescriptionDouble‐perturbation theory is applied to calculate the ground state of the hydrogen molecule. In this treatment the unperturbed system is formed by the two noninteracting electrons moving in the field of a virtual nucleus of charge Z located halfway between the two hydrogen nuclei. The rest of the molecular Hamiltonian—electronic repulsion and the part of the electron—nuclear attraction—is treated as a perturbation. We determine the virtual charge Z from the variational principle for the total energy through first order. With this approach the total molecular energy of H_{2} can be built up from the energy Z expansion of (1s)^{2} ^{1} S, twice the exact electronic energy of 1sσ H_{2} ^{+}, and correction terms of second and higher orders. Using the published results for (1s)^{2} ^{1} S and 1sσ H_{2} ^{+} we calculate the second‐order corrections to get the equilibrium distance within 4% of the very accurate result obtained by Kol/os and Roothaan; our dissociation energy is 4.207 eV, 11% smaller than their value 4.747 eV.

Polyhedral Clathrate Hydrates. XII. The Crystallographic Data on Hydrates of Ethylamine, Dimethylamine, Trimethylamine, n‐Propylamine (Two Forms), iso‐Propylamine, Diethylamine (Two Forms), and tert‐Butylamine
View Description Hide DescriptionThe crystallographic data for nine alkylamine hydrates are reported. The hydrates of C_{2}H_{5}NH_{2} and (CH_{3})_{2}NH are isostructural with the 12 Å cubic gas hydrates and have unit cells with symmetries Pm3n and Pm3, and dimensions a=12.17 and 12.55 Å, respectively. Those of (CH_{3})_{3}N and n‐C_{3}H_{7}NH_{2} have symmetry P6/mmm and unit cell dimensions a=12.41 Å, c=12.50 Å and a=12.20 Å, c=12.38 Å, respectively, while that of iso‐C_{3}H_{7}NH_{2} has symmetry P6_{3}/mmc and cell dimensions a=12.42 Å, c=25.22 Å. These hexagonal hydrates are related in their water structure to (iso‐C_{5}H_{11})_{4}N^{+}F^{−}·38H_{2}O. n‐C_{3}H_{7}NH_{2} forms a second hydrate with monoclinic symmetry P2_{1}/n and unit cell dimensions a=12.58 Å, b=21.20 Å, c=17.47 Å, β=89.3°; (C_{2}H_{5})_{2}NH forms two hydrates, one of orthorhombic symmetry Pbcn and unit cell dimensions a=13.44 Å, b=11.77 Å, c=27.91 Å, and one of monoclinic symmetry P2_{1}/c and cell dimensions a=13.86 Å, b=8.44 Å, c=10.93 Å, β=97.5°; (CH_{3})_{3}CNH_{2} forms a cubic hydrate with a unit cell of symmetry and dimensions a=18.81 Å. The total mass contents of the unit cells, calculated from the cell dimensions and experimental densities, are used to derive the probable stoichiometric formulas.

Polyhedral Clathrate Hydrates. XIII. The Structure of (CH_{3}CH_{2})_{2}NH·8⅔H_{2}O
View Description Hide DescriptionA three‐dimensional single crystal x‐ray analysis of (CH_{3}CH_{2})_{2}NH·8⅔H_{2}O has been carried out. The crystals are orthorhombic, with a=13.44 Å, b=11.77 Å, c=27.91 Å, and space group Pbcn. The compound is a clathrate hydrate, and the most notable feature of the water framework is a novel polyhedral cage, the 18‐hedron (octakaidecahedron), which has twelve pentagonal and six hexagonal faces. The 18‐hedra form a two‐dimensional network by sharing faces. The networks are then linked together by additional water molecules in a manner which gives rise to additional ``irregular'' cages having quadrilateral, pentagonal, and hexagonal faces. Diethylamine molecules are enclosed in two types of cages and in both the amine groups are hydrogen bonded to the water lattice. In the case of the 18‐hedra, this bonding somewhat distorts the cage from its ``ideal'' D _{3d } shape. In marked contrast to previous clathratestructures involving polyhedra with pentagonal and hexagonal faces, where the dodecahedron could be considered to be the basic structural unit, the pentagonal dodecahedron does not appear in this structure.

Polyhedral Clathrate Hydrates. XIV. The Structure of (CH_{3})_{3}CNH_{2}·9¾H_{2}O
View Description Hide DescriptionThe crystal structure of 16(CH_{3})_{3}CNH_{2}·156H_{2}O has been determined from three‐dimensional x‐ray‐diffraction data obtained at −30°C. The crystals are cubic, space group , with cell dimensions a=18.81±0.02 Å. The host framework of hydrogen‐bonded water molecules consists of face‐sharing heptakaidecahedra which have three square, nine pentagonal, two hexagonal and three heptagonal faces. The square and pentagonal faces also form octahedra which complete the space‐filling arrangement. The amine molecules occupy the larger polyhedra as nonbonded guests undergoing marked oscillatory motion.

On a Theory of Absolute Reaction Rates
View Description Hide DescriptionThe methods of multichannel collision theory are used to introduce a yield operator Y which is an observable that determines the rate and yield of a reaction. When the reactants are characterized by a statistical operator U _{0}, the reaction rate can be written as Tr(U _{0} Y)/Tr(U _{0}). By using Heisenberg's equation of motion it is possible to extend the formalism by introducing a yield operator Y_{A} that determines the rate of change of any measurable operator A in a system undergoing reactions. It is suggested to base semiempiricaltheories on approximations to the yield operator. Towards this aim the Arrhenius parameterization of the rate of thermal bimolecular reactions is discussed, and alternative forms for the yield operator are exhibited.

Vibrational Spectra and Rotational Isomerism in Acrylyl (Propenoyl) Chloride and Related α,β‐Unsaturated Acyl Halides
View Description Hide DescriptionThe complete vibrational spectra of acrylyl (propenoyl) chloride have been recorded and analyzed. This compound exists as a mixture of two discrete rotational isomers in the vapor and liquid states, their energy differing by about 0.6 kcal/mole in the vapor state. The spectra of the two isomers have been tentatively assigned and it has been found that all of the skeletal stretching modes are conformation dependent. Three other α,β‐unsaturated acyl chlorides have been studied and the results are compared with those of acrylyl chloride.

Perturbation Treatment of the Ground State of the Hydrogen Molecule
View Description Hide DescriptionPerturbation theory is used to obtain approximate energies and wavefunctions for the hydrogen molecule ground state. A function of simple form is chosen as zero‐order function, the zero‐order Hamiltonian is constructed, and the variational equation for the first‐order wavefunction is solved approximately by expansion in James—Coolidge basis functions, yielding the second‐ and third‐order energies. All integrals are calculated numerically. The binding energy and equilibrium internuclear distance are fair, but not as good as what one obtains from a comparable variational calculation.

Molecular Dynamics of Weakly Coupled Electric Dipoles on a Rigid Lattice. I. The Approach to Equilibrium
View Description Hide DescriptionThe approach to equilibrium of a finite two‐dimensional system of 400 rotating dipoles located on the sites of a square lattice is investigated by the technique of molecular dynamics. For all dipoles initially oriented at random and rotating in the same direction with equal velocities, it is verified that the system goes to its equilibrium state and that the relaxation time of the fourth moment of the angular momentum distribution is inversely proportional to the eighth power of the dipole moment, as expected from theory. A particular situation, such that the system does not approach its equilibrium state, is discussed.

Comments on Friction Constant Formalism
View Description Hide DescriptionExpressions for the molecular friction constant based on the acoustic continuum and small‐step diffusionmodels have been compared with experimental data. The integral describing ζ was evaluated by assuming an (n, m) potential and by substituting internal energy and pressure for terms involving integrals of the radial distribution function. The experimentally estimated values of the friction constant, from which a hard‐core contribution is removed, do not yield consistent or realistic values of the potential parameters n and m. The successful prediction of the coefficient of thermal conductivity and shear viscosity for liquid argon using the Rice—Allnatt theory is based on the extrapolation of experimental data for self‐diffusion. Statistical analysis of these data indicates that they do not permit a reliable test of the theory. Predicted values of the bulk viscosity coefficient of liquid argon are 40%—50% lower than recent experimental data, and the pressure dependence of the bulk viscosity coefficient at constant density calculated from the Rice—Allnatt theory is of the wrong sign.

Evaluation of Long‐Range Retarded Interaction Energies
View Description Hide DescriptionThe most important contributions to the expansion of the exact long‐range retarded interaction energy, between two nondegenerate atoms, are evaluated accurately for the H–H, H–He, and He–He interactions.

Integrated and Integral Hellmann—Feynman Formulas
View Description Hide DescriptionFor an isoelectronic molecular process X→Y, the energy change ΔW = W_{Y}—W_{X} may be computed from any one of three equivalent formulas if the exact molecular wavefunctions, ψ_{ X } and ψ_{ Y }, are known: the expectation‐value difference, the integrated Hellmann—Feynman formula, and the integral Hellmann—Feynman formula. Should only approximate wavefunctions be available, and , these formulas give different estimates of the energy change. If the Hamiltonians for X and Y differ in values of some parameter or parameters λ, say λ = 0 for X and λ = 1 for Y, one has , , , , , , and the three formulas are as follows:Relative advantages and disadvantages of these formulas are discussed, and illustrations are given of their use. Conditions for the equivalence of the formulas are established. It is shown that if and are selected by the linear variational method from a fixed basis set, the three formulas give the same ΔW̃. If each of and is selected variationally from a given class of functions, as is the case when each is an exact Hartree—Fock function, ΔW̃ _{ed} and ΔW̃_{d} are equal, but possibly different from ΔW̃_{l}. Examples are included which show that ΔW̃_{l} sometimes gives a better estimate of an actual energy change than does ΔW̃ _{ed}. Implications for the energy of interaction between two ions or ionic fragments in a molecule are discussed.

Fermi Doublet ν_{1}, 2ν_{2} in the Cyanate Ion
View Description Hide DescriptionCyanate ion enriched in ^{13}C, ^{15}N, or ^{18}O has been introduced into single crystals of KBr and KCl grown from the melt. The infrared absorption of such matrix‐isolated molecular ions has been observed between 1150 and 1350 cm^{−1} from room temperature down to liquid‐N_{2} temperature. On the basis both of isotopic frequency shifts and changes in the relative intensities, an earlier assignment of ν_{1} and 2ν_{2} is reversed; the new assignment parallels the situation recently brought to light for carbon dioxide.

Aromatic Carbonyl Spectra at High Pressures
View Description Hide DescriptionThe spectra of benzophenone (S _{ nπ* }←S _{0}; T _{ nπ* }→S _{0}), fluorenone (S _{ππ* }←S _{0}; S _{ππ* }→S _{0}), and anthrone (T _{ nπ* }→S _{0}) have been studied as a function of pressure to 25 kbar. The π^{*}←n absorption band of benzophenone shows a blue shift in compressed polar and hydrogen‐bonding plastics, in contrast to the absorption of fluorenone. The fluorescence of fluorenone shows a red shift for all plastics which is greater than the corresponding red shift in absorption at the same isobar. The phosphorescence also shifts red except for benzophenone in polyethylene, polyacrylonitrile, and polyvinyl alcohol, where an initial blue shift is observed. These plastics are evidently capable of restraining geometrical changes in the benzophenone molecule.

Microwave Spectrum of trans‐2,3‐Epoxybutane
View Description Hide DescriptionThe microwave spectrum of[Complex chemical formula]was studied from 8 to 40 Gc/sec. The rotational constants and the dipole moment of the main isotopic species in the ground torsional state were found to be A = 12 237.38 Mc/sec, B = 3 423.02 Mc/sec, C = 3 072.52 Mc/sec (κ=−0.9235122) and μ=2.03±0.04 D, respectively. An approximate structure was obtained by varying the two least‐well‐known structural parameters to fit the observed moments of inertia, and a barrier to internal rotation of 2444±150 cal/mole was obtained from the splittings of the lines in the ground torsional state. These results are discussed in terms of steric effects in this molecule and in the cis isomer studied by Sage.

Atomic Screening Constants from SCF Functions. II. Atoms with 37 to 86 Electrons
View Description Hide DescriptionMinimal basis‐set atomic functions for the ground‐state atoms from Rb(Z=37) to Rn(Z=86) are presented. These functions are analyzed in order to obtain systematic data for the screening constants and atomic radii following the work initiated by Slater.

Temperature Dependence, Orientation Correlation, and Molecular Fields in Second‐Harmonic Light Scattering from Liquids and Gases
View Description Hide DescriptionThe properties of second‐harmonic light scattering in fluids are derived in terms of the molecular polarizabilities, orientation correlation among molecules, and the molecular field F _{α}. Measurements of scattering intensity in CCl_{4} and water, from about 10° to 60°C, are reported. The variations with temperature, and therefore apparently the effects of changes of orientation correlation, are slight. The influence of preferred orientation in CCl_{4}, of the type deduced from x‐ray diffraction, is calculated. The third‐rank molecular polarizabilitytensor consists of a fourth‐rank tensor contracted with F _{α}, in addition to the term previously known, which is independent of F _{α}. With F _{α} arising from molecular multipole moments, the new term explains some measured depolarizations in liquids, and accounts for the spectral line, but not the background, observed in methane gas. In the case of molecular dipole moments, the new term can cause spectral narrowing.

Microwave Spectrum, Structure, and Quadrupole Interaction of Trifluoro‐iodo Silane
View Description Hide DescriptionRotational spectra of trifluoro‐iodo silane observed with a video microwave spectrometer were fitted to the following molecular constants: B=1118.84 Mc/sec, eqQ estimated to be −1450 Mc/sec. Since d _{SiF} and φ_{FSiF} have been found in other molecules to be 1.560±0.005 Å and 108°30′±1° these parameters were assumed, and d _{SiI} was found to be 2.387±0.02 Å. This observed Si–I bond shortening has been found in other molecules and is attributed to ionic and double‐bond character.

Vibrational Study of the Chain Conformation of the Liquid n‐Paraffins and Molten Polyethylene
View Description Hide DescriptionA vibrational and attendant conformational analysis of the liquid n‐paraffins and molten polyethylene is presented. For the purposes of the analysis a valence force field was derived which is applicable to both planar and nonplanar chains. The force field was evaluated from observed frequencies of trans (T) and gauche (G) n‐C_{4}H_{10}; TT and GT n‐C_{5}H_{12}; TTT, GTT, and TGT n‐C_{6}H_{14}; and (T)_{∞} polyethylene, all of whose infrared spectra were assigned in detail. Infrared spectra of the liquid‐n‐paraffins n‐C_{4}H_{10} through n‐C_{17}H_{36} were measured at room temperature and n‐C_{4}H_{10} through n‐C_{12}H_{26} also at a temperature just above their melting point. Frequencies and normal coordinates were calculated for the extended forms and for forms having one gauche bond of n‐C_{4}H_{10} through n‐C_{8}H_{18}. These quantities were also calculated for the conformations of n‐C _{5}H_{12} through n‐C_{7}H_{16} having two gauche bonds and for the nonplanar but regular conformations (TG)_{∞} and (G)_{∞} of polyethylene. Some bands attributable to forms of n‐C_{5}H_{12} and n‐C_{6}H_{14} having two gauche bonds were found. In the case of n‐C_{5}H_{12} the energy difference between the GT and TT states was found to be nearly the same as that between the GG and GT states. Bands in the region 1400–1300 cm^{−1} were found to be characteristic of specific conformations involving sequences of five or fewer methylenes, such as —GTTG— (1338 cm^{−1}), —GTG (1368 and 1308 cm^{−1}), —GG— (1352 cm^{−1}), and terminal —TG groups (1344 cm^{−1}). All these bands together with two broader ones centered near 1270 and 1080 cm^{−1} owe their intensity to the wagging of methylenes adjoining gauche bonds. An interpretation of the general features of the C–C‐stretching, methylene‐rocking, and methylene‐scissoring regions is given. Bands associated with molecules or chains having trans sequences involving at least four methylene groups are found. In the region 1300–1150 cm^{−1} there are chain‐length‐dependent band progressions resembling those observed for the crystalline n‐paraffins. These indicate the presence of molecules with gauche bonds, but these gauche bonds are few in number and are located near the ends of the chains. It is shown that for certain kinds of vibrations, particularly totally symmetric C–C stretching and ∠CCC bending, there is very little change in frequency in going from a fully extended chain to one having one or even two or more gauche bonds. Hence, it is very difficult in the case of the longer n‐paraffins to distinguish spectroscopically between fully extended and almost fully extended conformations.

Use of Optical Pumping to Detect Free Radicals during a Gas‐Phase Photolysis
View Description Hide DescriptionAn optically pumped system of rubidium has been used as a probe to measure the concentration of free radicals present during the vacuum‐ultraviolet photolysis of five hydrocarbons. The mechanism for this measurement is the reduction of the relaxation time of the oriented rubidium in the presence of radicals, due to the large spin exchange interaction between the two species. Measurements were made at two different pressures each on methane, ethane, propane, butane, and isobutane; from this both relative and absolute approximate quantum yields for radical production are determined. Separate detection of hydrogen atoms during the photolysis, through spin exchange coupled electron spin resonance, was reported briefly in an earlier note and is discussed more fully here. This method of directly detecting free‐radical intermediates appears to be a useful complement to standard experiments in which reaction mechanisms are deduced from analysis of final products of the photolysis.