Volume 51, Issue 10, 15 November 1969

De‐excitation of Electronically Excited Sodium by Nitrogen
View Description Hide DescriptionA semiquantitative calculation is made of the cross section for the quenching of Na(3^{2}P) by molecular nitrogen, as a function of initial kinetic energy and of final vibrational quantum number, , of the nitrogen molecule. The large observed cross section, which is of gas‐kinetic order, can be explained in terms of an intermediate ionic state, involving Na^{+} and . This state is unstable at infinite separation of Na and N_{2}, but because of the Coulomb attraction it becomes stable at collision distances below about 3 Å. As a result of the vibrational structure of both the intermediate and final states, we treat the reaction in terms of a diffusion of the probability flux through a two‐dimensional network of potential‐energy curves parametrized by both the electronic state and also the vibrational quantum numbers and . At each potential‐energy curve crossing we compute the transition matrix element for insertion into a Landau–Zener type of transition probability. The transition matrix element is represented as the product of an electronic interaction function (obtained from a correlation, due to Hasted and Chong, of results obtained from charge‐transfer processes involving multiply charged ions) and a vibrational overlap integral or Franck–Condon factor. Results are also presented on the quenching of by N_{2}, and on the quenching of by CO. All the results have the same general character: The total cross section is of gas‐kinetic order and depends only weakly on kinetic energy. The partial cross sections for excitation of the different final vibrational levels v_{f} show a rather broad distribution, with somewhat more than half the energy of electronic excitation ending up as vibrational excitation.

Theoretical Study of the Barriers to Internal Rotation in Hydrogen Persulfide, HSSH
View Description Hide DescriptionHydrogen persulfide, HSSH, has been studied by the ab initio self‐consistent‐field molecular‐orbital method for the four dihedral angles of 0°, 90°, 135°, and 180°. The basis set consisted of Gaussian orbital expansions of best‐atom Slater‐type orbitals through , tested in other calculations on H_{2}S. The molecule has a calculated energy minimum for a dihedral angle in the range 90°–100°, in fair agreement with experiment (about 90.5°). The cis barrier is high (7.4 kcal), but the smaller trans barrier (1.9 kcal) seems low for consistency with experimental studies of the torsional vibrational levels. The S–S overlap population shows a pronounced maximum near a dihedral angle of 90°, just where the total energy shows a minimum. This reflects larger S–S bonding character near equilibrium and furnishes semiquantitative support for the discussion based on hyperconjugation used by the experimentalists to explain the structure. A partitioning of the total energy into attractive and repulsive components shows that both cis and trans barriers are dominated by the repulsive component (this is also true if the wavefunctions are scaled to satisfy the virial theorem).

Magnetic‐Field Effects on a Compensated Cholesteric Liquid Crystal
View Description Hide DescriptionBy measuring changes in the dielectric constant of a 1.75:1 cholesteryl chloride–cholesteryl myristate (CM) mixture in the presence of magnetic fields up to 10 kG, the orientation of the molecular and helical axes with respect to the field direction can be deduced, and the possibility of a dependence of the alignment process on the pitch of the helix is explored. When the sample thickness is much greater than , there is no preferred direction for the helix axis in the bulk, and applying either ⊥ or ‖ to the sample causes the helix axis to align . This effect only occurs at , and only partial ordering occurs even at . The angle between the long molecular axis of cholesteryl chloride and a plane ⊥ to the helix axis is reduced by application of . Since is determined by the internal mechanical energy of the cholesteric structure, the decrease in becomes more pronounced as approaches infinity. A comparison is also made of the effects of electric and magnetic fields on CM; an electric field of 500 V/cm counteracts a magnetic field of the order of 10 kG. The anisotropy of the diamagnetic susceptibility is deduced to be ∼10^{−9}.

Matrix Isolation Studies of Group‐IV Oxides. I. Infrared Spectra and Structures of SiO, Si_{2}O_{2}, and Si_{3}O_{3}
View Description Hide DescriptionThe matrix isolation of silicon monoxide vapor leads to the formation of at least three distinct species: SiO, Si_{2}O_{2}, and Si_{3}O_{3}. Infrared absorptions for these molecules are observed at 1223.9 cm^{−1} (Si^{16}O); 804.7, 766.3 cm^{−1} (Si_{2} ^{16}O_{2}); 972.6, 631.5, 312.0 cm^{−1} (Si_{3} ^{16}O_{3}). Equations are given for the in‐plane vibrations of the ring and the ring, and using ^{18}O substitution, it is shown that these respective models account for the observed ir absorptions of Si_{2}O_{2} and Si_{3}O_{3}. Estimates are given for the molecular dimensions of and , and for their unobserved vibration frequencies. The reaction SiO + Si_{2}O_{2} → Si_{3}O_{3} is observed during diffusion studies, and a lower limit obtained for the mean bond energy in Si_{3}O_{3} of ∼104 kcal/mole.

Polarized Crystal Spectra of CoF_{2} and Co_{0.06}Zn_{0.94}F_{2}
View Description Hide DescriptionPolarized spectra of oriented single‐crystal CoF_{2} and Co_{0.06}Zn_{0.94}F_{2} are presented in the range 5000–25 000 cm^{−1} at 298, 77, and 20.4°K. Molar extinction coefficients and oscillator strengths are calculated. The spectra of CoF_{2} and of dilute Co^{2+} in ZnF_{2} are very similar. The principal bands are identified as transitions from the ground level to , , and levels. A value of is obtained. A sharp electric dipole line, 10 cm^{−1} wide, is seen at 22 768 cm^{−1} in CoF_{2} at 20.4°K.

On Symmetric Multicomponent Diffusion Coefficients
View Description Hide DescriptionThe symmetric set of isotropic multicomponent diffusion coefficients introduced by Curtiss in the context of the kinetic theory of dilute gases are given a general definition and shown to possess general symmetry properties by virtue of Onsager reciprocal relations. Their relationships to Onsager coefficients, Curtiss–Hirschfelder diffusion coefficients, and Bearman–Kirkwood multicomponent friction coefficients are established and employed in stability considerations to deduce results which include the vanishing of Curtiss–Hirschfelder thermal diffusion coefficients in dilute solution as a consequence of the second law of thermodynamics.

Hydrogen Bond Studies. XXXVII. The Crystal Structure of Sulfuric Acid Dihydrate (H_{3}O^{+})_{2}SO_{4} ^{2−}
View Description Hide DescriptionThe crystal structure of H_{2}SO_{4}·2H_{2}O has been determined from three‐dimensional single‐crystal x‐ray data recorded at −190°C. The crystals are monoclinic, space group , with 12 formula units in a cell with the dimensions: , , , and . The structure consists of H_{3}O^{+} and SO_{4} ^{2−} ions. Each of the three independent H_{3}O^{+} ions is hydrogen bonded to three different SO_{4} ^{2−} ions (0···0 distances, 2.520–2.590 Å) is such a way that a three‐dimensional hydrogen‐bond pattern is formed. The average S–O distance in the sulfate ion is 1.474 Å.

Electron Paramagnetic Resonance Study of the Stereochemistry of Nitrosylhemoglobin
View Description Hide DescriptionParamagnetic resonance spectra of single crystals of nitrosylhemoglobin (HbNO) have been obtained at − 195°C. There are four nonequivalent paramagnetic atoms which form two sets; the members of each set are related by the [010] dyad axis. The principal values of the gtensor are: , and ; the isotropic value is 2.039. The principal values of the hyperfine Atensors are: ; the isotropic coupling constant has a value of 50 MHz. The calculated principal values for the dipolar T′tensors are: . The principal axes of the gtensor do not coincide with these of the Ttensor; the results were interpreted to give a bent Fe–N–O angle of 110°. The N–O axes of the ligands of one set lie in the ab plane; those of the others are inclined at an angle of about 80° to the ab plane. The electrostatic interaction of the oxygen atom with the imidazolium group of the distal histidine and the nonpolar evnironment in the vicinity of the heme probably contribute to the stabilization of this particular Fe–N–O bond.

Quenching of Lyman‐α Fluorescence
View Description Hide DescriptionIntensities of scattered Lyman‐α radiation have been measured for mixtures of partially dissociated hydrogen in argon with variable amounts of O_{2}, N_{2}, NO, N_{2}O, CO, CO_{2}, or SO_{2}. Quenching cross sections measured for each of these gases, and obtained indirectly for H_{2} and Ar, have been corrected for radiation trapping using the theory of Holstein. We find values of 45 ± 15 (O_{2}), 33 ± 10 (N_{2}), 49 ± 25 (NO), 86 ± 30 (N_{2}O), 52 ± 20 (CO), 120 ± 45 (CO_{2}), 170 ± 50 (SO_{2}), 30 ± 15 (H_{2}), and 11 ± 5 (Ar) (all × 10^{−19} cm^{−2}).

Photoionization Study of the Dissociation Energy of Fluorine and the Heat of Formation of Hydrogen Fluoride
View Description Hide DescriptionMass spectra and photoionization yield curves are obtained for the molecular and atomic ions of fluorine and hydrogen fluoride. The atomic ions of both molecules are formed by ion‐pair and by dissociativeionization processes. The F_{2} ^{+} curve has a weak onset at 15.58 eV, ascribed to a hot band, followed by an abrupt, intense onset at 15.69 eV, ascribed to the 0–0 transition. Several broad bands of autoionization are observed. The onset of the dissociativeionization process occurs at 18.76 eV, from which we calculate . The only observed ion‐pair process is spin forbidden, producing , for which the thermodynamic threshold is not reached. The HF^{+} curve has a slightly tailing onset at 15.92 eV. No F^{+} ion is observed. The dissociativeionization process yielding H^{+} occurs at 19.34 eV, permitting the calculation of , and . Identical ion‐pair curves have a threshold at 15.87 eV resulting in . The indicated uncertainties are estimated limits of error.

Two‐Channel Model for Electron Transfer in Ion–Molecule Collisions
View Description Hide DescriptionA phenomenological model based on competition between charge‐transfer and atomic‐rearrangement (chemical reaction) channels is used to calculate the charge exchange cross section for Ar^{+}–H_{2} collisions below 1000 eV. The energy dependence of the calculated cross section is in good agreement with recent data.

Solvation of the Titanous Ion in Aqueous and Methanol Solutions
View Description Hide DescriptionThe solvation of the titanous ion in aqueous and methanol solutions has been studied by means of proton, deuteron, and oxygen‐17 magnetic resonance. Kinetic parameters for the exchange reaction of the solvent molecules between the coordination sphere and the bulk, hyperfine coupling constants, and relaxation times of the unpaired electron of the titanous ion have been determined. Attempts to interpret the results in view of the uniqueness of the titanous ion among the ions of the first transition‐metal series have also been made.

High‐Resolution Photoionization Study of the H_{2} Molecule near Threshold
View Description Hide DescriptionRelative photoionization and absorption cross sections of H_{2} (ordinary and para) have been measured from 745–810 Å at 300 and 78°K, with a resolution width of 0.04 Å. The photoionization data show the presence of extensive structure due to autoionization of vibrationally excited Rybderg states. Analysis of the data on the D–X(6, 0) band in the region of the ionization threshold leads to the conclusion that the ionization potential of H_{2} lies between 124 418.2 and 124 393.5 cm^{−1} and is probably very near the former value. Analysis of the data on the B″–X(4, 0) band requires either that the ionization potential lies below 124 407.2 cm^{−1} (which is rather unlikely) or that autoionization of the and lines occurs in violation of one of the autoionization selection rules proposed by Beutler and Jünger. Some Rybderg states that lie just below their ionization limits and do not autoionize spontaneously can be made to ionize in weak electric fields and by collision with unexcited H_{2} molecules. Direct ionization of appears to begin about 23 cm^{−1} below the expected threshold, probably as a result of collisional ionization of Rydberg states lying just below the ionization threshold. A series of peaks appearing in a short region immediately above threshold apparently coincides with a series which Herzberg has observed in absorption and identified as the Rydberg series converging to the rotationally excited state of the H_{2} ^{+} ion. The autoionization of these Rydberg states must occur by conversion of rotational to electronic energy. An intensity anomaly of this series is ascribed to channel interaction with a vibrationally excited Rydberg state. A large number of the autoionization peaks have been identified in the spectrum of parahydrogen at 78°K. By comparison of the absorption cross section with the photoionization cross section, it was found that all states that can autoionize with are strongly autoionized (∼40%–100%) while the autoionization probabilities of states that autoionize with vary widely. The dominance of autoionization with over predissociation extends to the very highest Rydberg states and leads to the absence of observable thresholds for formation of vibrationally excited H_{2} ^{+} ions. Some peaks that autoionize with have widths larger than the instrumental width, and the autoionization rates have been estimated. They are in fair quantitative agreement with recent calculations of Nielsen and Berry. The widths decrease rapidly with principal quantum number as Bardsley predicts. The autoionization rate decreases by about a factor of 10 or more when the of the transition changes from 1 to 2. For larger values of , the autoionization rate appears to decrease still more but not necessarily as a monotonic function of .

Vibrational Spectra of PCl_{ n }F_{5–n }
View Description Hide DescriptionThe frequencies of the title compounds are computed using a simple force‐field transference scheme. On the basis of these calculations, and gas‐phase Raman spectroscopy of PF_{5}, for this molecule is assigned at 175 cm^{−1}. An assignment of the species PF_{3}Cl_{2} is suggested.

Model for the Dynamics of Some Primary Photochemical Reactions
View Description Hide DescriptionA model similar to that proposed by Rice, McLaughlin, and Jortner [J. Chem. Phys. 49, 2756 (1968)] is examined in detail form the point of view of momentum space and is extended to include orthogonal decay channels. It is shown that a cutoff function in matrix elements between fragments and undissociated molecules is essential for convergent integrals over fragment energies. The explicit time dependence of molecular and fragment state amplitudes is investigated and formulas for the fragment energy profile given. The possibility of using this model to describe threshold and isotope effects is suggested.

Molecular Values, Magnetic Susceptibilities, Molecular Quadrupole Moments, and Second Moments of the Electronic Charge Distribution in OF_{2}, O_{3}, and SO_{2}
View Description Hide DescriptionThe rotational Zeeman effect has been observed in several transitions in OF_{2}, O_{3}, and SO_{2}. The absolute values of the molecular values , , and and the signs and magnitudes of the magnetic susceptibilityanisotropies and are obtained by high‐resolution microwavespectroscopy with the sample in the presence of high magnitude fields. Arguments are presented to show that all of the molecular values are negative leading to the molecular quadrupole moments, , , and also listed below. The , and axes are the principal inertial axes in each molecule. The axis bisects the interatomic angle and the axis is also in the molecular plane. The units of are 10^{−6}erg/G^{2}·mole and the units of are 10^{−26} esu·cm^{2}.The diagonal elements in the paramagnetic susceptibility tensor and the anisotropies in the second moment of the electronic charge distributions and are computed from the above results and the known molecular structures. The bulk susceptibilities are known for O_{3} and SO_{2} which leads to a direct determination of the diagonal elements of the total and diamagnetic susceptibilities and the individual values of in these two molecules. The bulk susceptibility for OF_{2} is estimated from a reliable estimate of for this molecule.

Analytical Evaluation of Multicenter Integrals of with Slater‐Type Atomic Orbitals. V. Four‐Center Integrals by Fourier‐Transform Method
View Description Hide DescriptionThe four‐center integral of with Slater‐type atomic orbitals is evaluated analytically. The Fourier‐transform convolution theorem is used to express the integral as an infinite sum in which the internuclear angles appear in spherical harmonics, and the internuclear distances in integrals over spherical Bessel functions and exponential‐type integrals. These “radial” integrals are evaluated as convergent infinite expansions by contour integration techniques. The formulas are valid for general values of the parameters of the orbitals and for general nonzero values of the internuclear distance vectors.

MagnetoOptical Investigation of Trivalent Dysprosium in Gadolinium Trichloride
View Description Hide DescriptionThe optical absorptionspectrum of 2% Dy^{3+} in the ferromagnet GdCl_{3} has been investigated and found to exhibit line shifts and splittings below the Curie temperature (2.2°K), which are attributable to magnetic dipole and exchange interaction between the various states of Dy^{3+} and the ordered Gd^{3+} system. These effects have enabled the exchange field to be measured for a number of different multiplets, at the lowest temperature obtainable (1.35°K). The exchange field is found to be reasonably constant within a particular multiplet, but the variation between multiplets is more complex than the simple model would indicate. The temperature dependence of the shifts and splittings suggests that the optical effects are a measure of the longrange, rather than the shortrange order, although the latter cannot be entirely ruled out.

Structure Studies of Solutions of Large Organic Molecules. I. C_{9}H_{19}I and C_{18}H_{36}I_{2} in Decalin
View Description Hide DescriptionThe x‐ray scattering from solutions of C_{9}H_{19}I and C_{18}H_{36}I_{2} in decalin, C_{10}H_{18}, at various concentrations has been studied. The principal aim of the research was to develop a technique for the direct determination of end‐to‐end distances of polymers in solution. This was achieved, and the method is outlined in detail. In the course of the work some interesting clustering phenomena were discovered in the monoiodide solutions. A model is proposed which has as its main feature the formation of quasi‐liquid‐crystal regions, with the alkane chains lying parallel to each other and the I atoms in contact.

Structure Studies of Solutions of Large Organic Molecules. II. End‐to‐End Distances of Alkanes from C_{8}− to C_{22}−
View Description Hide DescriptionEnd‐to‐end distances for a series of alkanes in the range C_{8}− to C_{22}− have been measured by the technique described in the preceding article. There appears to be good agreement with the theoretical values of the characteristic ratio cited by Flory. However, there is evidence that solvent effects are present. These are discussed.