Volume 54, Issue 3, 01 February 1971

Electric Dipole Moment of Diatomic Molecules by Configuration Interaction. I. Closed‐Shell Molecules
View Description Hide DescriptionA scheme has been developed for selecting a manageable number of configurations (less than 200) to be used in a configuration interaction calculation to obtain the electric dipole moments of closed‐shell diatomic molecules. Calculations have been performed on LiH , CO ( and ), CS , and NaLi . A dramatic improvement over the restricted Hartree–Fock value is obtained. At the RHF, CI, and experimental dipole moments (in debye) are LiH: 6.00, 5.86, 5.83; CO: − 0.27, 0.12, 0.11; and CS: 1.56, 2.03, 1.97.

Electron Spin Resonance of the CN Molecule Trapped in Gamma‐Ray Irradiated Potassium Cyanate
View Description Hide DescriptionElectron spin resonance(ESR) studies have been made on single crystals of potassium cyanate (KNCO) that have been irradiated with gamma rays at room temperature. Two ESRspectra resulted. One of these consisted of an center displaying a three‐line hyperfine structure. This spectra is assigned to a CN molecule. The molecule occupies two sites in the lattice in which the molecular axis is parallel to the [110] and the [11̄0] directions of the unit cell. The parameters of the spin Hamiltonian deduced from the spectra are , and . The is not determined.

EPR Linewidth Study of Vanadyl Complexes in Various Solvents
View Description Hide DescriptionThe temperature dependences of the EPRlinewidths for vanadyl acetylacetonate, VO(acac)_{2}, have been measured in ethanol,n‐propanol, isopropanol, n‐butanol, t‐butanol, trifluoroethanol, and trichloroethanol. A similar study has been carried out on vandayl trifluoroacetylacetonate, VO(tfac)_{2}, in methanol and the solvated vanadyl ion, VO^{2+}, in water. The EPRlinewidths have been measured at 25°C for VO^{2+} in dimethyl sulfoxide, trimethyl phosphate, acetonitrile, ,N‐dimethylformamide, and methanol. The results are interpreted in terms of the theory proposed by Kivelson et al. to obtain rotational correlation times for the various systems. The results generally conform to the predictions of the modified Debye theory, in that and solvent visocity show the expected temperature dependence. Only VO(tfac)_{2} in methanol appears to be anomalous in this respect. A detailed analysis has shown that one of the parameters in Kivelson's expression for the linewidths is less sensitive to experimental error and therefore best suited for calculations of . The results indicate that at low temperature some mechanism in addition to spin–rotational relaxation is contributing to the “residual” linewidth.

Relative Rates and Their Dependence on Kinetic Energy for Ion–Molecule Reactions in Ammonia
View Description Hide DescriptionIon cyclotron resonance techniques are used to measure the relative rates and their dependence on kinetic energy for the major ion–molecule reactions in ammonia. Charge transfer is shown to compete with proton transfer in the reaction of both NH_{2} ^{+} and NH_{3} ^{+} with ammonia over an energy range from thermal velocities to 50 eV: The rate for charge transfer increases with increasing kinetic energy while the rate for proton transfer decreases with kinetic energy. At thermal kinetic energies, and . Resonant charge transfer from NH_{3} ^{+} was observed only for translationally excited ions.

Spectroscopic Determination of the Pseudorotation Barrier in Selenacyclopentane
View Description Hide DescriptionThe infrared and Raman spectra of selenacyclopentane have been studied. A series of far‐infrared absorption peaks is interpreted to indicate that the five‐membered ring molecule has a large barrier to pseudorotation. The derived potential function is with the pseudorotation constant . Evidence that the molecule has a twisted configuration in its lowest few vibrational states has been obtained.

Electron Paramagnetic Resonance of V^{2+}, Mn^{2+}, Fe^{3+}, and Optical Spectra of V^{3+} in Blue Zoisite, Ca_{2}Al_{3}Si_{3}O_{12}(OH)
View Description Hide DescriptionElectron paramagnetic resonance and optical absorptionspectra have been used to clarify the local environments of transition metalions and their distributions among various Al and Ca sites in a gem quality zoisite crystal from Tanzania. The EPRspectra due to Mn^{2+}, Fe^{3+}, and two types of V^{2+} have been interpreted by the spin Hamiltonian in the principal axes system . The Mn^{2+}ions occupy one of the Ca sites, probably Ca(1), with point group symmetry ; and , both isotropic, and also , in general agreement with other oxides and hydrates. Highly anisotropic hyperfine and small zero‐field splittings are observed for V^{2+}, which is the opposite of the usual situation. One of the two types of V^{2+} apparently occupies the same site as Mn^{2+}; the other V^{2+} ion is in a general position, and probably occupies a double minima potential around the Ca(2) site. The Fe^{3+}ions occupy the Al_{II} site since the point group symmetry is ; the principal axes, however, are displaced approximately 45° from the NMR axes of ^{27}Al. Apparently, the local environment changes when Al^{3+}ions are replaced by Fe^{3+}. For Fe^{3+}, we found and . The optical absorption of V^{3+} and the trichroism of the zoisite single crystal are consistent with the two types of Al^{3+} site symmetries, with crystal field parameters at Al_{I} and Al_{II} sites.

Far‐Infrared Absorption Spectra of Mercurous Halides
View Description Hide DescriptionThe absorption spectra of mercurous halides Hg_{2}X_{2} (X=Cl, Br, and I) were measured at 300 and 90°K in the wavenumber region 400–10 cm^{−1}. Besides the two strong bands observed previously for each mercurous halide, some weak bands were found at 371, 310, and 156 cm^{−1} for chloride, at 310, 223, 156, and 113 cm^{−1} for bromide, and at 112 cm^{−1} for iodide. By use of a simple crystalline lattice model, the observed infrared spectra of halides together with the Raman spectra reported already could reasonably be explained. New assignments for the spectra are proposed and some force constants are determined.

ESR of ^{17}O‐Labeled CO_{2} ^{−} Radical Trapped in a Single Crystal of Sodium Formate
View Description Hide DescriptionThe ESR spectrum of x‐irradiated sodium formate enriched in ^{17}O is interpreted in terms of the CO_{2} ^{−} radical. Two magnetically inequivalent oxygens were observed. The hyperfine tensors of ^{13}C and ^{17}O were determined and the following principal values were obtained for ^{13}C: 155, 150, and 195 G, respectively, along the axis perpendicular to the molecular plane, along the O–O direction, and along the axis. These results agree with those previously reported. For ^{17}O the magnitudes of the principal values for both oxygens are practically identical, the averages being 22.0, 23.2, and 51.0 G. The direction of the largest value is in the molecular plane inclined at 13° to the axis. The results are used to derive the coefficients of the molecular orbital containing the unpaired electron.

Transport Properties of a Gas of Diatomic Molecules
View Description Hide DescriptionExplicit expressions, valid in the classical limit, are derived for the rotational relaxation time and viscosity of a low‐density gas of rotating, nonvibrating, diatomic molecules. These expressions are based on the quantum mechanical expressions in terms of the degeneracy‐averaged cross sections for a gas in which the average angular momentum of the molecules is zero. The use of an expression for the classical limit of the degeneracy‐averaged cross section leads to the evaluation of several of the summations and integrations.

Noniterative Solutions of Integral Equations for Scattering. V. Auxiliary T^{(kj)} Matrix Formalism
View Description Hide DescriptionThe homogeneous integral solution method is used to develop a scheme for direct computation of the T matrix. The method involves calculation of auxiliary matrices in terms of which the true T matrix is obtained. The auxiliary matrices can be obtained by solving either integral or first‐order linear non‐homogeneous differential equations. The relationship of calculations based on these equations to those based on the wavefunctionintegral equations is discussed. Numerical studies of the general behavior of the homogeneous integral solution procedure are presented. These studies deal with rotationally inelastic collisions of an atom and a rigid rotator interacting via a Morse‐type potential. An investigation of some higher‐order numerical schemes for solving the integral and differential equations for the auxiliary matrices and the integral equations for the wavefunction is reported. The results indicate that the use of higher‐order procedures such as the Runge–Kutta method or Simpson's quadrature scheme permit one to use step sizes 5–10 times larger than those required with the trapezoidal quadrature scheme (or equivalently, the uncorrected Euler method for the differential equation) to achieve a given accuracy. The role of the potential function is studied by a comparison of the matrix elements for Lennard‐Jones (12–6) and Morse potentials having the same well depth, curvature, and equilibrium position. In addition, hybrid potentials constructed by splicing together Morse and Lennard‐Jones potentials are studied. The results indicate that, at the energy considered, the long‐range portion of the potential has a dominant effect on the elastic and inelastic scattering.

On the Critical Region of a Simple Fluid. I. Two Elementary Index Inequalities
View Description Hide DescriptionThe continuity of the slopes of isochores of a simple fluid at its critical point is shown to imply, and be implied by, the strict index inequality, which is not a consequence of known index inequalities based on thermodynamic stability. Under certain assumptions relating to the index inequality, it is shown that diverges with index on the phase boundary, and that the saturated specific heat diverges with index

On the Critical Region of a Simple Fluid. II. Scaling‐Law Equation of State
View Description Hide DescriptionThe scaling‐law equation of state is used to illustrate some consequences of the elementary index inequalities. It is shown that evaluated on the phase boundary below from the homogeneous‐phase side diverges with index , where is the (scaling‐law) index for . Also, it is shown that diverges with index on the critical isobar, where is the degree of the critical isotherm.

Electronic Specific Heats of Alloys of the MgCu_{2−x }Zn_{ x } System
View Description Hide DescriptionSpecific‐heat measurements were made on 17 alloys of the pseudobinary system MgCu_{2−x }Zn_{ x } between 1.5 and 4.2°K. In addition to the two terminal phases MgCu_{2} and MgZn_{2}, the compositions studied included nine alloys having the cubic MgCu_{2} structure, four having the hexagonal MgZn_{2} structure, and two samples consisting of a mixture of two phases. The density of states at the Fermi levelN(E_{F} ) was calculated from the measured values of . The variation of with composition is compared with results from this laboratory previously reported on the MgCu_{2−x }Al_{ x } and Mg_{2−x }Si_{ x } systems. Variation of with composition in the cubic range exhibited, qualitatively, the same trends that were shown in the MgCu_{2−x }Al_{ x } system, namely, a maximum in at 1.44 electrons/atom, a rapid decrease in as the stability limit for the cubic phase at ≈ 1.73 electrons/atom is approached, and a shoulder on the falling curve at 1.59 electrons/atom. Values of the Debye , calculated from the slopes of the curves of vs are computed for the three systems.

Perturbation Theory in Terms of Reduced Density Matrices
View Description Hide DescriptionA simple perturbation theory has been developed for reduced density matrices which are known to be representable as functions of some set of independent parameters. Formulas are presented for single and double perturbations through second order. Extension to higher order would be possible, but involved. The results do not depend explicitly on the order of the density matrix, and when the N‐particle density matrix is used, the formulas can be reduced to those of conventional Rayleigh–Schrödinger theory. Details are given for the special cases of spin‐unrestricted or extended SCF density matrices and CI or optimized multiconfiguration density matrices which are known to be representable.

Optical Absorption Characteristics and Photobleaching Behavior of Trapped Electrons in γ‐Irradiated Alkaline Ice
View Description Hide DescriptionTrapped electrons,, are produced by irradiation of alkaline ice (10M NaOH) at 77°K. The absorption band maximum at 590 nm shifts to shorter for bleaching at 700 nm and shifts to longer for bleaching at 400 nm. After partial bleaching, electrons can be shifted back and forth between traps characterized by long and short . Although this suggests at least two trap depths, there is probably a broad spectrum of trap depths. The quantum efficiency, , for photobleaching is 0.15 and independent of when the optical density is measured at 590 nm. For the optical density measured at the bleaching wavelength, increases to 0.52 at 400 nm and to 0.26 at 700 nm; also increases in the presence of electron scavengers. decreases as the fraction of bleached, , increases and follows for . All of these changes are explained by retrapping and trap interconversion. is also independent of temperature between 4 and 77°K in agreement with photoconductivitymeasurements., and the oscillator strength is ≥ 0.86 for the band.

Microwave Spectrum, Structure, and Dipole Moment of Cyclopropylphosphine
View Description Hide DescriptionThe microwave spectra of three isotopic species of cyclopropylphosphine have been analyzed. The conformation of the molecule is the symmetric one allowing maximum interaction of the lone pair electrons of phosphorus with the intra‐annular orbitals of the cyclopropyl ring. A structure compatible with the observed moments of inertia yields, along with other parameters, a C–P bond distance of 1.834 Å, distinctly shorter than that observed in other organic phosphine derivatives. The dipole moment is found to be 1.16 D.

Infrared Spectrum and Structure of the Species CO_{3}
View Description Hide DescriptionUpon photolysis of solid CO_{2} by 1216‐Å radiation, very high yields of CO_{3} have been obtained. There is no evidence for the production of hydrogen‐containing species in experiments in which photolytically produced H or D atoms are also present. Experimental evidence supports a structure for CO_{3} in its ground state, as predicted by molecular orbital calculations. The vibrational frequency pattern for the planar modes of isotopically substituted species of CO_{3} has been fitted to a valence force potential having a minimal number of interaction force constants, assuming both an open structure having an O–C–O angle of 80° and a three‐membered ring structure having an O–C–O angle of 65°. Although the force constants obtained for the ring structure appear to be quite reasonable, exceptionally large values have been obtained for the O–C–O bending force constant and for all of the interaction constants for the open structure. On this basis, the three‐membered ring structure is favored for CO_{3} in its ground state.

Infrared Spectrum and Structure of Intermediates in the Reaction of OH with CO
View Description Hide DescriptionUpon vacuum‐ultraviolet photolysis of H_{2}O in a CO matrix at 14°K, infrared absorptions of HCO, H_{2}CO, HCOOH, and CO_{2} become prominent. Furthermore, new absorptions due to reactive product species appear at 615, 620, 1077, 1088, 1160, 1261, 1797, 1833, 3316, and 3456 cm^{−1}. These absorptions diminish in intensity when the sample is subjected to radiation in the 2000–3000‐Å spectral range. Detailed consideration of the processes which may occur in this system and extensive isotopic substitution studies support the assignment of these absorptions to the cis and trans stereoisomers of H–O–C=O, produced by the reaction of OH with the CO matrix. Valence force potentials having only small contributions from interaction terms have been found which correspond to a physically reasonable vibrational assignment and which satisfactorily reproduce the pattern of observed frequencies for the various isotopic species of both cis‐ and trans‐HOCO. Evidence suggests that cis‐ and trans‐HOCO photodecompose to produce H atoms and CO_{2}.

Absolute Rate of the Reaction H+H_{2}S
View Description Hide DescriptionFlash photolysis coupled with resonance fluorescence of Lyman‐α radiation at 121.6 nm has been used to investigate the rate of reaction of H atoms with H_{2}S over the temperature range 190–464°K. Conditions were chosen under which atom–radical and radical–radical reactions were unimportant and only the H‐atom–H_{2}S reaction occurred. The rate constant thus obtained can be expressed as . Comparison of the Arrhenius factor with that predicted by entropy considerations suggests a somewhat loose activated complex, but not as loose as expected on the basis of the exothermicity of the H+H_{2}S reaction.

Isothermal Compressibility of Deuterium Oxide at Various Temperatures
View Description Hide DescriptionThe isothermal compressibilities of deuterium oxide solutions have been measured from 5–65°K. The measurements were made by a piezometric technique from 1–34 bar and extrapolated to 1 atm. The results are briefly discussed and compared to the values for normal water.