Volume 70, Issue 12, 15 June 1979
Index of content:

Electron energy loss spectroscopy of pristine and radiation damaged polyethylene
View Description Hide DescriptionThe spectra of valence and core electronic excitations of polyethylene from 1 to 390 eV were measured with a resolution of 0.11 eV by transmission electron energy loss spectroscopy. Structure at 9.5, 13.2, 14.7, 16.6, 19.6, 21.6 eV and a continuum of core excitations beginning at 287.5 eV was measured and compared with theoretical calculations of molecular excitons and interband transitions. The momentum dependence of the fundamental absorption threshold at 7.2 eV indicates that the absorption edge is due to highly localized excitons. From the energy loss spectra the complex dielectric response function and optical properties were calculated and compared with existing optical data. Radiation induced changes in the electronic structure were observed by their characteristic excitation spectra which were shown to be due to formation of polyenyl chromophores in the polymer backbone.

Knudsen effusion mass spectrometric determination of the dissociation energy of diniobium, Nb_{2}(g), and the heat of sublimation of solid niobium
View Description Hide DescriptionThe dimer of niobium,Nb_{2}(g), has been observed under thermal equilibrium conditions by the high temperature mass spectrometric technique, employing an unconventional design for the Knudsen cell. From the partial pressures of Nb and Nb_{2} measured in the 2545–2677°K temperature range, the dissociation energy of Nb_{2}(g) has been determined to be D _{0}°=503±10 kJ mole^{−1} or 120.2±2.4 kcal mole^{−1} and D°_{298}=511±10 kJ mole^{−1} or 122.0±2.4 kcal mole^{−1}. By combining D(Nb_{2}) with the heat of vaporization of niobium, the heat of formation of Nb_{2}(g) is derived as ΔH°_{ f,298}=916±12 kJ mole^{−1} or 218.9±2.9 kcal mole^{−1}. Also, the heat of vaporization of Nb has been redetermined as ΔH°_{ v,298}=713±7 kJ mole^{−1} or 170.4±1.6 kcal mole^{−1} and ΔH°_{ v,0}=710±7 kJ mole^{−1} or 169.7±1.6 kcal mole^{−1}. The dissociation energy of Nb_{2}(g) is in good agreement with the value predicted previously and is consistent with the trends indicated for the dissociation energy of the diatomic molecules of the first and second transition series metals.

On the temperature dependence of the ^{14}N NQR in K‐TCNQ
View Description Hide DescriptionThe temperature dependence of the ^{14}N nuclear quadrupole resonance (NQR) spectrum of K‐TCNQ was measured from 77 to 300 K. The NQR frequency shifts with temperature can be explained by considering the effects of the thermal averaging of the quadrupole parameters and the rearrangement of the TCNQ^{−} and K^{+} stacks. The ^{14}N NQR data are consistent with the observed Peierls transition found for K‐TCNQ.

ESR studies of a nitrogen defect in irradiated potassium azide
View Description Hide DescriptionAn electron spin resonance study has been conducted on a new paramagneticdefect center in irradiatedpotassium azide. Irradiation of a single crystal of KN_{3} with x rays at 77 K resulted in the formation of the defect which was characterized by a single structureless resonance line having considerable anisotropy. Effective g values along the principal axes were measured at 77 K and were found to be 6.16, 1.719, and 0.579 along the crystal [001], [110] and [11̄0] directions, respectively. The rotational spectra could not be fit, however, with a spin one half Zeeman Hamiltonian, leading to the conclusion that only one transition of a spin greater than one half system was being observed. Measurements at temperatures other than 77 K showed a strong temperature dependence of the effective g values which would be consistent with a temperature dependent fine structure term in the spin Hamiltonian. The defect was found to be stable to about 130 K. Isothermal annealing measurements indicated a first order decay with an activation energy of 0.39 eV and a characteristic frequency of about 10^{12} Hz. Irradiation of a single crystal with ultraviolet light resulted in the formation of a defect with the same effective g values, but a narrower resonance line having hyperfine structure indicative of interaction with a single nitrogen nucleus.

Franck–Condon theory of chemical dynamics. VI. Angular distributions of reaction products
View Description Hide DescriptionWe calculate planar and three‐dimensional angular distributions for the products of atom–diatom chemical reactions by means of the Franck–Condon (FC) model. The wave functions on the reactant and product quasiadiabatic surfaces are expanded in partial wave series. A local uncoupling of the different degrees of freedom, as justified earlier, is assumed and consequently the individual members of the partial wave series can be separated into products of angular factors and rovibration–translation factors. To evaluate these factors, we consider the limit of weak and strong potential, and weak and strong kinematic couplings. The center of mass differential cross section is obtained by means of the T matrix formalism, where the T matrix is approximated by a generalized Franck–Condon overlap of the reactantlike and productlike wave functions. We use several further satisfactory approximations, e.g., linearization of the potential in the region of maximal overlap, and semiclassical approximation to the oscillator wave functions, beyond those of the FC model to obtain an analytic expression for the T matrix. For assumed LEPS surfaces of the systems H+H_{2} →H_{2}+H, H_{2}+F→HF+H and H+Cl_{2}→HCl+Cl, we calculate angular distributions of reaction products in the various coupling limits for ranges of final states. The angular distributions in the strong potential coupling limits have a Gaussian shape peaked about the backscattering angle (π) (the hard sphere deflection angle for the chosen critical configuration) for each of the three reactions studied. In all three cases the 3D angular distribution is narrower than the planar (2D) angular distribution. Our calculations show no difference between the angular distributions of the weak and strong kinematic coupling limits. The angular distribution of the 2D weak potential coupling case are broader than those of the strong potential coupling. For H+H_{2} we find our results in the strong potential limit to be in qualitative agreement with exact quantum mechanical calculations. The angular distribution for a given product state broadens as the initial relative kinetic energy is increased, in agreement with classical trajectory calculation (F+H_{2}). The angular distribution is also predicted to broaden as the final relative velocity increases, in agreement with experiment (H+Cl_{2}, F+H_{2}). Finally we introduce several simplifying approximations to our analytical model and find that, for exothermic reactions like F+H_{2}, the radial contribution to the T matrix is dominated by certain features of the potential: the barrier width, the slope of the potential on the reactant side, and force constants in the region of maximum overlap. Our analysis provides a basis for the formulation of reduced variables which may be of use in comparing reactions. Finally we discuss some sufficient conditions for the separability of product velocity and angular distributions.

Rotational dependence of the dipole moment of CH_{3}D
View Description Hide DescriptionRadio frequency modulated side bands of the C^{18}O_{2} P (18) laser line were used to perform infrared–infrared double resonance between the first order Stark components of the ν_{6} ^{ r } P (10,1) transition of CH_{3}D. The dipole moment in the J=10, K=1 level in the ground state has been measured to be (1.03±0.1) ×10^{−3} D, which is very different from the previously reported values of around 5.65×10^{−3} D. This difference has been explained as due to rotational dependence of the dipole moment. Combining the present result with the previous molecular beammeasurements by Wofsy, Muenter, and Klemperer, we have obtained the rotational dependence of the dipole moment derived from Stark measurements in the form μ_{Stark}(J,K) =∓{ (5.657±0.004)−(0.0427±0.0009) J (J+1) +(0.0696±0.0026) K ^{2}}×10^{−3} D. The upper sign would be consistent with a b i n i t i o calculations of the signs of the dipole derivatives. A theory was developed to calculate the above coefficients of J (J+1) and K ^{2} for CH_{3}D. It has been demonstrated that they can be completely predicted from the ϑ_{ z } ^{ x y } parameter of CH_{4}. The prediction agreed with the observed values within the quoted uncertainties. This theoreticalinformation was indispensable in determining which of the two observed double resonance signals corresponded to the ground state. The apparent contradiction of the present result with that of Ozier, Ho, and Birnbaum, who reported that the dipole moments of CH_{3}D determined from the intensities of R branch spectral lines are independent of J, is explained as due to the fact that the rotational dependence of the dipole moment is different depending on the method of determination. Their measurements are shown to be consistent with the above parameters.

NMR dynamic frequency shifts and the quadrupolar interaction
View Description Hide DescriptionA brief account of the quadrupolar interaction is presented. It is demonstrated that second‐order dynamic frequency shifts must be considered for multipolar nuclides relaxed by spacially isotropic quadrupolar interactions. Hence, each single quantum coherence is characterized by a unique precessional frequency. A short discussion of the intensities and evolution of these transverse magnetization composites is also included for completeness. The findings of this work supplement the theory of spin 3/2 quadrupolar labelling and exchange techniques as applied to biomolecular systems.

Deductions about the structure of phase III from thermodynamic measurements on solid isotopic methanes
View Description Hide DescriptionIn a continuing study of the solid isotopic methanes, the heat capacity of solid CHD_{3} has been measured in the range 0.15<T<3 K. Some structure is found in a Schottky anomaly in the region of the measurements and it is related to the composition of nuclear spin symmetry species in the solid. There is no evidence of spin conversion. The entropy of CHD_{3} has been calculated as a function of temperature from the heat capacity and other data, and is used to make deductions about quantum disorder in the solid. Combined results for CH_{3}D, CH_{2}D_{2} and CHD_{3} lead to the conclusion that the structure of phase III of solidmethane is quantum disordered and that it must contain at least three types of sublattice. A model consisting of two sublattices with tetrahedral molecular fields and one with symmetry lower than tetrahedral, accounts for the experimental observations satisfactorily.

Generalizations of the direct CI method based on the graphical unitary group approach. I. Single replacements from a complete CI root function of any spin, first order wave functions
View Description Hide DescriptionThe direct CI method is generalized to the class of wave functions, denoted as first order wave functions. With a first order wave function is meant a complete CI expansion in a small internal valence space and single excitations outside this space. The wave function can have any spin. The formalism of the graphical unitary group approach of Paldus and Shavitt is used to reduce the coupling coefficients of the direct CI method to expressions involving the internal space only. The necessary formula tape is therefore reduced drastically in size. An approximate and much faster method is suggested for very large CI expansions, based on the neglect of certain integrals. The method is applied to the singlet–triplet splitting of dioxymethane, CH_{2}O_{2}, which is a proposed intermediate in the ozonolysis of ethylene. The calculations predicts the ^{1} A _{1} to be the ground state, but the splitting between ^{1} A _{1} and ^{3} B _{2} is calculated to be very small, 2.0 kcal/mole, in the best calculations reported here.

Low energy x‐ray emission spectra and molecular orbital analysis of CH_{4}, CCl_{4}, and CHCl_{3}
View Description Hide DescriptionThe C–K and Cl–L_{II,III} low‐energy x‐ray spectra from solid CCl_{4}, CHCl_{3}, and the C–K x‐ray spectrum from solid CH_{4} have been obtained using monoenergetic x‐ray excitation and a lead myristate multilayeranalyzing crystal. The C–K spectrum of methane and Cl–L_{II,III}spectra of the chloromethanes were also measured in the gas/vapor phase and compared with those measured in the solid phase. The deconvolved spectral components are aligned on a common energy scale with the complementary x‐ray emission and photoelectron spectra by identifying the same molecular orbital in all spectra. Such an alignment procedure yields a C‐lsionizationenergy of gaseous CH_{4}, and solid CCl_{4} and CHCl_{3} as 290.0 293.5 and 293.1 eV, respectively; and the Cl‐2p _{3/2}ionizationenergy of solid CCl_{4} and CHCl_{3} as 206.5 and 204.8 eV. Results of the CNDO/2 and MINDO/3 MO calculations have been presented and compared with the available results of the extended Hückel MO method and with the deconvolved spectral components. From the geometry program in the MINDO/3 MO calculation, the C–H bond length in CH_{4} is 1.102 Å, the C–Cl bond length in CCl_{4} is 1.751 Å, and the C–H and C–Cl bond lengths in CHCl_{3} are 1.100 and 1.744 Å, respectively. Comparison with the vapor/gas phase spectra shows essentially the same energies for spectral components in the C–K and Cl–L spectra from CH_{4} and CCl_{4}, whereas the spectral components in the Cl–L spectra of CHCl_{3} have energies in the gas phase that are significantly higher than those for the solid phase.

The 2 ^{1} A _{ g }–1 ^{1} B _{ u } energy gap in the polyenes: An extended configuration interaction study
View Description Hide DescriptionFor a correct account of the ordering of excited states in the polyenes, in particular the low‐lying 2 ^{1} A _{ g } and 1 ^{1} B _{ u } states, single as well as double excited configurations must be included in a CI expansion. However, for longer π systems such expansion shows, in contrast to spectroscopic observations, a divergence of excitation energies and a reversal of the 2 ^{1} A _{ g } and 1 ^{1} B _{ u } state ordering. We have therefore extended the CI expansion to include all triple and quadruple excitations for the polyene series C_{ n }H_{ n+2’} n=4,6,8,10,12 and n=4,6,8,10, respectively. In our calculations we employed a PPP model Hamiltonian. The extended CI expansions correct the faults of previous treatments and predict an increase of the 2 ^{1} A _{ g }–1^{1} B _{ u }energy gap with increasing polyene length in agreement with recent spectroscopic observations. The effect of higher excitations is mainly due to triple excitations involving three simultaneous spin flips of ground state electrons.

Correlation effects in the spectra of polyacenes
View Description Hide DescriptionIn order to describe the electron correlation in the excited singlet π,π^{*} states of the polyacenes [C_{4n+2}H_{2n+4}], we have carried out PPP–SCF–CI calculations including all single and double excitations in the CI expansion up to n=5, including all triple excitations up to n=3, and all quadruple excitations up to n=2. Compared to previous CI descriptions which included single excitations only, e.g., the classic work of Pariser [J. Chem. Phys. 24, 250 (1956)], our calculations lead us to predict the following: (1) ’’new’’ excited states entailing the promotion of two electrons from the ground state (some of them predicted previously by other authors), and (2) a partial reordering of those (well‐known) excited states already accounted for by a S‐CI representation. Single and double excitations in a CI expansion (D‐CI) satisfactorily describe the ordering of all excited states up to 7 eV; the effect of higher excitations is to correct the excitation energies overestimated by the D‐CI description. Our predicted spectra provide a consistent assignment of all one‐ and two‐photon spectral data but do not yield a quantitative agreement.

Rate constants for the reactions of atomic boron with O_{2}, SO_{2}, CO_{2}, and N_{2}O
View Description Hide DescriptionThe gas phase reactions of atomic boron with O_{2}, SO_{2}, CO_{2}, and N_{2}O have been studied using a diffusionflame technique. Atomic boron is produced in a microwavedischarge of 1% B_{2}H_{6} in helium and diffuses into a chamber containing the oxidizer also diluted in helium. The temperature was approximately 300 °K. The rate constants were determined from atomic absorption measurements of boron density in the flame. The rate constants for the O_{2} and SO_{2}reactions are (9±7) ×10^{−12} cm^{3} molecule^{−1}sec^{−1} and (7±5) ×10^{−12} cm^{3} molecule^{−1}sec^{−1}, respectively. An upper limit of 5×10^{−13} cm^{3} molecule^{−1}sec^{−1} is estimated for the rate constants of the CO_{2} and N_{2}O reactions.

Two‐photon spectroscopy of dipole‐forbidden transitions. II. Calculation of two‐photon cross sections by the CNDO–CI method
View Description Hide DescriptionIn the first paper of this series we investigated the applicability of a CNDO/S scheme including double excited configurations for the calculation of excitation energies of larger unsaturated molecules. In this paper we show that the same scheme is very useful for the prediction of two‐photon transition probabilities. If the proper expansion is used, the results converge quite well with increasing number of intermediate states. We also show that the inclusion of double excited configurations is not only necessary to obtain better energies for dipole‐forbidden transitions to ’’covalent’’ excited states but also to obtain the correct order of magnitude for two‐photon cross sections.

Depolarized light scattering by simple liquids
View Description Hide DescriptionA new theory is presented for the scattering of light by simple fluids. The theory naturally leads to the idea that, in multiple scattering by a group of spherical particles, the shape of the region excluded (’’shaped cavity’’) by the group to the rest of the system is of considerable importance. The large existing disagreement between theoretical and experimental scattering intensities for simple liquids is explained using the shaped cavity idea, which has already been used most successfully for scattering from nonspherical molecules.

The role of intermolecular potential well depths in collision‐induced state changes
View Description Hide DescriptionA relationship is developed from two distinct theoretical approaches to correlate the rate constants k_{M} or cross sections σ_{M} for a series of added gases M which collisionally induce a state transformation A^{*}→B. The correlation derived from theory is where C is a constant and ε_{A*M} is the intermolecular well depth between A^{*} and M. We observe that experimental data can be described by a related correlation where β is a constant and ε_{MM} is the well depth between pairs of M molecules. This correlation is shown to be general. It works for electronic state deactivation in atoms, intersystem crossing and internal conversion in S _{1} polyatomics, rotational and also vibrational relaxation in S _{1} polyatomics, predissociation in diatomics and polyatomics, and vibrational relaxation in a free radical as well as in a molecular ion. The theory is appropriate only when attractive forces dominate the interaction, and this seems consistent with the experimental data. The correlation thus provides a simple means to distinguish between attractive and repulsive interactions. The correlation also reveals that collision partners do not substantially modify the intrinsic S _{1}‐T mixing during collision‐induced intersystem crossing.

A method to estimate intermolecular potential well depths for species in both ground and excited electronic states
View Description Hide DescriptionThe relationship lnσ_{M}=lnC+[(ε_{A}*_{A}*) (ε_{MM})]^{1/2}/kT correlates the cross sections σ_{M} for a state change A^{*}→B induced by a series of added M gases with the intermolecular potential well depths for A^{*}...A^{*} pairs and M...M pairs. This correlation is used with literature data concerning A*→B to deduce ε_{A}*_{A}* for electronically excited atoms (Na, Ne, Ar, Xe) and electronically excited molecules (I_{2}, SO_{2}, CH_{3}OH, glyoxal, propynal, benzene). The well depths are generally observed to exceed the ground state values by factors of 2–10. Large well depths are also observed for s e c‐butyl radicals and for the C_{5}H_{9} ^{+} ion with high vibrational excitation. The correlation also provides an alternate means to measure ground state well depths ε_{MM}. In cases where secure comparisons are available, the well depths so derived usually lie within 20% of values found from transport measurements or virial coefficients. The correlation seems a useful alternative to empirical estimating procedures when data from conventional methods are not available.

Dissociating states of the H^{−} _{3} system
View Description Hide DescriptionSingle determinant Hartree–Fock calculations for the lowest singlet and triplet potential energy surfaces of the H^{−} _{3} system are presented over a broad range of isosceles triangular configurations of the nuclei. The addition of a diffuse s function to the four‐term Gaussian expansion of Huzinaga for H(1s) together with p type polarization functions produces results which are in agreement with experiments on double electron capture by H^{+} _{3} to form H^{−} _{3}. The present calculations predict that capture to the ground singlet state produces H_{2}+H^{−}, with a dissociation energy in reasonable agreement with the experimental findings. Capture to the triplet state is predicted to resulted in the three body dissociation H+H+H^{−} with small dissociation energy. This is consistent with, but not positively confirmed by, the experimental data.

IR absorption of SF_{6} excited up to the dissociation threshold
View Description Hide DescriptionSF_{6} was pumped by a P20 TEA CO_{2} laser up to an average energy of 10 000 cm^{−1} in the absence of collisions and up to 20 000 cm^{−1} with a certain collisional relaxation. A second CO_{2} laser, very much attenuated, was used to determine absorption cross sections for frequencies from 915 to 985 cm^{−1}. No coherent effects and no collisionless relaxations were found, in contrast to measurements with a cw laser as a probe. The ν_{3} band continuously shifts to longer wavelengths, but the shift of the ν_{2}+ν_{6} band is 10 to 20 times smaller. Many more rotational states of the vibrational ground state are depopulated than expected. To explain it we suggest direct two‐photon excitation, for which independent evidence is also presented. Many peaks and holes were found, part of which we assign to high states. Evidence for inhomogeneity of these structures is found by comparison with single laser absorption spectra. Collisional relaxation of unidentified nature and with a time constant of 48±10 ns mbar generates new spectra, indicating large nonequilibrium rotational populations.

Coupled‐channel study of halogen (^{2} P) + rare gas (^{1} S) scattering
View Description Hide DescriptionQuantum mechanical coupled‐channel (CC) scattering calculations are reported using realistic adiabatic potentials for the ^{2} P+^{1} S interaction of F–Ar, F–Xe, and Cl–Xe. Differential cross sections dσ/dω derived from a simple elastic approximation appropriate for large spin orbit interactions accurately reproduce all the gross features computed by the coupled‐channel method. This finding supports the extraction of interaction potentials from laboratory differential cross sections I (ϑ) via an elasticanalysis. Integral inter and intramultiplet changing cross sections are expressed conveniently in terms of Grawert’s B(j, j’;g) coefficient. Information on the collision dynamics is extracted by following the partial wave dependence of selected B(j, j’;g). Classical turning point analysis, based on the values of the large l‐waves for which these partial wave contributions B_{ l }(j, j’;g) begin to rise above zero, leads to the conclusion that both intermultiplet and first order forbidden intramultiplet transitions are caused by a single localized nonadiabatic coupling region at the position of complex crossing of the Ω=1/2 adiabatic potentials. Small amplitude oscillations or perturbations in the CC calculated dσ/dω and in the experimental I (ϑ) are thought to be examples of Stükelberg oscillations, though quantitative agreement between these quantities is not obtained. The energy dependence and interference structure of the computed B(j, j;g) are briefly discussed, as is the approximation of the constant spin orbit interaction over the experimentally accessible range of internuclear distances.