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Volume 67, Issue 1, 01 July 1977

Molecular vibrations in crystalline environments: Normal mode analyses of Cs_{2}LiCo(CN)_{6} and Mn_{3}[Co(CN)_{6}]_{2}⋅xH_{2}O
View Description Hide DescriptionThe Raman and infrared spectra have been recorded for the ^{12}C^{14}N, ^{13}C^{14}N, ^{12}C^{15}N, and ^{13}C^{15}N isotopes for Mn_{3}[Co(CN)_{6}]_{2}⋅xH_{2}O. In addition to the above isotopic species, the ^{6}Li and ^{7}Li complexes of Cs_{2}LiCo(CN)_{6} were also observed. These data have been used to obtain a general quadratic potential function for Cs_{2}LiCo(CN)_{6} and the A _{1g } and E _{ g } potential constants for Mn_{3}[Co(CN)_{6}]_{2}⋅xH_{2}O. The Mn–N force constant has been estimated for Mn_{3}[Co(CN)_{6}]_{2}⋅xH_{2}O using the A _{1g } and E _{ g } symmetry force constants. The unusual strength of the Mn–N interaction has been attributed to a dπ–pπ* interaction between the manganese and the nitrogen end of the cyanide. Implications regarding intervalence transfer bands in Prussian blue and its analogs are discussed.

Observation of the set of three sublevel phosphorescence spectra of quinoxaline. Analysis of radiative mechanisms
View Description Hide DescriptionA method to observe phosphorescencespectra for the three triplet sublevels is proposed, and is applied to quinoxaline in a single crystal of naphthalene‐d _{8}. The method consists of measurements of the time resolvedphosphorescencespectra at temperatures where spin polarization is achieved and under the influence of the microwave field to saturate the magnetic transition between the spin sublevels. The method is best applied to the cases where total decay rate constants are small for two sublevels. The T _{ z } spectrum is identical to the known thermally averaged spectra observed at 4 K, whereas the T _{ x } and T _{ y }spectra are markedly different from the T _{ z } spectrum in the spectral distributions. The relative radiative rate constants as well as the total decay rate constants are obtained by the method of microwave induced delayed phosphorescence for some selected vibronic bands. On the basis of the observed spectra and the kinetic data, mechanisms in which vibronic bands gain intensity are discussed. Finally, from the qualitative analysis of the experimental results in conjunction with theoretical considerations, the magnitudes of the matrix elements with respect to spin–orbit coupling are estimated. In the matrix element over molecular orbitals the contribution of one center terms dominates. The sum of two center and three center terms contributes about 10%, and the sum of three center terms contributes about 3% of the matrix element.

Molecular statistical theory for inhomogeneous nematic liquid crystals with boundary conditions
View Description Hide DescriptionWe start with a multipole expansion of the London‐van der Waals dispersion forces between elongated cylindrically symmetric molecules as a model for the two‐particle interaction. This potential is rotationally invariant and anisotropic due to both the orientation and the position of two molecules. In the next step we define a self‐consistent description of orientational ordering. If a nematogenic substance is bounded by two parallel plates, a preferred direction of equilibrium orientation is induced depending on the alignment of the molecules next to the surface of the plates. The alignment near the plates will effect the degree of order throughout the whole sample thickness via the two‐particle interaction. For the two cases of parallel and perpendicular alignment to the walls, we describe the resulting inhomogeneous phase by locally‐variable‐order parameters and investigate the temperature dependence for several sample thicknesses. It is found that the ordering induced by alignment parallel to the walls is much weaker than in the case of alignment perpendicular to the walls. This behavior corresponds to the ratio of transverse to longitudinal correlation length in nematic liquid crystals. The ratio of the correlation lengths derived from the present interaction model is found to be in excellent agreement with the ratio of the elastic constants: k _{33}/(1/2)(k _{11}+k _{22}) determined from experiments.

Susceptibilities and electric and magnetic polarization fluctuations in nonoptically active media
View Description Hide DescriptionThe previous work which related electric polarizationfluctuations to the dielectric constant is extended to include magnetic polarizationfluctuations in nonoptically active media. To do this it is necessary to assume that electric fields induce changes only in the electric polarization and magnetic fields induce changes only in the magnetic polarization (in a well defined sense given in the text). This assumption is implemented after determining the relation between the average value of an arbitrary quantity and the average fields in the medium. The phenomenological parameters are related to the susceptibilities which, in turn, are related to the fluctuations by the Callen–Welton theorem. Finally, various approximate relations resulting from the neglect of certain specified electromagnetic interactions in the calculations of the susceptibilities are discussed.

Absolute rate constants for the reaction of O(^{3} P) atoms with a series of olefins over the temperature range 298–439 °K
View Description Hide DescriptionAbsolute rate constants for the reaction of O(^{3} P) atoms with ethylene, propylene, 1‐butene, isobutene, c i s‐2‐butene, and t r a n s‐2‐butene have been determined over the temperature range 298–439 °K using a flash photolysis–NO_{2}chemiluminescence technique. The Arrhenius expressions obtained are: k _{2}(ethylene) =9.23×10^{−12} e ^{−(1475±200)/R T }, k _{2}(propylene) =1.05×10^{−11} e ^{−(515±200)/R T }, k _{2}(1‐butene) =1.39×10^{−11} e ^{−(665±200)/R T }, k _{2}(isobutene) =1.76×10^{−11} e ^{−(85±200)/R T }, k _{2}(c i s‐2‐butene) =1.21×10^{−11} e ^{(235±200)} ^{ R T }, and k _{2}(t r a n s‐2‐butene) =2.26×10^{−11} e ^{(20±200)/R T } cm^{3} molecule^{−1} sec^{−1}. These data are in excellent agreement with a recent modulation–phase shift study.

Ionization potentials and vibrational structure in photoelectron spectra by a Green’s function method: t r a n s‐HNNH, c i s‐HNNH, and 1,1‐dihydrodiazine (H_{2}NN)
View Description Hide DescriptionThe ionization potentials of t r a n s‐diazene, c i s‐diazene and 1,1‐dihydrodiazine (in its singlet state) have been computed by a many‐body Green’s function method. For t r a n s‐diazene all calculated ionization potentials are within 0.3 eV of the measured values. Koopmans’ theorem supplies the correct ordering only for t r a n s‐diazene, but fails for the other two molecules. The electronic structures of the three molecules differ considerably. The ordering of the ionization potentials is for t r a n s‐diazene: n _{+}, π, n _{−}, σ_{+}(NH), σ_{−}(NH), and σ (NN); for c i s‐diazene: n _{−}, n _{+}, π, σ_{+}(NH), σ_{−}(NH), and σ (NN); and for H_{2}NN: n _{−}, n _{+}, π, σ_{−}(NH), σ_{+}(NH), and σ (NN). The n _{+}/n _{−} splitting is calculated to be 5.3, 3.6, and 5.7 eV, respectively. The vibrational structure in the photoelectron spectrum of t r a n s‐diazene and t r a n s‐diazene‐d _{2} is computed and compared to the experimental one. Similarly looking bands in the spectra of N_{2}H_{2} and N_{2}D_{2} may arise from quite different couplings.

Dynamics of confined polymer chains
View Description Hide DescriptionWe study the motions of a single polymer chain trapped inside a very thin capillary (or slit). We incorporate all excluded volume effects and hydrodynamic interactions through a scaling analysis. We find that the Debye–Bueche approximation, which was qualitatively correct for three‐dimensional dilute solutions, becomes completely incorrect for confined chains: the local fluctuations of the monomer concentration which are ignored in the Debye–Bueche picture allow for channels of easy flow of the solvent inside the chain. We obtain scaling formulas (with unknown numerical coefficients) for the diffusion constant and we also analyze the internal mode structure: inside a tube, for wavelengths larger than the diameter, we recover an unexpectedly simple structure of Rouse modes. Finally, we analyze the possibility of ’’sucking in’’ one chain inside a slightly tapered pore, by imposing a certain flow of the solvent. We find that the threshold pressure difference Δp _{ c } for aspiration of the chain depends only on the smallest diameter of the pore and is independent of the molecular mass. The magnitude of Δp _{ c } is not too large, and the experiment may be feasible.

Effects of exchange energy and orbital orthogonality on barriers to internal rotation
View Description Hide DescriptionIn order to determine the effect of the Pauli principle on internal rotation barriers, we have calculated exchange and orbital orthogonality contributions to barriers for a small group of molecules: ethane, methanol, acetaldehyde, and hydrogen peroxide. To evaluate exchange contributions it was necessary to formulate variation equations and to energy‐optimize simple product wavefunctions of orthogonal orbitals (Hartree‐product wavefunctions). The resulting orbitals resemble very closely the Edmiston–Ruedenberg localized Hartree–Fock orbitals. Our results indicate that exchange contributions to the barriers in ethane and acetaldehyde are quite small. For methanol and hydrogen peroxide, our calculated contributions are considerably larger and suggest that, at least in some molecules, exchange contributions cannot be ignored. For all of the molecules, however, the exchange contribution is greatly overshadowed by that of end‐to‐end orbital orthogonality.

Application of stochastic theory to vibration–rotation inelasticity in the He–H_{2} system
View Description Hide DescriptionPrevious papers considered describing molecular collisions by the techniques of nonequilibrium statistical mechanics. In the present work this stochastic theory of molecular collisions is applied to vibration–rotation inelasticity in the He^{4}–(para‐H_{2}) system. Some improvement in the theory is presented to better handle energetic effects, particularly important in the weak coupling limit. The resulting formulation leads to the solution of simultaneous Fokker–Planck and master equations for the rotational and vibrational motion, respectively. Scattering cross sections were computed for total energies from 1.3 to 4.0 eV. At this highest energy 85 vibration–rotation states of H_{2} are energetically accessible. Very strong near‐resonant vibration–rotation inelasticity was found from the high rotational levels (j∼18). The results are compared to quantum mechanical calculations and experimental measurements.

Theory for the influence of gravity on liquid–vapor interfaces
View Description Hide DescriptionThe van der Waals theory of surface tensions in the presence of gravity is discussed in detail. The physical two‐phase solution in the gravitational field is shown to exist and be unique. The relation between the chemical potential and the position of the interface in the gravitational field is elucidated. The solution approaches the solution given previously and the chemical potential approaches its coexistence value as the strength of the gravitational field is diminished. The gravitational effects are seen to be especially enhanced in the neighborhood of the critical point.

Lattice dynamics and phase transition in sodium azidea)
View Description Hide DescriptionWithin the context of the quasiharmonic theory of lattice dynamics, the zone center frequencies, dispersion curves, and frequency distribution of sodium azide are calculated using two potential models. Good agreement is obtained between the calculated zone center frequencies and the available Raman data. In particular, the calculated temperature dependence of the splitting of the E g librational mode in the β phase into A _{ g } and B _{ g } modes in the α phase is in excellent agreement with experiment.

On the j _{ z }‐conserving coupled states approximation: Magnetic transitions and angular distributions in rotating and fixed frames
View Description Hide DescriptionRecently Shimoni and Kouri have pointed out that a careful treatment of the j _{ z }‐conserving coupled states (CS) approximation results in a b o d y f r a m e T‐matrix T ^{ J }(jλ‖j _{0}λ_{0}) which is n o t diagonal in λ,λ_{0}. In addition they have shown that previous investigations of the CS did not optimally identify the body frame T‐matrix. In this paper, we explore the consequences of these observations. The exact T‐matrix is obtained in the R13‐ and P‐helicity frames, as well as in an uncoupled spaceframe (USF) representation. The resulting exact expressions for these T‐matrices are in terms of certain integrals, I ^{ J } _{ l }(jλ‖j _{0}λ_{0}), introduced earlier by Shimoni and Kouri. By obtaining the CS approximation to these integrals, we are able to derive the preferred CS approximation in the R‐ and P‐helicity and USF representations. We then employ the resulting CS T‐matrices to derive the differential scattering amplitude and cross section in the various possible reference frames. The result is a unified treatment of these quantities. We are then able to demonstrate the equivalence of the CS approximation to the R‐ and P‐helicity amplitudes. In addition, we show explicitly that the CS approximate degeneracy averaged differential cross section is frame independent. The CS approximation to the USF equation provides a rigorous basis for the original derivation of the CS method as given by McGuire and Kouri. In particular, our treatment shows that when the L^{2} operator is approximated by an eigenvalue form l (l+1) h/^{2} (as was suggested first by McGuire and Kouri), there is no longer any difference between the BF and USF i n t h e d y n a m i c a l e q u a t i o n s (for the wavefunction or amplitude density). Any differences are strictly kinematic in origin, and are the source of the λ transitions which occur in the BF CS approximation. In the USF, since there are no rotational kinematic effects, there are no magnetic transitions in the CS approximation. Thus, the name j _{ z }‐conserving coupled states is appropriate in two senses. First, in the USF, j _{ z } i s conserved in the CS approximation. Second, even though j _{ z } is n o t conserved in the BF CS‐approximation T‐matrices, j _{ z }‐conservation d o e s occur so far as the dynamics are concerned; i.e., the BF amplitude density and wavefunction both conserve j _{ z } in the CS approximation.

Vibrational relaxation studies of matrix isolated C^{−} _{2}
View Description Hide DescriptionAbsorption studies of C^{−} _{2} formed by 1216 Å photolysis of C_{2}H_{2} in Ar at 14 °K indicate that the C^{−} _{2} concentration approaches a limit of ∼1 ppm, possibly due to electron return tunneling to the unknown cation counterpart X^{+} for separations closer than ∼175 Å. A dual pulsed laser method was used to produce vibrationally excited C^{−} _{2} and to monitor the v ^{″}=1 nonradiative decay. Lifetime values were strongly dependent on C_{2}H_{2} concentration and increased to 147 msec at an Ar:C_{2}H_{2}=20 000 ratio. This value was reduced to 93 msec for a Ar:C_{2}D_{2} matrix, presumably because of near resonance of the C^{−} _{2}energy (1779 cm^{−1}) with the C≡C stretch (1762 cm^{−1}). Decay times were longer in Kr and Xe than in Ar. The absence of any temperature effect over the range 14 to 30 °K indicates that few lattice phonons are involved in the rate determining step, the transfer to C_{2}H_{2}. The rate constant for this transfer decreases as the third to fifth power of an average C^{−} _{2}–C_{2}H_{2} distance, a much slower drop than the tenth power dependence predicted for the first applicable electrostatic coupling term, a quadrupole–quadrupole interaction. A more direct coupling through the intermediate argon atoms is implied but ^{13}C studies show that this coupling does not extend so far as to permit ’’resonant’’ transfer of vibrational energy from one C^{−} _{2} to the next. Direct decay to lattice phonons is slow, with a lower lifetime limit of ∼160 msec in Ar.

Electronic spectrum and structure of the HSO radical
View Description Hide DescriptionA chemiluminescence spectrum in the range 5200–9600 Å is assigned to the ^{2} A′–^{2} Am’ transition of the HSO radical. The 0–0 band is observed at 6960 Å. The deuterated radical was also studied. The vibrational frequencies deduced from the vibronic transitions are ν′_{2}(HSO) =828, ν^{″} _{2}(HSO) =1063, ν′_{2}(DSO) =600±10, and ν^{″} _{2}(DSO) =770±10 for the bending vibration, and ν′_{3}(HSO) =702±5 and ν^{″} _{3}(HSO) =1013±5 cm^{−1} for the SO bond stretch. The latter does not change significantly upon deuteration. The SH bond stretch ν_{1} is not manifested in the spectrum, and is assumed to come close to the SH group frequency of 2570 cm^{−1} in the electronic ground state. The frequency increases slightly upon excitation to the ^{2} A′ state, as follows from the shift of the 0–0 band to 6958 cm^{−1} upon deuteration. Approximate bond lengths and angles of HSO in both electronic states are deduced from the partially resolved subband structure of the vibronic bands, which is compared with computed band contours. Relative Franck–Condon factors obtained from the intensities within the v ^{″} _{3} progressions are in accordance with an increase of the SO bond length from r ^{″} _{SO}=1.54 to r′_{SO}=1.69 Å. Emission from HSO (^{2} A′) is observed up to v′_{3}=7 in the system O/H_{2}S/O_{3}. Excitation is believed to occur through the chemiluminescent reaction SH+O_{3}→SHO*+O_{2}, leading to an upper limit of ΔH°_{ f }(HSO) ≲14.9 kcal/mole.

Spectra of centrosymmetric rare earth complexes: Pr^{3+} (HAPI) single crystal
View Description Hide DescriptionPolarized low‐temperature absorptionspectrum of centrosymmetric Pr^{3+}–antipyrene tri‐iodide single crystal has been recorded. Electronic transitions to the ^{1} D _{2} and ^{3} P _{0,1,2} states have been found to be forbidden. Associated vibronic lines have been analyzed. Lattice, metal–ligand, and ligand internal (such as C=0) modes appear in the spectrum. Crystal field parameters have been evaluated and found to be large. Participation of π electrons in the bonding has been suggested.

Method of the orthonormality‐constrained variation: A pair of basis sets and the pair‐orthogonality
View Description Hide DescriptionThe orthogonality between sets of basis vectors, referred below to as pair‐orthogonality, is examined from a variational point of view. Both how to constitute pair‐orthogonal vectors and how to retain the pair‐orthogonality conditions in the course of variation are presented. The relation of the vectors to canonically orthonormalized Löwdin vectors is noted.

Electron mobilities in liquid tetramethylsilane at temperatures up to the critical point
View Description Hide DescriptionElectron mobilities have been measured as a function of temperature over the whole liquid range of tetramethylsilane. Above the triple point, the mobility attained a minimum at 260 K and a maximum at 377 K then fell abruptly to a relatively low value near the critical point. This behavior has been shown by rare gas liquids as well as liquid 2,2,dimethylpropane; however, in tetramethylsilane the ratio of maximum to minimium mobilities was much smaller than in any of these other liquids.

A thermodynamic model of hysteresis in phase transitions and its application to rare earth oxide systems
View Description Hide DescriptionA thermodynamic model of hysteresis in phase reactions based on regular solution theory is developed by invoking metastabilities. The effect of enthalpy and entropy change, pressure, temperature, and interaction energy on the hysteresis curve term is explored. The influence of a variation of the interaction term with temperature and composition is also studied. Observed hysteresis for the phase reactions Tb_{7}O_{12}?7/2Tb_{2}O_{3}+3/4O_{2} and Pr_{9}O_{16} ?9/7Pr_{7}O_{12}+2/7O_{2} is discussed and the theory is applied to each case. The experimental details of data acquisition and the observed hysteresis in the praseodymium oxide reaction are given.

The spherical Compton profile of neopentane and the carbon–carbon single bond of diamond
View Description Hide DescriptionThe spherically averaged Compton profile of neopentane is measured and also calculated from an a b i n i t i o SCF–MO wave function. The measured Compton profile of diamond, corresponding to a carbon–carbon bond (C–C), is compared is empirical C–C profiles computed from experimental and theoretical profiles for neopentane, ethane, and methane. We conclude that the localized bond model works well in all cases examined.

Thermodynamic study of gaseous ternary europium–tungsten–oxygen molecules
View Description Hide DescriptionIn the course of a mass spectrometric Knudsen cell study of the vaporization of europium orthophosphate and mixtures of it with europium sesquioxide the molecules EuWO_{3}, EuWO_{4}, Eu_{2}WO_{5}, and EuW_{2}O_{7} were observed in the vapors. From the study of a number of pressure independent equilibrium reactions the atomization energies of these ternary molecules have been determined. In addition, the dissociation energy of EuO was determined and compared with previous results. The results obtained are D°_{0}(EuO) =111.6±1.7; D°_{0,at}(EuWO_{3}) =569.6±6.9; D°_{0,at}(EuWO_{4}) =714.6±6.5; D°_{0,at}(Eu_{2}WO_{5}) =960.0±10.9; D°_{0,at}(EuW_{2}O_{7}) =1276.3±9.0 kcal mol^{−1}.