Volume 45, Issue 4, 15 August 1966

Swarm Determination of the Cross Section for Momentum Transfer in Ethylene and in Ethylene Mixtures
View Description Hide DescriptionData are reported on the temperature dependence of electron‐swarm drift velocitiesw in ethylene. The analysis of the data gave a velocity‐independent cross section for momentum transfer, σ_{E} for ethylene at thermal electron energies. Using a constant σ_{E}, we investigated the dependence of w _{E}/w _{M} on gas concentration, where w _{E} is the drift velocity in ethylene and w _{M} that in mixtures of ethylene with a polar impurity P. Three regions of concentration were distinguished: initial, intermediate, and final. The initial region can provide information about the velocity dependence of σ_{P}, the intermediate (better suited for experimentation) can easily provide σ_{P} if the velocity dependence of σ_{P} is known, and the final region provides a new way to measure the drift velocity for pure polar compounds P by simply measuringw _{E}/w _{M} in mixtures of P with ethylene. The latter is extremely important when P cannot be studied alone.

On the Calculation of Autocorrelation Functions of Dynamical Variables
View Description Hide DescriptionIn this paper we develop a formalism for calculating the autocorrelation function of a dynamical variable in terms of a well‐defined memory function. Guided by simple physical arguments, an ansatz is adopted for the functional form of the memory function. This ansatz asserts that the memory of dynamical coherence decays exponentially. It is found that:
(a) Despite the monotonic exponential decay of the memory function, the autocorrelation function deduced can display negative regions in some circumstances and decay monotonically in other circumstances.
(b) The form of the autocorrelation function deduced is identical with that obtained from two other very different analyses, suggesting that the major properties of the function are of general validity.
(c) The computed linear momentum autocorrelation function and power spectrum for liquid Ar are in good agreement with the computer experiments of Rahman.
(d) The computed dipolar autocorrelation function reproduces all the features of the experimentally determined autocorrelation function, though at present insufficient data are available to provide a quantitative test of the theory.
(e) The ansatz used, although obviously not exact, is consistent with the theory of linear regression (Appendix B).

Momentum Autocorrelation Function for Systems with Finite Spatial Boundaries
View Description Hide DescriptionAn exact analytical expression is obtained for the momentum autocorrelation function of a particle moving in a one‐dimensional box and slowed by dynamical friction. Comparison is made with the results of Rahman's computer experiment for liquid argon.

Group‐Theoretical Classification of the Atomic States of g^{N} Configurations
View Description Hide DescriptionThe terms of the g^{N} configuration of equivalent electrons (or nucleons) are classified in both LS and jj coupling using the methods of group theory. It is suggested that the electronic structure of the g^{N} configurations, which should be important in an element of atomic number Z=126, could be most readily calculated in terms of the jj coupling scheme.

Exactly Solvable Nonlinear Relaxation Processes. Systems of Coupled Harmonic Oscillators
View Description Hide DescriptionA class of nonlinear relaxation processes is discussed which involves the interaction of two finite systems characterized by special forms of the transition probabilities. For these particular sets of transition probabilities it is possible to reduce the initial set of coupled nonlinear kinetic equations to a set of linear equations with time‐dependent coefficients which are amenable to exact analytical solutions. This reduction is effected through the use of summational invariants expressed in terms of the appropriate combinations of the moments of the distribution functions of the two systems. The vibrational—vibrational relaxation of two interacting systems of harmonic oscillators A and B with identical frequencies has been worked out as a specific example. For the type of relaxation processes discussed here it is found that the relaxation of System A is independent of the form of the initial distribution of System B (and thus of its time history) and vice versa.

Relaxation of Moments Derived from a Master Equation
View Description Hide DescriptionPrevious work on the relaxation of moments derived from a master equation has been extended to master equations for joint probability distributions and to nonlinear master equations involving product probability distributions. Necessary and sufficient conditions on the transition probabilities are given to obtain closed moment equations. The special case of a simple one‐term exponential relaxation of the moments is also discussed.

Electronically Excited NO by Photodissociation of NO_{2} and NOCl
View Description Hide DescriptionThe photodissociations of NO_{2} and NOCl yielding electronically excited NO are observed by the fluorescence of NO(γ) and NO(β) bands:
The dissociations of NO_{2} are observed at wavelengths 1165, 1236, and 1295 Å but not at 1470 Å and longer wavelengths, and the dissociation of NOCl is found at wavelengths from 1165 Å up to about 1600 Å. The NO(A ^{2}Σ^{+}) and NO(B ^{2}Π) molecules from NO_{2} and NOCl are strongly rotationally excited.

Nuclear Magnetic Resonance of Nitrogen−14 in Potassium Azide
View Description Hide DescriptionThe nuclear magnetic resonance of ^{14}N split by large quadrupole interactions has been observed in single crystals of potassium azide (KN_{3}). The observed spectrum at arbitrary orientation consists of eight resonance lines, which can be decomposed into two groups of four lines each. The resonances in each group are of the same apparent intensity, and one group is twice as intense as the other. The quadrupole coupling constants and asymmetry parameters of the two inequivalent nitrogens have been obtained from a rotation study. For the end nitrogen e ^{2} qQ/h=1.79±0.03 MHz with η=0.04±0.02. For the central nitrogen e ^{2} qQ/h=1.028±0.03 MHz with η=0.03±0.02. Unsuccessful attempts were also made to observe the pure quadrupole resonance of the end nitrogens.

Transition Probabilities for H_{2}, D_{2}, N_{2}, N_{2} ^{+}, and CO
View Description Hide DescriptionThe previously observed quenching of the a ^{3}Σ_{ g } ^{+} state of the hydrogen molecule by neutral collision has been confirmed by a study of deuterium. Lifetimes have also been measured for what are believed to be the B ^{2}Σ_{ u } ^{+} state of N_{2} ^{+}; the C ^{3}Π_{ u } state of N_{2}; and the b ^{3}Σ, d ^{3}Π, and B ^{1}Σ states of CO.

Emission Polarization and Circular Dichroism of Hexahelicene
View Description Hide DescriptionMeasurements of the relative polarization of electronic transitions and their circular dichroism are reported for hexahelicene (phenanthro[3,4‐c]phenanthrene). A new assignment scheme for the electronic spectrum is proposed in the light of these measurements.
The longest wavelength ^{1} L_{b} (375–425 mμ) transition shows evidence of mixed polarization in the fluorescence which would arise from vibronic coupling in the emission process. Its circular dichroism, which may contain ``forbidden'' character, is negative for the dextrorotatory molecule.
The ^{1} L_{a} (325–375 mμ) transition has a strong positive circular dichroism which determines the optical activity at visible wavelengths. The success of previous chirality calculations for hexahelicene hinges on a satisfactory treatment of this transition and the rather complex detailed polarization of its excited state. Discrepancies between predicted optical activity by free‐electron and by Hückel MO calculations are noted. The ^{1} B_{b} (280–325 mμ) transition has a weak circular dichroism whose sign is difficult to determine from experiment; calculations predict that it should have the same sign as ^{1} L_{a} . What appears to be the ^{1} B_{a} (or ^{1} C_{b} ) (230–280 mμ) transition has a stronger negative circular dichroism.
Because of the out‐of‐plane distortion of the molecule, relative transition polarizations somewhat peculiar for polynuclear aromatics are expected. These account for certain data in the emission polarization,phosphorescence lifetime, and phosphorescence—fluorescence relative quantum yield.

Absorption of Light by Pairs of Exchange‐Coupled Manganese and Nickel Ions in Cubic Perovskite Fluorides
View Description Hide DescriptionThe absorption of light by exchange‐coupled pairs of manganese and nickel ions in KZnF_{3} is reported. Three absorption regions are discussed, of which two (4000 and 3300 Å) are associated with electronic excitation of the manganese and the third (6600 Å) corresponds to electronic excitation of the nickel ion. The lines can be analyzed by means of an exchange interaction of the type J S·S and a value of J = 18 cm^{−1} for the manganese—nickel pair in its electronic ground state has been obtained. The mechanism of the electronic transitions has been discussed using the theory developed for like pairs in an earlier paper and reasons for the greater intensity of absorption by unlike pairs are considered. Corresponding effects of exchange interaction have also been observed in the spectra of KMn_{ x }Ni_{1−x }F_{3} crystals. The energies and intensities of the absorption bands have been measured as a function of x and a theoretical analysis of the main results has been given. The main features of these spectra can be interpreted satisfactorily using our model for a pair of exchange‐coupled ions.

Variational Calculation for Bound States in an Electric‐Dipole Field
View Description Hide DescriptionThe quantum‐mechanical problem of an electron moving in the field of a permanent electric dipole has been investigated in an attempt to determine whether negative energy eigenvalues, i.e., bound states, exist for small dipole moments. When the expectation value of the Hamiltonian is minimized in a variational calculation and then set equal to zero, the solution of the resulting equation gives a value of the dipole moment which is sufficient to assure the existence of a bound state. Use of the trial wavefunction ψ=exp (—αr^{t} ) (C _{0} Y _{00}+C _{1} Y _{10}) shows that 1.65×10^{−18} esu·cm is sufficient.

Nuclear Magnetic Double Resonance of a Single Nucleus of Spin ½
View Description Hide DescriptionThe nuclear magnetic double‐resonance spectrum of a single nucleus of spin ½ is theoretically described by perturbation theory and by the Bloch equations. The perturbation theory correctly predicts all experimental features except line shapes and saturation effects. The description in terms of the Bloch equations provides a clear physical picture of the spin‐½ problem. The analysis shows that the macroscopic moment is aligned with the effective field when the strong rf field is not in the immediate vicinity of the Larmor frequency. When the strong rf field is at the Larmor frequency, however, the macroscopic moment is perpendiclar to the effective field. This produces considerable changes in line shapes and intensities as the strong rf field approaches the Larmor frequency. The spectrum in this region is sensitive to the relaxation times, and provides a steady‐state method for measurement of relatively short relaxation times. The theory is confirmed by frequency‐sweep double‐resonance experiments on chloroform saturated with oxygen.

Quantum‐Theoretical Study on the Bond Angle for a Single Bond between Carbon Atoms
View Description Hide DescriptionBond energies and bond lengths of the single, double, and triple bonds between carbon atoms were studied with nonempirical calculations by one of the authors with the scheme of the electronic configurations of fictitious diatomic molecules; ≡C–C≡, –C–C–, and –C≡C–, where open bonds of the atoms were treated as suitably hybridized orbitals taking into account all possible spins. This treatment is examined for the bond angle of a single bond between carbon atoms. The result shows that the tetrahedrally hybridized bonding is the most stable.

Lattice Disorder in Some CaF_{2}‐Type Crystals
View Description Hide DescriptionThe ionic conductivity of BaF_{2}, SrF_{2}, and SrCl_{2}single crystalsdoped with monovalent and trivalent cations has been investigated from 300°C to within 100°C of the melting temperature. These measurements correct the intrinsic conductivity of SrF_{2} and show a consistent trend in the slopes of the Arrenhius plots of the conductivity for these and other fluorides: both the activation energy for conduction and the resistivity decreases with a decrease in the melting temperature of the materials. A Koch—Wagner‐type analysis of conductivity isotherms confirms an anion Frenkel thermal‐disorder model for the fluorides. The type of disorder for SrCl_{2} could not be determined unambiguously, however. Values for the energy of formation of the intrinsic defects and their motion energies have been deduced from the slopes of the conductivity curves. Estimates of concentration of the thermal defects were made in each case.

Competitive Unimolecular Decomposition Processes in Chemically Activated Systems
View Description Hide DescriptionA general formulation of the rates of competitive unimolecular reactions is given, and various relationships between the rates and between the energetics of competing processes are described. The relative and absolute rates of decomposition,have been measured at pressures from 0.004 to 90 mm Hg for vibrationally excited 3‐hexyl radicals, chemically activated by the addition of hydrogen atoms to trans−3‐hexene at 300°C. Use of a quantum‐statistical model for k_{E} in the general relations provides good theoretical agreement with the experimental data at all pressures. The results can also be used to lead to either of two alternative conclusions: that D _{0}(CH_{3}–H) — D _{0}(C_{2}H_{5}–H) is 5.4 kcal mole^{−1}, or that the difference in critical energies for addition of methyl to 1‐pentene, E _{0} ^{ m }, and of ethyl to 1‐butene, E _{0} ^{ e }, is E _{0} ^{ m }—E _{0} ^{ e }= −0.4 kcal.

Optical Spectrum of Re^{4+} in Single Crystals of K_{2}PtCl_{6} and Cs_{2}ZrCl_{6} at 4.2°K
View Description Hide DescriptionThe optical spectrum of Re^{4+}(5d ^{3}) has been studied at 4.2°K in single crystals of K_{2}PtCl_{6} and Cs_{2}ZrCl_{6}. The spectrum is characterized by extremely narrow lines in the region from 8500 to 36 000 cm^{−1}. Vibrational structure is observed which is assigned to the odd modes of the ReCl_{6} ^{2−} complex. A crystal‐field analysis of the 0–0 transitions fits the observed eight electronic transitions with an rms deviation of 209 cm^{−1} for the parameters A = 0, B = 327 cm^{−1}, C = 1818 cm^{−1}, V = 30 347 cm^{−1}, and λ_{5d }=2392 cm^{−1}. Magnetic‐field measurements of the excited states give g values which are compared with theory. A discussion of the intensities of the transitions is presented which demonstrates that some absorptions observed are magnetic‐dipole transitions. Finally, several conclusions about the study of optical spectra of d^{n} systems are presented.

Mössbauer‐Effect Studies of Weak Nuclear Quadrupole Interactions in ^{119}Sn
View Description Hide DescriptionNuclear quadrupole interaction in some tin compounds has been investigated by the use of the Mössbauer effect. Stannic oxide shows a partially resolvable quadrupole splitting of 0.49±0.06 mm/sec at 1 atm pressure. The origin of the nuclear quadrupole interaction is attributed to the characteristic rutile crystal structure in SnO_{2}. The absence of resolvable quadrupole splitting in stannic bromide and diphenyltin indicates that interpretations concerning the electric field gradient tensor based on the Mössbauer effect in ^{119}Sn alone are not always sufficient to warrant definitive conclusions about molecular structures. It has been shown that this restriction is largely due to the relatively broad total natural linewidth for ^{119}Sn, . Quadrupole‐splitting and isomer‐shift data for some phthalocyaninotin complexes indicate that simple correlations between chemical parameters, e.g., electronegativities, and Mössbauer parameters are not generally valid.

Mössbauer Effect in MnFeO_{3}
View Description Hide DescriptionThe Mössbauer spectrum of MnFeO_{3} was measured at 4.2°, 78°, and 300°K. At 300°K the spectrum consists of two overlapping sets of resonances having isomer shifts of +0.496 and +0.478 mm/sec and quadrupole splittings of 1.161 and 0.666 mm/sec, respectively. At 4.2°K the isomer shift increases to +0.61 mm/sec and a magnetic hyperfine splitting, corresponding to an effective field of 469 kOe, is observed. The distribution of Fe^{3+}ions over the available cation positions was determined from an analysis of the resonance curves.

Negative Temperature Coefficients of Electrical Conductance in Molten Salts
View Description Hide DescriptionThe electrical conductivities of molten CuCl, HgCl_{2}, HgBr_{2}, SnCl_{2}, InI_{3}, ZnI_{2}, ZnCl_{2}, TlCl, TlBr, TlI, and HgI_{2} were measured to temperatures as high as 1200°C. Maxima in conductivity as the temperature was increased were found in the first six salts. Since molten BiCl_{3}, BiBr_{3}, BiI_{3}, CdI_{2}, GaI_{3}, pure water, and aqueous solutions containing weak and strong electrolytes also exhibit a conductivity maximum at elevated temperatures, it is concluded that this behavior is general to all fluids at sufficiently high temperature and sufficiently reduced density. These maxima in fused salts are attributed to increasing covalency or ionic association as the density decreases.