Volume 60, Issue 4, 15 February 1974

A modification of the Herzberg‐Teller expansion for vibronic coupling
View Description Hide DescriptionFirst‐order perturbation theory is used to obtain approximate Born‐Oppenheimer wavefunctions, the zeroth‐order wavefunctions being of the SCF LCAO MO CI type, with atomic orbitals ``following'' the nuclei. A practical determination of these functions within a CNDO/S scheme is presented. The intensities of forbidden transitions of formaldehyde and benzene are calculated with these functions and a comparison is made with previously reported results obtained by the conventional Herzberg‐Teller expansion.

Correlation functions of classical fluids. III. The method of partition function variation applied to the chemical potential: Cases of PY and HNC2
View Description Hide DescriptionBy adopting the formalism of inhomogeneous systems, a variational expansion of the partition function as a functional of the singlet density is developed. Its successive derivatives are given in terms of correlation functions of increasing orders. A theorem is proven relating the inhomogeneous partition function caused by a source particle to that of the homogeneous medium, from which a general expression for the chemical potential μ is obtained as an infinite series in integrals involving correlation functions of all orders. This series is truncated or resummed by considering three approximate theories on correlation functions: the Percus‐Yevick approximation (PY), the hypernetted chain (HNC) approximation, and its extension HNC2. New expressions for μ in PY and HNC_{2} are given, while the results for HNC check with the formula given by Morita. To render our results on HNC2 open to the HNC2 distribution functions of Verlet and Levesque, we have generalized the Ornstein‐Zernike relation to third order correlation functions, called OZ3. Four alternative forms are obtained, two of which, first derived here, are of much simpler form. The convolution form of Wu‐Chien of the third order distribution function can be neatly summarized in light of OZ3 and is compared with other approximations. The μ formula for PY is found to be valid at low densities due to the convergence property. Examination of the hard sphere case shows that it is applicable to medium densities of ρd ^{3} up to 0.5.

Primary processes in the photolysis of water vapor at 174 nm
View Description Hide DescriptionThe quantum yield for the photolysis of HTO at 174 nm by Reaction (4) is estimated to be ≤0.003 relative to Reaction (5): These values were obtained by scavenging T atoms with C_{2}D_{4}, with measurement of the yields of HT, DT, and of tritiated hydrocarbons.

Formation of by reaction of metastable ions with H_{2}
View Description Hide DescriptionThe photoionization efficiency curves of , , and have been studied in a mixture of hydrogen and oxygen over the wavelength range 650–810 Å. The ion appears at 804 Å, the threshold for ionization of H_{2}, by the reaction. The relative photoionization efficiency curves of and are the same from 804 to 764 Å. Below 764 Å production of the a ^{4}Π_{μ} metastable electronic state of leads to the formation of by the reaction.

Detailed balance in chemical kinetics as a consequence of microscopic reversibility
View Description Hide DescriptionThe idea that the chemical principle of detailed balance is a consequence of microscopic reversibility is examined in terms of the stochastic theory of chemical reaction rates, particularly as developed by Snider. It is emphasized that detailed balance is a purely macroscopic requirement for all cases except those in which the chemical reaction mechanism contains a closed loop, or where forward and reverse rate constants for an elementary reaction step are measured in different experimental situations, each designed to isolate one unidirectional elementary reaction from its counterpart. Snider's theory is extended to a simpe triangular (closed‐loop) isomerization mechanism, and it is shown that detailed balance is not obtained as a result; this is in contrast to local‐equilibrium theories, for which the relationship between microscopic reversibility and detailed balance is well established. An attempt to overcome this difficulty by reformulating Snider's theory, in terms of the theory of lumping error, was only partly successful. The limitations of the present approach are discussed, and consequences for universally valid interpretations of phenomenological chemical kinetics are suggested.

Electron spin resonance studies of irradiated succinamic acid. I. Triclinic single crystals
View Description Hide DescriptionThe products formed by x‐irradiation of single crystals of triclinic succinamic acid have been studied by electron spin resonance in the temperature range from 77° to 300°K. The primary product observed at 77°K is the oxidation radical, CONH_{2}CH_{2}ĊH_{2}, (I), formed by decarboxylation. The two α‐hydrogens in I are exchanging rapidly and are equivalent at all orientations. Radical I decays by either an intermolecular or an intramolecular process to give two other products, CONH_{2}CH_{2}ĊHCOOH (II) or CONH_{2}ĊHCH_{3} (III), respectively. Both II and III are stable at room temperature, however, III predominates in crystals irradiated at 300°K, whereas II predominates in crystals irradiated at 77°K and warmed to 300°K.

Electron spin resonance studies of irradiated succinamic acid. II. Monoclinic single crystals
View Description Hide DescriptionThe radiation products and decay mechanisms have been studied in single crystals of monoclinic succinamic acid using electron spin resonance spectroscopy over the temperature range from 77° through 300°K. At 77°K the primary radical observed is the anion radical COOHCH_{2}CH_{2}(ĊONH_{2})^{−} where the unpaired electron is delocalized throughout the entire amide group. This radical decays at about 180°K to a nonparamagnetic species. The minor product at 77°K is the cation product and decays at about 157°K by intermolecular hydrogen abstraction to two radicals which are stable at room temperature, COOHĊHCH_{2}CONH_{2}, and COOHCH_{2}ĊHCONH_{2}. The spectra observed at 300°K are identical in crystals irradiated at 77°K and warmed to 300°K. The differences in the radiation products and mechanisms for the monoclinic and triclinic forms are discussed.

Associative ionization in U + O and U + O_{2} collisions
View Description Hide DescriptionCollisions between thermal energy uranium atoms and oxygen atoms and molecules have been studied in four experiments. A triple crossed beam experiment has determined that the ratio of effective cross sections for the associative ionization processes U + O → UO^{+} + e and U + O_{2} → UO_{2} + e is 97±20. An experiment measuring the number of ions formed per unit length by uranium atoms passing through O_{2} has determined that the absolute cross section for is 1.68±0.27 × 10^{−17} cm^{2}. A total attenuation experiment indicates that the total reaction cross section between U and O_{2} is 1.78±0.45×10^{−15} cm^{2}, implying that over 99% of the reactions lead to the neutral products UO+O while less then 1% give associative ionization. A modulated beam mass spectrometry experiment, employing phase spectrometry, indicates that the activation energy for is extremely small if existent at all. Two Appendices treat the relations between effective cross sections as measured in various experiments to true cross sections as derived from theory and the generation of phase shifts in modulated beam experiments where a beam is detected by reactions with a Maxwellian gas.

Infrared reflection from the internal mode of crystalline lithium hydroxide
View Description Hide DescriptionIn the lithium hydroxide crystal, the transition moment of the A _{2u } internal mode lies normal to the naturally occurring crystal face, so that the transverse frequency for the mode may not be directly observed in an infrared transmission spectrum. It has been demonstrated previously that under this condition, infrared reflection spectra using transverse magnetic polarization at finite incidence angles show a reflection maximum above the longitudinal frequency. A comparison of theoretically generated reflectivity curves with the experimental spectra reported here yield values for the longitudinal and transverse frequencies. The dipole derivative for the hydroxide stretching mode calculated from these frequencies is in good agreement with previously reported values.

Studies in molecular dynamics. XIII. Singlet and pair distribution functions for hard‐disk and hard‐sphere solids
View Description Hide DescriptionMolecular dynamics calculations have been carried out on the singlet distribution function (sdf) in hard‐disk and hard‐sphere solids. The dependence of the distribution function upon particle number and density and the deviations of this function from spherical symmetry are examined. The possible connection between the sdf and the entropy and the behavior of the sdf near the melting point are discussed. The surprisingly close resemblance between the extreme anharmonic hard particles solids and harmonic oscillator solids is emphasized. Calculations of the angular dependence of the pair distribution function at pair contact for hard‐disk and hard‐sphere solids are also presented.

Near‐Hartree‐Fock assessment of reorganization effects in ionic states of acetylene
View Description Hide DescriptionCalculations on acetylene ^{2}Π_{ u } and ^{2}Π_{ g } ions and the ^{1}Σ_{ g } neutral ground state using a series of wavefunctions with increasing basis set size converge to an estimated Hartree‐Fock vertical ionizationenergy near 10.0 eV and an estimated Hartree‐Fock vertical electron affinity near −4.2 eV. The calculations reveal that the near‐Hartree‐Fock σ orbitals change strongly with the state of ionization leading to σ‐electron energy errors (for transferring ground state σ orbitals to the ions) of − 4.5 eV for the cation and + 3.2 eV for the anion. Each carbon atom is calculated to lose only about 0.34 e upon π‐electron ionization and to gain about 0.42 e on π‐electron capture. Consequently there is poor transferability of the ground state HF σ core to the ionic states so that π‐electron energy changes of + 3.2 eV for the cation and − 3.8 eV for the anion are incurred. The error incurred by transferring π orbitals from the ground state to the ions with frozen σ core is −0.8 eV for the cation and − 0.35 eV for the anion. The σ‐ and π‐orbital reorganization effects largely cancel on going to the ions producing gross reorganization energy changes of − 1.3 eV in the cation and − 0.55 eV in the anion. Comparison with C(sp ^{2})→C^{+} and ethylene π‐electron ionization indicate that aside from extensive σ‐π cancellation reorganization effects are not transferable between these species. At least double zeta level basis sets are necessary for physically meaningful descriptions of ionic processes.

Study of the electronic structure of molecules. XXI. Correlation energy corrections as a functional of the Hartree‐Fock density and its application to the hydrides of the second row atoms
View Description Hide DescriptionA semiempirical functional of the Hartree‐Fock density is presented for estimates of the correlation energy correction. The functional is similar to the one proposed by Gombas and is (a) parametrized with reference to few atomic systems, and (b) is modified as to reproduce the atomic correlation correction not only for closed but also for open shell systems. The functional is then applied to the ground state function of the hydrides LiH(^{1}Σ^{+}), BeH(^{2}Σ^{+}), BH(^{1}Σ^{+}), CH(^{2}Π), NH(^{3}Σ^{−}), OH(^{2}Π), and HF(^{1}Σ^{+}). Several internuclear distances have been considered for each hydride, scanning the potential energy curve from the repulsive region to the dissociation products (∼ 10 a.u.). For these points a simple multiconfigurational function (consisting of no more than three configurations) was computed to obtain Hartree‐Fock functions with proper dissociation behavior (H‐F‐P‐D functions). The semiempirical functional was applied both to the traditional H‐F functions and the H‐F‐P‐D functions in order to study how to select a proper reference wavefunction. The computed binding and a number of spectroscopic constants from vibrational and rotational analysis are discussed. The new semiempirical functional of the electronic density appears to be a rather promising one for reliable estimates of the correlation energy correction.

Study of the electronic structure of molecules. XXII. Correlation energy corrections as a functional of the Hartree‐Fock type density and its application to the homonuclear diatomic molecules of the second row atoms
View Description Hide DescriptionA semiempirical functional of the Hartree‐Fock type density, previously obtained for the Hartree‐Fock atomic functions and applied with good success to the second row hydrides (in paper XXI of this series), is now applied to the molecules , , , , , , , and . For each molecule the potential energy curve is computed from the repulsive region to large internuclear distances. In order to follow the dissociation to the correct limits, we have added to the Hartree‐Fock configuration of each molecule those configurations which are needed for describing proper dissociation (HFPD functions). It is found that for certain molecules (Li_{2}, B_{2}, C_{2}, and O_{2}) there are configurations which contribute quite significantly in the bonding regions and must be added to the HFPD function to reach a proper reference state function as previously defined (see paper XXI). With our functional of the density applied to the HFPD functions, the calculated dissociation energies are, with the experimental values given in parentheses, 4.69 eV (4.75 eV), 0.65 eV (1.14 eV), 1.64 eV (3.0 eV), 3.48 eV (6.36 eV), 9.34 eV (9.91 eV), 3.75 eV (5.21 eV), and 1.37 eV (1.66 eV) for H_{2}, Li_{2}, B_{2}, C_{2}, N_{2}, O_{2}, and F_{2}, respectively. More realistic dissociation energies are obtained for Li_{2} (1.03 eV), B_{2} (3.06 eV), C_{2} (5.21 eV), and O_{2} (4.64 eV) if we use the proper reference state functions. The state of Be_{2} arising from the ground state atoms is repulsive. The agreement with the experimental dissociation energy is satisfactory but not as good as what we have previously obtained for the second row hydrides. However, owing to the extreme simplicity of the method it appears in a preliminary way that the combination of a Hartree‐Fock type function and the functional of its density (of the form that we have proposed) is capable of yielding sufficiently reliable results for very little computational and human effort. Since the parametrization of the density functional was made for the atomic systems and not changed in the molecular formation, our method does not suffer from the need of variation of parameters introduced ad hoc and differing from molecule to molecule.

Coexistence curve properties of Mermin's decorated lattice gas
View Description Hide DescriptionMermin's decorated lattice gas, noteworthy for its singular coexistence curve diameter and previously studied in connection with the breakdown of the law of rectilinear diameters, is shown to display in addition a rich variety of coexistence curve shapes and kinds of critical behavior as the interaction parameters of the model are varied. For an attractive decoration interaction, the coexistence curve of the model resembles, and can closely approximate, the liquid‐vapor coexistence curve of real fluids. For a sufficiently repulsive decoration interaction, however, the model is shown to possess (at fixed temperature) three transitions to increasingly dense phases. These coexistence curves may feature peculiar shapes, such as necks and cusps, and they can appear inverted near the critical point; these curves terminate at either a critical point or at a maxithermal point (an analog of an azeotropic point). For discrete values of the interaction parameters, the model possesses a critical double point (the coalescence of two critical points) or a cuspoidalcritical point (critical azeotropy), in which cases the critical exponents become renormalized. Qualitatively these results are found to be independent of lattice structure and spatial dimensionality d ≥ 2, and representative coexistence curves are plotted for the simple cubic lattice. Possible applications of these results are mentioned.

Vibrational potential function for diimide, HNNH
View Description Hide DescriptionThe general valence force field for the in‐plane motions of diimide has been determined from a total of 24 vibrational frequencies of HNNH, HNND, DNND, and ^{15}N substituted counterparts. The unusual upward shifts observed for the NN stretching frequency on deuteration can be obtained when these shifts are directly constrained, but an exact fit was not possible due to convergence problems. Most of the force constants are well determined and a comparison is offered with recent results for CH_{3}NNH, CH_{3}NNCH_{3}, FNNF, and C_{2}H_{4}. The latter force fields suggest that the unobserved torsional frequency of HNNH should lie above 1300 cm^{−1} and hence this spectral region has been carefully reexamined.

Molecular collisions. XXI. Semiclassical approximation to atom‐symmetric top rotational excitation
View Description Hide DescriptionIn Paper XIX of this series a distorted wave approximation to the T matrix for atom‐symmetric top scattering was developed which is correct to first order in the part of the interaction potential responsible for transitions in the component of rotational angular momentum along the symmetry axis of the top. A semiclassical expression for this T matrix is derived by assuming large values of orbital and rotational angular momentum quantum numbers.

Dielectric and pressure virial coefficients of imperfect gases: Hexadecapolar system
View Description Hide DescriptionDielectric and pressure virial coefficients of SF_{6} have been determined at 323.3, 348.3, and 373.9 K. Attributing the temperature dependent contribution of the second dielectric virial coefficient to dipole moments induced in one molecule by the hexadecapole moment of a second gives (5.40±0.7)×10^{−41} esu · cm^{4} for the molecular hexadecapole moment of SF_{6}. The hexadecapole moment of SF_{6} derived from pressure second virial coefficients is (5.75±0.3)×10^{−41} esu · cm^{4}.

Dispersion of the nonlinear optical susceptibilities of organic liquids and solutions
View Description Hide DescriptionThe dispersion of the third order optical nonlinear polarizabilities of benzene, chlorobenzene, and nitrobenzene is measured in the vicinity of Raman active vibrations. Observation of interference between resonant and nonresonant contributions determines the magnitude and phase of the electronic hyperpolarizability. Shifts in the frequency and linewidth of the interference minima occur when additional components such as CCl_{4}, CS_{2}, or 2,5‐diphenyloxazole are added to the solution. Analysis of the resulting line shape yields the hyperpolarizability of the solute species.

Mössbauer resonance studies in magnetically diluted Eu–Ca hexammines
View Description Hide DescriptionThe Mössbauer effect in ^{151}Eu is used to examine the mixed hexammines Eu_{ x } Ca_{1−x }(NH_{3})_{6}, with x = 0.012 and 0.092, and comparison is made to the apparent lack of conduction electron effects on the europium ionic and nuclear properties in Eu(NH_{3})_{6}. In zero external magnetic field, very broad lines are seen, indicative of weakened dipolar spin relaxation. For the 1.2% Eu sample, the single Lorentzian linewidth at 4.2 K is the broadest yet seen, 19 mm/sec, with little structure evident. The linewidth decreases with small applied fields, becoming some 30% narrower. Analysis of small field data in terms of slow‐relaxation‐limit parameters yields an effective axial electronic‐splitting parameter D≈ + 30 mK at 4.2 K. Spectra obtained in large external fields yield hyperfine fields H _{eff} = − 326 (3) and − 330 (3) kOe for the 1.2% and 9.2% samples, respectively. These values are in good agreement with H _{eff} = − 324 (3) kOe obtained with Eu(NH_{3})_{6}, quite similar to ESR results obtained in dilute Eu–NH_{3} solutions, and indicate the lack of conduction‐electron‐polarization effects on the hyperfine fields. Intermediate field spectra are analyzed in terms of relaxation. The Eu(NH_{3})_{6} rates and the rates obtained in the dilute samples at small external fields are consistent with an f ^{1/2} relaxation rate, where f is the Eu fractional concentration. For larger fields, the rate in the dilute samples slows as a function of applied field divided by the temperature. This is qualitatively explained by ionic line narrowing, with concomitant loss of ionic transitions due to energy conservation requirements. The data for the 1.2% Eu sample in high fields are also used to estimate an upper limit of Korringa relaxation to the conduction band, yielding a result considerably smaller than expected for Eu^{2+} in conductors.

Drift mobility of holes in phenanthrene single crystals
View Description Hide DescriptionThe temperature dependence of drift mobilities of holes in single crystals of phenanthrene was measured in the range 203–353°K in three crystallographic directions. Below the anomaly temperature of 72°C, the mobility temperature dependences are consistent with the Munn and Siebrand slow‐phonon hopping process in the b direction and the Munn and Siebrand slow‐phonon coherent mode in the a and c′ directions. The drift mobility temperature dependences in crystals that have been cooled through the anomaly temperature in the presence of illumination and an electric field are consistent with the model of Spielberg et al., in which the hindered vibration of the 4,5 hydrogens introduces a new degree of freedom above 72°C.