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Volume 68, Issue 7, 01 April 1978

Electron drift and diffusion in polyatomic gases: Calculations for CH_{4}, CD_{4}, and related models
View Description Hide DescriptionWe present the results of direct numerical calculations of electron drift velocities and diffusion coefficients in polyatomic gases as a function of applied electric fieldE. Modelscattering cross sections appropriate to CH_{4} and CD_{4} and others of related form are used. The kinetic theory ideas presented in previous work are more extensively tested. We find good agreement with available experimental results for CH_{4} and CD_{4}. The diffusion is found to be strongly anisotropic, consistent with the anisotropy of the (space‐independent) velocity distribution calculated previously. The diffusion parallel to the field has a strong maximum as a function of E, in a region where apparently no experimental work has been done. Drift and diffusion results for some CH_{4} cross sections derived by comparison of experiment with approximate analytical treatments of the Boltzmann equation are discussed. We demonstrate that these treatments depend on parameters inadequate to specify the problem completely. The effects on drift velocity of angle dependence in the elasticscattering cross section are tested as are those of a resonance in the inelastic scattering. By comparison of our results for drift and diffusion with a proposed generalization of the Nernst–Einstein relation to large E, we show that this generalization is quantitatively invalid for gases with electron–molecule cross sections similar to those of CH_{4} and CD_{4}.

A statistical theory for collisionless multiphoton dissociation of SF_{6}
View Description Hide DescriptionA statistical thermodynamictheory is used to calculate the dissociation efficiency of SF_{6} by CO_{2} laser photons. The dissociation efficiency calculated with the model presented is compared to that calculated with two other statistical models, one a more sophisticated model (RRKM) and the other a very crude model. We find that the calculated dissociation efficiency is insensitive to the particular statistical model used.

The effects of basis set and configuration interaction on the predicted geometries of AH_{2} molecules
View Description Hide DescriptionThe effects of basis set size and type on the theoretical optimum geometries calculated by a b i n i t i o SCF and CI methods is studied for the molecular species H_{2}O ^{1} A _{1}, NH_{2} ^{2} B _{1}, CH^{2} ^{1} A _{1}, H_{2}O^{+} ^{2} B _{1}, NH_{2} ^{2} A _{1}, CH_{2} ^{3} B _{1}, BH_{2} ^{2} A _{1}, H_{2}O^{+} ^{2} A _{1}, over the range from minimum to much extended basis sets. The difference in optimum geometry between SCF and CI calculations is also noted. Calculations made specially for this study have used double‐zeta and double‐zeta‐plus‐polarization Gaussian basis sets. The geometries predicted by these and many published calculations are plotted as points on diagrams of bond angle ϑ versus bond length r. It is observed that there are striking similarities between such diagrams for different species, and thus it is possible to use the diagrams in order to predict a molecular geometry with greater accuracy than by one method alone (except CI with a very extended basis). Such a prediction is made from calculations of the species NH^{−} _{2} ^{1} A _{1}.

Pressure dependence of the reaction of He_{2}(^{3}Σ) metastable molecules with Ar
View Description Hide DescriptionThis paper reports the re‐examination and analysis of data characterizing the excitation transfer reaction of metastable He_{2}(^{3}Σ_{ u }) helium molecules with argon atoms. Data were originally obtained from measurements of the transient optical absorption of the 4650 Å, ^{3}Σ_{ u }→^{3}π_{ g } helium transition in high pressure,e‐beam afterglows, and in low pressure, electric discharges. Rate coefficients have been obtained from the data and resolved into components describing the bimolecular and termolecular reactions of He_{2}(^{3}Σ_{ u }) with Ar. Values of 1.5×10^{−10} cm^{3} sec^{−1} and 2.4±0.8×10^{−30} cm^{6} sec^{−1}, respectively, were found. The former corresponds to a reaction probability of 0.18 and the latter represents the first measurements of a termolecular excitation transfer reaction of He_{2}(^{3}Σ_{ u }).

A classical trajectory study of collisional energy transfer in thermal unimolecular reactions
View Description Hide DescriptionClassical trajectory calculations have been carried out to study energy transfer in atom–triatom collisions.Collisions between O_{3} and He, Ar and Xe have been studied at energies corresponding to the temperature range 300–2500 K and between H_{2}O and Ar in the range 2500–10 000 K. The results allow a comparison between the multistep and strong collision models of unimolecular decay. For both O_{3} and H_{2}O the multistep model gives good agreement with experimental results and the energy transfer characteristics of He, etc. conform to those expected for an inefficient heat‐bath gas. Rotational energy transfer is found to be more efficient than vibrational and energy transfer in general is sensitive to the R ^{−6} term in the atom–triatom potential.

Semiclassical theory of unimolecular dissociation induced by a laser field
View Description Hide DescriptionA semiclassical nonperturbative theory of direct photodissociation in a laser field is developed in which photon absorption and dissociation are treated in a unified fashion. This is achieved by visualizing nuclear dynamics as a representative particle moving on electronic‐field surfaces. Methods are described for calculating dissociation rates and probabilities by Monte Carlo selection of initial conditions and integration of classical trajectories on these surfaces. This unified theory reduces to the golden rule expression in the weak‐field and short‐time limits, and predicts nonlinear behavior, i.e., breakdown of the golden rule expression in intense fields. Field strenghts above which lowest‐order perturbation theory fails to work have been estimated for some systems. Useful physical insights provided by the electronic‐field representation have been illustrated. Intense field effects are discussed which are amenable to experimental observation. The semiclassical methods used here are also applicable to multiple‐surface dynamics in fieldfree unimolecular and bimolecular reactions.

The quadrupole moment of the H_{2} molecule
View Description Hide DescriptionWe present an improved adiabatic calculation of the quadrupole moment of the H_{2} molecule and of its matrix elements between various vibrational rotational states. Particular attention is paid to making a reasonable estimate of the accuracy of transition elements between widely different vibrational states. An order of magnitude estimate of the nonadiabatic contribution to the quadrupole moment is also given and we show that it is typically of the order of a tenth of a percent of the adiabatic value.

A b i n i t i o effective core potentials for molecular calculations. II. All‐electron comparisons and modifications of the procedure
View Description Hide DescriptionRecently methods have been developed [L. R. Kahn, P. Baybutt, and D. G. Truhlar, J. Chem. Phys. 65, 3826 (1976)] to replace the core electrons of atoms by a b i n i t i o effective core potentials (ECP). Valence‐electron calculations are reported on the ground states of HF, F_{2}, HCl, LiCl, and Cl_{2} using ECP’s for F and Cl, and the results are compared to all‐electron calculations. Significant discrepancies are found (as much as 20 kcal/mol for D _{ e } and 0.3 bohr for R _{ e } in the case of Cl_{2}) between the two sets of calculations. The original formulation of generating ECP’s can lead to artificial attractive tails in the potential at large values of r which leads to potential energy curves which are too attractive. The procedure of generating ECP’s is modified to remove the long‐range attractive tails. Excellent agreement between the valence‐electron and all‐electron calculations is then obtained.

^{129}I Mössbauer spectra of the tellurium iodides
View Description Hide DescriptionThe ^{129}I spectra of Cs_{2}TeI_{6}, α‐Me_{2}TeI_{2}, α‐TeI and TeI_{4} are reported and the compound p‐EtOC_{6}H_{4}TeI_{3} was also studied. The iodine coupling constant in Cs_{2}TeI_{6} is comparable with that previously reported from NQR data. The other compounds each contain a number of inequivalent iodine atoms and complex spectra are observed. Computed Mössbauer parameters were obtained for all but p‐EtOC_{6}H_{4}TeI_{3}. A simple relationship is observed between bond length and the ^{129}I isomer shift and coupling constant.

The effect of spin delocalization on the proton magnetic relaxation in transition metal hexaaquo ions
View Description Hide DescriptionThe calculation of the effect of covalency on the electron–nuclear dipolar relaxation in low spin d ^{5} complexes was extended to include all octahedral transition metal complexes. In particular, an expression was given for hexaaquo complexes and numerical calculations were performed for the hexaaquomanganese (II) ion. Taking into account spin delocalization, the calculated dipolar relaxation is larger than the value obtained using the point dipole appproximation. This effect was found to be relatively small for hexaaquo complexes owing to cancellations in the contributions from spin densities in the various water molecular orbitals. The result of the proton–manganese distance obtained from NMRrelaxation times is compared with the available crystallographic data.

Pressure and temperature dependence of molecular motion in organic plastic crystals
View Description Hide DescriptionThe proton NMRrelaxation timesT _{1} and T _{1} _{ρ} have been measured as a function of temperature and pressure in the plastic crystals cyclohexane, hexamethylethane (HME) and hexamethyldisilane (HMDS) for pressures up to 2.8 kbar. The T _{1} data provide information on the molecular reorientation. This motion is only weakly dependent on pressure. The reorientational activation volumes for the three materials studied were found to be temperature dependent and generally less than 10% of the molar volume V _{ m }. The T _{1ρ} data have been analysed in terms of the translational molecular self‐diffusion, using a weak‐collision theory. A value of 1.1V _{ m } was obtained for the activation volume for self‐diffusion in HME, independent of pressure and temperature over most of the range studied. Diffusional activation volumes for the other two substances were found to be dependent on both pressure and temperature, ranging from 0.9 to 0.3V _{ m } in cyclohexane and from 0.55 to 0.2V _{ m } in HMDS. The observed temperature and pressure dependences of the activation enthalpies and volumes are discussed in relation to the mechanisms of the molecular motion. The complexity of the diffusive motion appears to correlate with the entropy of fusion of the material. While the dominant defect responsible for self‐diffusion is usually thought to be a relaxed vacancy, there is some evidence to suggest that, in parts of the plastic phase, translational motion may proceed by more than one mechanism.

Long and short range correlations in the Brownian motion of charged particles
View Description Hide DescriptionLong range electrical forces are shown to produce a long range correlation of the dipolar type between the Brownian motion of charged particles in a conducting solution. A modification of the short range correlation of the displacement of the particles is shown to be associated with the long range correlation.

Dipole correlations in conducting media
View Description Hide DescriptionIt is shown that the lack of static long range correlation of permanent dipoles in a conducting medium follows simply from the assumption that the phenomenological coefficients are short ranged. The long range correlation which develops in time can be looked at as being induced by a dipole formed by ions which shield a static dipole.

Effect of centrifuging on fluctuations in the critical liquid–liquid region
View Description Hide DescriptionThis paper presents a reassessment of an earlier paper on the elevation of the critical temperature, t _{ c }, of liquid–liquid mixtures in a centrifugal field and in a uniform pressure field. Two systems are used: one whose components have nearly the same density, the other whose densities differ widely. We find that with the first pair pressure raises t _{ c } by the same amount whether applied by external compression or by a centrifuge, where the centrifugal force produces the same pressure. With the second pair there is a small additional increase in t _{ c } which we attribute to stretching of the range of the thermal fluctuations. We confirm this effect and its magnitude by a theoretical analysis.

A perturbation theory calculation on the ^{1}ππ* state of formamide
View Description Hide DescriptionA hybrid orbital basis and a partitioning perturbation theory procedure were developed to calculate the ^{1}ππ* state of formamide. The calculated energies for the ^{1}ππ* state are uncertain by about 1 eV with the predicted energies ranging from 6.96 to 8.21 eV. The ^{1}ππ* state is extensively mixed with several Rydberg states. To calculate the true ^{1}ππ* state this interaction must be properly accounted for and the calculations cannot be biased in favor of any one state. It is also shown that the common practice of using ground state or triplet ππ* orbitals to describe the ^{1}ππ* state of amides is qualitatively incorrect and can lead to completely wrong conclusions.

Solid‐state reaction kinetics in single‐phase polymerizations
View Description Hide DescriptionThe kinetics of single‐phase solid‐state polymerization reactions are evaluated using two different approximations for the effect of structural changes at intermediate conversions. Conversion curves are calculated for monomer phases which undergo large dimensional changes in the reaction direction (crystal strain approximation) and for monomer phases which are essentially dimensionally invariant during reaction (nearest neighbor approximation). Using the crystal strain approximation and experimentally derived elastic constants, the different autocatalytic reaction curves observed for thermal and radiation‐induced polymerization of a diacetylenic monomer are successfully predicted. The dramatic autocatalytic effect for thermal polymerization can be explained quantitatively by a strain‐dependent rate of chain initiation and chain propagation, while the weaker autocatalytic effect for γ‐ray induced polymerization suggests that radiation‐induced chain initiation is relatively insensitive to crystal strain. Chain propagation lengths as a function of conversion and the effects of external stress and impurities on reaction kinetics are also predicted using the model.

ESR investigations of VO^{2+} doped ferroelectric tris sarcosine calcium chloride
View Description Hide DescriptionESR studies of vanadyl ions doped in ferroelectric tris sarcosine calcium chloride single crystals are carried out. The room temperature spectra indicate four magnetically inequivalent complexes which become equivalent along the crystallographic axes. The z axes of two of these correspond to two Ca–O bond directions, suggesting substitutional sites for the paramagnetic ion. The molecular orbital coefficients are estimated from the ESR and optical absorption data which indicate the complex to be ionic except for the extremely low value for e*_{π} ^{2}. A new band is observed in the optical absorptionspectrum which might be due to the b _{2}↔a transition. The equivalency at room temperature is lost at liquid nitrogen temperature.

Substituent effects in benzene cation spectroscopy. I. Perturbation theory
View Description Hide DescriptionThe spectroscopy of substituted benzene radical ions is considered within the context of perturbation methods successfully developed for neutrals. Expressions are given for substituent perturbation of the two spectroscopic peaks in the visible–uv spectral region; the positions of the peaks are perturbed by both first‐ and second‐order terms, and the intensities by second‐order terms. As an example, the information on ion state positions in the methylbenzenes from photoelectron spectroscopy and ionization potential measurements is discussed and parametrized in relation to the perturbation expressions.

Substituent effects in benzene cation spectroscopy. II. Photodissociation spectra of methylbenzene ions
View Description Hide DescriptionPhotodissociationspectra have been obtained for the complete series of methylbenzene cations. The spectra are similar in pattern, showing a visible peak and a uv peak, and the positions, widths, and intensities of the peaks are reported for all 13 ions. The peak positions, and to some extent intensities, are discussed in terms of the perturbation expressions derived in the preceding paper. Substituent effects on the visible peak positions are reasonbly well accounted for by the simplest first‐order inductive perturbation model. However, the uv peak positions are in extreme disagreement with the predictions of this simplest model. It is shown that second‐order perturbations can account for nearly all of the uv peak shifts, and a successful quantitative model is described, although the complexity of possible second‐order effects precludes any definitive conclusion about the uv peak situation.

On the application, breakdown, and near‐dissociation behavior of the higher‐order JWKB quantization condition
View Description Hide DescriptionNumerical studies and analytic results show that singularities in the appropriate contour integrals cause the higher‐order JWKB eigenvalue criteria to break down for energies near the dissociation limit of any potential with an attractive inverse power (C _{ n }/R ^{ n }) tail for which n≳2. However, the expressions derived for the characteristic near‐dissociation behavior of these contour integrals provide a simple way of predicting the range of binding energies over which this occurs from a knowledge of only n, the potential constant C _{ n }, and the reduced mass μ. This analysis also shows that for more than 70% of all diatomic molecule electronic states, no vibrational levels lie in the very narrow region near dissociation where this breakdown occurs. A related near‐dissociation analysis shows that for levels in the upper part of a potential well, applying the Langer–Kemble correction to the first‐order quantization condition reduces the errors in calculated eigenvalues by the fraction 3/(n+1), for n?2. In contrast, for the (n=6) model problem studied numerically, use of the two‐term (third‐order) or three‐term (fifth‐order) quantization conditions reduces these errors by four or eight orders of magnitude, respectively.