Index of content:
Volume 65, Issue 7, 01 October 1976

Extended time dependent Hartree theory of van der Waals interaction: Inclusion of electric quadrupoles
View Description Hide DescriptionExpressions are derived for the van der Waals interactionfree energy, to infinite order, which include dipole and quadrupole interactions. The treatment is an extension of the time‐dependent Hartree approximation developed previously for dipolar interactions. The results are obtained via linear response theory. Just as in the dipolar case, the results are expressed in terms of the eigen frequencies of a normal mode matrix. In the present formulation, however, the normal modes are determined not only by electric dipolar coupling but also by coupling of electric quadrupoles with each other and with dipoles. The method is also useful in generating the perturbation terms of the free energy shift. It is found that the second order term, when applied to isotropic oscillators at zero degrees, reduces to the result derived earlier by Margenau. The nonadditive three‐body potential, derived here, reduces to the Axilrod–Teller triple dipole potential in the absence of quadrupoles. Numerical results are given for the interaction between two and between three isotropic oscillators.

Alkyl–metal surface complexes: Methyl and lithium
View Description Hide DescriptionClusters containing 4 and 10 atoms of lithiuminteracting with methyl groups were investigated as models for alkyl–lithium surface complexes. Pople’s a b i n i t i o Gaussian 70 procedure was used to optimize geometrical arrangements starting from sites having a C _{3v } site symmetry and selected on the basis of known chemical and physical properties. Two sites were identified as rational possibilities for binding of methyl to lithiumsurfaces. One of the two sites was calculated to be about 40 kcal more favorable than the other. Both sites are prevalent on Li(111). The position of CH_{3} above Li(111) and orientation of CH_{3} relative to the Li surface network, as well as binding strengths, orbital parentage, and charge distributions were qualitatively the same on both 4 and 10 atom models of substrate. The change in quantitative factors among the 4 and 10 atom models suggest that 7 to 13 atoms in the substrate are sufficient to approximate properties of surface complexes of lithium with alkyl hydrocarbon groups. A potential surface for motion of CH_{3} on Li(111) estimated with 10 points suggests that an activation energy of 35–40 kcal is to be experienced for associative desorption of methyl to ethane.

Test of inert gas interatomic potentials: Virial coefficients for argon adsorption on xenon‐plated graphite
View Description Hide DescriptionVirial coefficients have been calculated for argon adsorption on xenon‐plated graphite. Good agreement for the lowest order coefficients is obtained using the accurate inert gas interatomic potentials currently available. Agreement with the higher order coefficients is still poor, however, implying the necessity of either the inclusion of additional effects or reinterpretation of the experimental data. The discrepancies occasioned by the former use of 6–12 potentials are examined, and the result of including three‐body terms is considered.

A modified CNDO method for saturated hydrocarbons, amines, alcohols, and ethers
View Description Hide DescriptionA modified CNDO method for the calculations of binding energies and conformational properties of saturated organic molecules is proposed. Modifications concern the evaluation of the core integrals only. Results of calculations on selected compounds containing hydrogen, carbon, nitrogen, and oxygen using standard geometrical models are reported. For binding energies, the mean deviations between calculated and experimental values are ±1.6 kcal mole^{−1} for 16 hydrocarbons including adamantane, ±2.0 kcal mole^{−1} for 12 amines, and ±2.2 kcal mole^{−1} for 14 alcohols and ethers. The calculated relative energies of conformational isomers are generally acceptable, but those for the skeletal isomers are unsatisfactory. Further comparisons with experimental values are made for the first ionization potentials, the dipole moments, and the equilibrium geometries of a few small molecules.

Photodissociation spectroscopy of CO_{3} ^{−}
View Description Hide DescriptionThe photodissociation cross section of gas‐phase CO_{3} ^{−} has been measured over the wavelength range from 4579 to 6940 Å, and reveals detailed structure reflecting the vibrational spacings of a predissociating excited electronic state. From an analysis of the structure, we identified three vibrational modes of the excited state having energies of 990, 1470, and 880 cm^{−1}. The bond energy D (CO_{2}–O^{−}) of the ground state CO_{3} ^{−} was determined to be 1.8±0.1 eV, and the electron affinity of CO_{3} was found to be 2.9±0.3 eV. By comparison with theoretical calculations, the lowest predissociating state was identified as 1 ^{2} A _{1}. Observations regarding other excited states of CO_{3} ^{−} are made.

Exact static dipole polarizabilities for the excited S states of the hydrogen atom
View Description Hide DescriptionThe exact static dipole polarizabilities for the excited S states of the hydrogen atom are determined by using the reduced free‐particle Green’s function method developed by McDowell and Porter [J. Chem. Phys. 65, 658 (1976)]. The general formula for the polarizabilities is found to be α_{1} ^{(n)}(S) =n ^{4}(2n ^{2}+7)/2.

An NMR study of molecular reorientation processes in solid n‐butane
View Description Hide DescriptionProtonmagnetic resonance line shapes for polycrystallinen‐butane have been studied over the temperature interval 20 K to the melting point. Spin–lattice relaxation timemeasurements have been made in the low temperature solid phase but no minimum found. The results show that methyl group tunneling persists to very low temperatures at a rate sufficiently high to narrow the absorptionspectrum. In the high temperature solid phase long axis rotational motion of the molecules occurs. A model for this form of motion is discussed.

Comments on the classical theory of energy transfer. II. Extension to higher multipoles and anisotropic media
View Description Hide DescriptionThe classical electromagnetic theory of the fluorescence emission and energy transfer in layered systems is extended to describe magnetic dipole and electric quadrupoleradiation and anisotropic media. A general formulation is developed for energy transfer from various emitter types and orientations to isotropic acceptors. The description is exact within the classical framework and requires none of the usual assumptions as to the nature of the acceptor layer. The theory is further extended to describe one‐ and two‐dimensional acceptors and electric dipole radiation in an anisotropic medium. The latter case is the actual situation in the fatty‐acid layer experiments. The coupling to the surface plasmon modes of the acceptor is discussed as it relates to the various systems described here.

Higher time derivatives of the generalized entropy
View Description Hide DescriptionUsing the generalized N‐body expression for a Liapunov functional developed by Prigogine, George, and Henin, a condition is obtained whereby the successive time derivatives of this functional alternate in sign for weakly coupled systems. This condition is applied and seen to hold true for generalized Bose and Fermi systems. An N‐body entropy is defined in terms of this functional, which contains diagonal as well as off‐diagonal elements of the density matrix. This ’’generalized entropy’’ is seen to be concave close to equilibrium, similar to the results of Harris. It does not appear that this property holds for the entropy far from equilibrium.

Far infrared spectra of ring compounds. XV. The far infrared spectrum of 7‐oxabicyclo‐[4.1.0]‐hept‐3‐ene
View Description Hide DescriptionThe far infrared spectrum of 7‐oxabicyclo‐[4.1.0]‐hept‐3‐ene has been studied using the Jarrell–Ash 78‐900 spectrophotometer at MIT. A series of nine Q branch transitions exhibiting slight negative anharmonicity has been observed beginning at 121.9 cm^{−1}. The fact that the rocking of the oxirane ring with respect to the six‐membered ring has a frequency ∼3 times that of the ring‐puckering leads to near coincidence between pairs of levels and this is reflected in some irregularity in the positions of the 2→3, 3→4, and 4→5 ring‐puckering transitions. In contrast to analogs of bicyclo‐[3.1.0]‐hexane, where the anharmonicity is substantial and the effect of the quartic term in the potential is quite noticeable, it is possible to account for the data for 7‐oxabicyclo‐[4.1.0]‐hept‐3‐ene with a harmonic potential with a small cubic perturbation. H=ν_{0}/2(P ^{2}+Q ^{2}) +C Q ^{3}, where P=−i d/d Q, Q = dimensionless ring‐puckering coordinate, ν_{0}=123.7 cm^{−1}, C=5.49 cm^{−1}.

Inelastic cross sections for molecules interacting through dipole and/or quadrupole potentials
View Description Hide DescriptionFormal expressions for the lowest order inelastic contribution to the degeneracy averaged total cross section for both distinguishable and indistinguishable rigid diatomic molecules are obtained for molecules interacting through a multipole potential. Explicit expressions for the inleastic cross section are obtained for molecules interacting through permanent dipole–dipole, dipole–quadrupole, or quadrupole–quadrupole potentials. These results require the summation over only a single quantum number; the relative angular momentum quantum number. Thus, they are useful for analytic or numerical calculations.

Rainbow structure and g–u‐interference effects in the elastic scattering of low energy protons on deuterium and hydrogen atoms
View Description Hide DescriptionElastic differential cross sections for the scattering of low energyprotons (E _{c.m.}=11–142 eV) on H and D atoms have been obtained. The curves exhibit clearly rainbow structure, g–u oscillations and a type of rapid interference, if coherent scattering of both σ_{ g } and σ_{ u } potential curves is taken into account. For comparison, partial wave calculations have been performed using WKB phases and a two‐state (1sσ_{ g }, 2pσ_{ u }) approximation. The agreement with both experimental results and three‐state (1sσ_{ g }, 2pσ_{ u }, 2pπ_{ u }) calculations of Knudson e t a l. is excellent, which implies that rotational coupling between the 2pσ_{ u } and 2pπ_{ u } potential curves can be neglected. It is shown that the reduced phases a=√E/2μN can be described as a single function of the reduced angle τ=Eϑ for all energies and both isotopes. This function agrees with both two‐state calculations of the authors and three‐state calculations of Knudson e t a l.

Shift of emission band upon the excitation at the long wavelength absorption edge. III. Temperature dependence of the shift and correlation with the time dependent spectral shift
View Description Hide DescriptionThe edge‐excitation red shift previously observed for quinine and related compounds has been shown to exist also for 8‐anilinonaphthalene‐1‐sulfonic acid. The excitation energy dependent spectral shift observed here and the time dependent spectral shift observed by Chakrabarti and Ware have been interpreted satisfactorily in terms of one and the same mechanism. The previously suggested mechanism of the red shift in which the solute–solvent interaction plays an essential role is thus supported. The solvent reorientation relaxation time has been estimated from two different sets of experimental data, one concerned with the excitation energy dependent shift and the other with the time dependent shift. The estimated relaxation times are shown to be entirely different from the dielectric relaxation times of the solvent.

The perfect‐pairing valence bond model for the water molecule
View Description Hide DescriptionOptimized orbitals for the water molecule have been obtained within the perfect‐pairing valence bond model by an a b i n i t o self‐consistent field calculation. Each split pair is optimized by approximating the remaining electron distribution with a localized doubly‐occupied orbital sea. In addition, the overlaps between orbitals of different pairs are optimized by considering higher order pair–pair interactions. The expansion of the energy in the cumulative order of intrapair orbital splittings converges rapidly. The total energy obtained is 49.0 kcal/mole below restricted Hartree–Fock, thus accounting for 21.0% of the correlation energy. The orbitals are well localized into a 1s core pair on oxygen, two equivalent O–H bond pairs and two equivalent lone pairs on oxygen. The hybridization of these orbitals differs considerably from what is expected on the basis of ordinary chemical intuition, the split lone pair orbitals being s p ^{0.56} and s p ^{1.83} and the bonding orbital centered on oxygen being s p ^{1.84}. No artificial orthogonality restrictions are imposed on the orbitals in this method. The interpair orbital overlaps are typically on the order of 0.0–0.3, rising to over 0.7 for the overlap between the diffuse orbitals of each lone pair! The energy lowering over a valence bond calculation carried out with a strong orthogonality constraint is small (3.4 kcal/mole). However, the nonorthogonal orbitals are the appropriate ones for transferring from one molecule to another and for chemical interpretation in general. Furthermore, the artificial radial nodes that appear in the strongly orthogonal orbitals hamper the perturbation calculation of correlation energies and the application of pseudopotential techniques as well.

Survey of chemi‐ionization reactions in accelerated atom–O_{2} crossed‐molecular beams
View Description Hide DescriptionThe chemi‐ionization reactions,associative ionization, and rearrangement (reactive) ionization, and the electron transferreaction have been investigated in the crossed‐molecular beam collisions of more than 20 accelerated (by sputtering) metal and nonmetal atoms with O_{2} molecules. The observations support a generalization on the scope of these chemi‐ionization reactions and their relation to electronic structure, namely that associative and rearrangement ionizationreactions do not occur for collision partners for which the thermodynamic threshold energy for electron transfer is lower than the thresholds for the chemi‐ionizations. On the other hand, rearrangement and associative ionization may be prominent reaction channels when their thermodynamic thresholds are less than that for electron transfer. Relative cross sections for Ce^{+}, CeO^{+}, and CeO_{2} ^{+} formation for collision energies of Ce+O_{2} up to 50 eV (cm) are presented. A substantial threshold for associative ionization is observed for this system.

Hindered rotational energy levels of a tetrahedron in a trigonal crystalline field
View Description Hide DescriptionThe energy levels for the motion of a rigid tetrahedral molecule in a trigonal crystalline field have been computed. The symmetry group of the Hamiltonian is ?×C _{3}, where ? is the tetrahedral group of rotations about body‐fixed axes and C _{3} is the trigonal group of rotations about space‐fixed axes. The effect on the tunneling frequencies, heat capacity, and activation energy of lowering the symmetry of the crystalline field from tetrahedral to trigonal is discussed. The energy levels of a symmetric top molecule in a tetrahedral crystalline field have been computed and used to determine tunneling frequencies.

Ion–molecule reaction mechanisms: Thermal energy gas phase reactions of ^{12}C^{+} and ^{13}C^{+} ions with CH_{4}, C_{2}H_{4}, C_{2}H_{6}, C_{3}H_{6}, C_{3}H_{8}, and CD_{3}CH_{2}CD_{3}
View Description Hide DescriptionThe results of a tandem Dempster–ICR mass spectrometric study of carbon ion reactions with several hydrocarbons are reported. The reactions of ground state (^{2} P) ^{12}C^{+} and ^{13}C^{+} ions at near thermal translational energies (0.1 eV) with methane, ethylene, ethane, propylene, propane, and propane 1,1,1,3,3,3‐d _{6} were investigated. Reaction branching ratios show several reactions with varying degrees of ^{13}C insertion in the ionic products. On progression from smaller to larger neutral reactants the results are characterized by less retention of the reactant ion nucleus in the ionic products. Reaction of C^{+} with methane gives a product distribution in line with that predicted by Quasiequilibrium Theory (QET) for excited C_{2}H_{4} ^{+} species. However, propylene shows little correlation with QET predictions. Moreover, ^{13}C^{+}reactions with ethane and propane exhibit reaction channels in which ^{13}C retention in the ionic products is considerably greater than predicted from statistical considerations. It is concluded that the results are best rationalized by a combination of direct processes and an indirect mechanism involving C^{+} insertion at a C–H bond.

Translational energies from ionic fragmentation
View Description Hide DescriptionStatistical theories of unimolecular reactions are applied to determine the translational energies of fragments of ionic decomposition. The results are found to be in conflict with experimental measurements of translational energies of ions formed by electron or photon impact. However, a full application of phase‐space theory results in much better agreement with ion–molecule experiments than the theory of Safron e t a l. [S. A. Safron, N. D. Weinstein, D. R. Herschbach, and J. C. Tully, Chem. Phys. Lett. 12, 564 (1972)]. A classical model of a triatomic molecule is constructed, and the partitioning of energy in dissociating trajectories is examined and compared to statistical theories. Discrepancies between the trajectories and statistical theories are noted and possible explanations discussed.

Analytic energy shifts, linewidths, and line profiles in predissociation
View Description Hide DescriptionC^{+} and C^{−}predissociations are treated in the linear potential approximation. Using the appropriate Green’s function, analytic expressions are obtained for ΔE and Γ, the energy shifts and linewidth. These parameters are shown to be strongly energy dependent and their effect on predissociation line shapes are illustrated.

Fano line shapes in predissociation
View Description Hide DescriptionThe absorption line shapes for C^{+}predissociations are examined in the case of an optically active continuum which gives rise to Fano profiles. Using the model of linear potentials at the crossing point, all relevant parameters are obtained analytically from the appropriate Green’s function. It is shown that the energy dependence of linewidths and energy shifts has important effects on these profiles, introducing sometimes new zeros or peaks in the classical Fano profile.