Volume 67, Issue 10, 15 November 1977
Index of content:

Quantum‐dynamical model for thermal desorption of gases from solid surfaces
View Description Hide DescriptionThe Montroll–Shuler model for the kinetics of dissociation of a diatomic molecule in a heat bath is adapted to thermal desorption of gases from solid surfaces. The rate constant k _{MS} is compared with that predicted by transition‐state theory,k _{TST}, and that extracted from experimental data for the system Xe/W. A central feature of the present model is that k _{MS} shows a strong explicit dependence (ϑ^{−3} _{ D } in the Debye approximation) upon the lattice dynamics, whereas k _{TST} has none at all.

Entropy and chemical change. III. The maximal entropy (subject to constraints) procedure as a dynamical theory
View Description Hide DescriptionAn equivalence between the dynamical (equations of motion) and the information theoretic (maximal entropy) approaches to collision phenomena is established. The connection is demonstrated in both directions. The variational procedure of maximal entropy is shown to converge to an exact solution of the equations of motion (be they classical or quantal) throughout the collision. In particular, a stationary precollision state is proved to be a state of maximal entropy (subject to constants of the unperturbed motion) and to remain a state of maximal entropy throughout the collision. Conversely, the exact solution of the equations of motion is shown to be of maximal entropy. In this fashion one obtains an algebraic procedure for the specification of the constraints which determine (via the procedure of maximal entropy) an exact solution of the equations of motion. Surprisal analysis does not require the solution of differential equations. These must be solved to determine the magnitude of the Lagrange parameters (i.e., for surprisal synthesis). The number of coupled differential equations that have to be solved (to obtain an exact solution) equals the number of constraints. Sum rules (which express the mean value of any constraint as a linear function of the initial mean values of the constraints) are derived and offer an alternative route to surprisal synthesis. The information theoretic result for the branching ratio (as the ratio of two partition functions) is shown to be a rigorous result of the present formalism. As an illustration, a simple Hamiltonian for a collinear reactive collision is analytically treated in detail (for a classical motion along the reaction coordinate). The constraints are identified (with special reference to reactive collisions, where the Hamiltonians for the reactants and products do differ); the time dependence of the Lagrange parameters is established and the vibrational state distribution (both during and after the collision) is determined. A sum rule for the mean products vibrational energy is discussed. For a stationary initial state (e.g., a particular vibrational state or a thermal distribution), 〈E′_{vib}〉 is linearly dependent on 〈E _{vib}〉 alone. The slope and intercept are determined only by the dynamics and are essentially proportional to the ratio of the final to initial vibrational frequencies. For a family of related reactions where this ratio is nearly unchanged, the vibrational energy disposal would be quite similar. Inefficient products vibrational excitation is expected when this ratio is low.

Product distributions for some thermal energy charge transfer reactions of rare gas ions
View Description Hide DescriptionIon cyclotron resonance methods were used to measure the product distributions for thermal energycharge transferreactions of He^{+}, Ne^{+}, and Ar^{+} ions with N_{2}, O_{2}, CO, NO, CO_{2}, and N_{2}O. Except for the He^{+}–N_{2}reaction, no molecular ions were formed by thermal energycharge transfer from He^{+} and Ne^{+} with these target molecules. The propensity for dissociative ionization channels in these highly exothermic charge transferreactions at thermal energies contrasts with the propensity for formation of parent molecular ions observed in photoionization experiments and in high energycharge transfer processes. This difference is explained in terms of more stringent requirements for energy resonance and favorable Franck–Condon factors at thermal ion velocities.

The correlation energy in the random phase approximation: Intermolecular forces between closed‐shell systems
View Description Hide DescriptionA new expression for the correlation energy within the random phase approximation (RPA) is presented. It has the following properties: it is (1) size consistent, (2) invariant to unitary transformations of degenerate orbitals, (3) correct to second order in perturbation theory, and (4) when applied to a supermolecule comprised of two interacting closed‐shells, it describes the dispersive part of the interaction at the c o u p l e d Hartree–Fock (HF) level, i.e., the van der Waals’ coefficient extracted from its long‐range behavior is identical to that obtained from the Casimir–Polder expression using the dynamic coupled Hartree–Fock polarizabilities of the isolated systems. This expression, which requires only particle–hole two‐electron integrals for its evaluation, is expected to yield considerably more accurate potential energy curves between closed‐shell systems than second‐order Moller–Plesset perturbation theory which, as is shown, describes dispersion forces at the less accurate u n c o u p l e d HF level. In addition, since it is shown how this RPA correlation energy can be obtained from the zeroth iteration of a self‐consistent RPA procedure such as that of McKoy and co‐workers, our result can be systematically improved. Finally, illustrative calculations of He and (He)_{2} are presented.

The adsorption of benzene on the Pt(111) surface studied by low‐energy electron diffraction intensity measurements and quantitative Auger electron spectroscopy
View Description Hide DescriptionBenzene, when chemisorbed on the Pt(111) crystal face forms an ordered metastable ‖^{4} _{0} _{4} ^{−2}‖ surface structure which transforms, slowly, to a stable ‖^{4} _{0} _{5} ^{−2}‖ surface structure. A complete set of intensity–voltage (I vs V) curves are presented in the appendix to aid in solving the surface structures of this complex organic molecule. The size of the unit cells and the larger than monolayercarbonsurface concentrations (determined by quantitative Auger spectroscopy) indicate that most of the adsorbed benzene molecules are inclined at an angle to the surface. The similarity of the (I–V) profiles for the same diffraction beams from the two structures indicate that the carbon–platinum layer spacing changes very little during the order–order transformation.

Simulation of the bound‐free KrF* emission spectra from reactive quenching of Kr(5s[3/2]_{2}) and Kr(5s[3/2]_{1}) atoms
View Description Hide DescriptionThe low pressure KrF emission spectra, which includes the KrF(III,1/2−I,1/2 or B–X) and the KrF(II,3/2−I,3/2 or C–A) transitions arising from the reaction of metastable or resonance states of Kr with F_{2}, NF_{3}, and CF_{3}OF, have been simulated by computer. Since a broad distribution of very high v′ levels is produced by the chemical reactions, the dependence of the spectrum upon various properties of the upper and lower states was first investigated. A general discussion of the types of emission spectra that can be expected from bound‐free transitions from high v levels is first presented. As a starting point for fitting the KrF spectra, the a b i n i t i o potential curves and the dependence of the transition moments upon internuclear separation calculated by Hay and Dunning for KrF were used. The I,1/2 and III,1/2 curves are generally satisfactory but some modification of the I,3/2 potential curve was necessary in order to fit the observed spectra. As the final step, KrF* vibrational distributions from the Kr*+F_{2}, CF_{3}OF, and NF_{3}reactions were assigned that gave simulated spectra in agreement with the low pressure spectra. The fraction of the available energy released as KrF* vibrational energy was ≳50%. The assignment of the initial vibrational distribution as well as 〈f _{ V }〉, and to the dependence of the transition moment upon internuclear separation. Within some general limitation, this spectrum is not very sensitive to the I,1/2 or III,1/2 potential curves.

Infrared intensities: A comprehensive quantitative analysis for transition metal carbonyls M(CO)_{6} (M=Cr, Mo, and W) and Ni(CO)_{4}
View Description Hide DescriptionA comprehensive analysis of infrared intensities has been made for Cr(CO)_{6}, Mo(CO)_{6}, W(CO)_{6}, and Ni(CO)_{4} molecules. Making use of the isotopic frequencies reported by Jones, McDowell, and Goldblatt, α matrices have been evaluated. The atomic polar tensors and dipole moment derivatives δμ_{ g }/δS _{ j } for all possible sign combinations have been reported. The correct sign combination has been determined from the criterion of maximum ξ^{2} value as reported earlier. The bond moment parameters and atomic charges have been determined using the modified first order approach. The atomic charges obtained for Cr, Mo, W, and Ni, respectively, are 0.55, 0.64, 0.65, and 0.11e. The atomic polar tensors are found to show systematic trends in the molecules considered and indicate that they may be predicted qualitatively for other similar molecules. The analysis of bond moment parameters and polar tensors have led to the support of general ideas about the nature of bonding between metal and CO ligands.

Structure and energy transfer within isolated (O_{2})_{2} dimers via high resolution electronic spectroscopy
View Description Hide DescriptionPolarized, high resolution ^{1}Δ_{ g }+^{1}Δ_{ g } ↔^{3}Σ_{ g } ^{−}+^{3}Σ_{ g } ^{−}(^{1} A _{ g }) and ^{3}Σ_{ g } ^{−}+^{1}Σ_{ g } ^{+}→^{3}Σ_{ g } ^{−}+^{3}Σ_{ g } ^{−} (^{3} B _{3u }) (O_{2})_{2} dimer spectra have been observed in solid neon host at 4.2 K. Excited state electronic fine structure components are resolved and assigned. The ^{1}Δ_{ g }+^{1}Δ_{ g } transition is both allowed and vibronically induced by b _{3u } antisymmetric O_{2} stretch quanta. The ^{1}Δ_{ g }+^{1}Δ_{ g } geometry is identical to that of the ground ^{3}Σ_{ g } ^{−}+^{3}Σ_{ g } ^{−} state; the ^{3}Σ_{ g } ^{−}+^{1}Σ_{ g } ^{+} state appears to have slightly different structure. The spectra are entirely consistent with D _{2h } structure, and less likely with D _{2d } structure. The dimer triplet (^{3} B _{3u }) ground state subcomponents lie ∼55 cm^{−1} above the dimer singlet (^{1} A _{ g }) ground state. The dimer vibrational constants are unperturbed from the O_{2} in vacuum values. The nearest neighbor vibrational energy transfer time from one O_{2}(^{1}Δ_{ g }) to another is ∼14 ps, as revealed by zero phonon line splittings in emission. The nearest neighbor electronic energy transfer time of the ^{1}Σ_{ g } ^{+}(v=0) state appears to be 0.6 ps, as revealed by spectral shifts. Both these processes appear to result from electron exchange, and not multipole–multipole interactions. Isotopic substitution experiments show that unfavorable Franck–Condon factors ’’trap’’ the ^{1}Σ_{ g } ^{+} (v) state on one side of the dimer for v?1. Energy transfer of ^{1}Σ_{ g } ^{+} (v) from dimers to nearby monomers also occurs. Comparison is made with the calculations of Bhandari and Falicov. Values for the intermolecular exchange integrals are obtained. Gas phase energy transfer is also discussed.

Local mode involvement in the vibrational relaxation of isolated (O_{2})_{2} dimers
View Description Hide DescriptionStudy of five isotopic species of isolated (O_{2})_{2} dimer in solid neon host near 4.2 °K shows that the mechanism of ^{1}Δ_{ g }+^{1}Δ_{ g }excited state vibrational relaxation involves intersystem crossing into the ^{3}Σ^{−} _{ g }+^{1}Σ^{+} _{ g } state. Several reversible dynamic equilibria are observed between nearly degenerate ^{1}Δ_{ g }+^{1}Δ_{ g } and ^{3}Σ^{−} _{ g }+^{1}Σ^{+} _{ g } vibronic states. Indirect arguments suggest that the nearest neighbor, nonresonant vibrational energy transfer time from ^{16}O_{2}(^{1}Δ_{ g }) to ^{18}O_{2}(^{1}Δ_{ g }) is order‐of‐magnitude 10^{−9}–10^{−10} s. Vibrational relaxation rates for (0+v) ^{3}Σ^{−} _{ g }+^{1}Σ^{+} _{ g } states (v?3) are slower with heavier reduced masses. The relaxation rate depends not only on the nuclei in the excited O_{2}, but also on the nuclei in the unexcited nearest neighbor O_{2}. These results are consistent with O_{2} rotation accepting energy during the vibrational relaxation process. This appears to be the first such observation for a nonhydride molecule in condensed phase. The relation between spectral polarization and rotation as the accepting mode is discussed.

Internal dynamics of van der Waals complexes. I. Born–Oppenheimer separation of radial and angular motion
View Description Hide DescriptionAn efficient method has been developed for calculating ground stateproperties of atom–diatomic van der Waals complexes. The wide amplitude bending motion is decoupled from the radial motion in a way analogous to the Born–Oppenheimer separation of electronic and nuclear motion. The treatment furnishes rigorous upper and lower bounds to the ground state energy that are typically ±3 cm^{−1} for the Ar–HCl surfaces considered. Extensive comparison of this technique with the close‐coupling method of Dunker and Gordon [J. Chem. Phys. 64, 354 (1976)] using intermolecular potentials for the Ar HCl complex indicates excellent agreement in the prediction of angular expectation values and rotational constants for the ground state, while realizing an approximate 700‐fold reduction in computation time.

Far infrared absorption of diatomic polar molecules in simple liquids and statistical properties of the interactions. I. Spectral theory
View Description Hide DescriptionA theory of the far infrared spectra of diatomic polar molecules dissolved in simple liquids is presented. The starting point is a basic spectrum of additive Lorentzian lines, whose widths and shifts are expressed up to second order with respect to the interaction. This basic spectrum is distorted by the finite correlation time of the interaction, by the correlation between initial states, and by the overlap between the lines which are not completely resolved for the liquid state. All these deviations, including the overlap correction, which leads to a nonadditivity effect of the lines, are also treated up to second order with respect to the interaction.

Far infrared absorption of diatomic polar molecules in simple liquids and statistical properties of the interactions. II. Statistical theory and spectral application
View Description Hide DescriptionThe statistical properties of the directing intermolecular field, which describes the anisotropic action to which polar molecules are submitted when immersed in a simple liquid, are expressed in terms of equilibrium averages. These averages are obtained by means of a convenient cell model for the liquid structure. This statistical information is inserted in the spectraltheory of Paper I. The different spectral effects are numerically analyzed. It is shown that only the overlapping line effect must be retained in the far‐infrared absorption of such a liquid solution. When using this (nonadditivity) overlapping line effect the theoretical and experimental band profiles are in agreement.

Overlapping effects and motional narrowing in molecular band shapes: Application to the Q branch of HDa)
View Description Hide DescriptionA new formulation of the theory of strong overlapping effects in molecular line broadening is presented in terms of the intermolecular potential. This formulation takes into account the vibrational degrees of freedom and includes in an acceptable form the close collisions. A detailed analysis of such effects is carried out for the motional narrowing arising in the Q branch of HD at sufficiently high densities. A very good consistency is obtained between the experimental data and the present calculation at room and low temperatures. The nonadditivity effects in infrared absorption and anisotropic Raman overlapping lines treated in the general frame of this paper may also be easily calculated when required.

Electronic to vibrational energy transfer from Br(4^{2} P _{1/2}) to CO_{2}, COS, and CS_{2}
View Description Hide DescriptionIn this paper, we report a study of the quenching of Br(4^{2} P _{1/2}) by CO_{2}, COS, and CS_{2}. Laser photolysis of gas samples containing Br_{2} and the molecular species of interest produces Br(4^{2} P _{1/2}), and the subsequent quenching of this species results in vibrational excitation of the molecule of interest. By monitoring the time resolved ir fluorescence from Br(4^{2} P _{1/2}) and the (001) states of CO_{2}, COS, and CS_{2}, we are able to measure the quenching rate coefficients for these species as well as rate coefficients for a number of V–V,T,R processes. By comparing the intensities of the Br(4^{2} P _{1/2}) and (001) state fluorescences, we measure directly the rate coefficients for electronic to vibrational (E→V) energy transfer into the product states that contain at least one quantum of ν_{3} vibration.

Semiclassical theory of the effects of collisions between rotors on molecular spectral line shapes. I
View Description Hide DescriptionThe semiclassical (WKB) limit of the quantum mechanical expression for the collisional line broadening cross section of the microwave spectrum of gaseous molecules is derived. For the present purpose of considering binary collisions between such species as OCS and CO_{2}, action‐angle‐like variables for the classical mechanics of two interacting rotors are developed. Applications can be made to the evaluation of T _{2}(microwave line broadening) and T _{1}(microwave transient experiments) cross sections and to calculations of rotational and vibrational energy transfer for linear molecule–linear molecule systems.

Semiclassical theory of the effects of collisions between rotors on molecular spectral lineshapes. II. Calculations for several systems
View Description Hide DescriptionThe T _{2}(microwave line broadening) and T _{1}(microwave transient experiments) collisional cross sections are obtained by Monte Carlo trajectory evaluations of semiclassical (WKB) expressions for those quantities derived in a previous paper in this series. The calculated values of the cross sections presented here yields the relation T _{1}?T _{2} (within standard error) for the systems OCS–OCS, OCS–N_{2}, OCS–H_{2}, OCS–CO_{2}, and HCN–HCN, a result which agrees with recent experimental findings. Reasonable agreement was also found between the calculated values of the T _{2} cross section and those observed spectroscopically.

An optically pumped molecular bromine laser
View Description Hide DescriptionMolecular bromine has been observed to lase when optically pumped on individual vibration–rotation lines. With no dispersive elements in the laser cavity the output consists of several doublets, corresponding to P‐ and R‐branch transitions from the excited (B) state populated by the pump pulse to various vibrational levels of the ground state. The insertion of an intracavity prism causes a single doublet to lase, with a corresponding reduction in output power. In the current experiments the output wavelength was tunable from 550 nm in the green to 750 nm in the red for each transition pumped near 532 nm. The broadband efficiency was a few tenths of a percent, with the single‐line output efficiency one‐tenth of that. The theoretical gain at 10 torr and 300 K was estimated to be 0.05–0.40 per cm. This system offers a quasicontinuous tunable source of radiation ranging from the visible to 3.5 μm in the infrared.

Dynamics of three‐body half collisions. I. Secondary product decomposition in the photodissociation of acetyl iodide
View Description Hide DescriptionPhotofragment spectroscopy of acetyl iodide (CH_{3}COI) at 266 nm shows evidence of a two‐step dissociation into three products. Initial photodissociation yields an iodine atom and a highly internally excited acetyl radical containing on average 80% of the energy available in the dissociation process. The transitiondipole moment of the initial absorption lies in the C–C–O plane near the C–I bond axis, and breakup of the photoexcited acetyl iodide is rapid, on the order of 10^{−13} sec. The acetyl fragment is found to live for several rotational periods, ∼10^{−11} sec. Its subsequent decomposition to CO and CH_{3} can be modeled by statistical theories of unimolecular decay. It is found that an average 30% of the energy residing in the acetyl radical ultimately appears as relative translational energy of the CO and CH_{3} fragments.

Diagrammatic perturbation theory. The ground state of the carbon monosulfide molecule
View Description Hide DescriptionDiagrammatic many‐body perturbation theory is employed in a study of the ground state of the carbon monosulfide molecule for bond lengths close to the equilibrium value. The calculations are complete through third order in the energy within the algebraic approximation. Two different zero‐order Hamiltonians are considered and all two‐, three‐, and four‐ body terms are determined for the corresponding perturbation expansions. Many‐body effects are found to be very important. Padé approximants to the energy expansion are constructed and upper bounds are evaluated. Almost 53% of the estimated correlation energy is recovered. The variation of components of the correlation energy with nuclear separation is investigated. Spectroscopic constants are also calculated.

A CNDO/S study on the electronic structure of some methyl and phenyl substituted pyryliums
View Description Hide DescriptionThe semiempirical molecular orbital CNDO/S spectral parameterization of Del Bene and Jaffe has been used to elucidate the electronic structure of a series of methyl and phenyl substituted pyrylium cations. This study demonstrates that the CNDO/S technique, without additional parameterization, provides a quantitative basis for the understanding of various ground and excited singlet state properties of the five pyrylium molecules considered. Of particular importance is the favorable comparison of experimental and calculated relative oscillator strengths and the magnitude and direction of shifts of the singlet transitions. The nature of the low‐lying singlet states are further elucidated through a study of the calculated wavefunctions. Comparisons of potential energy diagrams for the interaction of the ground and excited state static charge density distributions with a negative test charge demonstrates that the nature of the transition could be important in the determination of relative spectral sensitization properties.