Statistical Branching Ratios Research Articles

Electronic structure of GaN nanowall network analysed by XPS

This work examines the changes in bonding of GaN nanowall network samples with varying morphology grown by rf-plasma assisted molecular beam epitaxy system. X-ray photoelectron spectroscopy is employed to study the valence band spectra of two samples and the difference in bonding with change in morphology is observed. Compared to a standard epilayer, the nanostructured samples display a higher binding energy for different hybridization levels appearing near the top of valence band. Higher than statistical branching ratio of Ga 2p spin split levels is also observed unlike in the case of epilayer. The higher bonding energy is understood as having more stable electronic structure which is possible because of reduction of defects in the nanostructured films.

Spin-orbit coupling in iridium-based 5dcompounds probed by x-ray absorption spectroscopy

We have performed x-ray absorption spectroscopy (XAS) measurements on a series of Ir-based 5d transition metal compounds, including Ir, IrCl3, IrO2, Na2IrO3, Sr2IrO4, and Y2Ir2O7. By comparing the intensity of the "white-line" features observed at the Ir L2 and L3 absorption edges, it is possible to extract valuable information about the strength of the spin-orbit coupling in these systems. We observe remarkably large, non-statistical branching ratios in all Ir compounds studied, with little or no dependence on chemical composition, crystal structure, or electronic state. This result confirms the presence of strong spin-orbit coupling effects in novel iridates such as Sr2IrO4, Na2IrO3, and Y2Ir2O7, and suggests that even simple Ir-based compounds such as IrO2 and IrCl3 may warrant further study. In contrast, XAS measurements on Re-based 5d compounds, such as Re, ReO2, ReO3, and Ba2FeReO6, reveal statistical branching ratios and negligible spin-orbit coupling effects.

Product branching ratios in photodissociation of phenyl radical: A theoretical ab initio/Rice–Ramsperger–Kassel–Marcus study

Ab initio CCSD(T)/CBS//B3LYP/6-311G** calculations of the potential energy surface for possible dissociation channels of the phenyl radical are combined with microcanonical Rice-Ramsperger-Kassel-Marcus calculations of reaction rate constants in order to predict statistical product branching ratios in photodissociation of c-C(6)H(5) at various wavelengths. The results indicate that at 248 nm the photodissociation process is dominated by the production of ortho-benzyne via direct elimination of a hydrogen atom from the phenyl radical. At 193 nm, the statistical branching ratios are computed to be 63.4%, 21.1%, and 14.4% for the o-C(6)H(4) + H, l-C(6)H(4) ((Z)-hexa-3-ene-1,5-diyne) + H, and n-C(4)H(3) + C(2)H(2) products, respectively, in a contradiction with recent experimental measurements, which showed C(4)H(3) + C(2)H(2) as the major product. Although two lower energy pathways to the i-C(4)H(3) + C(2)H(2) products are identified, they appeared to be kinetically unfavorable and the computed statistical branching ratio of i-C(4)H(3) + C(2)H(2) does not exceed 1%. To explain the disagreement with experiment, we optimized conical intersections between the ground and the first excited electronic states of C(6)H(5) and, based on their structures and energies, suggested the following photodissociation mechanism at 193 nm: c-C(6)H(5) 1 → absorption of a photon → electronically excited 1 → internal conversion to the lowest excited state → conversion to the ground electronic state via conical intersections at CI-2 or CI-3 → non-statistical decay of the vibrationally excited radical favoring the formation of the n-C(4)H(3) + C(2)H(2) products. This scenario can be attained if the intramolecular vibrational redistribution in the CI-2 or CI-3 structures in the ground electronic state is slower than their dissociation to n-C(4)H(3) + C(2)H(2) driven by the dynamical preference.

Ion Imaging Study of NO3Radical Photodissociation Dynamics: Characterization of Multiple Reaction Pathways

The photodissociation of NO(3) has been studied using velocity map ion imaging. Measurements of the NO(2) + O channel reveal statistical branching ratios of the O((3)P(J)) fine-structure states, isotropic angular distributions, and low product translational energy consistent with barrierless dissociation along the ground state potential surface. There is clear evidence for two distinct pathways to the formation of NO + O(2) products. The dominant pathway (>70% yield) is characterized by vibrationally excited O(2)((3)Σ(g)(-), v = 5-10) and rotationally cold NO((2)Π), while the second pathway is characterized by O(2)((3)Σ(g)(-), v = 0-4) and rotationally hotter NO((2)Π) fragments. We speculate the first pathway has many similarities to the "roaming" dynamics recently implicated in several systems. The rotational angular momentum of the molecular fragments is positively correlated for this channel, suggesting geometric constraints in the dissociation. The second pathway results in almost exclusive formation of NO((2)Π, v = 0). Although product state correlations support dissociation via an as yet unidentified three-center transition state, theoretical confirmation is needed.

Formation of nitriles and imines in the atmosphere of Titan: combined crossed-beam and theoretical studies on the reaction dynamics of excited nitrogen atoms N(2D) with ethane

The dynamics of the H-displacement channels in the reaction N(2D) + C2H6 have been investigated by the crossed molecular beam technique with mass spectrometric detection and time-of-flight analysis at two different collision energies (18.0 and 31.4 kJ mol(-1)). From the derived center-of-mass product angular and translational energy distributions the reaction micromechanisms and the product energy partitioning have been obtained. The interpretation of the scattering results is assisted by new ab initio electronic structure calculations of stationary points and product energetics for the C2H6N ground state doublet potential energy surface. C-C bond breaking and NH production channels have been theoretically characterized and the statistical branching ratio derived at the temperatures relevant for the atmosphere of Titan. Methanimine plus CH3 and ethanimine plus H are the main reaction channels. Implications for the atmospheric chemistry of Titan are discussed.

A theoretical study of the O( 1D) + CH 4 reaction II

The titled reaction is assumed to proceed via an insertion mechanism. Statistical branching ratios for various product channels are predicted with RRKM rate constants that are obtained based on ab initio calculations. A modified collision-complex model is utilized in the estimation of absolute reaction cross-sections for primary channels. The product energy partitions for H and H 2 formation pathways are obtained. Subsequently, the RRKM rate constants for secondary reactions are calculated with correction for the translational and rotational energies of primary products. The results give insight to reaction mechanism and provide probable explanations to disputes among previous experimental findings.

Angle-differential and momentum-transfer cross sections for low-energy electron-Cs scattering.

Based on a previous Dirac [ital R]-matrix calculation [U. Thumm and D. W. Norcross, Phys. Rev. A 45, 6349 (1992)], we have derived elastic and inelastic angle-differential and elastic momentum-transfer cross sections for slow electrons ([ital E][sub kin][le]2.8 eV) colliding with neutral Cs atoms. Our results for the angle-differential cross sections are in good agreement with scaled experimental data and, depending on the incident electron energy, in qualitative or fair quantitative agreement with previously published theoretical work. The inelastic angle-differential cross sections for 6[ital p][sub 1/2] and 6[ital p][sub 3/2] excitation differ by more than a statistical branching ratio due to relativistic effects. For the momentum-transfer cross sections, we hope to resolve existing discrepancies in the literature and to provide more reliable input for transport calculations.

Non-statistical branching ratios for excitation of (np2(n+1)s) 1.3P degrees 0,1,2 states in noble gases

Previous relativistic DWBA calculations based on the Pauli form of the Schrodinger equation have been extended to excitation of the (np5(n+1)s)1.3Po1 states and the metastable (np5(n+1)s)3Po0.2 states of neon, argon, krypton and xenon. Results for several collision energies are presented and compared with experiment. In agreement with experimental evidence, strong deviations from the statistical branching ratio of 5:1 in the cross sections for excitation of the states with J=2 and j=0 were found for the xenon target. When comparing relativistic and non-relativistic DWBA calculations, it becomes evident that these effects are mainly due to the energy dependence of the T-operator because of different fine-structure excitation energies rather than to explicitly spin-dependent terms in the projectile-target interaction.

Nonadiabaticity and the competition between alpha and beta bond fission upon 1[n,π*(C=O)] excitation in acetyl- and bromoacetyl chloride

This work investigates how molecular dissociation induced by local 1[n(O),π*(C=O)] electronic excitation at a carbonyl functional group can result in preferential fission of an alpha bond over a weaker bond beta to the functional group and how nonadiabaticity in the dynamics drives the selectivity. The experiment measures the photofragment velocity and angular distributions from the photodissociation of acetyl chloride and bromoacetyl chloride at 248 nm, identifying the branching between bond fission channels and the mechanism for the selectivity. The anisotropic angular distributions measured shows dissociation occurs on a time scale of less than a rotational period, resulting in primary C–X (X=Cl, Br) bond fission, but no significant C–C bond fission. While the selective fission of the C–Cl over the C–C alpha bond can be predicted from the adiabatic correlation diagram for this special class of Norrish type I cleavage, the preferential fission of the C–Cl alpha bond over the C–Br bond beta to the carbonyl group would not be predicted on the adiabatic potential energy surface. In bromoacetyl chloride, fission of the C–Cl and C–Br bonds occurs with a branching of 1.0:1.1 (approximately 1.0:0.5 from the 1nπ* transition) compared with a predicted statistical branching ratio of 1:30. This preferential α-bond fission is attributed to a dissociation mechanism on the coupled [n,π*(C=O)] and [n(X),σ *(C–X)] electronic states, a model consistent with the lack of C–C fission and the measured kinetic energy and angular distributions. The selectivity results from the relative strengths of the electronic coupling between the initially excited [n,π*(C=O)] bound configuration and the two [n(X),σ *(C–X)] states, the weaker coupling inhibiting the adiabatic crossing over the barrier to C–Br bond fission. The results demonstrate the need to go beyond the Born–Oppenheimer approximation to gain predictive ability in any reactive system where the electronic configuration changes along the reaction coordinate, particularly at barriers due to configuration crossings. In addition, the Cl product angular distribution determines the orientation of the 1[n(O),π*(C=O)] transition dipole moment and shows it is governed by the C2v symmetry of the localized carbonyl electronic orbitals and not by the asymmetric substitution at the carbonyl group. Spectra of the Br atoms from direct dissociation at 193 nm help separate the contribution from the overlapping nσ *(C–Br) transition at 248 nm.

Desorption of a two-state system: Laser probing of gallium atom spin-orbit states from silicon (100)

The interactions of gallium atom spin-orbit states with silicon (100) surfaces are studied by temperature programmed desorption (TPD) using laser-induced fluorescence detection. State-resolved sticking coefficients are measured and are found to be unity for both spin-orbit states ( 2 P 1 2 , 2 P 3 2 , ΔE = 2.5 kcal mol −1, 10.5 kJ mol −1 ) up to surface temperatures of 1000 K. A Redhead analysis of the state-specific TPD spectra yields essentially identical energies and pre-exponential factors for both spin-orbit states. A statistical branching ratio is observed between the 2P 1 2 and 2P 3 2 Ga states at the peak of the TPD curves. These results may be accounted for by a rapid interconversion between the two states during the desorption. Since the spin-orbit splitting in this case is small, a rapid interconversion may be anticipated; however, modeling the desorption kinetics yields important features for the desorption of a two-state system. The model shows that the Redhead analysis is not adequate to measure the desorption kinetic parameters of the individual states. The TPD spectra of the two states differ only very slightly because their shape is mainly controlled by the overall rate of desorption for the sum of the two channels. The population ratio between the states allows a direct comparison of the desorption energetics of the two channels. Errors of 5–10 kcal mol −1 can occur in a determination of the desorption energy of a hypothetical, slowly desorbing state if the presence of a rapid desorption channel is ignored. The model can be generalized to describe any multiple channel surface process, including multi-state desorption of the competition between desorption and diffusion into the bulk. These results are of interest in the epitaxial growth of GaAs on Si(100).

Nonstatistical behavior of photoeffect subshell branching ratios at high energies

Deviations of subshell photoionization branching ratios from the statistical ratio are examined, using full numerical calculations in screened central potentials and high-energy-limit results, focusing on the intermediate- and high-energy regimes of photoelectron energies greater than 1 keV. For intermediate- and high-$Z$ elements there are no regions characterized by statistical branching ratios. At intermediate energies ratios for fixed photoelectron energy fall below the statistical value since at the smaller distances which have then become important the $J=L\ensuremath{-}\frac{1}{2}$ bound state is pulled in and becomes larger in comparison to the $J=L+\frac{1}{2}$ state. However, at high energies, once retardation and higher multipole effects become important, ratios rise again for low-$Z$ elements and also for higher-angular-momentum states.

Statistical and dynamical influences on electronic branching in reactions of ground- and excited-state alkaline earth atoms with molecular oxidants

We develop statistical predictions for the branching ratios into the various energetically allowed product electronic states in the reaction of Ca(4s4p 3p) + O 2, CO 2, and N 2O as well as Ba(6s 2 1S) + N 2O. The statistical branching ratios, based solely on the total volume of translational phase space associated with each electronic channel, can be constrained to be consistent with the conservation of electronic spin and/or electronic adiabaticity. By making use of earlier formal work of Levine, Bernstein, and co-workers, it is further possible to incorporate available information on the internal energy distributions in the various product electronic channels. In the reactions of metastable calcium the experimentally determined branching ratios into electronically excited CaO products are larger than would be predicted by a purely statistical model, whereas the converse seems to be true for the oxidation of Ba( 1S) by N 2O. Also, the experimental branching ratios appear consistent with a dynamical model which allows surface crossings and changes in electronic multiplicity. These oxidation reactions are interpreted in terms of an electron-jump mechanism involving a single charged ion-pair intermediate.