CH2 + O2: reaction mechanism, biradical and zwitterionic character, and formation of CH2OO, the simplest Criegee intermediate.

The singlet and triplet potential surfaces for the title reaction were investigated using the CBS-QB3 level of theory. The wave functions for some species exhibited multireference character and required the CASPT2/6-31+G(d,p) and CASPT2/aug-cc-pVTZ levels of theory to obtain accurate relative energies. A Natural Bond Orbital Analysis showed that triplet 3CH2OO (the simplest Criegee intermediate) and 3CH2O2 (dioxirane) have mostly polar biradical character, while singlet 1CH2OO has some zwitterionic character and a planar structure. Canonical variational transition state theory (CVTST) and master equation simulations were used to analyze the reaction system. CVTST predicts that the rate constant for reaction of 1CH2 + 3O2 is more than ten times as fast as the reaction of 3CH2 (X3B1) + 3O2 and the ratio remains almost independent of temperature from 900 K to 3000 K. The master equation simulations predict that at low pressures the 1CH2O + 3O product set is dominant at all temperatures and the primary yield of OH radicals is negligible below 600 K, due to competition with other primary reactions in this complex system.

Predicted Chemical Activation Rate Constants for HO2 + CH2NH: The Dominant Role of a Hydrogen-Bonded Pre-reactive Complex.

The reaction of methanimine (CH2NH) with the hydroperoxy (HO2) radical has been investigated by using a combination of ab initio and density functional theory (CCSD(T)/CBSB7//B3LYP+Dispersion/CBSB7) and master equation calculations based on transition state theory (TST). Variational TST was used to compute both canonical (CVTST) and microcanonical (µVTST) rate constants for barrierless reactions. The title reaction starts with the reversible formation of a cyclic prereactive complex (PRC) that is bound by ∼11 kcal/mol and contains hydrogen bonds to both nitrogen and oxygen. The reaction path for the entrance channel was investigated by a series of constrained optimizations, which showed that the reaction is barrierless (i.e., no intrinsic energy barrier along the path). However, the variations in the potential energy, vibrational frequencies, and rotational constants reveal that the two hydrogen bonds are formed sequentially, producing two reaction flux bottlenecks (i.e., two transition states) along the reaction path, which were modeled using W. H. Miller's unified TST approach. The rate constant computed for the formation of the PRC is pressure-dependent and increases at lower temperatures. Under atmospheric conditions, the PRC dissociates rapidly and its lifetime is too short for it to undergo significant bimolecular reaction with other species. A small fraction isomerizes via a cyclic transition state and subsequent reactions lead to products normally expected from hydrogen abstraction reactions. The kinetics of the HO2 + CH2NH reaction system differs substantially from the analogous isoelectronic reaction systems involving C2H4 and CH2O, which have been the subjects of previous experimental and theoretical studies.

Comparison of Three Isoelectronic Multiple-Well Reaction Systems: OH + CH2O, OH + CH2CH2, and OH + CH2NH.

Methylenimine (CH2NH) has been predicted to be a product of the atmospheric photo-oxidation of methylamine, but its atmospheric reactions have not been measured. In this paper, we report potential energy surfaces (PESs) and rate constants for OH + CH2NH and its isoelectronic analogues OH + CH2O and OH + CH2CH2, which are more fully understood. The PESs were computed using the BHandHLYP/aug-cc-pVTZ and CCSD(T)/aug-cc-pVTZ levels of theory. Canonical variational transition state theory and Rice-Ramsperger-Kassel-Marcus and master equation modeling were used to calculate temperature- and pressure-dependent rate constants, with particular emphasis on the OH + reactant entrance channels and the effects of prereactive complexes. The computed results are in reasonable agreement with experimental data where they can be compared and also with the results of previous theoretical calculations. The results show that to some extent OH radicals both add to the carbon center double bond in CH2NH and abstract methylene hydrogen atoms, as in the OH + CH2O and OH + CH2CH2 reactions, respectively, but the dominant pathway is abstraction of the hydrogen from N-H. The computed rate constants are suitable for both atmospheric and combustion modeling.

When Rate Constants Are Not Enough.

Real-world chemical systems consisting of multiple isomers and multiple reaction channels often react significantly prior to attaining a steady state energy distribution (SED). Detailed elementary reaction models, which implicitly require SED conditions, may be invalid when non-steady-state energy distributions (NSED) exist. NSED conditions may result in reaction rates and product yields that are different from those expected for SED conditions, although this problem is to some extent reduced by using phenomenological models and rate constants. The present study defines pragmatic diagnostics useful for identifying NSED conditions in stochastic master equation simulations. A representative example is presented for each of four classes of common combustion species: RO2 radicals, aliphatic hydrocarbons, alkyl radicals, and polyaromatic radicals. An example selected from the seminal work of Tsang et al. demonstrates that stochastic simulations and eigenvalue methods for solving the master equation predict the same NSED effects. NSED effects are common under relatively moderate combustion conditions, and accurate simulations may require a master equation analysis.

HO + OClO Reaction System: Featuring a Barrierless Entrance Channel with Two Transition States.

Chlorine-containing compounds play a significant role in the troposphere and are key players in the stratosphere. The free radical compound OClO reacts with HO free radicals, but the existing experimental kinetics data are limited and uncertain. In the present theoretical investigation, the reaction mechanism, rate constants, and product branching ratios for the HO + OClO reaction system were computed over wide temperature and pressure ranges and compared with the existing experimental data. Stationary points on the singlet potential energy surface (PES) were calculated at high levels of theory, and the kinetics parameters were computed using several methods, including variational transition state theory (VTST) and RRKM/master equation techniques. The computed PES is in reasonable agreement with previous calculations, and the computed rate constants and branching ratio are in good agreement with the recent experiments. The results are used as the basis for recommendations for atmospheric chemistry modeling. The PES along the reaction path forming the peroxy bond has a steplike structure and only a very weakly bound prereactive complex, and yet it still supports two transition states along the reaction path. This feature may also be present in other reactions in which electrostatic forces align the approaching reactants in an unfavorable orientation at long distances, thus requiring a dramatic geometry change before reaction can take place.

Theoretical study on the kinetics of the reaction CH2Br + NO2.

The mechanism for the reaction CH2Br + NO2 was investigated by quantum chemical calculation, and the kinetic calculations were carried out by means of multichannel RRKM and variational transition-state theory method. Both singlet and triplet potential energy surfaces (PESs) were considered at the CCSD(T)/6-311++G(d,p)//B3LYP/6-311G(d,p) level. The results show that the singlet PES is preferred, and the initial association is a barrierless process (CH2Br + NO2 → CH2BrNO2), consistent with previous study, while the reaction occurring on the triplet PES is unfavorable due to the high barriers at the entrance channels. The calculated overall rate constants agree well with the experimental data within the measured temperature range of 221-363 K, fitted to the expression of k(T) = 2.61 × 10(-10)T(-0.76) exp(461/T) cm(3) molecule(-1) s(-1) over the temperature range of 200-2000 K. The product ratios were obtained by using master equation modeling and show that the formation of product CH2O + BrNO (P1) is dominant, in line with the experimental observation.

CH2NH2 + O2 and CH3CHNH2 + O2 reaction kinetics: photoionization mass spectrometry experiments and master equation calculations.

Two carbon centered amino radical (CH2NH2 and CH3CHNH2) reactions with O2 were scrutinized by means of laboratory gas kinetics experiments together with quantum chemical computations and master equation modeling. In the experiments, laser photolysis of alkylamine compounds at 193 nm was used for the radical production and photoionization mass spectrometry was employed for the time-resolved detection of the reactants and products. The investigations were performed in a tubular, uncoated borosilicate glass flow reactor. The rate coefficients obtained were high, ranging from 2.4 × 10(-11) to 3.5 × 10(-11) cm(3) molecule(-1) s(-1) in the CH2NH2 + O2 reaction and from 5.5 × 10(-11) to 7.5 × 10(-11) cm(3) molecule(-1) s(-1) in the CH3CHNH2 + O2 reaction, showed negative temperature dependence with no dependence on the helium bath gas pressure (0.5 to 2.5 Torr He). The measured rate coefficients can be expressed as a function of temperature with: k(CH2NH2 + O2) = (2.89 ± 0.13) × 10(-11) (T/300 K)(-(1.10±0.47)) cm(3) molecule(-1) s(-1) (267-363 K) and k(CH3CHNH2 + O2) = (5.92 ± 0.23) × 10(-11) (T/300 K)(-(0.50±0.42)) cm(3) molecule(-1) s(-1) (241-363 K). The reaction paths and mechanisms were characterized using quantum chemical calculations and master equation modeling. Master equation computations, constrained by experimental kinetic results, were employed to model pressure-dependencies of the reactions. The constrained modeling results reproduce the experimentally observed negative temperature dependence and the dominant CH2NH imine production in the CH2NH2 + O2 reaction at the low pressures of the present laboratory investigation. In the CH3CHNH2 + O2 reaction, similar qualitative behavior was observed both in the rate coefficients and in the product formation, although the fine details of the mechanism were observed to change according to the different energetics in this system. In conclusion, the constrained modeling results predict significant imine + HO2 production for both reactions even at atmospheric pressure.

HO + CO reaction rates and H/D kinetic isotope effects: master equation models with ab initio SCTST rate constants.

Ab initio microcanonical rate constants were computed using Semi-Classical Transition State Theory (SCTST) and used in two master equation formulations (1D, depending on active energy with centrifugal corrections, and 2D, depending on total energy and angular momentum) to compute temperature-dependent rate constants for the title reactions using a potential energy surface obtained by sophisticated ab initio calculations. The 2D master equation was used at the P = 0 and P = ∞ limits, while the 1D master equation with centrifugal corrections and an empirical energy transfer parameter could be used over the entire pressure range. Rate constants were computed for 75 K ≤ T ≤ 2500 K and 0 ≤ [He] ≤ 10(23) cm(-3). For all temperatures and pressures important for combustion and for the terrestrial atmosphere, the agreement with the experimental rate constants is very good, but at very high pressures and T ≤ 200 K, the theoretical rate constants are significantly smaller than the experimental values. This effect is possibly due to the presence in the experiments of dimers and prereactive complexes, which were not included in the model calculations. The computed H/D kinetic isotope effects are in acceptable agreement with experimental data, which show considerable scatter. Overall, the agreement between experimental and theoretical H/D kinetic isotope effects is much better than in previous work, and an assumption of non-RRKM behavior does not appear to be needed to reproduce experimental observations.

Kinetic isotope effects for Cl + CH4 ⇌ HCl + CH3 calculated using ab initio semiclassical transition state theory.

Calculations were carried out for 25 isotopologues of the title reaction for various combinations of (35)Cl, (37)Cl, (12)C, (13)C, (14)C, H, and D. The computed rate constants are based on harmonic vibrational frequencies calculated at the CCSD(T)/aug-cc-pVTZ level of theory and X(ij) vibrational anharmonicity coefficients calculated at the CCSD(T) /aug-cc-pVDZ level of theory. For some reactions, anharmonicity coefficients were also computed at the CCSD(T)/aug-cc-pVTZ level of theory. The classical reaction barrier was taken from Eskola et al. [J. Phys. Chem. A 2008, 112, 7391-7401], who extrapolated CCSD(T) calculations to the complete basis set limit. Rate constants were calculated for temperatures from ∼100 to ∼2000 K. The computed ab initio rate constant for the normal isotopologue is in good agreement with experiments over the entire temperature range (∼10% lower than the recommended experimental value at 298 K). The ab initio H/D kinetic isotope effects (KIEs) for CH(3)D, CH(2)D(2), CHD(3), and CD(4) are in very good agreement with literature experimental data. The ab initio (12)C/(13)C KIE is in error by ∼2% at 298 K for calculations using X(ij) coefficients computed with the aug-cc-pVDZ basis set, but the error is reduced to ∼1% when X(ij) coefficients computed with the larger aug-cc-pVTZ basis set are used. Systematic improvements appear to be possible. The present SCTST results are found to be more accurate than those from other theoretical calculations. Overall, this is a very promising method for computing ab initio kinetic isotope effects.

Water effect on the OH + HCl reaction.

Hydrochloric acid is a major reservoir for chlorine radicals in the atmosphere. Chlorine radicals are chemically reactivated by the relatively slow attack of OH radical on HCl. Through the formation of hydrogen-bonded complexes, water has a dramatic effect on the rate of this reaction. The introduction of water opens several new reaction pathways with rate coefficients that are faster than the "bare" reaction. Accounting for the low fraction of hydrogen bonded water complexes in the atmosphere, the present results suggest that these new mechanisms involving water can contribute, although modestly, to the total chemical reactivation of chlorine from HCl in the lower troposphere. The first reported value for the equilibrium constant for the formation of H(2)O·HCl complex, which is important in understanding the removal of HCl from the atmosphere by deposition, is presented.

Ab initio reaction rate constants computed using semiclassical transition-state theory: HO + H2 → H2O + H and isotopologues.

A new algorithm [Nguyen, T. L.; Stanton, J. F.; Barker, J. R. Chem. Phys. Lett. 2010, 9, 499] for the semiclassical transition-state theory (SCTST) formulated by W. H. Miller and co-workers is used to compute rate constants for the isotopologues of the title reaction, with no empirical adjustments. The SCTST and relevant results from second-order vibrational perturbation theory (VPT2) are summarized. VPT2 is used at the CCSD(T) level of electronic structure theory to compute the anharmonicities of the fully coupled vibrational modes (including the reaction coordinate) of the transition structure. The anharmonicities are used in SCTST to compute the rate constants over the temperature range from 200 to 2500 K. The computed rate constants are compared to experimental data and theoretical calculations from the literature. The SCTST results for absolute rate constants and for both primary and secondary isotope effects are in excellent agreement with the experimental data for this reaction over the entire temperature range. The sensitivity of SCTST to various parameters is investigated by using a set of simplified models. The results show that multidimensional tunneling along the curved reaction path is important at low temperatures and the anharmonic coupling among the vibrational modes is important at high temperatures. The theoretical kinetics data are also presented as fitted empirical algebraic expressions.

Mechanism and kinetics of the reaction NO3 + C2H4.

The reaction of NO(3) radical with C(2)H(4) was characterized using the B3LYP, MP2, B97-1, CCSD(T), and CBS-QB3 methods in combination with various basis sets, followed by statistical kinetic analyses and direct dynamics trajectory calculations to predict product distributions and thermal rate constants. The results show that the first step of the reaction is electrophilic addition of an O atom from NO(3) to an olefinic C atom from C(2)H(4) to form an open-chain adduct. A concerted addition reaction mechanism forming a five-membered ring intermediate was investigated, but is not supported by the highly accurate CCSD(T) level of theory. Master-equation calculations for tropospheric conditions predict that the collisionally stabilized NO(3)-C(2)H(4) free-radical adduct constitutes 80-90% of the reaction yield and the remaining products consist mostly of NO(2) and oxirane; the other products are produced in very minor yields. By empirically reducing the barrier height for the initial addition step by 1 kcal mol(-1) from that predicted at the CBS-QB3 level of theory and treating the torsional modes explicitly as one-dimensional hindered internal rotations (instead of harmonic oscillators), the computed thermal rate constants (including quantum tunneling) can be brought into very good agreement with the experimental data for the overall reaction rate constant.

Collisional energy transfer probability densities P(E, J; E', J') for monatomics colliding with large molecules.

Collisional energy transfer remains an important area of uncertainty in master equation simulations. Quasi-classical trajectory (QCT) calculations were used to examine the energy transfer probability density distribution (energy transfer kernel), which depends on translational temperature, on the nature of the collision partners, and on the initial and final total internal energies and angular momenta: P(E, J; E', J'). For this purpose, model potential energy functions were taken from the literature or were formulated for pyrazine + Ar and for ethane + Ar collisions. For each collision pair, batches of 10(5) trajectories were computed with three selected initial vibrational energies and five selected values for initial total angular momentum. Most trajectories were carried out with relative translational energy distributions at 300 K, but some were carried out at 1000 or 1200 K. In addition, some trajectories were computed for artificially "heavy" ethane, in which the H-atoms were assigned masses of 20 amu. The results were binned according to (ΔE, ΔJ), and a least-squares analysis was carried out by omitting the quasi-elastic trajectories from consideration. By trial-and-error, an empirical function was identified that fitted all 45 batches of trajectories with moderate accuracy. The results reveal significant correlations between initial and final energies and angular momenta. In particular, a strong correlation between ΔE and ΔJ depends on the smallest rotational constant in the excited polyatomic. These results show that the final rotational energy distribution is not independent of the initial distribution, showing that the plausible simplifying assumption described by Smith and Gilbert [Int. J. Chem. Kinet. 1988, 20, 307-329] and extended by Miller, Klippenstein, and Raffy [J. Phys. Chem. A 2002, 106, 4904-4913] is invalid for the systems studied.

Sums and densities of fully coupled anharmonic vibrational states: a comparison of three practical methods.

Three practical methods for computing sums and densities of states of fully coupled anharmonic vibrations are compared. All three methods are based on the standard perturbation theory expansion for the vibrational energy. The accuracy of the perturbation theory expansion is tested by comparisons with computed eigenvalues and/or experimental vibrational constants taken from the literature for three- and four-atom molecules. For a number of examples, it is shown that the X(ij) terms in the perturbation theory expansion account for most of the anharmonicity, and the Y(ijk) terms also make a small contribution; contributions from the Z(ijkl) terms are insignificant. For molecules containing up to approximately 4 atoms, the sums and densities of states can be computed by using nested DO-loops, but this method becomes impractical for larger species. An efficient Monte Carlo method published previously is both accurate and practical for molecules containing 3-6 atoms but becomes too slow for larger species. The Wang-Landau algorithm is shown to be practical and reasonably accurate for molecules containing approximately 4 or more atoms, where the practical size limit (with a single computer processor) is currently on the order of perhaps 50 atoms. It is shown that the errors depend mostly on the average number of stochastic samples per energy bin. An automated version of the Wang-Landau algorithm is described. Also described are the effects of Fermi resonances and procedures for deperturbation of the anharmonicity coefficients. Computer codes based on all three algorithms are available from the authors and can also be downloaded freely from the Internet (http://aoss.engin.umich.edu/multiwell/).

Quantum Transport in a Silicon Nanowire FET Transistor: Hot Electrons and Local Power Dissipation.

A review and perspective is presented of the classical, semiclassical and fully quantum routes to the simulation of electrothermal phenomena in ultrascaled silicon nanowire fieldeffect transistors. It is shown that the physics of ultrascaled devices requires at least a coupled electron quantum transport semiclassical heat equation model outlined here. The importance of the local density of states (LDOS) is discussed from classical to fully quantum versions. It is shown that the minimal quantum approach requires selfconsistency with the Poisson equation and that the electronic LDOS must be determined within at least the selfconsistent Born approximation. To bring in this description and to provide the energy resolved local carrier distributions it is necessary to adopt the nonequilibrium Green function (NEGF) formalism, briefly surveyed here. The NEGF approach describes quantum coherent and dissipative transport, Pauli exclusion and nonequilibrium conditions inside the device. There are two extremes of NEGF used in the community. The most fundamental is based on coupled equations for the Green functions electrons and phonons that are computed at the atomically resolved level within the nanowire channel and into the surrounding device structure using a tight binding Hamiltonian. It has the advantage of treating both the nonequilibrium heat flow within the electron and phonon systems even when the phonon energy distributions are not described by a temperature model. The disadvantage is the grand challenge level of computational complexity. The second approach, that we focus on here, is more useful for fast multiple simulations of devices important for TCAD (Technology Computer Aided Design). It retains the fundamental quantum transport model for the electrons but subsumes the description of the energy distribution of the local phonon subsystem statistics into a semiclassical Fourier heat equation that is sourced by the local heat dissipation from the electron system. It is shown that this selfconsistent approach retains the salient features of the fullscale approach. For focus, we outline our electrothermal simulations for a typical narrow Si nanowire gate allaround fieldeffect transistor. The selfconsistent Born approximation is used to describe electronphonon scattering as the source of heat dissipation to the lattice. We calculated the effect of the device selfheating on the current voltage characteristics. Our fast and simpler methodology closely reproduces the results of a more fundamental computeintensive calculations in which the phonon system is treated on the same footing as the electron system. We computed the local power dissipation and "local lattice temperature" profiles. We compared the selfheating using hot electron heating and the Joule heating, i.e., assuming the electron system was in local equilibrium with the potential. Our simulations show that at low bias the source region of the device has a tendency to cool down for the case of the hot electron heating but not for the case of Joule heating. Our methodology opens the possibility of studying thermoelectricity at nanoscales in an accurate and computationally efficient way. At nanoscales, coherence and hot electrons play a major role. It was found that the overall behaviour of the electron system is dominated by the local density of states and the scattering rate. Electrons leaving the simulated drain region were found to be far from equilibrium.

Oxidation of ethyne and But-2-yne. 2. Master equation simulations.

The aim of this study is to improve understanding of the tropospheric oxidation of ethyne (acetylene, C2H2) and but-2-yne, which takes place in the presence of HO and O2. The details of the potential energy hypersurface have been discussed in a previous article [Maranzana et al., J. Phys. Chem. A 2008, 112, XXXX]. For both molecules, the initial addition of HO radical to the triple bond is followed by addition of O2 to form peroxyl radicals. In both reaction systems, the peroxyl radicals take two isomeric forms, E1 and E2 for ethyne and e1 and e2 for but-2-yne. Energy transfer parameters (alpha = 250 cm-1) for the ethyne system were obtained by simulating laboratory data for N2 buffer gas, where O2 was not present. In simulations of C2H2 + HO when O2 is present, E1 reacts completely and E2 reacts almost completely, before thermalization. Radical E1 produces formic acid ( approximately 44%) and E2 gives glyoxal ( approximately 53%), in quite good agreement with experiments. For but-2-yne, pressure-dependent laboratory data are too scarce to obtain energy transfer parameters directly, so simulations were carried out for a range of values: alpha = 200-900 cm-1. Excellent agreement with the available experimental yields at atmospheric pressure was obtained with alpha = 900 cm-1. Two reaction channels are responsible for acetic acid formation, but one is clearly dominant. Biacetyl is produced by reactions of e1 and, to a minor extent, e2. The peroxyl radical e2 leads to less than 8% of all products. Vinoxyl radical (which has been reported in experiments involving C2H2 + HO) and products of its reactions are predicted to be negligible under atmospheric conditions.

Non-RRKM dynamics in the CH3O2 + NO reaction system.

Quasi-classical trajectory (QCT) calculations on a model potential energy surface (PES) show strong deviations from statistical Rice-Ramsperger-Kassel-Marcus (RRKM) rate theory for the decomposition reaction (1) CH3OONO* --> CH3O + NO2, where the highly excited CH3OONO* was formed by (2) CH3O2 + NO --> CH3OONO*. The model PES accurately describes the vibrational frequencies, structures, and thermochemistry of the cis- and trans-CH3OONO isomers; it includes cis-trans isomerization in addition to reactions 1 and 2 but does not include nitrate formation, which is too slow to affect the decay rate of CH3OONO*. The QCT results give a strongly time-dependent rate constant for decomposition and damped oscillations in the decomposition rate, not predicted by statistical rate theory. Anharmonicity is shown to play an important role in reducing the rate constant by a factor of 10 smaller than predicted using classical harmonic RRKM theory (microcanonical variational transition state theory). Master equation simulations of organic nitrate yields published previously by two groups assumed that RRKM theory is accurate for reactions 1 and 2 but required surprising parametrizations to fit experimental nitrate yield data. In the present work, it is hypothesized that the non-RRKM rate of reaction (1) and vibrational anharmonicity are at least partly responsible for the surprising parameters.

Tropospheric oxidation of ethyne and But-2-yne. 1. Theoretical mechanistic study.

This paper (part 1) and the following one (part 2) aim to assess the viability of some tropospheric oxidation channels for two symmetrical alkynes, ethyne (acetylene) and but-2-yne. Paper 1 defines the features of the DFT(B3LYP)/6-311G(3df,2p) energy hypersurface and qualitatively considers the practicability of different pathways through the estimate of free energy barriers. Paper 2 will assess this in more detail by way of master equation simulations. Oxidized in the presence of HO and O2 (with the possible intervention of NO), ethyne and but-2-yne are known to produce mainly glyoxal or dimethylglyoxal and, to a lesser extent, formic or acetic acid. The initial attack by HO gives an adduct, from which several pathways (1a-c, 2a-e) originate. Pathway 1a passes through the 2-oxoethyl (vinoxyl) radical, or the analogous dimethyl-substituted intermediate, which could in principle undergo O2 addition (and subsequently, but through a demanding step, give the dialdehydes). However, in paper 2 it is assessed that the vinoxyl, as a nonthermalized intermediate, will preferentially follow unimolecular pathways to ketene or acetyl. Pathway 2a is the most important pathway: a very steep free energy cascade, started by O2 addition to the initial HO adduct with a concerted barrierless 1,5 H shift, gives a hydroperoxyalkenyloxyl radical intermediate. Peroxy bond cleavage finally produces the dialdehydes and regenerates HO. Pathways 2b and 2c originate from O2 addition to the initial HO adduct and produce, via different ring closures, either dioxetanyl or alkyl dioxiranyl radicals, respectively. Two subsequent fragmentations occur in both cases and give the carboxylic acids and a carbonyl radical, which can indirectly generate hydroxyl. Two further pathways (1c and 2e) see NO intervention onto the peroxyl radicals formed along pathways 1 and 2. Both could enhance dialdehyde production, while simultaneously depressing the carboxylic acid yield.

Image charge models for accurate construction of the electrostatic self-energy of 3D layered nanostructure devices.

Efficient analytical image charge models are derived for the full spatial variation of the electrostatic self-energy of electrons in semiconductor nanostructures that arises from dielectric mismatch using semi-classical analysis. The methodology provides a fast, compact and physically transparent computation for advanced device modeling. The underlying semi-classical model for the self-energy has been established and validated during recent years and depends on a slight modification of the macroscopic static dielectric constants for individual homogeneous dielectric regions. The model has been validated for point charges as close as one interatomic spacing to a sharp interface. A brief introduction to image charge methodology is followed by a discussion and demonstration of the traditional failure of the methodology to derive the electrostatic potential at arbitrary distances from a source charge. However, the self-energy involves the local limit of the difference between the electrostatic Green functions for the full dielectric heterostructure and the homogeneous equivalent. It is shown that high convergence may be achieved for the image charge method for this local limit. A simple re-normalisation technique is introduced to reduce the number of image terms to a minimum. A number of progressively complex 3D models are evaluated analytically and compared with high precision numerical computations. Accuracies of 1% are demonstrated. Introducing a simple technique for modeling the transition of the self-energy between disparate dielectric structures we generate an analytical model that describes the self-energy as a function of position within the source, drain and gated channel of a silicon wrap round gate field effect transistor on a scale of a few nanometers cross-section. At such scales the self-energies become large (typically up to ~100 meV) close to the interfaces as well as along the channel. The screening of a gated structure is shown to reduce the self-energy relative to un-gated nanowires.