Chemical Physics Letters (v.344, #1-2)
Chemical structure, aggregate structure and optical properties of adsorbed dye molecules investigated by scanning tunnelling microscopy by G. Janssens; F. Touhari; J.W. Gerritsen; H. van Kempen; P. Callant; G. Deroover; D. Vandenbroucke (1-6).
We describe in this Letter experiments on three related cyanine dye molecules and their aggregation on silver bromide model surfaces. By using a combination of diffuse reflectance spectroscopy, scanning tunnelling microscopy and molecular modelling, insight has been gained in the relationship between chemical structure, aggregate structure and optical properties. Our results confirm the three types of aggregate structures (J-, H- and Herringbone) expected from theories on absorption spectra.
Multiple bonding structures of C2H2 chemisorbed on Si(1 0 0) by S. Mezhenny; I. Lyubinetsky; W.J. Choyke; R.A. Wolkow; J.T. Yates (7-12).
Adsorption of acetylene on the Si(1 0 0)–(2×1) surface was studied at room temperature by scanning tunneling microscopy (STM) and theoretical modeling. Acetylene molecules adsorb nondissociatively in three distinctive bonding configurations, not one, as reported previously. In Configuration I, C2H2 molecules adsorb in di-σ form over a single silicon dimer with a relative population of 0.33 at low coverage. Configuration II has an initial formation probability of 0.51 and involves adsorption across the ends of two adjacent dimers in the same row. In Configuration III (r-bridge) C2H2 forms four bonds as it symmetrically bridges two neighboring dimers. Relative populations depend strongly on coverage. Above a coverage of ∼0.13 an acceleration in the rate of formation of Configuration III (r-bridge) is observed.
X-ray diffraction characterization on the alignment degree of carbon nanotubes by Anyuan Cao; Cailu Xu; Ji Liang; Dehai Wu; Bingqing Wei (13-17).
X-ray diffraction (XRD) studies were performed on carbon nanotubes (CNTs) with various alignment degrees synthesized by catalytic pyrolysis of ferrocene and xylene. A qualitative relationship between the peak intensities of the XRD patterns and the degrees of nanotube alignments was established. The intensity of the (0 0 2) peak decreases monotonically with higher nanotube alignment. This method provides a simple way to characterize the alignment degree of as-grown large-area CNTs.
A new purification method of single-wall carbon nanotubes using H2S and O2 mixture gas by Tak Jeong; Wan-Young Kim; Yoon-Bong Hahn (18-22).
A purification process of single-wall carbon nanotubes (SWNTs) combining both the acid treatment to remove metal particles and the gas-phase purification to remove impurity carbon particles has been developed. Acid solution of 3 M HCl was used to remove catalyst metal particles out of the arc-discharge grown SNWTs. Thermal oxidation method using H2S–O2 gas mixture was followed to preferentially remove carbon particles. Hydrogen sulfide played a role of enhancing the removal of carbon particles as well as suppressing the oxidation of nanotubes. After the combined liquid–gas cleaning process, we achieved carbon nanotubes purity of >95% with yield of 20–50%.
Concentration modulation spectroscopy with a pulsed slit supersonic discharge expansion source by Scott Davis; Michal Fárnı́k; Dairene Uy; David J. Nesbitt (23-30).
Frequency modulated discharges are combined with pulsed slit supersonic expansions to provide an intense, long path source of jet-cooled radicals/molecular ions for direct absorption laser spectroscopy. The high modulation frequency (100 kHz) permits lock-in detection of the modulated absorbance signals at sensitivities down to 7.3×10−7 absorbance/Hz1/2 (within 40% of the shot noise limit) and provides excellent discrimination for radical or molecular ion spectra in the presence of much higher precusor concentrations. The sensitivity of these methods is demonstrated with direct absorption spectral data on sample jet-cooled molecular ions (H+ 3) and hydrocarbon radicals (CH3CH2).
Spin polarization mechanisms in early stages of photoinduced charge separation in surface-modified TiO2 nanoparticles by T. Rajh; O. Poluektov; A.A. Dubinski; G. Wiederrecht; M.C. Thurnauer; A.D. Trifunac (31-39).
Steady-state and time-resolved electron paramagnetic resonance (EPR) experiments reveal that photoinduced charge separation in surface-modified nanoparticles yields interacting electron–hole radical pairs with spectral features indicative of a range of dynamic properties (Radical Pair Model and emissive Triplet Model CIDEP). Fast exchange in the radical pair is indicated by the presence of a central line at the midpoint, (g ave=(g h+g e)/2) , of electron and hole g-factors. Excess emission is consistent with the triplet character of the exciton precursor. A subset of electron–hole radical pairs exhibits the spin feature characteristic of correlated radical pair polarization (CRPP) reflecting a weak interaction between photogenerated holes and electrons.
Interaction of benzidine with DNA: experimental and modelling studies by R. Amutha; V. Subramanian; Balachandran Unni Nair (40-48).
Interaction of benzidine with DNA has been studied using spectroscopic and molecular simulation techniques. A binding constant of (6.2±0.4)×103 M −1 has been obtained by spectroscopic technique for benzidine, which indicates the existence of weak interaction between benzidine and DNA. The experimental analysis including spectroscopic and viscometric techniques reveal the possibility of groove as well as partial intercalation mode of binding of benzidine with DNA. The calculated binding energy for minor groove and intercalated complex from modelling studies are 64.15 and 67.27 kcal/mol, respectively. The calculations clearly bring out the significance of non-bonding interactions between DNA and benzidine. Both experimental and modelling studies show that benzidine interacts with DNA through minor groove binding as well as partial intercalation mechanism.
Observation of radical pair zero quantum coherence effects in the FT-EPR spectra of SO3 − and eaq − generated by photoionization of sulfite ions by Alejandro Bussandri; Hans van Willigen (49-54).
The time evolution of the intensities of FT-EPR signals from the hydrated electron (eaq −) and SO3 − radical formed by photoionization of SO3 2− in aqueous solution shows an oscillatory pattern. The effect is attributed to the coherent S–T0 spin state evolution in the [eaq −⋯SO3 −] radical pair producing spin polarization in the free radicals. The damping of these oscillations is not as strong as that predicted by the radical pair mechanism (RPM) chemically induced dynamic electron polarization (CIDEP) theory formulated by Adrian [Chem. Phys. Lett. 272 (1997) 120]. The experimental data can serve to test alternative theoretical descriptions of RPM CIDEP in terms of coherent radical pair spin state evolution combined with diffusive motion of the radicals.
A single-molecule study of the relation between the resonance frequency and the orientation of a guest molecule in a Shpol'skii system by Andreas Bloeß; Yannig Durand; Michio Matsushita; Jan Schmidt; Edgar J.J. Groenen (55-60).
An optical single-molecule study is reported of a quickly frozen solution of 2.3,8.9-dibenzanthanthrene (DBATT) in n-tetradecane at 1.4 K. The orientation has been measured of several hundreds of DBATT molecules within a confocal detection volume of ∼10 μm 3 as a function of their resonance frequency in the range of the two 0–0 bands in the fluorescence-excitation spectrum. Each band is found to correspond to a distinct distribution of orientations of DBATT molecules. A particular resonance frequency within a band is not correlated with a specific molecular orientation.
Kinetic and mechanistic studies of the OH-initiated oxidation of dimethylsulfide at low temperature – A reevaluation of the rate coefficient and branching ratio by M.B. Williams; P. Campuzano-Jost; D. Bauer; A.J. Hynes (61-67).
The pulsed laser photolysis–pulsed laser induced fluorescence (PLP–PLIF) technique has been used to study the reactions of OH with DMS and DMS-d6. The effective rate coefficient for the reaction of OH with DMS-d6 has been determined as a function of O2 partial pressure at 600 Torr total pressure in N2/O2 mixtures at 298 and 261 K and for both DMS and DMS-d6 at 240 K. Currently recommended rates are based on an empirical fit to a two-channel mechanism. This work shows that at low temperatures the currently recommended expression underestimates both the effective rate coefficient for reaction together with the branching ratio between addition and abstraction.
Line-splitting and broadening effects from 19 F in the 13 C NMR of liquid crystals and solids by Giancarlo Antonioli; Deborah E. McMillan; Paul Hodgkinson (68-74).
The NMR resonances of 13 C spins in proximity to 19 F are often unusually broad, degrading resolution and limiting the ability to quantify the C–F interactions. We observe line-splittings and selective broadenings in a liquid crystal sample that strongly depend on the 1 H decoupling. We propose a simple rationalisation that successfully reproduces the experimental behaviour, and find that suitably adapted decoupling sequences effectively eliminate the line-broadenings. Experiments on solid samples show similar variations with decoupling sequence, and the same effects may be general to H–X–Y systems.
Transition metal sulfide studies: the pure rotational spectrum of the CuS radical (X2 Π i ) by J.M. Thompsen; L.M. Ziurys (75-84).
The pure rotational spectrum of CuS in its X2 Π i ground state has been recorded using direct absorption techniques in the range 140–540 GHz. This radical was produced by the reaction of copper vapour with CS2. Both the v=0 and v=1 states of 63 CuS were observed, as well as the 65 CuS (v=0) isotopomer. 25, 13, and 8 rotational transitions were recorded for these three species, respectively. Both the Ω=1/2 and Ω=3/2 spin–orbit ladders were observed. Accurate rotational, spin–orbit, and lambda-doubling constants were subsequently determined for these molecules. These data suggest that 3d-sulfides have subtle bonding differences relative to the corresponding 3d-oxides.
Infrared predissociation reaction of the hydrogen bonds in the ternary cluster cation of aniline–water–benzene+ by T Nakanaga; F Ito (85-91).
The infrared predissociation reaction of the hydrogen bonds of aniline–water–benzene cluster cation (AWB+) in NH and OH stretching region has been investigated. It has been found that an infrared photon can decompose the cluster cation AWB+ into fragments in two different reaction paths; AWB + →
Infrared laser spectrum of the fundamental band of the boron monoxide free radical by M. Osiac; J. Röpcke; P.B. Davies (92-96).
The infrared diode laser absorption spectrum of the fundamental band of the boron monoxide (BO) radical in its ground 2Σ+ state has been observed. The source of the radical was the reaction of BCl3 with O 3 P in the absence of molecular oxygen. 15 lines of 11 BO and three lines of 10 BO have been measured. The 10 BO lines show a small, partially resolved, doublet structure of about 0.01 cm −1 which is not present in the 11 BO species. This is attributed to the complex hyperfine pattern expected for the 10 B (I=3) nucleus. The band origins are 1861.92465(48) and 1915.30554(16) cm −1 , respectively. Combining the diode laser value of B1=1.756829(11) cm −1 with the microwave determination of B 0 leads to a value of r e=1.204068(7) Å for 11 BO .
Characterization of zinc oxide crystal whiskers grown by thermal evaporation by J.Q. Hu; X.L. Ma; Z.Y. Xie; N.B. Wong; C.S. Lee; S.T. Lee (97-100).
ZnO crystal whiskers were prepared via a simple thermal evaporation of a mixture of ZnS and Fe(NO3)3. The growth process was carried out in an alumina tube at 1300°C using Ar mixed with 5% H2 as the carrier gas. The ZnO whiskers obtained had diameters ranging from 200 to 500 nm and lengths up to several hundreds of micrometers. The photoluminescence spectrum of as-grown ZnO whiskers was studied. The influences of reaction temperature, time, and carrier gases on the formation of the whiskers were investigated. A preliminary growth mechanism of the ZnO crystal whiskers was proposed.
Electron affinities of germanium anion clusters, Ge n − (n=2–5) by P.W. Deutsch; L.A. Curtiss; J.-P. Blaudeau (101-106).
Gaussian-2 (G2) theory for third-row non-transition elements is used to calculate accurate electron affinities of germanium clusters, Ge n (n=2–5). The results for n=2–4 are in agreement with experiment while there is some disagreement for Ge5. The electron affinities are also calculated using G2 theory modified by adding a diffuse function to the basis set for MP2 geometry optimizations and using the B3LYP density functional method with the 6-311+G(3df,2p) basis set.
A comparative study of two QM/MM methods testing the validity of the mean field approximation by M.E Martı́n; M.A Aguilar; S Chalmet; M Ruiz-López (107-112).
We compared the performances of two methods that combine quantum mechanics and molecular mechanics for the study of liquid systems. They differ in the description of the solute–solvent interaction. One makes use of the mean field approximation and the other does not. We show that the introduction of this approximation does not introduce significant errors into the induced dipole moment of the solute, the interaction energy or the solvent structure, while it permits a considerable reduction (from several thousand to four or five) of the number of quantum calculations and hence of the computational demands.
OH stretching vibrations of the phenol(H2O)1 + cation by M. Gerhards; A. Jansen; C. Unterberg; K. Kleinermanns (113-119).
In this Letter, we report on the application of infrared/photo induced Rydberg ionisation (IR/PIRI) spectroscopy to the hydrogen-bonded phenol(H2O)1 + cluster yielding the frequency of the symmetric OH stretching vibration of the bare cluster ion. By comparing IR/PIRI and IR-photodissociation spectra the symmetric OH stretching mode of the water moiety turns out to be a localised uncoupled vibration. Furthermore, CASSCF calculations for the phenolic OH stretching vibration of phenol(H2O)1 in the S 0, S 1 , and D0 states are performed by using a very large active space including σ- and π-orbitals. These calculations yield OH stretching frequencies which are in good agreement with the experimentally observed vibrational frequencies of the S0 and S1 states. The OH stretching vibration of the D0 state is predicted to be lower than 2800 cm−1.
On the electron–electron coalescence function in Hartree–Fock theory by Toshikatsu Koga (120-124).
In many-electron systems, the electron–electron coalescence function I0( R ) represents the probability density that any two electrons are simultaneously located at a position R in three-dimensional space. For the Hartree–Fock wavefunctions, it is shown that the coalescence function I0( R ) is rigorously expressible in terms of the familiar single-electron density ρ( r ) and spin density S( r ). The same is also true in momentum space.
Sequential STIRAP-based control of the HCN→CNH isomerization by Vandana Kurkal; Stuart A. Rice (125-137).
We have examined the use of successive stimulated Raman adiabatic passage (STIRAP) excitations to control the isomerization reaction HCN→CNH. We show that this method generates virtually complete transfer from an arbitrary initial vibrational state of HCN to an arbitrary final vibrational state of CNH. This result is valid even in the presence of a substantial number of background states that have non-zero dipole transition moments among themselves and with the subset of STIRAP states, and when pairs of background states are in resonance with the applied field.
Photoinduced electron transfer from chloropromazine and promethazine to chloroalkanes accompanied by cleavage of C–Cl bond by Sukhendu Nath; Avinash V. Sapre (138-146).
Electron transfer from two phenothiazine derivatives namely promethazine and chloropromazine to chloroalkanes namely carbontetrachloride and chloroform has been studied by steady state fluorescence and transient absorption techniques. These phenothiazine derivatives also form weak charge transfer complexes with the above two chloroalkanes. Picosecond transient absorption studies provide direct evidence for two processes: (1) charge separation in the charge transfer complex and (2) electron transfer from the excited state of phenothiazines to chloroalkanes. A modified Marcus electron transfer theory proposed by Saveant [J. Am. Chem. Soc. 109 (1987) 6788], which incorporates the bond cleavage, has been used to explain the observed experimental results.
Inelastic neutron scattering spectra of zeolite frameworks – experiment and modeling by Hervé Jobic; Konstantin S. Smirnov; Daniel Bougeard (147-153).
Inelastic neutron scattering spectra of silicalite, Na-ZSM-5, zeolites X, and Y are measured and compared with the spectra obtained by molecular dynamics simulations of the zeolitic frameworks. Comparison of the spectra shows a good general agreement of the experimental and modeling results, indicating that a generalized force field correctly describes the dynamics of the frameworks. Some discrepancies are observed. They are assigned to defects in the samples and to the neglect of electrostatic interactions in the force field model.
The measurements of picosecond fluorescence lifetimes with high accuracy and subpicosecond precision by J Karolczak; D Komar; J Kubicki; T Wróżowa; K Dobek; B Ciesielska; A Maciejewski (154-164).
Systematic studies of the fluorescence picosecond lifetimes determination by laser-excited time-correlated single-photon-counting (TCSPC) have been undertaken. The results have been used to develop methods for determining lifetimes with much smaller error and much greater reproducibility than any hitherto reported. The error in the determination of the lifetimes (±three standard deviations) can be as low as that in simulations and amounts to 0.01 FWHM of the IRF. The lifetimes determined for the second excited singlet state of xanthione in toluene (5.1±0.3 ps) and in benzene (8.1±0.3 ps) can be treated as reliable standards of picosecond lifetimes.
A comparison of the renormalized and active-space coupled-cluster methods: Potential energy curves of BH and F2 by Karol Kowalski; Piotr Piecuch (165-175).
The renormalized noniterative CCSD(T) and CCSD(TQ) methods, which are the examples of the method of moments of coupled-cluster (CC) equations, and the active-space CC approach with internal and semi-internal triexcited clusters (CCSDt) are applied to the potential energy curves of BH and F2. It is shown that the renormalized CCSD(T) and CCSD(TQ) methods are practically as effective in removing the failing of the standard noniterative CC approaches at larger internuclear separations as the CCSDt method. The results of the CCSDt and renormalized CCSD(T) and CCSD(TQ) calculations are also compared with those obtained with other perturbative CC approaches that focus on bond breaking.
Can ordinary single-reference coupled-cluster methods describe the potential energy curve of N2? The renormalized CCSDT(Q) study by Piotr Piecuch; Stanisław A. Kucharski; Karol Kowalski (176-184).
The recently proposed renormalized and completely renormalized CCSDT(Q) methods, which result from the method of moments of coupled-cluster equations, have been implemented and applied to the potential energy curve of N2. It is shown that the renormalized and completely renormalized CCSDT(Q) methods, employing the restricted Hartree–Fock reference, provide very good description of the potential energy curve of N2, in spite of the failure of the full CCSDT and perturbative CCSDT(Qf) approaches at large N–N separations.
Ab initio calculation of the torsional potential for 2-alkenylanthracene in the ground and excited states by Ken Sakata; Noritsugu Kometani; Kimihiko Hara (185-192).
Torsional potentials between the anthracene ring and alkene planes for two 2-alkenylanthracene derivatives both in the ground- and excited-states were calculated using ab inito method as a function of dihedral angle. Molecular geometries were optimized at the restricted Hartree–Fock level in the ground-state, whereas in the excited-state at the level of configuration interaction with single excitation. In the ground-state it is s-trans conformation that is more stable and more planar. While in the excited-state both are planar and the potential shape is more like symmetrical for 2-vinylanthracence, although somewhat distorted for 2-(2′ propenyl) anthracene. Stabilization energies, barrier energies, and barrier top frequencies of both ground- and excited-states were determind
Theoretical study of the internal rotation of cubylcubane and cubylcubane difluoride by Bárbara Herrera; Alejandro Toro-Labbé (193-199).
We present a theoretical study of the internal rotation of cubylcubane (CCB) (C8H7)2 and cubylcubane difluoride (CCB-2F) (C7H6F)2. Calculations at the ab initio HF//6-311G**, MP2 and DFT/B3LYP levels show that CCB presents an energy barrier at α=0° of about 4.8 kcal/mol, the addition of two fluorine atoms on each cage leads to a potential profile presenting two maxima, at α=0° (8.6 kcal/mol) and 120° (4.6 kcal/mol). The potential barriers hindering the internal rotation have been characterized by partitioning the potential function in terms of contributions due to interactions through bond and through space. It is found that the potential barriers are basically due to the through space electrostatic interactions.
Ab initio study on the electronic structures of styrene at the conical intersection by Yoshiaki Amatatsu (200-206).
Ab initio complete active space self-consistent field calculations have been performed to determine the conical intersection (CIX) of styrene where the radiationless relaxation into S0 takes place. The CIX is a crossing region between zwitterionic and diradical covalent states. In the zwitterionic state, the electron is partially transferred from the methylene into the benzylidene group. It has been also examined how the truncation of the active space affects the optimized geometry of the CIX.
Spin–orbit coupling within a two-component density functional theory approach: theory, implementation and first applications by Laura Gagliardi; Bernd Schimmelpfennig; Laurent Maron; Ulf Wahlgren; Andrew Willetts (207-212).
An implementation of spin–orbit coupling within a two-component generalization of the density functional code MAGIC is described. The spin–orbit operator is represented in the effective one-electron mean-field approximation and included into the Fock matrix within an iterative self-consistent scheme. First tests have been carried out for the spin–orbit splitting of several atoms. The spin–orbit effect on the bond distance and harmonic frequency of some diatomics has also been determined. This scheme allows to include spin–orbit in a simple way and can be efficiently used to treat large systems.
A Quantum chemical study on the potential energy surface of Mg(1 S)+N 2 O reaction by Boggavarapu Kiran; Chris Vinckier; Minh Tho Nguyen (213-220).
The singlet (1 A ′) potential energy surface (PES) of the Mg+N2O reaction has been studied at both MP2/6-311+G ∗ and CCSD(T)/6-311+G ∗ levels. Two kinds of reaction channels have been identified: the first one is when the Mg atom approaches N2O in a perpendicular fashion (⌊Mg–O–N≈90.0°) and the second is when Mg approaches from the end-on (oxygen side) of N2O (⌊Mg–O–N≈148.0°). The CCSD(T) activation barrier for the perpendicular approach is 48.8 kJ/mol and compares well with the experimentally determined value (44.3±1.3 kJ/mol). The transition structure for the end-on approach has higher energy barrier, 95.7 kJ/mol. Charges analysis and electron density calculations by atoms-in-molecule theory showed that the reaction mechanism is controlled by covalent interactions between the Mg atom and the O end of N2O rather than by an electron transfer from the Mg atom to the N2O molecule.
Density functional investigation of atmospheric sulfur chemistry II. The heat of formation of the XSO2 radicals X=H,CH3 by Pablo A Denis; Oscar N Ventura (221-228).
The Δ f H 0 (298 K) of HSO2 is estimated as −42.6±2 kcal/mol through calculations using Dunning's basis sets up to cc-pV6Z and Pople's 6-311+G(3df,2p). This estimation differs from previous G2 calculations and from our own G3 result of −37.1 kcal/mol. Similarly, the Δ f H 0 (298 K) CH3SO2 is estimated as −56.3 kcal/mol, in good agreement with Benson's prediction, −55.0 kcal/mol, and again in disagreement with the G2 value, −47.6 kcal/mol. Finally, we propose a revision of the enthalpy of formation of the CH3S radical. On the basis of the density functional theory (DFT) calculations, we propose a value of 28.8±1 kcal/mol , slightly lower than the presently accepted value of 29.78±0.44 kcal/mol .
Franck–Condon spectral calculations on trans-hydroquinone by G.N. Patwari; S. Wategaonkar; M. Durga Prasad (229-235).
In this Letter we present an application of the correlation function approach to calculate the Franck–Condon spectra of polyatomic molecules. A coupled-cluster method was used for the time propagation of the wavefunction using a quadratic Hamiltonian. The dispersed fluorescence spectra from various single vibronic excitations of trans-hydroquinone were calculated and compared with the experimentally observed spectra. The agreement between the calculated and experimental spectra was found to be excellent after some empirical adjustments to the potential displacements.
The potential energy surfaces for AlO2 using multi-reference wave functions by Michael V Pak; Mark S Gordon (236-240).
We report a systematic multi-configurational study of several low lying states of AlO2 in a wide region of the coordinate space, in order to provide additional insight into the electronic structure of the AlO2 molecule. This work attempts to resolve the question of the global minimum energy structure for the AlO2 molecule. A symmetry breaking observed in the vicinity of the linear geometry at the multi-configurational self-consistent field (CASSCF) level of theory is shown to be due to insufficient accounting of dynamic correlation, since it does not appear in multi-reference configuration interaction (MRCI) or multi-reference perturbation theory calculations (MCQDPT).
Kinetic study for the reactions of chlorine atoms with hexamethyldisiloxane, 1,1,3,3-tetramethyldisiloxane, and 1,3-dimethyldisiloxane by Alexandros V. Prosmitis; Vassilis C. Papadimitriou; Josef Pola; Panos Papagiannakopoulos (241-248).
The absolute rate constants for the reactions of chlorine atoms with (CH3)3SiOSi(CH3)3, (CH3)2HSiOSiH(CH3)2, and (CH3)H2SiOSiH2(CH3) were measured in the gas phase over the temperature range 273–363 K, using the very low pressure reactor (VLPR) in a molecular flow system. The absolute rate constants were temperature independent and take the values (in cm 3 molecule −1 s −1 , 2σ uncertainties): k1=(1.00±0.19)×10−10, k2=(1.98±0.29)×10−10 , and k 3=(2.42±0.25)×10−10. All title reactions proceed via the abstraction of C–H and/or Si–H hydrogen leading to the formation of HCl. The results show that the reactivity of Si–H bond towards Cl atom attack is higher than the reactivity of the C–H bond.