Dependence of the rate constants on the treatment of internal rotation modes: the reaction OH + CH3SH --> CH3S + H2O as an example

The title reaction has been used as an example to test the importance of using a hindered rotor treatment instead of a harmonic oscillator model for calculating vibrational partition functions corresponding to low-frequency internal rotation modes. First, a normal-mode analysis according to the Ayala and Schlegel's algorithm has been used to identify the internal rotation modes of methanethiol and the transition state structure. Then, after calculation of the energy barrier for each internal rotation, the corresponding hindered rotor partition functions have been calculated following the CW scheme of Chuang and Truhlar. The results show that the anharmonic treatment produces a rather modest improvement of the rate constants at room temperature or below.     

Control of rotor function in light-driven molecular motors

A study is presented on the control of rotary motion of an appending rotor unit in a light-driven molecular motor. Two new light driven molecular motors were synthesized that contain aryl groups connected to the stereogenic centers. The aryl groups behave as bidirectional free rotors in three of the four isomers of the 360° rotation cycle, but rotation of the rotors is hindered in the fourth isomer. Kinetic studies of both motor and rotor functions of the two new compounds are given, using (1)H NMR, 2D-EXSY NMR, and UV-vis spectroscopy. In addition, we present the development of a new method for introducing a range of aryl substituents at the α-carbon of precursors for molecular motors. The present study shows how the molecular system can be photochemically switched between a state of free rotor rotation and a state of hindered rotation and reveals the dynamics of coupled rotary systems.     

Ab initio thermochemistry and kinetics for carbon-centered radical addition and beta-scission reactions

A quantitative comparison of ab initio calculated rate coefficients using five computational methods and five different approaches of treating hindered internal rotation and tunneling with experimental values of rate coefficients for nine carbon-centered radical additions/beta scissions at 300, 600, and 1000 K is performed. The high-accuracy compound methods, CBS-QB3 and G3B3, and the density functionals, MPW1PW91, BB1K, and BMK, have been evaluated using the following approaches: (i) the harmonic oscillator approximation; (ii) the hindered internal rotor approximation for the internal rotation about the forming/breaking bond in the transition state and product; and the hindered internal rotation approximation combined with (iii) Wigner, (iv) Skodje and Truhlar, and (v) Eckart zero-curvature tunneling corrections. The density functional theory (DFT) based values for beta-scission rate coefficients deviate significantly from the experimental ones at 300 K, and the DFT methods do not accurately predict the equilibrium coefficient. The hindered rotor approximation offers a significant improvement in the agreement with experimental rate coefficients as compared to the harmonic oscillator treatment, especially at higher temperatures. Tunneling correction factors are smaller than 1.40 at 300 K and 1.03 at 1000 K. For both the CBS-QB3 method, including the hindered rotor treatment but excluding tunneling corrections, and the G3B3 method, including hindered rotor and Eckart tunneling corrections, a mean factor of deviation with experimentally observed values of 3 is found.     

An analytic hindered rotor model for calculating microcanonical variational unimolecular rate constants from reaction path properties

A model is proposed for performing microcanonical variational transition state theory calculations which incorporates ideas from vibrator and flexible variational transition state models. Vibrational frequencies, moments of inertia, and potential energy for the variational transition state are found by reaction path following as for the vibrator model. However, the transitional modes are treated as hindered rotors using an analytic potential and an analytic density of states, which are fit to barriers for hindered rotation determined from reaction path following. The model proposed here differs from the flexible transition state model in that the density of states for the transitional modes is analytic and transitional modes and external rotational angular momenta are uncoupled. For the H + CH₃ ? CH₄ system, rate constants calculated with this new model are only 6–23% smaller on average from those of the flexible transition state model for values of total angular momentum which correspond to average rotational temperatures of 0–2000 K. Harmonic frequencies calculated for the transitional modes from the hindered rotor Hamiltonian are in good agreement with the exact values found by a reaction path analysis. © 1994 John Wiley & Sons, Inc.     

Fine tuning of molecular rotor function in photochemical molecular switches

Molecular switches are used as scaffolds for the construction of controlled molecular rotors. The internal position of the switching entity in the molecule controls the dynamic behaviour of the rotor moiety in the molecule. Six new molecular motors with o-xylyl rotor moieties were prepared on the basis of an overcrowded alkene, and their dynamics were systematically studied by 2D EXSY NMR. Variation of the (hetero-)atoms in the upper and lower halves of the overcrowded alkene allows fine tuning of the rate of rotation of the o-xylyl rotor in the lower half of the molecule. For all rotors it was observed that the rotation barrier for the trans-isomer was higher than that of the corresponding cis-isomer. The results are analyzed and discussed in terms of differences in steric interactions in the presented system.     

Experimental characterization of the weakly anisotropic CN X 2Σ+ + Ne potential from IR-UV double resonance studies of the CN-Ne complex

IR-UV double resonance spectroscopy has been used to characterize hindered internal rotor states (n(K) = 0(0), 1(1), and 1(0)) of the CN-Ne complex in its ground electronic state with various degrees of CN stretch (ν(CN)) excitation. Rotationally resolved infrared overtone spectra of the CN-Ne complex exhibit perturbations arising from Coriolis coupling between the closely spaced hindered rotor states (1(1) and 1(0)) with two quanta of CN stretch (ν(CN) = 2). A deperturbation analysis is used to obtain accurate rotational constants and associated average CN center-of-mass to Ne separation distances as well as the coupling strength. The energetic ordering and spacings of the hindered internal rotor states provide a direct reflection of the weakly anisotropic intermolecular potential between CN X (2)Σ(+) and Ne, with only an 8 cm(-1) barrier to CN internal rotation, from which radially averaged anisotropy parameters (V(10) and V(20)) are extracted that are consistent for ν(CN) = 0-3. Complementary ab initio calculation of the CN X (2)Σ(+) + Ne potential using MRCI+Q extrapolated to the complete one-electron basis set limit is compared with the experimentally derived anisotropy by optimizing the radial potential at each angle. Experiment and theory are in excellent accord, both indicating a bent minimum energy configuration and nearly free rotor behavior. Analogous experimental and theoretical studies of the CN-Ne complex upon electronic excitation to the CN B (2)Σ(+) state indicate a slightly more anisotropic potential with a linear CN-Ne minimum energy configuration. The results from these IR-UV double resonance studies are compared with prior electronic spectroscopy and theoretical studies of the CN-Ne system.     

On the internal rotations in p-cresol in its ground and first electronically excited states

The overall rotation and internal rotation of p-cresol (4-methyl-phenol) has been studied by comparison of the microwave spectrum with accurate ab initio calculations using the principal axis method in the electronic ground state. Both internal rotations, the torsions of the methyl and the hydroxyl groups relative to the aromatic ring, have been investigated. The internal rotation of the hydroxyl group can be approximately described as the motion of a symmetrical rotor on an asymmetric frame. For the methyl group it has been found that the potential barrier hindering its internal rotation is very small with the first two nonvanishing Fourier coefficients of the potential V(3) and V(6) in the same order of magnitude. Different splittings of b-type transitions for the A and E species of the methyl torsion indicate a top-top interaction between both internal rotors through the benzene ring. An effective coupling potential for the top-top interaction could be estimated. The hindering barriers of the hydroxyl and methyl rotation have been calculated using second-order Moller-Plesset perturbation theory and the approximate coupled-cluster singles-and-doubles model (CC2) in the ground state and using CC2 and the algebraic diagrammatic construction through second order in the first electronically excited state. The results are in excellent agreement with the experimental values.     

Average orientation of a molecular rotor embedded in a Langmuir-Blodgett monolayer

A molecular rotor in which a naphthalene rotator is attached through a silicon atom to three fatty acid chains has been synthesized, and Langmuir-Blodgett techniques were used to deposit on silica surfaces monolayers of its calcium salt, both neat and diluted with stearic acid salts. The monolayer films have been characterized by ellipsometry and Fourier transform infrared (FT-IR) grazing-incidence attenuated total internal reflection (GATR) spectroscopy on Si-SiO(2) and by UV-vis absorption spectroscopy on SiO(2). The measurements were combined with calculations of the electronic (INDO/S) and vibrational (DFT) transition moment directions to deduce the average orientation of the rotor molecules, including the naphthalene ring, relative to the surface. In both neat and mixed films, the naphthalene ring is found to preferentially tilt toward the surface, enough that its rotation is most likely hindered. A comparable picture was obtained from molecular mechanics calculations on a mixed film of the naphthalene rotor and stearic acid.     

Effects of entropy on the gas-phase pyrolysis of ethyl N,N-dimethylcarbamate

In this study, we examined the gas-phase pyrolysis of ethyl N,N-dimethylcarbamate theoretically at various theoretical levels. The reaction consists of a two-step mechanism, with N,N-dimethylcarbamic acid and ethylene as reaction intermediates. In the first step, the reaction proceeds via a six-membered cyclic transition state (TS), which is more favorable than that via a four-membered cyclic TS. Here, the contribution of entropy to the overall potential energy surface was found to play an important role in determining the rate-limiting step, which was found to be the second step when viewed in terms of the enthalpy of activation (DeltaH(not equal)), but the first step when entropy changes (-TDeltaS(not equal)) were considered. These results are consistent with experimental findings. Moreover, the experimental activation entropy can be reproduced by using the hindered rotor approximation, which converts some low vibration frequencies that correspond to internal rotational modes into hindered rotors.     

Topological and symmetry features of internal rotation potetial in molecules with two rotors

The detailed knowledge of the potential energy surface features of a molecule in a given electronic state (within the Born-Oppenheimer approximation), is very interesting both from the spectroscopic and from configurational analysis point of view.The study of the topological and symmetry properties of potential energy can be great help in order to characterize and understand it, especially when the number of internal coordinates increases.In the present work, we show an application of these methods to the study of the internal rotation potential in a molecule with two three-fold tops as ether.     

Experimentally measured permanent dipoles induced by hydrogen bonding. The Stark spectrum of indole-NH3

Hydrogen bond pairs involving the chromophore indole have been extensively studied in the gas phase. Here, we report high resolution electronic spectroscopy experiments on the indole-NH(3) hydrogen bond pair in the absence and presence of an electric field. The S(1)-S(0) origin band of this complex recorded in zero field at high resolution reveals two overlapping spectra; a consequence of NH(3) hindered internal rotation. The barrier to internal rotation is predicted by theory to be less than 20 cm(-1) in the ground state, therefore requiring a non-rigid rotor Hamiltonian to interpret the spectra. Conducting the experiment in the presence of an applied electric field further perturbs the already congested spectrum of the complex, but makes possible the measurement of the permanent electric dipole moments in its S(0) and S(1) states. These values reveal significant changes in electron distribution that arise from hydrogen bonding effects.     

Barmer to internal rotation in the methylammonium ion

As experimentally available data only give indirect information about geometrical and electronic properties of the methylammonium ion, ab initio MO-LCAO-SCF calculations, with different minimal and extended basis sets, have been performed on this ion to determine its optimized geometry and internal rotation barrier. Results suggest the existence of a hindered internal rotation with a barrier of about 2 kcal mole^?1.     

Variational analysis of the phenyl + O2 and phenoxy + O reactions

Variational transition state analysis was performed on the barrierless phenyl + O2 and phenoxy + O association reactions. In addition, we also calculated rate constants for the related vinyl radical (C2H3) + O2 and vinoxy radical (C2H3O) + O reactions and provided rate constant estimates for analogous reactions in substituted aromatic systems. Potential energy scans along the dissociating C-OO and CO-O bonds (with consideration of C-OO internal rotation) were obtained at the O3LYP/6-31G(d) density functional theory level. The CO-O and C-OO bond scission reactions were observed to be barrierless, in both phenyl and vinyl systems. Potential energy wells were scaled by G3B3 reaction enthalpies to obtain accurate activation enthalpies. Frequency calculations were performed for all reactants and products and at points along the potential energy surfaces, allowing us to evaluate thermochemical properties as a function of temperature according to the principles of statistical mechanics and the rigid rotor harmonic oscillator (RRHO) approximation. The low-frequency vibrational modes corresponding to R-OO internal rotation were omitted from the RRHO analysis and replaced with a hindered internal rotor analysis using O3LYP/6-31G(d) rotor potentials. Rate constants were calculated as a function of temperature (300-2000 K) and position from activation entropies and enthalpies, according to canonical transition state theory; these rate constants were minimized with respect to position to obtain variational rate constants as a function of temperature. For the phenyl + O2 reaction, we identified the transition state to be located at a C-OO bond length of between 2.56 and 2.16 A (300-2000 K), while for the phenoxy + O reaction, the transition state was located at a CO-O bond length of 2.00-1.90 A. Variational rate constants were fit to a three-parameter form of the Arrhenius equation, and for the phenyl + O2 association reaction, we found k(T) = 1.860 x 1013T-0.217 exp(0.358/T) (with k in cm3 mol-1 s-1 and T in K); this rate equation provides good agreement with low-temperature experimental measurements of the phenyl + O2 rate constant. Preliminary results were presented for a correlation between activation energy (or reaction enthalpy) and pre-exponential factor for heterolytic O-O bond scission reactions.     

Molecular compasses and gyroscopes. II. Synthesis and characterization of molecular rotors with axially substituted bis[2-(9-triptycyl)ethynyl]arenes

We have developed a simple convergent procedure for the synthesis of molecular rotors consisting of a central aromatic group coupled with two axially positioned ethynyltriptycenes. Molecular rotors with 1,4-phenylene (1), 1,4'-1,1'-biphenylene (2), 9,10-anthracenylene (3), and 2,7-pyrenylene (4) groups were prepared by Pd(0)-catalyzed coupling of ethynyl triptycenes with the corresponding dibromoarenes. Although compounds 1-4 were not expected to have free rotation in the solid state, the rotational potentials of 1 and 3 were analyzed by semiempirical methods and the crystal packing of 1 was analyzed to design the structures most likely to yield a functional rotor in the solid state. Semiempirical PM3 calculations predict compounds 1, 2, and 4 to have frictionless internal rotation even at temperatures as low as 25 K, while compound 3 is expected to have a barrier of ca. 4 kcal/mol.     

Origin of diastereoselectivity in the synthesis of chiral bicyclic lactams: pi-facial selective attack of singlet oxygen induced by hindered internal rotation

Previously reported experimental results indicate that photooxygenation of homochiral N-(hydroxyalkyl)-2-methylpyrroles with singlet oxygen yields trans-rather than cis-bicyclic lactams as the major product. In this study, the origin of selectivity in this reaction has been investigated with computational methods. Relative stabilities of homochiral N-(hydroxyalkyl)-2-methylpyrrole conformers and their effect on pi-facial selectivity of 1O2 were extensively studied. Stepwise and concerted reaction mechanisms, starting from the endoperoxide intermediates, were proposed and modeled in vacuum using the UB3LYP method with the 6-31+G** basis set. Solvent calculations were carried out in CH2Cl2, by means of the integral equation formalism-polarizable continuum model (IEF-PCM) at the UB3LYP/6-31+G** level of theory. Free energies of activation leading to both diastereomers were analyzed in an effort to explain the stereoselectivity and product distribution. Steric interactions among the pyrrole substituents were shown to lead to a rotational barrier higher than 10 kcal/mol. Hence, hindered internal rotation is suggested to cause one pyrrole conformer to be substantially overpopulated. This in turn has a major effect on pi-facial selectivity of 1O2, thereby favoring one endoperoxide over the other and leading to the diastereoselective synthesis of trans-pyrrolooxazolones. The importance of hindered internal rotors, for an accurate calculation of the frequency factors of a chemical reaction, has already been mentioned in the literature many times; however, in this work hindered internal rotors also seem to dictate the diastereoselective outcome of the reaction.     

Theory of damped quantum rotation in NMR spectra. I. Fundamental aspects

The damped quantum rotation (DQR) theory, formulated originally for methyl-like atomic groupings, is now extended to hindered (N>3)-fold molecular rotors, such as the cyclopentadienyl, benzene, and cycloheptatrienyl rings in solid phase environments. It heightens the significance of the Pauli principle in shaping up the stochastic dynamics of such objects, reflected in NMR line shapes. The corresponding NMR line-shape equation is derived; its stochastic part is shown for the first time to have the double commutator form for any values of the quantum-mechanical (coherence-damping) rate constants entering it. Constraints on the relative magnitudes of such constants are determined under which the DQR line-shape equation is converted into the phenomenological Alexander-Binsch equation describing classical jumps of the rotor. When all the quantum rate constants happen to be equal, the phenomenological model of equal jump rates between any two of the N (equivalent) orientations of the rotor is reproduced. On the other hand, the seemingly most plausible (for N>3) nearest-neighbor hopping model does not have any peculiar grounds in the DQR approach. For the special instances of stochastic molecular motions addressed in this work, the extended DQR formalism affords a quantification of the "degree of classicality" represented by a complete set of the relevant quantum rate constants. In view of our earlier experimental findings for the methyl rotors, the very occurrence of the nonclassical DQR effects seems unquestionable even for the objects of the size of benzene. The question of under what circumstances such effects can be big enough to be detected experimentally will be addressed in Part II of this work.     

Methyl rotational tunneling dynamics of p-xylene confined in a crystalline zeolite host

The methyl rotational tunneling spectrum of p-xylene confined in nanoporous zeolite crystals has been measured by inelastic neutron scattering (INS) and proton nuclear magnetic resonance (NMR), and analyzed to extract the rotational potential energy surfaces characteristic of the methyl groups in the host-guest complex. The number and relative intensities of the tunneling peaks observed by INS indicate the presence of methyl-methyl coupling interactions in addition to the methyl-zeolite interactions. The INS tunneling spectra from the crystals (space group P2(1)2(1)2(1) with four crystallographically inequivalent methyl rotors) are quantitatively interpreted as a combination of transitions involving two coupled methyl rotors as well as a transition involving single-particle tunneling of a third inequivalent rotor, in a manner consistent with the observed tunneling energies and relative intensities. Together, the crystal structure and the absence of additional peaks in the INS spectra suggest that the tunneling of the fourth inequivalent rotor is strongly hindered and inaccessible to INS measurements. This is verified by proton NMR measurements of the spin-lattice relaxation time which reveal the tunneling characteristics of the fourth inequivalent rotor.     

Auxiliary Methoxy Aided Triphenylamine and Dicyanoisophorone Based Flurophores with Viscosity and Polarity Sensitive Intramolecular Charge Transfer

Novel, multibranched “triphenylamine based donor with added auxiliary methoxy donor and dicyanovinyl acceptor” based fluorescent molecules are developed. The dicyanoisophorone moiety is used as a configurationally locked polyene system for π-conjugation linking between donor and acceptor, to control the unnecessary intramolecular rotations in the molecule, which can to act as a rotor. The synthesized dyes show good fluorescent molecular rotor properties and strong emission solvatochromism. Auxiliary methoxy donors shift both the absorption and emission maxima towards longer wavelengths compared to known analogues, along with increased Stokes shifts. Fluorescent molecular rotor properties of the dyes are influenced by a local excited state to twisted intramolecular charge transfer state transition, which is discussed in terms of emission solvatochromism and Lippert–Mataga, Weller and Rettig polarity plots. Three different viscous solvent systems i.e., paraffin oil–dichloromethane, polyethylene glycol-400–dichloromethane and polyethylene glycol-400–N,N-dimethylformamide are used to investigate the sensitivity of rotors towards the viscosity of the environment. A maximum 16-fold enhancement in emission intensity and 0.616 × value is achieved for rotor Dye-3. The polarity effect of a binary viscous solvent system, by the virtue of intramolecular charge transfer, on the viscosity sensing properties of rotors is explained by constructing the Weller and Rettig’s plots for different viscous systems.     

Magnetic moments of hindered rotators by off‐center impurity ions

Off‐center impurity ions in solids often perform rotations around their regular lattice sites. Unlike quasifree rotors with rotational line spectra subject to textbook attention in quantum mechanics, the off‐center species are hindered rotors with spectra quantized in rotational bands. These bands occur because of tunneling through barriers arising along the orbital path. For an off‐center ion rotating along a planar orbit, such as the Li⁺ impurity nearest‐neighboring an F center in alkali halide, the hindered rotation will give rise to specific magnetic moments that couple to and quantize external magnetic fields normal to the orbital plane. We present a simple theory and estimates of Li⁺ magnetic dipoles and rotational bands to find conditions for an experimental verification. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Pnictogen Interactions with Nitrogen Acceptors

Stabilizing nitrogen pnictogen bond interactions were measured using molecular rotors. Intramolecular C=O⋅⋅⋅N interactions were formed in the bond rotation transition states which lowered the rotational barriers and increased the rates of rotation, as measured by EXSY NMR. The pnictogen interaction energies show a very strong correlation with the positive electrostatic potential on nitrogen, which was consistent with a strong electrostatic component. In contrast, the NBO perturbation and pyramidalization analyses show no correlation, suggesting that the orbital-orbital component is minor. The strongest C=O⋅⋅⋅N pnictogen interactions were comparable to C=O⋅⋅⋅C=O interactions and were stronger than C=O⋅⋅⋅Ph interactions, when measured using the same N-phenylimide rotor system. The ability of the nitrogen pnictogen interactions to stabilize transition states and enhance kinetic processes demonstrates their potential in catalysis and reaction design.