Design and evaluation of a crystalline hybrid of molecular conductors and molecular rotors

Combining recent concepts from the fields of molecular conductivity and molecular machinery we set out to design a crystalline molecular conductor that also possesses a molecular rotor. We report on the structures, electronic and physical properties, and dynamics of two solids with a common 1,4-bis(carboxyethynyl)bicyclo[2.2.2]octane (BABCO) functional rotor. One, [nBu(4)N(+)](2)[BABCO][BABCO(-)](2), is a colorless insulator where the dicarboxylic acid cocrystallizes with two of its monoanionic conjugated bases. The other is self-assembled by electrocrystallization in the form of black, shiny needles, with highly conducting molecular slabs of (EDT-TTF-CONH(2))(2)(+) (EDT-TTF = ethylenedithiotetrathiafulvalene) and anionic [BABCO(-)] rotors. Using variable-temperature (5-300 K) proton spin-lattice relaxation, (1)H T(1)(-1), we were able to assign two types of Brownian rotators in [nBu(4)N(+)](2)[BABCO][BABCO(-)](2). We showed that neutral BABCO groups have a rotational frequency of 120 GHz at 300 K with a rotational barrier of 2.03 kcal mol(-1). Rotors on the BABCO(-) sites experience stochastic 32 GHz jumps at the same temperature over a rotational barrier of 2.72 kcal mol(-1). In contrast, the BABCO(-) rotors within the highly conducting crystals of (EDT-TTF-CONH(2))(2)(+)[BABCO(-)] are essentially "braked" at room temperature. Notably, these crystals possess a conductivity of 5 S cm(-1) at 1 bar, which increases rapidly with pressure up to 50 S cm(-1) at 11.5 kbar. Two regimes with different activation energies E(a) for the resistivity (180 K above 50 and 400 K below) are observed at ambient pressure; a metallic state is stabilized at ca. 8 kbar, and an insulating ground state remains below 50 K at all pressures. We discuss two likely channels by which the motion of the rotors might become slowed down in the highly conducting solid. One is defined as a low-velocity viscous regime inherent to a noncovalent, physical coupling induced by the cooperativity between five C(sp3)-H···O hydrogen bonds engaging any rotor and five BABCO units in its environment. The rotational barrier calculated with the effect of this set of hydrogen bonds amounts to 7.3 kcal mol(-1). Another is quantum dissipation, a phenomenon addressing the difference of dynamics of the rotors in the two solids with different electrical properties, by which the large number of degrees of freedom of the low dimensional electron gas may serve as a bath for the dissipation of the energy of the rotor motion, the two systems being coupled by the Coulomb interaction between the charges of the rotors (local moments and induced dipoles) and the charges of the carriers.     

Quadrupole-bound anions: efficacy of positive versus negative quadrupole moments

A pseudopotential method is utilized to study the critical stability of model anions formed by long-range quadrupolar molecular potentials. Results indicate that critical quadrupole moments of simple point-charge triads do not serve well as predictors of real quadrupole-bound anions of systems with negative moments.     

Translational to rotational energy transfer in molecule-surface collisions

A theoretical approach that combines classical mechanics for treating translational and rotational degrees of freedom and quantum mechanics for describing the excitation of internal molecular modes is applied to the scattering of diatomic molecules from metal surfaces. Calculations are carried out for determining the extent of energy transfer to the rotational degrees of freedom of the projectile molecule. For the case of observed spectra of intensity versus final rotational energy, quantitative agreement with available experimental data for the scattering of NO and N(2) from close packed metal surfaces is obtained. It is shown that such measurements can be used to determine the average rotational energy of the incident molecular beam. Measurements of the exchange of energy between translational and rotational degrees of freedom upon collision are also described by calculations for these same systems.     

Ultra-fast rotors for molecular machines and functional materials via halogen bonding: crystals of 1,4-bis(iodoethynyl)bicyclo[2.2.2]octane with distinct gigahertz rotation at two sites

As a point of entry to investigate the potential of halogen-bonding interactions in the construction of functional materials and crystalline molecular machines, samples of 1,4-bis(iodoethynyl)bicyclo[2.2.2]octane (BIBCO) were synthesized and crystallized. Knowing that halogen-bonding interactions are common between electron-rich acetylenic carbons and electron-deficient iodines, it was expected that the BIBCO rotors would be an ideal platform to investigate the formation of a crystalline array of molecular rotors. Variable temperature single crystal X-ray crystallography established the presence of a halogen-bonded network, characterized by lamellarly ordered layers of crystallographically unique BIBCO rotors, which undergo a reversible monoclinic-to-triclinic phase transition at 110 K. In order to elucidate the rotational frequencies and the activation parameters of the BIBCO molecular rotors, variable-temperature (1)H wide-line and (13)C cross-polarization/magic-angle spinning solid-state NMR experiments were performed at temperatures between 27 and 290 K. Analysis of the (1)H spin-lattice relaxation and second moment as a function of temperature revealed two dynamic processes simultaneously present over the entire temperature range studied, with temperature-dependent rotational rates of k(rot) = 5.21 × 10(10) s(-1)·exp(-1.48 kcal·mol(-1)/RT) and k(rot) = 8.00 × 10(10) s(-1)·exp(-2.75 kcal·mol(-1)/RT). Impressively, these correspond to room temperature rotational rates of 4.3 and 0.8 GHz, respectively. Notably, the high-temperature plastic crystalline phase I of bicyclo[2.2.2]octane has a reported activation energy of 1.84 kcal·mol(-1) for rotation about the 1,4 axis, which is 24% larger than E(a) = 1.48 kcal·mol(-1) for the same rotational motion of the fastest BIBCO rotor; yet, the BIBCO rotor has three fewer degrees of translational freedom and two fewer degrees of rotational freedom! Even more so, these rates represent some of the fastest engineered molecular machines, to date. The results of this study highlight the potential of halogen bonding as a valuable construction tool for the design and the synthesis of amphidynamic artificial molecular machines and suggest the potential of modulating properties that depend on the dielectric behavior of crystalline media.     

Estimation of the absolute internal-rotation entropy of molecules with two torsional degrees of freedom from stochastic simulations

A method of statistical estimation is applied to the problem of evaluating the absolute entropy of internal rotation in a molecule with two torsional degrees of freedom. The configurational part of the entropy is obtained as that of the joint probability density of an arbitrary form represented by a two-dimensional Fourier series, the coefficients of which are statistically estimated using a sample of the torsional angles of the molecule obtained by a stochastic simulation. The internal rotors in the molecule are assumed to be attached to a common frame, and their reduced moments of inertia are initially calculated as functions of the two torsional angles, but averaged over all the remaining internal degrees of freedom using the stochastic-simulation sample of the atomic configurations of the molecule. The torsional-angle dependence of the reduced moments of inertia can be also averaged out, and the absolute internal-rotation entropy of the molecule is obtained in a good approximation as the sum of the configurational entropy and a kinetic contribution fully determined by the averaged reduced moments of inertia. The method is illustrated using Monte Carlo simulations of isomers of stilbene and halogenated derivatives of propane. The two torsional angles in cis-stilbene are found to be much more strongly correlated than those in trans-stilbene, while the degree of the angular correlation in propane increases strongly on substitution of hydrogen atoms with chlorine.     

Far-from-equilibrium processes without net thermal exchange via energy sorting

Many important processes at the microscale require far-from-equilibrium conditions to occur, as in the functioning of mesoscopic bioreactors, nanoscopic rotors, and nanoscale mass conveyors. Achieving such conditions, however, is typically based on energy inputs that strongly affect the thermal properties of the environment and the controllability of the system itself. Here, we present a general class of far-from-equilibrium processes that suppress the net thermal exchange with the environment by maintaining the Maxwell-Boltzmann velocity distribution intact. This new phenomenon, referred to as ghost equilibrium, results from the statistical cancellation of superheated and subcooled nonequilibrated degrees of freedom that are autonomously generated through a microscale energy sorting process. We provide general conditions to observe this phenomenon and study its implications for manipulating energy at the microscale. The results are applied explicitly to two mechanistically different cases, an ensemble of rotational dipoles and a gas of trapped particles, which encompass a great variety of common situations involving both rotational and translational degrees of freedom.     

Coherent Rayleigh-Brillouin scattering measurements of bulk viscosity of polar and nonpolar gases, and kinetic theory

We investigate coherent Rayleigh-Brillouin spectroscopy as an efficient process to measure the bulk viscosity of gases at gigahertz frequencies. Scattered spectral distributions are measured using a Fizeau spectrometer. We discuss the statistical error due to the fluctuating mode structure of the used pump laser. Experiments were done for both polar and nonpolar gases and the bulk viscosity was obtained from the spectra using the Tenti S6 model. Results are compared to simple classical kinetic models of molecules with internal degrees of freedom. At the extremely high (gigahertz) frequencies of our experiment, most internal vibrational modes remain frozen and the bulk viscosity is dominated by the rotational degrees of freedom. Our measurements show that the molecular dipole moments have unexpectedly little influence on the bulk viscosity at room temperature and moderate pressure.     

Dynamic arrest in a liquid of symmetric dumbbells: reorientational hopping for small molecular elongations

We present extensive equilibrium and out-of-equilibrium molecular-dynamics simulations of a liquid of symmetric dumbbell molecules, for constant packing fraction, as a function of temperature and molecular elongation. We compute diffusion constants as well as odd and even orientational correlators. The notations odd and even refer to the parity of the order l of the corresponding Legendre l polynomial, evaluated for the orientation of the molecular axis relative to its initial position. Rotational degrees of freedom of order l are arrested if, in the long-time limit, the corresponding orientational l correlator does not decay to zero. It is found that for large elongations translational and rotational degrees of freedom freeze at the same temperature. For small elongations only the even rotational degrees of freedom remain coupled to translational motions and arrest at a finite common temperature. On the contrary, the odd rotational degrees of freedom remain ergodic at all investigated temperatures. Hence, in the translationally arrested state, each molecule remains trapped in the cage formed by its neighboring molecules, but is able to perform 180 degrees rotations, which lead to relaxation only for the odd orientational correlators. The temperature dependence of the characteristic time of these residual rotations is well described by an Arrhenius law. Finally, we discuss the evidence in favor of the presence of the type-A transition for the odd rotational degrees of freedom, as predicted by mode-coupling theory for small molecular elongations. This transition is distinct from the type-B transition, associated with the arrest of the translational and even rotational degrees of freedom for small elongations, and with all degrees of freedom for large elongations. Odd orientational correlators are computed for small elongations at very low temperatures in the translationally arrested state. The obtained results suggest that hopping events restore the ergodicity of the odd rotational degrees of freedom at temperatures far below the A transition.     

On the degeneracy of the Hessian matrix

A widespread notion in the computational chemistry literature about the Hessian matrix has been revisited, namely, that the Hessian matrix over Cartesian space is sixfold degenerate due to the three translational and three rotational degrees of freedom. It has been shown that this is true only at critical points on the potential energy hypersurface, otherwise the Hessian matrix is only threefold degenerate. The rotational degrees of freedom generally do not cause degeneracy in the Hessian matrix away from critical points.On leave until January 1993 from the Department of General and Analytical Chemistry, Technical University Budapest, Szt. Gellért 4, H-1111 Budapest, Hungary.     

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     

Structural relaxation and glass transition behavior of binary hard-ellipse mixtures

Structural relaxation and glass transition in binary hard-spherical particle mixtures have been reported to exhibit unusual features depending on the size disparity and composition. However, the mechanism by which the mixing effects lead to these features and whether these features are universal for particles with anisotropic geometries remains unclear. Here, we employ event-driven molecular dynamics simulation to investigate the dynamical and structural properties of binary two-dimensional hard-ellipse mixtures. We find that the relaxation dynamics for translational degrees of freedom exhibit equivalent trends as those observed in binary hard-spherical mixtures. However, the glass transition densities for translational and rotational degrees of freedom present different dependencies on size disparity and composition. Furthermore, we propose a mechanism based on structural properties that explain the observed mixing effects and decoupling behavior between translational and rotational motions in binary hard-ellipse systems.     

Importance of correlated motions on the low barrier rotational potentials of crystalline molecular gyroscopes

The energetic and structural changes taking place upon rotation of the central phenylene of 1,4-bis(3,3,3-triphenylpropynyl)benzene in the solid state were computed using molecular mechanics calculations. Pseudopolymorphic crystals of a benzene clathrate (1A) and a desolvated form (1B) were analyzed with models that account for varying degrees of freedom within the corresponding lattices. The calculated rotational barriers in a rigid lattice approximation, 78 kcal/mol for 1A and 72 kcal/mol for 1B, are about 5 times greater than those previously measured by variable-temperature 13C CPMAS NMR and quadrupolar echo 2H NMR line-shape analysis: 12.8 kcal/mol for 1A and 14.6 kcal/mol for 1B. The potential energy barriers calculated with a model that restricts whole body rotation and translational motions but allows for internal rotations give results that are near the experimental free-energy barriers. The calculated barriers for 1A and 1B are 15.5 and 16.2 kcal/mol, respectively. The differences between the rigid and partially relaxed models are attributed to the effect of correlated motions of the lattice and the rotating group, which are evident from the structural analysis of the atomic position data as a function of the dihedral angle of the rotator. The displacements of neighboring molecules near the rotary transition states for 1A and 1B can be as large as 2.7 and 1.1 A, respectively. The displacement and oscillation (C2) of interpenetrating phenyl rings from neighboring rotors proximal to the event are significant for both 1A and 1B. In addition, 6-fold (C6) benzene rotations in clathrate 1A were found to be directly correlated to the rotation of the phenylene rotator.     

Molecular dynamics with quantum transitions study of the vibrational relaxation of the HOD bend fundamental in liquid D2O

The molecular dynamics with quantum transitions method is used to study the vibrational relaxation of the HOD bend fundamental in liquid D(2)O. All of the vibrational bending degrees of freedom of the HOD and D(2)O molecules are described by quantum mechanics, while the remaining translational and rotational degrees of freedom are described classically. The effect of the coupling between the rotational and vibrational degrees of freedom of the deuterated water molecules is analyzed. A kinetic mechanism based on three steps is proposed in order to interpret the dynamics of the system. It is shown that intermolecular vibrational energy transfer plays an important role in the relaxation process and also that the transfer of energy into the rotational degrees of freedom is favored over the transfer of energy into the translational motions. The thermalization of the system after the relaxation is reached in a shorter time scale than that of the recovery of the hydrogen bond network. The relaxation and equilibration times obtained compare well with experimental and previous theoretical results.     

Identifiability analysis of models for reversible intermolecular two-state excited-state processes coupled with species-dependent rotational diffusion monitored by time-resolved fluorescence depolarization

A deterministic identifiability analysis of the kinetic model for a reversible intermolecular two-state excited-state process with species-dependent rotational diffusion described by Brownian reorientation is presented. The cases of both spherically and cylindrically symmetric rotors, with no change in the principal axes of rotation on interconversion in the latter case, are specifically considered. The identifiability analysis is carried out in terms of compartmental modeling based on the S(t) identical with I( parallel)(t)+2I( perpendicular)(t) and D(t) identical with I( parallel)(t)-I( perpendicular)(t) functions, where I( parallel)(t) and I( perpendicular)(t) are the delta-response functions for fluorescence, polarized, respectively, parallel and perpendicular to the electric vector of linearly polarized excitation. It is shown that, from polarized time-resolved fluorescence data collected at two concentrations of coreactant and three appropriately chosen emission wavelengths, (a) a unique set of rate constants for the overall excited-state process is always obtained by making use of polarized measurements and (b) the rotational diffusion constants and geometrical factors associated with the different anisotropy decay components can be uniquely determined and assigned to each species. The geometrical factors are determined by the absorption and emission transitions in the two rotating species. For spherical rotors, these factors depend directly on the relative orientations of the transition moments, while for cylindrically symmetric rotors they depend on the orientations with respect to each other and to the symmetry axis.     

Rotational correlation and dynamic heterogeneity in a kinetically constrained lattice gas

We study the dynamical heterogeneity and glassy dynamics in a kinetically constrained lattice-gas model which has both translational and rotational degrees of freedom. We find that the rotational relaxation time tracks the structural relaxation time as density is increased whereas the translational diffusion constant exhibits a strong decoupling. We investigate distributions of exchange and persistence times for both the rotational and translational degrees of freedom and compare our results on the distributions of rotational exchange times to recent single molecule studies.     

光驱动单向分子转子的研究进展

分子转子是分子马达设计的要件, 有关分子转子的讨论已经引起广泛的关注. 主要介绍2003年以来单向转动型分子转子的研究状况, 重点讨论其构效关系和应用方面的最新进展, 展望了分子转子的发展前景并指出其面临的挑战.     

Product energy distribution for exothermic reactive collisions

A statistical-dynamic model for calculating product state distributions for reactive collisions is presented. For the vibrational-translational coupling Franck-Condon type approximations are adopted which lead to very good agreement with exact quantum calculations in the limit of the collinear arrangement. The rotational degrees of freedom are treated statistically. The energy distribution among vibrational translational and rotational degrees of freedom is discussed as a function of the masses and the attractive part of the potential. Extension from triatomic to polyatomic exchange reactions are considered. A detailed comparison with other simple models is made.     

Infrared spectroscopy of HCN-salt complexes formed in liquid-helium nanodroplets

Rotationally resolved infrared spectra are reported for the binary complexes of HCN and LiF, LiCl, NaF, and NaCl, formed in helium nanodroplets. Stark spectroscopy is used to determine the dipole moments for these complexes. Ab initio calculations are also reported for these complexes, revealing the existence of several different isomers of these binary systems. In the frequency region examined in this experimental study we only observe one of these, corresponding to the salt binding to the nitrogen end of the HCN molecule. The experimental rotational constants, dipole moments, and vibrational frequency shifts are all compared with the results from ab initio calculations for this isomer.