A redesign of light-driven rotary molecular motors

Structural modification of unidirectional light-driven rotary molecular motors in which the naphthalene moieties are exchanged for substituted phenyl moieties are reported. This redesign provides an additional tool to control the speed of the motors, and should enable the design and synthesis of more complex systems.     

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.     

Universal optimal working cycles of molecular motors

Molecular motors capable of directional track-walking or rotation are abundant in living cells, and inspire the emerging field of artificial nanomotors. Some biomotors can convert 90% of free energy from chemical fuels into usable mechanical work, and the same motors still maintain a speed sufficient for cellular functions. This study exposed a new regime of universal optimization that amounts to a thermodynamically best working regime for molecular motors but is unfamiliar in macroscopic engines. For the ideal case of zero energy dissipation, the universally optimized working cycle for molecular motors is infinitely slow like Carnot cycle for heat engines. But when a small amount of energy dissipation reduces energy efficiency linearly from 100%, the speed is recovered exponentially due to Boltzmann's law. Experimental data on a major biomotor (kinesin) suggest that the regime of universal optimization has been largely approached in living cells, underpinning the extreme efficiency-speed trade-off in biomotors. The universal optimization and its practical approachability are unique thermodynamic advantages of molecular systems over macroscopic engines in facilitating motor functions. The findings have important implications for the natural evolution of biomotors as well as the development of artificial counterparts.     

MHz unidirectional rotation of molecular rotary motors

A combination of cryogenic UV-vis and CD spectroscopy and transient absorption spectroscopy at ambient temperature is used to study a new class of unidirectional rotary molecular motors. Stabilization of unstable intermediates is achieved below 95 K in propane solution for the structure with the fastest rotation rate, and below this temperature measurements on the rate limiting step in the rotation cycle can be performed to obtain activation parameters. The results are compared to measurements at ambient temperature using transient absorption spectroscopy, which show that behavior of these motors is similar over the full temperature range investigated, thereby allowing a maximum rotation rate of 3 MHz at room temperature under suitable irradiation conditions.     

Non-non-crossings in molecular potential energy curves

This article points out a new aspect of approximate calculations of molecular potential curves. Two curves that cross in an exact solution of the electronic wave equation may avoid each other when an approximate method is used. This is in direct contradiction to the usual interpretation of the von Neumann-Wigner non-crossing rule. Examples of this behavior are shown in one-electron systems. The question is, to what extent are calculated avoidances real, and to what extent are they artifacts of incomplete calculations? We suggest that this question is unanswered at present and mention possible molecules for critical theoretical investigations.     

A unified electrostatic and cavitation model for first-principles molecular dynamics in solution

The electrostatic continuum solvent model developed by [Fattebert and Gygi J. Comput. Chem. 23, 662 (2002); Int. J. Quantum Chem. 93, 139 (2003)] is combined with a first-principles formulation of the cavitation energy based on a natural quantum-mechanical definition for the surface of a solute. Despite its simplicity, the cavitation contribution calculated by this approach is found to be in remarkable agreement with that obtained by more complex algorithms relying on a large set of parameters. Our model allows for very efficient Car-Parrinello simulations of finite or extended systems in solution and demonstrates a level of accuracy as good as that of established quantum-chemistry continuum solvent methods. We apply this approach to the study of tetracyanoethylene dimers in dichloromethane, providing valuable structural and dynamical insights on the dimerization phenomenon.     

New mechanistic insight in the thermal helix inversion of second-generation molecular motors

The introduction of dibenzocyclohepten-5-ylidene as part of a unidirectional light-driven molecular motor allows a more complete picture of the pathway of thermal helix inversion to be developed. The most stable conformation is similar to that found in related motors in that it has, overall, an anti-folded structure with the substituent at the stereogenic centre adopting an axial orientation. Photochemical cis/trans isomerisation at -40 degrees C results in the formation of an isomer in a syn-folded conformation with the methyl group in an axial orientation. This contrasts with previous studies on related molecular rotary motors. The conformation of the higher energy intermediate typically observed for this class of compound is the anti-folded conformation, in which the methyl group is in an equatorial orientation. This conformation is available through an energetically uphill upper half ring inversion of the observed photochemical product. However, this pathway competes with a second process that leads to the more stable anti-folded conformation in which the methyl group is oriented axially. It has been shown that the conformations and pathways available for second-generation molecular motors can be described by using similar overall geometries. Differences in the metastable high-energy species are attributable to the relative energy and position on the reaction coordinate of the transition states. Kinetic studies on these new molecular motors thus provide important insights into the conformational dynamics of the rotation cycle.     

Maximum directionality and systematic classification of molecular motors

Track-walking molecular motors are widely used in living cells for transport purposes, and artificial mimics are being vigorously pursued in engineered molecular systems. The defining character for a motor is its intrinsic capability to utilize energy input to rectify a sustained directional motion out of stochastic thermal motion. The energy injection can be coupled to a motor's mechanical steps in different ways, leading to different motor mechanisms. We derive here a formulation for maximum motor performance in terms of a new quantity called directionality based on a general representation of the track-walking motors. Compared to performance measures like velocity and processivity, directionality is a cleaner and more robust indicator of the rectification mechanism that amounts to a motor's inner design/working principles. Meaningful and distinctly different upper limits of directionality were found to exist for a wide variety of experimentally demonstrated and theoretically proposed motors and their biological counterparts. The maximum directionality provides a conceptual framework by which all of these different motors were quantitatively compared and systematically classified according to their mechanistic advancement. The results yield a series of guidelines for artificial motor development, and expose important evolutionary traits of biomotors.     

A unified mechanistic view on the Morita-Baylis-Hillman reaction: computational and experimental investigations

The thermodynamic properties and reaction mechanism of the Morita-Baylis-Hillman (MBH) reaction have been investigated through experimental and computational techniques. The impossibility to accelerate this synthetically valuable transformation by increasing the reaction temperature has been rationalized by variable-temperature experiments and MP2 theoretical calculations of the reaction thermodynamics. An increase in temperature results in a switching of the equilibrium to the reactants occurring at even moderate temperature levels. The complex reaction mechanism for the MBH reaction has been investigated through an in-depth analysis of the suggested alternative pathways, using the M06-2X computational method. The results provided by this theoretical approach are in agreement with all the experimental/kinetic evidence such as reaction order, acceleration by protic species (methanol, phenol), and autocatalysis. In particular, the existing controversy about the character of the key proton transfer in the MBH reaction (Aggarwal versus McQuade pathways) has been resolved. Depending on the specific reaction conditions both suggested pathways are competing mechanisms, and depending on the amount of protic species and the reaction progress (early or late stage) either of the two mechanisms will be favored.     

The art of building small: from molecular switches to molecular motors

Molecular switches and motors are essential components of artificial molecular machines. In this perspective, we discuss progress in our design, synthesis, and functioning of photochemical and electrochemical switches and chemical and light-driven molecular motors. Special emphasis is given to the control of a range of functions and properties, including luminescence, self-assembly, motion, color, conductance, transport, and chirality. We will also discuss our efforts to control mechanical movement at the molecular level, a feature that is at the heart of molecular motors and machines. The anchoring of molecular motors on surfaces and molecular motors at work are discussed.     

A unified view of the theoretical description of magnetic coupling in molecular chemistry and solid state physics

The magnetic interactions in organic diradicals, dinuclear inorganic complexes and ionic solids are presented from a unified point of view. Effective Hamiltonian theory is revised to show that, for a given system, it permits the definition of a general, unbiased, spin model Hamiltonian. Mapping procedures are described which in most cases permit one to extract the relevant magnetic coupling constants from ab initio calculations of the energies of the pertinent electronic states. Density functional theory calculations within the broken symmetry approach are critically revised showing the contradictions of this procedure when applied to molecules and solids without the guidelines of the appropriate mapping. These concepts are illustrated by describing the application of state-of-the-art methods of electronic structure calculations to a series of representative molecular and solid state systems.     

A unified scheme for the calculation of differentiated and undifferentiated molecular integrals over solid-harmonic Gaussians

Utilizing the fact that solid-harmonic combinations of Cartesian and Hermite Gaussian atomic orbitals are identical, a new scheme for the evaluation of molecular integrals over solid-harmonic atomic orbitals is presented, where the integration is carried out over Hermite rather than Cartesian atomic orbitals. Since Hermite Gaussians are defined as derivatives of spherical Gaussians, the corresponding molecular integrals become the derivatives of integrals over spherical Gaussians, whose transformation to the solid-harmonic basis is performed in the same manner as for integrals over Cartesian Gaussians, using the same expansion coefficients. The presented solid-harmonic Hermite scheme simplifies the evaluation of derivative molecular integrals, since differentiation by nuclear coordinates merely increments the Hermite quantum numbers, thereby providing a unified scheme for undifferentiated and differentiated four-center molecular integrals. For two- and three-center two-electron integrals, the solid-harmonic Hermite scheme is particularly efficient, significantly reducing the cost relative to the Cartesian scheme.     

A method for analysis of DMFC performance curves

Our recent analytical model of direct methanol fuel cell is used to fit experimental performance curves. Based on evolutionary genetic algorithm, a new fitting procedure is developed. The idea is to fit simultaneously a set of performance curves, which have several common fitting parameters. On the first stage of evolution all parameters are determined independently. Starting from certain step a mean values of common parameters are calculated and further evolution corrects the mean values. For different sets of experimental curves the method gives well reproducible results. The physical parameters resulted from fitting and the effect of crossover on cell performance are discussed.     

On velocity scaling in molecular dynamics simulations

The effect of scaling the molecular velocities to a fixed total energy in molecular dynamics simulations within the (N,V,E) ensemble has been investigated. The effect of using different time steps is also discussed. It is found that, even for small time steps, velocity scaling has a substantial influence on the resulting molecular trajectories, velocities, and forces. Furthermore, velocity rescaling and larger time step seem to have an additive effect on the calculated trajectories, but not on the average thermodynamic properties, such as temperature, pressure, and energy.     

Fine tuning of the rotary motion by structural modification in light-driven unidirectional molecular motors

The introduction of bulky substituents at the stereogenic center of light-driven second-generation molecular motors results in an acceleration of the speed of rotation. This is due to a more strained structure with elongated C=C bonds and a higher energy level of the ground state relative to the transition state for the rate-limiting thermal isomerization step. Understanding the profound influence that variation of the substituent at the stereogenic center holds over the rotational speed of the light-driven molecular motor has enabled the development of the fastest molecular motor reported thus far.