Chemical processes in closed systems inevitably relax to equilibrium. Living systems avoid this fate and give rise to a much richer diversity of phenomena by operating under nonequilibrium ...conditions. Recent experiments in dissipative self-assembly also demonstrated that by opening reaction vessels and steering certain concentrations, an ocean of opportunities for artificial synthesis and energy storage emerges. To navigate it, thermodynamic notions of energy, work and dissipation must be established for these open chemical systems. Here, we do so by building upon recent theoretical advances in nonequilibrium statistical physics. As a central outcome, we show how to quantify the efficiency of such chemical operations and lay the foundation for performance analysis of any dissipative chemical process.
Information is physical, a realization that has transformed the physics of measurement and communication. However, the flow between information, energy and mechanics in chemical systems remains ...largely unexplored. Here we analyse a minimalist autonomous chemically driven molecular motor in terms of information thermodynamics, a framework that quantitatively relates information to other thermodynamic parameters. The treatment reveals how directional motion is generated by free energy transfer from chemical to mechanical (conformational and/or co-conformational) processes by 'energy flow' and 'information flow'. It provides a thermodynamic level of understanding of molecular motors that is general, complements previous analyses based on kinetics and has practical implications for machine design. In line with kinetic analysis, we find that power strokes do not affect the directionality of chemically driven machines. However, we find that power strokes can modulate motor velocity, the efficiency of free energy transfer and the number of fuel molecules consumed per cycle. This may help explain the role of such (co-)conformational changes in biomachines and illustrates the interplay between energy and information in chemical systems.
Reaction currents in chemical networks usually increase when increasing their driving affinities. But far from equilibrium the opposite can also happen. We find that such negative differential ...response (NDR) occurs in reaction schemes of major biological relevance, namely, substrate inhibition and autocatalysis. We do so by deriving the full counting statistics of two minimal representative models using large deviation methods. We argue that NDR implies the existence of optimal affinities that maximize the robustness against environmental and intrinsic noise at intermediate values of dissipation. An analogous behavior is found in dissipative self-assembly, for which we identify the optimal working conditions set by NDR.
Chemically fueled autonomous molecular machines are catalysis-driven systems governed by Brownian information ratchet mechanisms. One fundamental principle behind their operation is kinetic ...asymmetry, which quantifies the directionality of molecular motors. However, it is difficult for synthetic chemists to apply this concept to molecular design because kinetic asymmetry is usually introduced in abstract mathematical terms involving experimentally inaccessible parameters. Furthermore, two seemingly contradictory mechanisms have been proposed for chemically driven autonomous molecular machines: Brownian ratchet and power stroke mechanisms. This Perspective addresses both these issues, providing accessible and experimentally useful design principles for catalysis-driven molecular machinery. We relate kinetic asymmetry to the Curtin–Hammett principle using a synthetic rotary motor and a kinesin walker as illustrative examples. Our approach describes these molecular motors in terms of the Brownian ratchet mechanism but pinpoints both chemical gating and power strokes as tunable design elements that can affect kinetic asymmetry. We explain why this approach to kinetic asymmetry is consistent with previous ones and outline conditions where power strokes can be useful design elements. Finally, we discuss the role of information, a concept used with different meanings in the literature. We hope that this Perspective will be accessible to a broad range of chemists, clarifying the parameters that can be usefully controlled in the design and synthesis of molecular machines and related systems. It may also aid a more comprehensive and interdisciplinary understanding of biomolecular machinery.
The structures and relative stabilities as well as the rotational and vibrational spectra of the three low-energy conformers of pyruvic acid (PA) have been characterized using a state-of-the-art ...quantum-mechanical approach designed for flexible molecules. By making use of the available experimental rotational constants for several isotopologues of the most stable PA conformer, Tc-PA, the semiexperimental equilibrium structure has been derived. The latter provides a reference for the pure theoretical determination of the equilibrium geometries for all conformers, thus confirming for these structures an accuracy of 0.001 Å and 0.1 deg for bond lengths and angles, respectively. Highly accurate relative energies of all conformers (Tc-, Tt-, and Ct-PA) and of the transition states connecting them are provided along with the thermodynamic properties at low and high temperatures, thus leading to conformational enthalpies accurate to 1 kJ mol–1. Concerning microwave spectroscopy, rotational constants accurate to about 20 MHz are provided for the Tt- and Ct-PA conformers, together with the computed centrifugal-distortion constants and dipole moments required to simulate their rotational spectra. For Ct-PA, vibrational frequencies in the mid-infrared region accurate to 10 cm–1 are reported along with theoretical estimates for the transitions in the near-infrared range, and the corresponding infrared spectrum including fundamental transitions, overtones, and combination bands has been simulated. In addition to the new data described above, theoretical results for the Tc- and Tt-PA conformers are compared with all available experimental data to further confirm the accuracy of the hybrid coupled-cluster/density functional theory (CC/DFT) protocol applied in the present study. Finally, we discuss in detail the accuracy of computational models fully based on double-hybrid DFT functionals (mainly at the B2PLYP/aug-cc-pVTZ level) that avoid the use of very expensive CC calculations.
Molecular nonequilibrium systems hold great promises for the nanotechnology of the future. Yet, their development is slowed by the absence of an informative representation. Indeed, while potential ...energy surfaces comprise in principle all the information, they hide the dynamic interplay of multiple reaction pathways underlying nonequilibrium systems, i.e., the degree of kinetic asymmetry. To offer an insightful visual representation of kinetic asymmetry, we extended an approach pertaining to catalytic networks, the energy span model, by focusing on system dynamics – rather than thermodynamics. Our approach encompasses both chemically and photochemically driven systems, ranging from unimolecular motors to simple self‐assembly schemes. The obtained diagrams give immediate access to information needed to guide experiments, such as states’ population, rate of machine operation, maximum work output, and effects of design changes. The proposed kinetic barrier diagrams offer a unifying graphical tool for disparate nonequilibrium phenomena.
A graphical approach is presented that allows visualizing molecular nonequilibrium systems displaying kinetic asymmetry with monodimentional profiles, retrieving at a glance information on directionality, speed, states population, controlling steps, and the energy available to do work. The work comprises a tutorial in the form of a Jupyter Notebook that can be used to familiarize with the concept of kinetic asymmetry.
Lecture notes after the doctoral school (Post)Modern Thermodynamics held at the University of Luxembourg, December 2022, 5-7, covering and advancing continuous-time Markov chains, network theory, ...stochastic thermodynamics, large deviations, deterministic and stochastic chemical reaction networks, metastability, martingales, quantum thermodynamics, and foundational issues.
The B2PLYP double hybrid functional, coupled with the correlation-consistent triple-ζ cc-pVTZ (VTZ) basis set, has been validated in the framework of the semiexperimental (SE) approach for deriving ...accurate equilibrium structures of molecules containing up to 15 atoms. A systematic comparison between new B2PLYP/VTZ results and several equilibrium SE structures previously determined at other levels, in particular B3LYP/SNSD and CCSD(T) with various basis sets, has put in evidence the accuracy and the remarkable stability of such model chemistry for both equilibrium structures and vibrational corrections. New SE equilibrium structures for phenylacetylene, pyruvic acid, peroxyformic acid, and phenyl radical are discussed and compared with literature data. Particular attention has been devoted to the discussion of systems for which lack of sufficient experimental data prevents a complete SE determination. In order to obtain an accurate equilibrium SE structure for these situations, the so-called templating molecule approach is discussed and generalized with respect to our previous work. Important applications are those involving biological building blocks, like uracil and thiouracil. In addition, for more general situations the linear regression approach has been proposed and validated.
This work aims at extending the semi-experimental (SE) approach for deriving accurate equilibrium structures to large molecular systems of organic and biological interest. SE equilibrium structures ...are derived by a least-squares fit of the structural parameters to the experimental ground-state rotational constants of several isotopic species corrected by vibrational contributions computed by quantum mechanical (QM) methods. A systematic benchmark study on 21 small molecules (CCse set) is carried out to evaluate the performance of hybrid density functionals (in particular B3LYP) in the derivation of vibrational corrections to rotational constants. The resulting SE equilibrium structures show a very good agreement with the corresponding geometries obtained employing post-Hartree–Fock vibrational corrections. The use of B3LYP in conjunction with the double-ζ SNSD basis set strongly reduces the computational costs, thus allowing for the evaluation of accurate SE equilibrium structures for medium-sized molecular systems. On these grounds, an additional set of 26 SE equilibrium structures including the most common organic moieties has been set up by collecting the most accurate geometries available in the literature together with new determinations from the present work. The overall set of 47 SE equilibrium structures determined using B3LYP/SNSD vibrational corrections (B3se set) provides a high quality benchmark for validating the structural predictions of other experimental and/or computational approaches. Finally, we present a new strategy (referred to as the template approach) to deal with the cases for which it is not possible to fit all geometrical parameters due to the lack of experimental data.
The first study in which stochastic simulations of a two‐component molecular machine are performed in the mass‐action regime is presented. This system is an autonomous molecular pump consisting of a ...photoactive axle that creates a directed flow of rings through it by exploiting light energy away from equilibrium. The investigation demonstrates that the pump can operate in two regimes, both experimentally accessible, in which light‐driven steps can be rate‐determining or not. The number of photons exploited by an individual molecular pump, as well as the precision of cycling and the overall efficiency, critically rely on the operating regime of the machine. This approach provides useful information not only to guide the chemical design of a self‐assembling molecular device with desired features, but also to elucidate the effect of the environment on its performance, thus facilitating its experimental investigation.
The fate of individual molecules is typically neglected in the context of mass action chemical kinetics. Adopting a molecular viewpoint in the analysis of reaction networks allows the mechanisms underlying collective behaviors to be disclosed, such as using an energy source to reach nonequilibrium states. Insights are gained on the use of photons to afford dissipative pumping in an artificial supramolecular motor.
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