The miniaturization of components used in the construction of working devices is being pursued currently by the large-downward (top-down) fabrication. This approach, however, which obliges solid-state physicists and electronic engineers to manipulate progressively smaller and smaller pieces of matter, has its intrinsic limitations. An alternative approach is a small-upward (bottom-up) one, starting from the smallest compositions of matter that have distinct shapes and unique properties-namely molecules. In the context of this particular challenge, chemists have been extending the concept of a macroscopic machine to the molecular level. A molecular-level machine can be defined as an assembly of a distinct number of molecular components that are designed to perform machinelike movements (output) as a result of an appropriate external stimulation (input). In common with their macroscopic counterparts, a molecular machine is characterized by 1) the kind of energy input supplied to make it work, 2) the nature of the movements of its component parts, 3) the way in which its operation can be monitored and controlled, 4) the ability to make it repeat its operation in a cyclic fashion, 5) the timescale needed to complete a full cycle of movements, and 6) the purpose of its operation. Undoubtedly, the best energy inputs to make molecular machines work are photons or electrons. Indeed, with appropriately chosen photochemically and electrochemically driven reactions, it is possible to design and synthesize molecular machines that do work. Moreover, the dramatic increase in our fundamental understanding of self-assembly and self-organizational processes in chemical synthesis has aided and abetted the construction of artificial molecular machines through the development of new methods of noncovalent synthesis and the emergence of supramolecular assistance to covalent synthesis as a uniquely powerful synthetic tool. The aim of this review is to present a unified view of the field of molecular machines by focusing on past achievements, present limitations, and future perspectives. After analyzing a few important examples of natural molecular machines, the most significant developments in the field of artificial molecular machines are highlighted. The systems reviewed include 1) chemical rotors, 2) photochemically and electrochemically induced molecular (conformational) rearrangements, and 3) chemically, photochemically, and electrochemically controllable (co-conformational) motions in interlocked molecules (catenanes and rotaxanes), as well as in coordination and supramolecular complexes, including pseudorotaxanes. Artificial molecular machines based on biomolecules and interfacing artificial molecular machines with surfaces and solid supports are amongst some of the cutting-edge topics featured in this review. The extension of the concept of a machine to the molecular level is of interest not only for the sake of basic research, but also for the growth of nanoscience and the subsequent development of nanotechnology.

Artificial Molecular Machines.

In the present chapter, as well as throughout the entire book, we assume that the reader knows the basic facts about the Huckel molecular orbital (HMO) theory [35, 51, 62]. Hence HMO theory is an approximate quantum-mechanical approach to the description of the π-electrons in unsaturated conjugated molecules. The wave function for a π-electron is presented in the LCAO form 

$$ {\psi_i} = \sum\limits_{{j = 1}}^n {{c_{{ij}}}} \left| {{p_j} >} \right. $$

(1)

where {p j > symbolizes a p π -vorbital located on the j-th atom of the conjugated molecule, and the summation goes over all n atoms which participate in the conjugation.

Graph theory and molecular orbitals

Looking back to the introductory section, it appears that in recent years appreciable progress has been made in understanding and controlling the process of spherical recognition of alkali and alkaline-earth cations by organic ligand molecules. Information stored in various structural features allows the thermodynamic and kinetic features of the complexation process to be monitored. Further progress may be achieved by making use of the feedback from present results to adjust and improve the model and to analyze the information-property relationship.

Design of organic complexing agents Strategies towards properties

Comparison of Phosphorus and Silicon: Hypervalency, Stereochemistry, and Reactivity.

Kinetics and Mechanisms for the Cleavage and Isomerization of the Phosphodiester Bonds of RNA by Brønsted Acids and Bases

Berry pseudorotation and turnstile rotation

Non‐rigid Molecular Skeletons—Berry Pseudorotation and Turnstile Rotation

Displacement Reactions of Phosphorus(V) Compounds and Their Pentacoordinate Intermediates

Molekule konnen sich unter Erhaltung von Bindungen und Koordinationszahlen durch regulare Prozesse umordnen – oder aber durch irregulare Prozesse unter Spaltung und erneuter Knupfung von Bindungen sowie Durchlaufen von Zustanden mit veranderten Koordinationszahlen. Beide Arten von Prozessen an Molekulen mit n-platzigem Molekulgerust konnen mittels Permutationsoperatoren aus der symmetrischen Gruppe Sn beschrieben werden. Diese Operatoren werden in einfacher Weise aus den Deskriptoren der Molekule erhalten; die denkbaren Reaktionsmechanismen entsprechen Klassen konjugierter Permutationen. Regulare Prozesse – z. B. Umordnungsvorgange bei. Phosphoran-Derivaten mit monozentrischem Gerust oder konformationelle Umwandlungen bei Athan-Derivaten mit dizentrischem Gerust – beruhen auf der Beweglichkeit des Molekulgerustes. Flexible Molekulgeruste konnen durch eine Anzahl starrer Gerustmodelle reprasentiert werden, die durch Verformung von Bindungswinkeln und/oder Drehungen um Bindungsachsen ineinander uberfuhrbar sind. Fur das mechanistische Verstandnis regularer Prozesse ist es notwendig, die Symmetrien der starren Gerustmodelle und die gegebenen Ligandenaquivalenzen sowie auch Gerustflexibilitaten und deren Beeinflussung durch den Ligandensatz durch Permutationsgruppen, Untergruppen von Sn, wiederzugeben. Solches Vorgehen beruht auf Polyas, von DeBruijn und Ruch erweiterter Konzeption der Aufspaltung einer permutationellen Molekulsymmetrie in Gerustsymmetrie und Symmetrie des Ligandensatzes in Kombination mit der von Longuet-Higgins fur flexible, symmetrische Molekule – wie Ammoniakeingefuhrten totalen Molekulsymmetrie, woraus man die von uns definierte dynamische Gerustsymmetrie ableiten kann. Die regularen Prozesse pentakoordinierter Phosphorverbindungen werden auf der Grundlage dieser Vorstellungen in einer auch fur mathematisch wenig vorgebildete Chemiker verstandlichen Weise diskutiert, und es ergibt sich unter Berucksichtigung der quantenmechanischen Eigenschaften des P-Bindungssystems, insbesondere der Beteiligung der d-Orbitale, das neben dem bisher fur die Deutung der beobachteten Phanomene ausschlieslich herangezogenen BPR-Mechanismus[2] auch einfache und multiple TR-Prozesse[2] in Betracht zu ziehen sind. Es gibt Beobachtungen, die sowohl durch BPR- als auch durch TR-Prozesse interpretierbar sind, und es gibt Vorgange, die als regulare Prozesse nur auf der Grundlage des TR-Mechanismus zu verstehen sind, aber man kennt noch keine regularen Umordnungen, welche sich allein durch BPR-Prozesse und nicht durch TR-Prozesse deuten lassen.

Bewegliche Molekülgerüste – Pseudorotation und Turnstile-Rotation pentakoordinierter Phosphorverbindungen und verwandte Vorgänge†

The utility of the basic structures of modern mathematics for chemistry is discussed; general set theory, topology, and group theory are shown to pervade almost all static and dynamic aspects of chemistry. Chemical analogy, the systematic classification of molecules and a corresponding nomenclature system, conformational transformations, polyhedral rearrangements, and the relations between starting materials, transition complexes, and final products of chemical reactions are examples of where we apply the elements of modern mathematics to the solution of chemical problems.

Paul Gillespie

Papers

Berry pseudorotation and turnstile rotation

Non‐rigid Molecular Skeletons—Berry Pseudorotation and Turnstile Rotation

Displacement Reactions of Phosphorus(V) Compounds and Their Pentacoordinate Intermediates

Bewegliche Molekülgerüste – Pseudorotation und Turnstile-Rotation pentakoordinierter Phosphorverbindungen und verwandte Vorgänge†

Chemistry and Logical Structures