Abstract Quantum mechanical and classical aspects are of equal importance in chemistry, and theoretical chemistry must be able to deal with this situation. Classical quantities with which a chemist has to deal include, for example, the temperature and the chemical potential of a substance, and chirality, knot‐type and tertiary structures of molecules. Classical concepts of this type are no more consequences of traditional quantum chemistry than is the theory of complex chemical processes (for example adsorption, heterogeneous catalysis) and macroscopic systems. Algebraic quantum mechanics affords a general framework for the discussion of classical quantities and large systems. There are other independent approaches for the theoretical treatment of chemical problems; these can be summarized by using the keywords “fractals”, “chaotic motion”, “quasicrystals” and “knot theory”. The relationships between these four research topics and their connection with algebraic quantum mechanics, as well as their importance for theoretical chemistry, were discussed at a NATO Workshop in 1987 (see Ref. [1]). In an extended theoretical chemistry, the notion of “molecules” will not play a role as central as it does in quantum chemistry. In the theory of large systems in particular, the introduction of complementary approaches appears to be appropriate; the term “molecule” as used by the chemist does not appear either in the description of disordered systems by means of fractals or in the thermodynamic limit of algebraic statistical mechanics.
Abstract Quantum mechanical and classical aspects are of equal importance in chemistry, and theoretical chemistry must be able to deal with this situation. Classical quantities with which a chemist has to deal include, for example, the temperature and the chemical potential of a substance, and chirality, knot‐type and tertiary structures of molecules. Classical concepts of this type are no more consequences of traditional quantum chemistry than is the theory of complex chemical processes (for example adsorption, heterogeneous catalysis) and macroscopic systems. Algebraic quantum mechanics affords a general framework for the discussion of classical quantities and large systems. There are other independent approaches for the theoretical treatment of chemical problems; these can be summarized by using the keywords “fractals”, “chaotic motion”, “quasicrystals” and “knot theory”. The relationships between these four research topics and their connection with algebraic quantum mechanics, as well as their importance for theoretical chemistry, were discussed at a NATO Workshop in 1987 (see Ref. [1]). In an extended theoretical chemistry, the notion of “molecules” will not play a role as central as it does in quantum chemistry. In the theory of large systems in particular, the introduction of complementary approaches appears to be appropriate; the term “molecule” as used by the chemist does not appear either in the description of disordered systems by means of fractals or in the thermodynamic limit of algebraic statistical mechanics.
This introductory chapter provides an overview of quantum mechanics, which is a subject of central importance in chemistry, and is by nature a mathematical theory. The chemist's approach to the understanding of matter and its chemical transformations is to take a microscopic view, connecting experimental observation with the properties of constituent molecules. However, at the microscopic level, atoms, molecules, and their constituent particles do not obey the familiar laws of mechanics that pertain to the everyday macroscopic world. For example, the existence of molecular line spectra indicates that molecules can be found only at certain well-defined energies, unlike objects at our own scale whose energy appears to be continuously variable. This book aims to explain the fundamentals of quantum mechanics from the point of view of chemistry; describe the areas of chemistry where quantum mechanics is most important; and show how quantum mechanics is applied to chemical problems.
The Quantum Chemist’s Companion: Background Classical and Quantum Mechanics is the first part of a comprehensive two volume reference designed for students and researchers seeking a deeper, more intuitive understanding of quantum chemistry. Filling a long standing gap in the traditional chemistry curriculum, this volume builds the essential bridge between classical mechanics, quantum mechanics and the mathematical tools that underpin them. Ideal as both a course companion and a long-term desk reference, this book brings clarity to concepts that often challenge chemists especially those rarely explored in standard chemistry training. Detailed treatments of Lagrangian and Hamiltonian mechanics, the structure of vector spaces and the role of linear algebra in quantum theory make this volume an indispensable resource. Every derivation is presented step by step, ensuring that even the most mathematically inexperienced reader can follow the logic with confidence. Inside this volume: • Part 1 provides a guided introduction to the central ideas of classical and quantum mechanics, emphasizing how the two theories connect; • Part 2 dives deeper into classical mechanics, exploring key systems, such as the harmonic oscillator, that form the backbone of later quantum discussions; • Part 3 covers systematic development of quantum mechanics built directly on top of the foundations established in Parts 1 and 2; and • Part 4 consolidates the tools and techniques needed for the mathematical material in this volume and beyond. Whether you are navigating quantum mechanics for the first time or revisiting the fundamentals with a fresh perspective, this book supports learning at every stage. Use it cover to cover or consult it as a precise, cross referenced guide to specific topics. Either way, it provides the clarity and depth needed to transform quantum theory from an abstract challenge into a coherent, intuitive framework.
When compared to classical mechanics (CM), quantum mechanics (QM) clearly appears as a difficult topic to the beginner. However, some knowledge of the basics of QM is a real need also for learners with predominant interest in experimental chemistry. Indeed, QM is the physical theory explaining most fundamental aspects of Chemistry, such as the periodic table of the elements and the chemical bond now called covalent, found by 19th century chemists and for a long time recognized as incompatible with the physical theories of the time (CM and classical electromagnetism). Going beyond the historical point of view, many peculiar aspects of QM and its very language permeate all modern chemistry so that a trustworthy understanding is required to deal with the matter in a sensible way.
The field of quantum chemistry is concerned with the modelling and simulation of the behaviour of molecular systems on the basis of the fundamental equations of quantum mechanics. Since these equations exhibit an extreme case of the curse of dimensionality (the Schrödinger equation for N electrons being a partial differential equation on \mathbb R^{3N} ), the quantum-chemical simulation of even moderate-size molecules already requires highly sophisticated model-reduction, approximation, and simulation techniques. The workshop brought together selected quantum chemists and physicists, and the growing community of mathematicians working in the area, to report and discuss recent advances on topics such as coupled-cluster theory, direct approximation schemes in full configuration-interaction (FCI) theory, interacting Green’s functions, foundations and computational aspects of density-functional theory (DFT), low-rank tensor methods, quantum chemistry in the presence of a strong magnetic field, and multiscale coupling of quantum simulations.
The molecular view haunted chemists for a long time. Since this vision promised an outline of chemical reality in terms of basic building blocks, complementary approaches were neglected. Nowadays, the molecular program of chemistry has arrived at its successful termination so that the theoreticians find themselves challenged by new ways of looking at familiar facts of chemistry.Our modern theoretical first principles allow a precise mathematical definition of Bohr’s notion of complementarity and enforce a pluralism in looking at the nature of things. In particular, complementarity is revealed with conspicious clarity everywhere in chemistry. The complementary aspects of classical and quantal descriptions of molecules and the complementarity between molecules and chemical substances are discussed. The discourse is concluded with a hint of how chemistry could help in learning complementary ways of thinking and to place complementarity into a wider perspective.
The United Nations General Assembly has officially designated 2025 as the International Year of Quantum Science and Technology (IYQ). This global initiative, supported by UNESCO and co-sponsored by several countries, marks the centenary of quantum sciences, which encompass quantum mechanics, quantum chemistry, and related fields. These disciplines serve as the foundation for fundamental research across the natural sciences. Quantum mechanics provides the theoretical framework for understanding matter and energy at the microscopic scale. While public celebrations of the International Year of Quantum Science and Technology often showcase quantum technologies to engage a broader audience, it is crucial to remember that the emergence of quantum theory primarily represented a ground-breaking shift in the basic sciences. This article explores the complex relationship between quantum mechanics and concepts of traditional chemistry, particularly concerning the microscopic world of atoms and molecules. It highlights how quantum mechanics, a holistic and nonlocal theory, features concepts such as entanglement and the indistinguishability of components that challenge classical chemical notions of distinct interatomic interactions and well-defined molecular structures. While quantum mechanics excels at determining the overall stability and dynamics of the system, the article explains that quantum chemistry relies on the classical Born-Oppenheimer approximation to maintain the view of local interactions and identifiable atoms within a molecule. Then, the article discusses the historical development and limitations of transition state theory in explaining chemical reactions, highlighting chemistry’s specific focus on bond breaking and bond making as a fundamental explanatory principle.