Principles of Quantum Chemistry

Nikos L. Doltsinis

Ricardo Vivas‐Reyes

Abstract In this contribution, the role of epistemology in understanding quantum chemistry is discussed. Quantum chemistry is the study of the behavior of atoms and molecules using the principles of quantum mechanics. Epistemology helps us evaluate claims to knowledge, distinguish between justified and unjustified beliefs, and assess the reliability of scientific methods. In quantum chemistry, the epistemology of knowledge is heavily influenced by the mathematical nature of quantum mechanics, and models can be tested, proven, and validated through experimentation. This paper also discusses key concepts used in quantum chemistry, such as the wave-particle duality of matter and the uncertainty principle. This work utilizes Kant’s philosophy of science to frame debates and discussions in quantum chemistry, particularly with regard to the interplay between empirical observation and theory. Additionally, the text explores how Kant’s ideas about the role of the mind in constructing our understanding of the world can help us comprehend the counterintuitive phenomena of quantum mechanics and its applications in quantum chemistry theory.

Thomas Peacock

Yasuaki Ito, Satoki Tsuji, Haruto Fujii +4 more

Computational quantum chemistry is a theoretical approach that utilizes the principles of quantum mechanics to perform computations on the electronic structure of molecules and atoms. This method enables the prediction of properties such as molecular structure, energy, electron orbitals, and electron density. In the field of the first principles, or ab initio, which relies solely on computation and not on experimental data, mathematical understanding allows even those without a background in chemistry to perform molecular orbital computations. The computation of quantum chemistry is computationally intensive, making them highly applicable in the field of high-performance computing. However, initiating quantum chemistry can be challenging for newcomers due to the numerous specialized terms and complex equations from quantum mechanics and chemistry. Therefore, this paper aims to provide a clear and accessible compilation of the fundamental and essential algorithm of the Hartree- Fock method, from theory to implementation. The goal is to offer the minimum required knowledge, in an approachable manner, serving as a starting point for those interested in computational quantum chemistry.

Ilya G. Kaplan

Abstract General ideas, on which the quantum chemistry without spin is based, are discussed. Three important applications of quantum chemistry without spin are presented in detail: (1) the methods for finding the molecular spin‐multiplets allowed by the Pauli principle; (2) the symmetry properties of the electron density that determines the Kohn‐Sham equations in the density functional theory; and (3) the foundations of the Pauli principle. In particular, it was demonstrated that, on the one hand, the Pauli exclusion principle cannot be derived from other fundamental principles of quantum mechanics; on the other hand, it cannot be considered as a postulate, since all other symmetry options for the total wave function of identical particles, except the one‐dimensional representations, are forbidden. © 2012 Wiley Periodicals, Inc. This article was published online on 18 June 2012. An error was subsequently identified. This notice is included in the online and print version to indicate that both have been corrected on 25 July 2012.