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arXiv:2405.00203

All molecules are entangled in the number of electrons following a general physical principle

Jing Kong

Published Apr 30, 2024• 1 citation
arXivHTMLPDF

Abstract

A physically motivated equation that determines the number of electrons of a molecule is proposed based on some generally accepted basic chemical knowledge. It permits a complete local definition of molecules and shows that all molecules are entangled in the number of electrons. It also results in the extensivity and convexity of molecular energy, which underpin molecular quantum mechanics. The proposed physical principle includes the molecular size consistency principle as a special case and reveals an intrinsic relationship between molecular locality, size consistency, and energy convexity. Application of wavefunction theory to the new principle shows that an individual molecule with a noninteger number of electrons is locally physical. The energy of a molecule is piecewise linear with respect to its number of electrons. The realness of the number of electrons allows the definition of the electronic chemical potential of a single molecule. A state function equivalent to the energy of a molecule can be defined using the chemical potential as a variable and used to express the physical principle as a simple additivity. The latter also shows that the quantum entanglement in the number of electrons can be viewed as all molecules sharing one chemical potential. When the energy of a molecule with a definite number of electrons is not convex with respect to the number of electrons, the state of the molecule is not always locally determinable even with a known number of electrons.

DOI
10.48550/arxiv.2405.00203

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A physically motivated equation that determines the number of electrons of a molecule is proposed based on some generally accepted basic chemical knowledge. It permits a complete local definition of molecules and shows that all molecules are entangled in the number of electrons. It also results in the extensivity and convexity of molecular energy, which underpin molecular quantum mechanics. The proposed physical principle includes the molecular size consistency principle as a special case and reveals an intrinsic relationship between molecular locality, size consistency, and energy convexity. Application of wavefunction theory to the new principle shows that an individual molecule with a noninteger number of electrons is locally physical. The energy of a molecule is piecewise linear with respect to its number of electrons. The realness of the number of electrons allows the definition of the electronic chemical potential of a single molecule. A state function equivalent to the energy of a molecule can be defined using the chemical potential as a variable and used to express the physical principle as a simple additivity. The latter also shows that the quantum entanglement in the number of electrons can be viewed as all molecules sharing one chemical potential. When the energy of a molecule with a definite number of electrons is not convex with respect to the number of electrons, the state of the molecule is not always locally determinable even with a known number of electrons.
We theoretically investigate the quantum correlations (in terms of concurrence of indistinguishable electrons) in a prototype molecular system (hydrogen molecule). With the assistance of the standard approximations of the linear combination of atomic orbitals and the configuration interaction methods we describe the electronic wavefunction of the ground state of the H 2 molecule. Moreover, we managed to find a rather simple analytic expression for the concurrence (the most used measure of quantum entanglement) of the two electrons when the molecule is in its lowest energy. We have found that concurrence does not really show any relation to the construction of the chemical bond.
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The use of the mutual information (MI) as a measure of the entanglement in quantum systems has gained a consensus in recent years, even if there is an ongoing effort to distinguish the classical and quantum contributions contained therein. This quantity has been first introduced in condensed matter physics, in particular, in studies based on the density matrix renormalization group method. This method has been successfully adapted to quantum chemistry problems, opening the way to compute MI also in molecular systems. A key aspect of this quantity is its dependence on the one-electron (orbital) basis set, even for wave functions that are invariant under unitary transformation of the orbitals. In this work, we investigate the role of the orbital basis set (delocalized or localized, following different strategies) for wave functions expressed as linear combinations of Slater determinants and we give the analytic expression for the MI for a few special cases. This study aims to improve the knowledge of the relationship between the characteristics of the chemical bond (considering a few paradigmatic molecules, H 2, F 2, N 2, and short linear polyenes) and the properties of interest in the field of quantum information theory.
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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.