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arXiv:2406.06171

Exact Entanglement correlation complements the chemical bond description

Józef Spałek, Maciej Hendzel

Published Jun 10, 2024• 0 citations
arXivHTMLPDF

Abstract

We analyze the properties of the exact solution obtained by us recently for the extended Hetiler-London model for chemical bonding which has an analytic form. The emphasis is put on defining two-particle entanglement correlation as the complementary characterization of the chemical bond and relating it to the partial atomicity and the so-called true covalency. The newly introduced characteristics remove the deficiency of the standard definition of covalency which now vanishes in the limit of the separated atoms. In effect, a gradual evolution of the system of two indistinguishable electrons in a bound state into their distinguishable correspondents can be traced systematically. The present analysis has a universal meaning and may also be applied to more complex systems.

DOI
10.48550/arxiv.2406.06171

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We analyze the properties of the exact solution obtained by us recently for the extended Hetiler-London model for chemical bonding which has an analytic form. The emphasis is put on defining two-particle entanglement correlation as the complementary characterization of the chemical bond and relating it to the partial atomicity and the so-called true covalency. The newly introduced characteristics remove the deficiency of the standard definition of covalency which now vanishes in the limit of the separated atoms. In effect, a gradual evolution of the system of two indistinguishable electrons in a bound state into their distinguishable correspondents can be traced systematically. The present analysis has a universal meaning and may also be applied to more complex systems.
We analyze the properties of the exact solution obtained by us recently for the extended Heitler-London model of the chemical bonding in an analytic form. The emphasis, put on defining the two-particle entanglement correlation, and expressing it by the von Neumann entropy, which provides the complementary characterization of the chemical bond and is directly related to the partial atomicity and the true covalency. The newly introduced concepts refine the standard analysis of covalency based solely on the wave-function and related energy description of the bond as a pure state. We show that a gradual evolution of the system with the increasing interatomic distance of the indistinguishable two electrons composing the bond into their distinguishable correspondents in the atomic (dissociation) limit can be traced out systematically. In particular, only by taking into account the atomicity the true covalency vanishes in the latter limit.
A precise discussion of a single bond requires consideration of two-particle wave function for the particles involved. Here we define and determine rigorously the intrinsic covalency and connected characteristics on the canonical example of H2 molecule. This is achieved by starting from analytic form for the two-particle wave function for electrons forming the bond, in which we single out the atomic contribution (\textit{atomicity}) in an unequivocal manner. The presence the of atomicity and ionicity factors complements the existing attributes of the bond. In this way, a gradual evolution of the molecular state to its two-atomic correspondant is traced systematically with increasing interatomic distance. In effect, a direct relation to the onset of incipient Mott-Hubbard atomicity (Mottness) to the intrinsic covalency and ionicity is established. This goal is achieved by combining the single--particle wave function readjustment with a simultaneous determination of two-particle states in the particle (second--quantization) representation
Abstract We analyze two-particle binding factors of H2, LiH, and HeH+ molecules/ions with the help of our original exact diagonalization ab initio approach. The interelectronic correlations are taken into account rigorously within the second quantization scheme for restricted basis of renormalized single-particle wave functions, i.e., with their size readjusted in the correlated state. This allows us to determine the many-particle covalency and ionicity factors in a natural and intuitive manner in terms of the microscopic single-particle and interaction parameters, also determined within our method. We discuss the limitations of those basic characteristics and introduce the concept of atomicity, corresponding to the Mott and Hubbard criterion concerning localization threshold in many-particle systems. This addition introduces an atomic ingredient into the electron states and thus removes a spurious behavior of covalency with the increasing interatomic distance, as well as provides a more complete physical interpretation of bonding.
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.
Abstract The second quantum revolution is all about exploiting the quantum nature of atoms and molecules to execute quantum information processing tasks. To boost this growing endeavor and by anticipating the key role of quantum chemistry therein, our work establishes a framework for systematically exploring, quantifying and dissecting correlation effects in molecules. By utilizing the geometric picture of quantum states we compare—on a unified basis and in an operationally meaningful way—total, quantum and classical correlation and entanglement in molecular ground states. To unlock and maximize the quantum informational resourcefulness of molecules an orbital optimization scheme is developed, leading to a paradigm-shifting insight: a single covalent bond equates to the entanglement 2 ln ( 2 ) . This novel and more versatile perspective on electronic structure suggests a generalization of valence bond theory, overcoming deficiencies of modern chemical bonding theories.
The chemical bond is an important local concept to understand chemical compounds and processes. Unfortunately, like most local concepts, the chemical bond and the bond order do not correspond to any physical observable and thus cannot be determined as an expectation value of a quantum chemical operator. We recently demonstrated [Boguslawski et al., J. Chem. Theory Comput., 2013, 9, 2959-2973] that one- and two-orbital-based entanglement measures can be applied to interpret electronic wave functions in terms of orbital correlation. Orbital entanglement emerged as a powerful tool to provide a qualitative understanding of bond-forming and bond-breaking processes, and allowed for an estimation of bond orders of simple diatomic molecules beyond the classical bonding models. In this article we demonstrate that the orbital entanglement analysis can be extended to polyatomic molecules to understand chemical bonding.