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Quantum Entanglement and Reactivity of the Water Molecule

Sidra Azam, Tauqeer Ahmad, S. M. Zangi

Published Nov 25, 2025• 0 citations
Publisher

Abstract

Entanglement is a quantum mechanical correlation that effects the chemical reactivity of a molecule. In this study, we vary the bond length and bond angle of the water molecule in order to see how changes in its shape affect entanglement and reactivity. Entanglement is measured with three quantifiers of entanglement that are Von Neumann Entropy, Negativity and Concurrence. The results indicate that at compressed geometry, entanglement is higher due to high electron sharing and a reactive state. At near equilibrium, entanglement is moderate and the structure is stable. When the bond is stretched, entanglement is least because of electron localization and low reactivity. Each metric highlights a unique aspect of electron behavior. Entropy is the measure of total correlation, negativity is the early bond and concurrence is the pair electrons relation. It has been found that quantum entanglement can effectively describe chemical bonding and predict molecular reactivity beyond traditional energy-based approaches.

DOI
10.22541/au.176405960.08116969/v1

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Entanglement is a quantum mechanical correlation that effects the chemical reactivity of a molecule. In this study, we vary the bond length and bond angle of the water molecule in order to see how changes in its shape affect entanglement and reactivity. Entanglement is measured with three quantifiers of entanglement that are Von Neumann Entropy, Negativity and Concurrence. The results indicate that at compressed geometry, entanglement is higher due to high electron sharing and a reactive state. At near equilibrium, entanglement is moderate and the structure is stable. When the bond is stretched, entanglement is least because of electron localization and low reactivity. Each metric highlights a unique aspect of electron behavior. Entropy is the measure of total correlation, negativity is the early bond and concurrence is the pair electrons relation. It has been found that quantum entanglement can effectively describe chemical bonding and predict molecular reactivity beyond traditional energy-based approaches.
The water molecule and a hydrogenic abstraction reaction are used to explore in detail some quantum entanglement features of chemical interest. We illustrate that the energetic and quantum-information approaches are necessary for a full understanding of both the geometry of the quantum probability density of molecular systems and the evolution of a chemical reaction. The energy and entanglement hypersurfaces and contour maps of these two models show different phenomena. The energy ones reveal the well-known stable geometry of the models, whereas the entanglement ones grasp the chemical capability to transform from one state system to a new one. In the water molecule the chemical reactivity is witnessed through quantum entanglement as a local minimum indicating the bond cleavage in the dissociation process of the molecule. Finally, quantum entanglement is also useful as a chemical reactivity descriptor by detecting the transition state along the intrinsic reaction path in the hypersurface of the hydrogenic abstraction reaction corresponding to a maximally entangled state.
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.
The dynamics of quantum entropy, energy, and entanglement is studied for various initial states in an important spectroscopic Hamiltonian of bent triatomic molecules H2O, D2O, and H2S. The total quantum correlation is quantified in terms of the mutual information and the entanglement by the concurrence borrowed from the theory of quantum information. The Pauli entropy and the intramolecular energy usually used in the theory of molecules are calculated to establish a possible relationship between both theories. Sections of two quantities among these four quantities are introduced to visualize such relationship. Analytic and numerical simulations demonstrate that if an initial state is taken to be the stretch- or the bend-vibrationally localized state, the mutual information, the Pauli entropy, and the concurrence are dominant-positively correlated while they are dominantly anti-correlated with the interacting energy among three anharmonic vibrational modes. In particular, such correlation is more distinct for the localized state with high excitations in the bending mode. The nice quasi-periodicity of those quantities in D2O molecule reveals that this molecule prepared in the localized state in the stretching or the bending mode can be more appreciated for molecular quantum computation. However, the dynamical correlations of those quantities behave irregularly for the dislocalized states. Moreover, the hierarchy of the mutual information and the Pauli entropy is explicitly proved. Quantum entropy and energy in every vibrational mode are investigated. Thereby, the relation between bipartite and tripartite entanglements is discussed as well. Those are useful for the understanding of quantum correlations in high-dimensional states in polyatomic molecules from quantum information and intramolecular dynamics.
By using quantum information theory metrics, we have studied the relationship between quantum correlation and bond dissociation in hydrogen fluoride. Von Neumann entropy, concurrence and quantum discord are calculated as the bond length of H-F is stretched. These are analyzed in comparison with classical descriptor like dipole moment of H-F and Mulliken charge fluorine. Laplacian contour maps also visualize electron concentration and depletion during bond stretching. At equilibrium bond length, quantum correlations and bond polarization both are optimally balanced. As the bond length increases, charge localize on Fluorine but entanglement reduces leading to bond dissociation. At large separations, quantum correlation which are still residual persist near dissociation. These findings provides a critical role of quantum correlations that are involve in stabilizing strongly polar bond. It gives quantitative insights into interplay electronic structure and quantum information theory properties during bond dissociation.
Recent proposals of measuring bipartite Renyi entropy experimentally involve techniques that hold exactly for non-interacting quantum particles. Here we consider the difference between such measurements and the actual Renyi entropy for ground state fermion ab initio molecular systems. To calculate various entanglement measures we extended several different techniques for use with variational Monte Carlo, Hartree-Fock and quantum chemistry methods. Our results show that in systems with strong electron correlations the Renyi entropy may not be accurately determined with the proposed measurements. In addition, we find significant physical insight can be gained by calculating entanglement properties in molecular systems. We see that the Renyi entropy and the entanglement Hamiltonian encode information about the character of the covalent bonds in a molecular system and that such information may lead to better descriptions of bonded systems that have been traditionally hard to describe with standard techniques. In particular our results for the C2_{2}2​ dimer suggests all eight valence electrons play a significant role in covalent bonding.
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.