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Quantum Entanglement and Dissociation Behavior in Hydrogen Fluoride

Sidra Azam, S. M. Zangi, Tauqeer Ahmad, Khurram Shahzad Munawar, Hazrat Ali

Published Feb 19, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.26434/chemrxiv.15000221/v1

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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.
Quantum Information Theory is a new field with potential implications for the conceptual foundations of Quantum Mechanics through density matrices. In particular, information entropies in Hilbert space representation are highly advantageous in contrast with the ones in phase space representation since they can be easily calculated for large systems. In this work, novel von Neumann conditional, mutual, and joint entropies are employed to analyze the dissociation process of small molecules, Cl2 and HCl, by using the spectral decomposition of the first reduced density matrix in natural atomic orbital-based representation which allows us to assure rotational invariance, N- and v-representability in the Atoms-in-Molecules (AIM) scheme. Quantum information entropies permit to analyze the dissociation process through quantum mechanics concepts such as electron correlation and entanglement, showing interesting critical points which are not present in the energy profile, such as charge depletion and accumulation, along with bond breaking regions.
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.
Quantum correlations characterized by quantum entanglement and quantum discord play important roles in many quantum information processing. We study the relations among the entanglement of formation, concurrence, tangle, linear entropy-based classical correlation and von Neumann entropy-based classical correlation . We present analytical formulae of linear entropy-based classical correlation for arbitrary d⊗2d\otimes 2d⊗2 quantum states and von Neumann entropy-based classical correlation for arbitrary 2⊗22\otimes 22⊗2 rank-2 quantum states. From the von Neumann entropy-based classical correlation, we derive an explicit formula of quantum discord for arbitrary rank-2 two-qubit quantum states.
The accurate calculation of the (differential) correlation energy is central to the quantum chemical description of bond-formation and bond-dissociation processes. In order to estimate the quality of single- and multireference approaches for this purpose, various diagnostic tools have been developed. In this work, we elaborate on our previous observation [J. Phys. Chem. Lett.2012, 3, 3129] that one- and two-orbital-based entanglement measures provide quantitative means for the assessment and classification of electron correlation effects among molecular orbitals. The dissociation behavior of some prototypical diatomic molecules features all types of correlation effects relevant for chemical bonding. We demonstrate that our entanglement analysis is convenient to dissect these electron correlation effects and to provide a conceptual understanding of bond-forming and bond-breaking processes from the point of view of quantum information theory.
The interplay between electron interaction and geometry in a molecular system can lead to rather paradoxical situations. The prime example is the dissociation limit of the hydrogen molecule. While a significant increase of the distance r between the two nuclei marginalizes the electron–electron interaction, the exact ground state does, however, not take the form of a single Slater determinant. By first reviewing and then employing concepts from quantum information theory, we resolve this paradox and its generalizations to more complex systems in a quantitative way. To be more specific, we illustrate and prove that thermal noise due to finite, possibly even just infinitesimally low, temperature T will destroy the entanglement beyond a critical separation distance r crit ( T ) entirely. Our analysis is comprehensive in the sense that we simultaneously discuss both total correlation and entanglement in the particle picture as well as in the orbital/mode picture. Our results reveal a conceptually new characterization of static and dynamical correlation in ground states by relating them to the (non)robustness of correlation with respect to thermal noise.
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.