The present manuscript revisits one of the earliest approaches to treating molecular systems within the Schrödinger formalism of quantum mechanics: the Heitler-London (HL) model. Originally proposed in 1927 and based on a linear combination of atomic orbitals, the HL model provided a foundational description of covalent bonds and has served as the basis for numerous variational methods. Focusing on the hydrogen molecule, we begin by revisiting the analytical calculations of the original HL model, from which the qualitative physics of bonding and antibonding states can be obtained. Subsequently, we propose including electronic screening effects directly in the original HL wave function. We then compare our proposal with variational quantum Monte Carlo (VQMC) calculations, whose trial wave function allows us to optimize the electronic screening potential as a function of the inter-proton distance. We obtain the bond length, binding energy, and vibrational frequency of the H $_2$ molecule. Beyond revisiting this foundational approach in quantum mechanics, our proposal can serve as improved input for constructing new, but still analytically simple, variational wave functions to describe dissociation or bond formation.The present manuscript revisits one of the earliest approaches to treating molecular systems within the Schrödinger formalism of quantum mechanics: the Heitler-London (HL) model. Originally proposed in 1927 and based on a linear combination of atomic orbitals, the HL model provided a foundational description of covalent bonds and has served as the basis for numerous variational methods. Focusing on the hydrogen molecule, we begin by revisiting the analytical calculations of the original HL model, from which the qualitative physics of bonding and antibonding states can be obtained. Subsequently, we propose including electronic screening effects directly in the original HL wave function. We then compare our proposal with variational quantum Monte Carlo (VQMC) calculations, whose trial wave function allows us to optimize the electronic screening potential as a function of the inter-proton distance. We obtain the bond length, binding energy, and vibrational frequency of the H$_2$ molecule. Beyond revisiting this foundational approach in quantum mechanics, our proposal can serve as improved input for constructing new, but still analytically simple, variational wave functions to describe dissociation or bond formation.

physics.chem-phCross-listedarXiv:2511.01132Nov 4, 2025

Quantum Distribution Functions

Springer eBooksDec 9, 20070 citations

Entropy and Wigner Distribution Functions Revisited

Joachim J. Włodarz

International Journal of Theoretical PhysicsMay 1, 200333 citations

Quantum-mechanical distribution functions: Conditions for uniqueness

Robert F. O’Connell, Eugene Paul Wigner

Physics Letters AMay 1, 1981172 citations

Quantum Non-Locality in Systems with Open Boundaries: Failure of the Wigner-Function Formalism

Luigi Genovese, David Taj, Fausto Rossi

We shall revisit the conventional treatment of open quantum devices based on the Wigner-Function formalism. Our analysis will show that the artificial spatial separation between device active region and external reservoirs -properly defined within a semiclassical simulation scheme- is intrinsically incompatible with the non-local character of quantum mechanics. More specifically, by means of an exactly-solvable semiconductor model, we shall show that the application of the conventional boundary-condition scheme to the Wigner transport equation may produce highly non-physical results, like thermal injection of coherent state superpositions and boundary-driven negative probability distributions.We shall revisit the conventional treatment of open quantum devices based on the Wigner-Function formalism. Our analysis will show that the artificial spatial separation between device active region and external reservoirs -properly defined within a semiclassical simulation scheme- is intrinsically incompatible with the non-local character of quantum mechanics. More specifically, by means of an exactly-solvable semiconductor model, we shall show that the application of the conventional boundary-condition scheme to the Wigner transport equation may produce highly non-physical results, like thermal injection of coherent state superpositions and boundary-driven negative probability distributions.

arXiv:cond-mat/0506757Jun 29, 20050 citations

_2

molecule. Beyond revisiting this foundational approach in quantum mechanics, our proposal can serve as improved input for constructing new, but still analytically simple, variational wave functions to describe dissociation or bond formation.