Exact ODE Framework for Classical and Quantum Corrections for the Lennard-Jones Second Virial Coefficient
Year: 2025
Type: article
Abstract: The second virial coefficient (SVC) of the Lennard-Jones fluid is a cornerstone of molecular theory, yet its calculation has traditionally relied on the complex integration of the pair potential. This work introduces a fundamentally different approach by reformulating the problem in terms of ordinary differential equations (ODEs). For the classical component of the SVC, we generalize the confluent hypergeometric and Weber-Hermite equations. For the first quantum correction, we present entirely new ODEs and their corresponding exact-analytical solutions. The most striking result of this framework is the discovery that these ODEs can be transformed into Schrödinger-like equations. The classical term corresponds to a harmonic oscillator, while the quantum correction includes additional inverse-power potential terms. This formulation not only provides a versatile method for expressing the virial coefficient through a linear combination of functions (including Kummer, Weber, and Whittaker functions) but also reveals a profound and previously unknown mathematical structure underlying a classical thermodynamic property.
Source: Entropy
DOI: 10.3390/e27101059
Language: English
Subfield: Biomedical Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
OpenAlex ID: W4415100997