A variational formulation for modeling a protium hydrogen molecular ionization and detailed notes on the Energy equation and the first Maxwell one

This article develops a variational formulation for modeling a protium hydrogen molecular ionization obtained through a high temperature scalar field and an appropriate electric one action. The results are based on standard tools of calculus of variations and optimization theory. Finally, we highlight the context here addressed is essentially an Euler-Bernoullian one and includes the establishment of a new approximate Bernoulli-interacting-gas type equation.