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The stability of the hydrogen molecule interacting with the environment according to the balanced gain and loss energy scheme was studied. We determined the properties of the molecule taking into account all electronic interactions, the parameters of the Hamiltonian being computed by the variational method. The interaction of the hydrogen molecule with the environment was modeled parametrically ( γ ) by means of the non-Hermitian,    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$${\mathscr{P}}{\mathscr{T}}$$\end{document}        -symmetric Hamiltonian. We showed that the hydrogen molecule is dynamically unstable. Its dissociation time ( T   D  ) decreases if the  γ  parameter increases (for  γ  → 0 we got  T   D   → + ∞). The dynamic instability of the hydrogen molecule is superimposed on the decrease in its static stability as  γ  increases. Then we can observe the decrease in the dissociation energy value and the existence of the metastable state of the molecule as  γ   MS   reaches 0.659374 Ry. The hydrogen molecule is statically unstable when  γ  >  γ   D   = 1.024638 Ry. Moreover, we can also observe the    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$${\mathscr{P}}{\mathscr{T}}$$\end{document}        symmetry breaking effect for the electronic Hamiltonian when    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$${\gamma }_{{\mathscr{P}}{\mathscr{T}}}$$\end{document}γ     = 0.520873 Ry. This effect does not affect such properties of the hydrogen molecule as: the electronic Hamiltonian parameters, the phonon and the rotational energies, and the values of the electron-phonon coupling constants neither it disturbs the dynamics of the electronic subsystem. However, the number of available quantum states goes down to four.

Interaction of the hydrogen molecule with the environment: stability of the system and the $${\mathscr{PT}}$$ symmetry breaking