Chemistry in a Strong Magnetic Field and the Atmosphere of Neutron Star 1E1027.4 - 5209

At 2002 the data collected by CHANDRA X-ray observatory (and later confirmed by XMM-Newton) led to a discovery of two absorption features in the spectra of radiation at 0.7 and 1.4 KeV of the isolated neutron star 1E1027.4-5209 characterized by enormous magnetic field $>10^{12}\,$G. A natural question about a content of the neutron star atmosphere occurs. It is demonstrated that in a strong magnetic field $B>10^11$\,G traditional molecular systems like the $H_2^+$ molecular ion and the $H_2$ molecule can cease to exist but exotic ones $H_3^{++} (pppe)$, $H_4^{+++} (ppppe)$ and even $He_2^{3+}$, $(HeH)^{2+}$ can occur. The same time it turns out the neutral $H$-atom is the least bound one-electron system in a magnetic field. In general, studies in a strong magnetic are extremely complicated technically. Novel approach to study of molecular systems, which provides very accurate results, based on variational calculus with physically relevant trial functions is presented. It is argued that the atmosphere of the neutron star 1E1027.4-5209 with surface temperature $~10^6 K$ may consist of the exotic molecular ions $H_3^{++}$.