Abstract: Based on the variational principle of quantum mechanics, this study applied the Heitler-London valence bond theory to the hydrogen molecule wave function after parameter optimization. Through the high-performance computing framework of the Julia language (the multi-threading parallel and vectorization optimization techniques increased the overall computing efficiency by 6 times, and the @fastmath macro further reduced the computational cost by 15 %), the electron cloud distribution law of the hydrogen molecule system was systematically explored. The results show that at the equilibrium bond length (R = 1.4 atomic units), the peak value of the electron density between the nuclei reaches 0.35 a.u.-3, presenting typical covalent bond characteristics; when the nuclear distance increases to R = 3.0 atomic units, the electron density between the atoms approaches zero, corresponding to the molecular dissociation process.

Key words: hydrogen molecule, Schrdinger equation, variational method, Julia language, electron cloud distribution