The Ground State Energy of Helium Using Hartree-Fock Roothaan With Six Expansion Terms of Gaussian Type Orbital (GTO-6G)

An implementation of the Hartree-Fock Roothaan with six expansion terms of Gaussian Type Orbitals (GTO-6G) is described and used to study the Helium atom’s ground state accurately. The objective of this research is to calculate the ground state energy of the Helium atom. The analysis was conducted using the numerical method using Matlab2017b. By using the Hartree-Fock Roothaan method, the complexity of Hartree-Fock in integrating the differential equations of eigenvalues for each electron is repeatedly successfully overcome by expressing Hartree-Fock orbitals in the form of linear combinations, known as STO (Slater Type Orbitals) and GTO (Gaussian Type Orbital). The Hartree-Fock Roothaan approximation procedure begins by assigning an initial guess value to the elements of the density matrices and then constructing the first Fock matrix from these matrices. The calculation is performed using the various iterations in multiples of 50, show that the error value expressed in relative uncertainty is getting smaller at the 150th iteration, which is around 1.84%. Compared with some literature, the relative uncertainty value is still within tolerance (below 5%). The contribution of theoretical implications in this study can be used as input for other researchers to review the Hartree-Fock Roothaan method and improve accuracy