Quantum Chemistry¶
My ongoing learning path:
Modern Quantum Chemistry [T6]
About approximations in Quantum Chemistry, cited from [60]
To reach the second quantized formulation, one typically first approximates the nuclei as fixed classical point charges under the Born-Oppenheimer approximation and chooses a basis φi in which to represent the electronic wave function. Often, one chooses a basis of N molecular orbitals, constructed as a linear combination of atomic orbitals (LCAO), which are computed using a mean-field procedure known in chemistry as the Hartree-Fock (HF) method [71]. The atomic orbital basis functions are derived from variations of hydrogenlike atomic orbitals for differ- ent values of Z. They are numerically optimized to match desired physical properties across a range of systems and to be compatible with systematic improvement [72]. Usually, the basis functions are expressed as sums of Gaussian functions rather than the original Slater-type orbitals to enhance the efficiency of integral evaluation. This choice is convenient for small problems but not mandatory, and much work has been done recently to improve the Hamiltonian representation for electronic structure problems [40,41].