Multicenter Molecular Integrals over Dirac Wave Functions for Relativistic Kinetic Energy Terms

Multicenter molecular integrals over Dirac wave functions can be derived by using the Gaussian-transform for the Dirac wave function, which was derived by the author, for relativistic kinetic energy integrals; i.e., the integral for 𝐴⃗ ∙ 𝐴⃗, where 𝐴⃗ is the vector potential of the magnetic field due to the nuclear spin, that for 𝑝⃗ ∙ 𝐴⃗ + 𝐴⃗ ∙ 𝑝⃗, where 𝑝⃗ = −𝑖ℏ∇ is the momentum of the electron, and that for 𝑖𝜎⃗ ∙ (𝑝⃗ × 𝐴⃗ + 𝐴⃗ × 𝑝⃗), where 𝜎⃗ is the Pauli spin matrices. These integral formulas can be derived for the first time.

Keywords: Molecular integrals, Relativistic kinetic energy, Dirac wave function, NMR spectra.