The use of gaussian nuclear charge distributions for the calculation of relativistic electronic wavefunctions using basis set expansions

Relativistic Hamiltonians for Chemistry: A Primer

“…Carrying out the decoupling transformation W 1 , Equation (46), of the Dirac Hamiltonian leads to the ZORA, [81][82][83] whereas subsequent renormalization W 2 , Equation (47), gives the infiniteorder (IORA) variant. [84] The variationally stable ZORA Hamiltonian [Eq.…”

“…With the introduction of a finite nuclear charge model, typically a Gaussian, the singularity is replaced by a Gaussian shape at the origin, favoring the use of Gaussian-type basis functions. [45][46][47] The implementation of Equation (26) at the basis-set level has been denoted kinetic balance, [48] since it provides a correct representation of the kinetic energy operator in the non-relativistic limit. It is, however, important to have sufficient flexibility in the basis such that the exact coupling can be obtained.…”

Relativistic virial theorem for atoms

“…In the GCD and FCD nucleus models, the nuclear potential is commonly written as [1,2] m r ÀZ ds q s 1 r À s j j ; 22…”

“…In nonrelativistic atomic and molecular calculations, atomic nuclei are usually treated as point charges (PCs), while in relativistic calculations they are often assumed to have ®nite sizes and such nucleus models are adopted as a uniformly charged sphere (UCS), a Gaussian charge distribution (GCD), and a Fermi charge distribution (FCD) [1,2].…”

Full configuration-interaction calculations with the simplest iterative complement method: Merit of the inverse Hamiltonian

“…This problem is called the singularity problem. Finite size of the nucleus [7] does not solve this problem. However, when we use the second-quantized Hamiltonian, the singularity problem is not obvious.…”