# SCF.jl

A Julia library for the self-consistent field method, mainly intended to solve problems on the form

\[\begin{equation} E(\vec{P},\vec{c}) = \frac{\vec{c}^H \mat{H}\vec{c}}{\vec{c}^H\vec{c}} \end{equation}\]

where $\vec{P}$ is a set of orbitals, $\vec{c}$ is a vector of mixing coefficients, and

\[\begin{equation} \mat{H}_{ij} \defd \matrixel{P_i}{\Hamiltonian}{P_j}. \end{equation}\]

Such equations arise in the *multi-configurational (Dirac–)Hartree–Fock* approximation, used in theoretical atomic and molecular physics.

This library only implements the SCF procedure. The actual equations that are to be solved have to be setup by the user (for atoms, the Atoms.jl library may be used).

## References

- Fischer, C. F. (1986). Self-Consistent-Field (SCF) and Multiconfiguration (MC) Hartree-Fock (HF) Methods in Atomic Calculations: Numerical Integration Approaches. Computer Physics Reports,
**3**(5), 274–325. DOI: 10.1016/0167-7977(86)90001-8