Roothaan-Hall-Gleichungen

The Roothaan equations are a representation of the Hartree-Fock equation in a non orthonormal basis set which can be of Gaussian-type or Slater-type. It applies to closed-shell molecules or atoms where all molecular orbitals or atomic orbitals, respectively, are doubly occupied. This is generally called Restricted Hartree-Fock theory.

The method was developed independently by Clemens C. J. Roothaan and George G. Hall in 1951, and is thus sometimes called the Roothaan-Hall equations. The Roothaan equations can be written in a form resembling generalized eigenvalue problem, although they are not a standard eigenvalue problem because they are nonlinear:

$\mathbf {F} \mathbf {C} =\mathbf {S} \mathbf {C} \mathbf {\epsilon }$

Where F is the so-called Fock matrix (which depends on the coefficients C due to electron-electron interactions), C is a matrix of coefficients, S is the overlap matrix of the basis functions, and $\epsilon$ is the (diagonal, by convention) matrix of orbital energies. In the case of an orthonormalised basis set the overlap matrix, S, reduces to the identity matrix.

External links

• http://www.cachesoftware.com/mopac/Mopac2002manual/node443.html
• http://www.physik.unizh.ch/~sam/diss/node8.html

See also

• Hartree-Fock