Fractional occupation numbers and density functional energy gradients within the linear combination of Gaussian-type orbitals approach

Gradients of the total energy with respect to nuclear displacements using fractionally occupied orbitals within a linear combination of Gaussian-type orbitals density-functional theoretical appraoch are discussed. Expressions for the gradient in the fractional occupation number solution as well as for Fermi and Gaussian broadening are presented and related to previously described methods.