The convergence properties of direct energy minimisation with respect to linear coefficients in the MC-LCAO-MO-SCF approach

It is shown that in the LCAO-MO-MC-SCF problem, if the molecular orbital orthonormality constraints are introduced in the manner suggested by Kari and Sutcliffe or indeed by any similar method then the Hessian of the problem with respect to the linear coefficients is singular. The nature of this singularity is analysed and it is shown that in general it is possible to remove it in a level-shifting-like scheme, but that only in certain special cases is this procedure likely to be quickly convergent.