Augmented Hessian procedure

A comparison of the present algorithm with every one of the various MCSCF procedures used at present in literature is a task beyond the scope of this paper. But some kind of test must be done at least with one of the best procedures described so far. According to Werner /14/ the Augmented Hessian (AH) procedure of Lengsfield /62/ constitutes one of the best... 

The later procedure of Knowles and Werner uses instead an augmented Hessian method to define the orbital corrections. An approximate Hamiltonian operator is constructed that accounts for the simultaneous change of the entire vector of orbital rotations. This procedure may be summarized by the following steps ... 

The super-CI method can be regarded as an approximation in the augmented Hessian variant of the Newton-Raphson (NR) procedure (see for example Ref 43). However, in its original formulation, it does not eonstitute any simplification when compared with the NR method. The matrix elements between the Brillouin states (41) are actually more difficult to compute than the corresponding Hessian matrix elements, since they involve third-order density matrix elements" . 

As already pointed out, the super-CI procedure can be regarded as an approximate version of the augmented Hessian approach. This is of course also true for the method described above, the only difference being that the approximations made are more severe. 

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