A quadratically convergent MCSCF method for the simultaneous optimization of several states

A quadratically convergent MCSCF method is described which allows one to optimize an energy average of several states with arbitrary weight factors. An analysis of the problems connected with the variational determination of excited states is given and it is concluded that the averaging method is a natural solution to these problems. In the energy expansion minimized in each iteration, certain cubic and higher order terms can be included. It is demonstrated that this greatly facilitates convergence in cases where the Hessian matrix of second energy derivatives has many negative eigenvalues. Several approximations to the exact quadratically convergent scheme, which are useful when calculating potential surfaces, are discussed.