Second-order optimization MCSCF theory

MOs and the configuration expansion. To be successful, we must choose the parametrization of the MCSCF wave function with care and apply an algorithm for the optimization that is robust as well as efficient. The first attempts at developing MCSCF optimization schemes, which borrowed heavily from the standard first-order methods of single-configuration Hartree-Fock theory, were not successful. With the introduction of second-order methods and the exponential parametrization of the orbital space, the calculation of MCSCF wave functions became routine. Still, even with the application of second-order methods, the optimization of MCSCF wave functions can be difficult - more difficult than for the other wave functions treated in this book. A large part of the present chapter is therefore devoted to the discussion of MCSCF optimization techniques. 

In this section, we shall ply the second-order Newton method to the optimization of the Hartree-Fock energy, considering both a method that works with the AO density matrix and is applicable to large systems, and a method that carries out rotations among the MOs and is applicable to general single-configuration states [16-18]. Our discussion is here restricted to minimizations - in the discussion of MCSCF theory in Chapter 12, we shall consider also the second-order localization of saddle points. 

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