Iterative natural orbitals

While it is impossible to determine the full impact of the Edmonton conference, Ernest Davidson recalls that it was while he was driving back to Seattle through the Canadian Rockies that he got the idea for iterative natural orbitals.16 Also, Fritz Grein remembers a long discussion with Chris Wahl in the Faculty Club which gave him the idea for the work on MCSCF methods that is cited later in this chapter. 

The effectiveness of NSO s in reducing the expansion size in systems with more than two electrons is not as great and, in fact, for larger systems, their use is not practical. The loss in practicality is immediately obvious when one realizes that in order to obtain them, one must diagonalize the first-order density matrix of the exact wavefunction, i.e. a full configuration interaction must first be performed. Two methods have been introduced in order to regain the initial usefulness of natural orbitals the pseudonatural orbital method and the approximate or iterative natural orbital method. 

Hartree-Fock with Proper Dissociation Internally Consistent Self Consistent Orbitals Independent Electron Pair Approximation Intermediate Neglect of Differential Overlap Intermediate Retention of Differential Overlap Iterative Natural Orbital Ionization Potential... 

Hartree -Fock or Self-Consistent Field (SCF) Method Spin Optimized Self-Consistent Field Method Configuration Interaction Iterative Natural Orbital Method Multi-Configuration SCF Many Body Perturbation Theory Valence-Bond Method Pair-Function or Geminal Method... 

The ab initio calculations which have so far been performed have, on the whole, been rather limited. The most extensive treatments have been for the systems H3, 62-95 H385-97 and H2F.108 The ab initio method which at present seems to offer the most practical means of calculating reliable surfaces is the iterative natural orbital (INO) method.92 108 Relatively little effort has as yet been put into the application of valence-bond methods which, from a theoretical point of view, provide the most natural description of processes involving the breaking and making of chemical bonds. The Hartree-Fock or SCF method, which is the most convenient and widely used of all the ab initio methods, gives an inadequate description of these processes and often yields qualitatively incorrect results.13107... 

The first applications of natural orbitals were the factorization of the two electron wave function of He and H2. Iterative natural orbitals were used to develop accurate wave functions for many small molecules in ground and excited states. Natural orbitals provide a powerful tool for reducing wave functions expanded using an arbitrary set of molecular orbitals to a more compact canonical form that shows rapid convergence. Used in this way, they are a useful interpretive tool. 

For nonlinear geometries, the most recent calculations on excited potential energy surfaces of water find the A A state to be repulsive. These calculations, which employed a double zeta basis set augmented by polarization functions and Rydberg orbitals coupled with an iterative natural orbital procedure, also find the state ( A" in Cs symmetry) to be totally repulsive. The repulsive nature of the Cg pathways is in agreement with earlier results obtained by Miller et at the SCF level. The latter authors... 

---