Iterative natural orbital method

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 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... 

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 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 super-CI method now implies solving the corresponding secular problem and using tpq as the exponential parameters for the orbital rotations. Alternatively we can construct the first order density matrix corresponding to the wave function (4 55), diagonalize it, and use the natural orbitals as the new trial orbitals in I0>. Both methods incorporate the effects of lpq> into I0> to second order in tpq. We can therefore expect tpq to decrease in the next iteration. At convergence all t will vanish, which is equivalent to the condition ... 

R. Ahhichs and E. Driessler, Determination of pair natural orbitals. A new method to solve the multiconfiguration Hartree-Eock problem for two-electron wave functions, Theor. Chim. Acta, 36 (1975) 275. W. Meyer, Theory of self-consistent electron pairs. An iterative method for correlated many-electron... 

The three-dimensional nature of the electrostatic potential makes it difficult to simultaneously visualize its spatial distribution and its magnitude. However, we can deal with the electrostatic potential on the van der Waals surface of a molecule, which is of major importance for the molecular contact between a ligand and a receptor. The electrostatic potential can be calculated by a point charges derived from partial atomic charges, the latter of which can be calculated by iterative partial equalization of orbital electronegativity (PEOE), a well-established empirical method for the rapid calculation of charge distributions [104]. 

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