Pseudonatural orbitals

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. 

He + H - HeH+ + H.—Two different approaches of He to the HJ ion were investigated by Edmiston et al.im using the same method they applied to H3.184 20 An uncontracted GTO basis set with polarization functions (6s, 2pt, 3px,y on helium and 4s, 1 pz, 3px,u on each hydrogen) was used and pseudonatural orbitals were calculated for the la2 pair. A 65-configuration Cl followed in which ca. 90% of the correlation energy was accounted for. The energies of 22 different linear He-H-H + geometries were calculated. A minimum which lies about 21 kJ mol 1 below the separated reactants is found at He-H and H-H+ bond distances of ca. 2.0 a.u. 

W. Meyer, Configuration Expansion by Means of Pseudonatural Orbitals, Modern Theoretical... 

W. Meyer, Configuration expansion by means of pseudonatural orbitals, in Methods of Electronic Structure Theory, edited by H. F. Schaefer, pages 413-446. Plenum Press, New York, 1977. 

ANO = atomic natural orbital CSF = configuration state function DRT = distinct row table FCI = full configuration interaction GUGA = graphical unitary group approach PNO = pseudonatural orbital or pair natural orbital UGA =... 

The most important from the viewpoint of the correlation are the NOs with NO occupancies large occupancies, i.e. D ag)ii values. Inclusion of only the most important in the Q expansion creates a short and quite satisfactory wave fimction. Meyer in-pseudonalural troduced the PNO Cl, i.e. pseudonatural orbitalsP In the first step, we perform orbitals (PNO) the Q calculations for excitations obtained by replacement of two selected spinorbitals. The process is repeated for all spinorbital pairs and at the end we carry out a large Cl, which includes all important determinants engaged in the partial calculations (i.e. those with large weights). 

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