Pair natural orbital method

A MP2/6-311- -G(2df,2p) calculation is carried out, which automaticaUy yields the corresponding HF energy. The MP2 result is extrapolated to the basis set limit by the pair natural orbital method. 

A Complete Basis Set Model Chemistry. IV. An Improved Atomic Pair Natural Orbital Method. 

Montgomery, J.A., Ochterski, J.W., Petersson, G.A. A complete basis-set model chemistry. 4. An improved atomic pair natural orbital method. J. Chem. Phys. 1994,101(7), 5900-09. 

Neese, R, Wennmohs, E, and Hansen, A. (2009). Efficient and accurate local approximations to coupled-electron pair approaches An attempt to revive the pair natural orbital method, / Chem. Phys. 130, p. 114108, doi 10.1063/l.3086717. 

J. A. Montgomery, J. W. Ochterski, and G. A. Petersson,/. Chem. Phys., 101, 5900-5909 (1994). A Complete Basis Set Model Chemistry. IV. An Improved Atomic Pair Natural Orbital Method. 

The CEPA computer programs, developed by two German groups78,104 are based on the use of pair natural orbitals and, therefore, it is appropriate to refer to their approach as the CEPA-PNO method. The construction of H-matrix elements over the PNO s is the same as with the PNO-CI (this was noted in the preceding section). 

Even though computers were an essential tool in quantum chemical calculations, the main challenge was the further development of methods and concepts to describe even more facets of chemistry and with higher accuracy. Methods that account for electron correlation were extended to be able to describe energy surfaces more reliably. Several variants of the CEPA Ansatz (CEPA-1, CEPA-2) were developed as well as the method of self-consistent electron pairs (SCEP). Formulations using canonical or localized orbitals (e.g., pair natural orbitals, PNO, as a kind of optimized virtual orbitals) were put forth. These methods were extensively used for two decades, primarily in Germany, until coupled cluster formulations became more popular. ... 

Electron Pair Approximation with Pair Natural Orbitals) Calculations of Molecular Systems. I. Outline of the Method for Closed-Shell States. 

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... 

MO calculations have been reported for the BH and BH3 molecules, using the pair natural orbital configuration interaction (PNO—Cl) and coupled electron pair approximation with natural orbitals (CEPA—PNO) methods." The force constant and equilibrium distance of BH agreed very well with experimental values. 

There are three basic CBS methods CBS-4 (for fourth-order extrapolation), CBS-Q (for quadratic Cl) and CBS-APNO (or CBS-QCI/APNO, for asymptotic pair natural orbitals), in order of increasing accuracy (and increasing computer time). These methods are available with keywords in the Gaussian 94 and 98 programs. 

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... 

Two ab initio methods, which were well known and much discussed in the 1970s and 1980s, were the pair natural orbital Cl (PNO-CI) method and the coupled electron pair approximation (CEPA) method. They were proposed by Meyer [67] in 1973 and 2 years later improved by Ahlrichs et al. [68]. In 1983, Burton and Senff [69] applied the method of Ahlrichs et al. to an analysis of the anisotropy of (H2)2 interaction near the minimum in the van der Waals interaction energy. 

We normalize Pci such that the coefficient of is equal to 1. The spin orbitals (pa, natural spin orbitals of the respective lEPA pair correction function My 22) jhis will be the case for all of the methods considered and we shall not stress this again. One ought to add the abbreviation PNO (for Pair-Natural-Orbitals, sometimes interpreted as Pseudo-Natural-Orbitals) to the terms lEPA and CEPA as well, i.e. to speak of lEPA-PNO and CEPA-PNO rather than just of lEPA and CEPA. Using the PNO s one gets mutually orthogonal 0if though the PNO s of different pairs are nonorthogonal. Also the explicit expressions for Hab are not too complicated. 

Complete Basis Set Methods Petersson et al.61-63 developed a series of methods, referred to as complete basis set (CBS) methods, for the evaluation of accurate energies of molecular systems. The central idea in the CBS methods is an extrapolation procedure to determine the projected second-order (MP2) energy in the limit of a complete basis set. This extrapolation is performed pair by pair for all the valence electrons and is based on the asymptotic convergence properties of pair correlation energies for two-electron systems in a natural orbital expansion. As in G2 theory, the higher order correlation contributions are evaluated by a sequence of calculations with a variety of basis sets. 

In the pseudo-natural orbital (PSNO) method,188 a natural orbital calculation is performed on selected pairs of electrons in the Hartree-Fock field of the n-2 electron core. These orbitals are then used as a basis for a Cl calculation. In their work on the HeH+ system, for which the orbital occupancy is 1 first-order density matrix, only 45 configurations were found to have significant occupation numbers. The results of the application of this method to Hs184 and HeH 185 will be discussed below. 

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