Geminal power method

The centrality of the FNA has spawned considerable research into improvement of the approach. The strategies for obtaining better nodes are numerous. Canonical HF orbitals, Kohn-Sham orbitals from density functional theory (DFT), and natural orbitals from post-HF methods have been used. The latter do not necessarily yield better nodes than single configuration wave functions [39-41]. More success has been found with alternative wave function forms that include correlation more directly than sums of Slater determinants. These include antisymmetrized geminal power functions [42,43], valence-bond [44,45] and Pfaffian [46] forms as well as... 

Historically, MO methods have dominated trial-function construction because these functions are readily obtained from widely distributed computer codes. Recently, however, some QMC practitioners have renewed interest in a broader variety of wave functions including valence bond (VB) functions [44, 45], pairing wave functions, such as the antisymmetrized geminal power (AGP) [42, 43], Pfafflan, and perfect pairing forms [46]. 

Progress in Heterocyclic Chemistry (PHC) Volume 8 reviews critically the heterocyclic literature published mainly in 1995. The first two chapters are review articles. Chapter 1 by T. Kappe deals with Geminal Diazides of Heterocycles, and Chapter 2 by M. Sibi and J. Ji provides extensive coverage of the important emerging area of Radical Methods in the Synthesis of Heterocyclic Compounds. The unusual length of the latter contribution attests to the rising power of this methodology in heterocycle construction. 

We also note that there are other, more advanced techniques for the treatment of electron correlation such as the r 2 approaches [101], geminal techniques [101], or quantum Monte Carlo methods [102]. Although these approaches are undeniably very powerful treatments for obtaining accurate ground-state energies, they are still awaiting implementations of analytic derivatives and therefore are outside the scope of this chapter. 

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