Strongly orthogonal antisymmetrized geminal

The earliest such attempts go back to 1953, when strongly orthogonal antisymmetrized geminal products (SOAGP) were employed [1, 2]. A strongly orthogonal geminal is such that Jgi(l,2)g2(2,3)d2 = 0, while the weaker... 

The antisymmetrized product of strongly orthogonal geminals is denoted by the acronym APSG. Properties of this wave function, its construction and use, will be discussed in the forthcoming sections. 

Since our wave function is most conveniently written in the form (69), i.e. as an antisymmetrized product of strongly orthogonal geminals i), the name APSG is now commonly used for this ansatz. 

We have in fact to compare the energy of an APG function (Antisymmetrized Product of Geminals, without strong orthogonality) with the sum of individual pair energies (without factorization of the Hilbert space). The difference... 

The separated electron pair concept, which was first proposed by Hurley et al. [14] and which was later referred to as antisymmetrized product of strongly orthogonal geminals (APSG) [15], is also a special case of the group function concept. This kind of wave function is qualitatively correct at all internuclear distances and it can be improved either perturbationally [16, 17] or variationally [18]. 

These equations are expressed in the spin-orbital formalism and the products of orbitals are assumed to be antisymmetrized. The coefficients are the explicitly correlated analogues of the conventional amplitudes. The xy indices refer to the space of geminal replacements which is usually spanned by the occupied orbitals. The operator Q12 in Eq. (21) is the strong orthogonality projector and /12 is the correlation factor. In Eq. (18) the /12 correlation factor was chosen as linear ri2 term. It is not necessary to use it in such form. Recent advances in R12 theory have shown that Slater-type correlation factors, referred here as /12, are advantageous. Depending on the choice of the Ansatz of the wave function, the formula for the projector varies, but the detailed discussion of these issues is postponed until Subsection 4.2. The minimization of the Hylleraas functional... 

The first pair theory was proposed as long ago as 1953 the antisymmetrized product of strongly orthogonal geminals (APSG) of Hurley et a ... 

The perturbation theory has widely been used in quantum chemistry to account for the dynamical electron correlation in single Slater [i.e., Hartree-Fock (HF)] and multideter-minantal states [1]. Suijdn has woiked on the perturbation theories for both HF and non-HF references. For non-HF reference functions, he and his cowoikers proposed a series of multiconfiguration perturbation (MCPT) theories [2-6]. Because the MCPT theories are applicable to any reference functions, they have occasionally been applied to the antisymmetric product of strongly orthogonal geminals wave functions [7-9]. 

The total wave function of a many-electron system can be constructed as an antisymmetrized product of individual geminals [see Eq. (3)]. Dealing with this product is substantially simpler if the geminals are kept orthogonal to each other in the strong sense, i.e. 

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