FSGO

Table 18.1 Input and output from an FSGO calculation on ammonia...

Some authors also recommended that the inner-shell octet of a second-row atom should be represented by four doubly occupied FSGOs arranged tetrahe-drally round the nucleus. 

FSGO Hartree-Fock Instabilities of Hydrogen in External Electric Fields... 

With respect to correlation, the behaviour of the hydrogen molecule studied in a subminimal FSGO basis set is still more striking than the one observed in a minimal basis set. By symmetry arguments, the single FSGO which describes the electron pair of the hydrogen molecme is centred at the middle of the H-H bond. As the intemuclear distance increases and ultimately when the molecule dissociates, such a description would lead to a physical nonsense. Indeed, at the dissociation limit, this would correspond to two protons (2H ) and an isolated pair of electrons (2e ). 

Thus, we understand that, in the FSGO model, for some critical distance, the single Gaussian will jump from its symmetric position at the middle of the H-H bond to a dissymetric one represented below. Thus, the FSGO dissociation scheme corresponds to one electron pair on one of the proton (H )and no electron on the second proton (H+) H2 H- + H+... 

FSGO HARTREE-FOCK INSTAB HUES OF HYDROGEN... 

In the RHF method, the FSGO describing the electron pairs is doubly occupied and the wave-function has the form ... 

Table 1. shows the total energies obtained using the RHF method for 1. LCAO minimal basis set STO-IG for the sake of comparison with FSGO, 2. FSGO in its symmetric and broken symmetry solutions and, 3. LCAO minimal basis set STO-3G in order to allow a safer comparison with the quality of the subminimal basis used in the FSGO technique. The dissociation curves are given in Figure 1. 

The equilibrium FSGO-hydrogen molecule is found for the parameters ... 

In both cases, the energy formula (E(UHF-FSGO)) is the same ... 

Note that the PHF wave function is no longer a single determinant and is a sum of two terms. This PHF function both satisfies the Pauli principle and is a pure singlet state. The energy formula E(PHF-FSGO) is easily derived ... 

Table 2. Total energy as a function of the internuclear distance R, in FSGO...

In the Extended Hartree-Foek (EHF) technique, the minimization is performed on the form of the PHF wave function. This type of wave function should produce for each interatomic distance a further lowering of the energy with respect to the RHF, UHF, and PHF total energies. The values of E(PHF-FSGO), and E(EHF-FSGO) for internuclear distances from 1.0 a.u. to 7 a.u. (step 0.5 a.u.) are also given in Table 2. As in the UHF... 

In all the other sehemes (UHF, PHF, EHF), the dissociation limit is the correct one corresponding to two neutral hydrogen atoms (2H-) each FSGO-hydrogen atom energy is thus obtained by the simple variational procedure ... 

When expressing the nuclear attraction integrals in the FSGO basis, one has explicitly ... 

The optimal positions of the FSGO orbital correspond to the minima of the function E(zg). They may be found by imposing the necessary condition dE... 

By performing the derivative of the error function, one finds easily that the optimal position ZG of the FSGO necessarily satisfies the following equation ... 

FSGO Hartree-Fock instabilities of hydrogen in external electric fields... 

Development of the OLPA/FSGO treatment of molecular stopping 341... 

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