SCF approximation

SCF approximation. The indices //, v, A, and o denote four atomic orbital centers, so that the number of such orbitals that needs to be calculated increases proportionally scales with ) N, where N is the number of AOs, This was an intractable task in 1965, so Pople, Santry, and Segal introduced the approximation that only integrals in which = v and J. = o (i.e., li)) would be considered and that, further-... 

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The bonding properties of dimeric SiO and SiS have also been investigated by means of quantum chemical methods. The most stable isomer of Si202 is found within the SCF approximation to be a... 

Kevan (1974) and Tachiya (1972) point out that CKJ use an SCF approximation to calculate the medium polarization energy, but in everything else they use the adiabatic approximation. This somewhat inconsistent procedure, which may be called the modified adiabatic approximation, gives results similar to those obtained by FFK. Varying the dipole moment and the polarizability in the semicontinuum models varies the result qualitatively in the same direction. It increases the electron-solvent attraction in the first shell and also increases the dipole-dipole repulsion. Both hv and I increase with the dipole moment, but not proportionately. 

The most simple approach is the Hartree-Fock (HF) self-consistent field (SCF) approximation, in which the electronic wave function is expressed as an antisymmetrized product of one-electron functions. In this way, each electron is assumed to move in the average field of all other electrons. The one-electron functions, or spin orbitals, are taken as a product of a spatial function (molecular orbital) and a spin function. Molecular orbitals are constructed as a linear combination of atomic basis functions. The coefficients of this linear combination are obtained by solving iteratively the Roothaan equations. 

In most work reported so far, the solute is treated by the Hartree-Fock method (i.e., Ho is expressed as a Fock operator), in which each electron moves in the self-consistent field (SCF) of the others. The term SCRF, which should refer to the treatment of the reaction field, is used by some workers to refer to a combination of the SCRF nonlinear Schrodinger equation (34) and SCF method to solve it, but in the future, as correlated treatments of the solute becomes more common, it will be necessary to more clearly distinguish the SCRF and SCF approximations. The SCRF method, with or without the additional SCF approximation, was first proposed by Rinaldi and Rivail [87, 88], Yomosa [89, 90], and Tapia and Goscinski [91], A highly recommended review of the foundations of the field was given by Tapia [71],... 

We now turn to the problem of simplifying the recovery of the dynamic correlation energy. We consider the simplest situation, viz., where the zeroth-order wavefunction can be chosen as the SCF approximation. A challenging disparity exists between the energetic smallness of these refinements and the complexity and magnitude of the computational efforts required for their variational determination. In order to reduce this disproportion, various semiempirical approaches have been proposed (56-61), notably in particular the introduction of semiempirical elements into MP2 theory which has led to the successful Gn methods (62-64). 

A solution to the many-electron problem, including correlation, can be obtained directly, without the use of the SCF approximation. 

The inclusion of relativistic effects is essential in quantum chemical studies of molecules containing heavy elements. A full relativistic calculation, i.e. based upon Quantum Electro Dynamics, is only feasible for the smallest systems. In the SCF approximation it involves the solution of the Dirac Fock equation. Due to the four component complex wave functions and the large number of basis functions needed to describe the small component Dirac spinors, these computations are much more demanding than the corresponding non-relativistic ones. This limits Dirac Fock calculations, which can be performed using e.g. the MOLFDIR package [1], to small molecular systems, UFe being a typical example, see e.g. [2]. 

It is well known that in the SCF approximation the Be clusters are stable only for N > 4.The inclusion of the electron correlation makes stable the Be2 E = 1.8 kcal/mol) and the = 25.8 kcal/mol) clusters and... 

Table I Interelectronic repulsion energy in the frozen orbital approximation (C) and in the SCF approximation (C )(l).

Pople refers to a specific set of approximations as defining a theoretical model. Hence the ab initio or Hartree-Fock models employ the Born-Oppenheimer, LCAO and SCF approximations. If the system under study is a closed-shell system (even number of electrons, singlet state), the constraint that each spatial orbital should contain two electrons, one with a and one with P spin, is normally made. Such wavefunctions are known as restricted Hartree-Fock (RHF). Open-shell systems are better described by unrestricted Hartree-Fock (UHF) wavefunctions, where a and P electrons occupy different spatial orbitals. We have seen that Hartree-Fock (HF) models give rather unreliable energies. 

Flouquet and Horsley145 have recently published a study of the potential energy surface of the BlAi surface of HaO in the SCF approximation and with some limited configuration interaction. They found the form of the surface for this state... 

Kouba and Ohm have gone beyond the SCF approximation and calculated a limited Cl wavefunction, using NSO.389 The lowest energy obtained was —129.2599 hartree. This is still above the estimated HF limit. The computed dipole moment of 0.121 D is in fair agreement with the experimental value of 0.148 D. The spin density at the two nuclei was also computed. 

The 7r-electron structures and energies of the singlet tt-tt transitions for a number of l//-pyrrolo[l,2-a jimidazoles (39), l/f-pyrrolo[l,2-f>]-s-triazoles (40) and l//-pyrrolo[2,l-c]-s-triazoles (41) were calculated by the MO LCAO method within the semiempirical self-consistent field (SCF) approximation. A comparison of the data shows that the maximum... 

Fig. 4. Distributions of integral probabilities of electron excitations to the energy ranges of [5n, 5(n + 1)] eV in fl decay of (a) LiT, (b) LiOT, (c) CH3T, (d) C2H3T, (e) C2H5T, (f) C3H7T, (g) NH2-C2HT, and (h) NH2-C2H4T in the SCF approximation.

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