Self-consistent field , ground

The calculations are based on the INDO/s method of Zerner et al., and include the lowest 225 singly excited configurations from the self-consistent field ground state. The calculations utilized the crystallographic data for P. aestuarii reported by Tronrud et al. For modifications to the BCHL molecule, the Mg or substituents were replaced by hydrogens at idealized positions. 

The self-consistent field function for atoms with 2 to 36 electrons are computed with a minimum basis set of Slater-type orbitals. The orbital exponents of the atomic orbitals are optimized so as to ensure the energy minimum. The analysis of the optimized orbital exponents allows us to obtain simple and accurate rules for the 1 s, 2s, 3s, 4s, 2p, 3p, 4p and 3d electronic screening constants. These rules are compared with those proposed by Slater and reveal the need for the screening due to the outside electrons. The analysis of the screening constants (and orbital exponents) is extended to the excited states of the ground state configuration and the positive ions. 

The self-consistent field functions for the ground state of the first- and second-row atoms (from He to Ar) are computed with a basis set in... 

As an example of the insufficiency of present usefulness and self-consistency as grounds for belief in a scientific construct, it may be in order to recall some scientific history. In our own field we have the familiar example of phlogiston and in astronomy the example of epicycles. By the use of epicycle superimposed on epicycle, the geocentric theory was able to give a self-consistent, popular, and accurate description of apparent planetary motions. The epicycle treatment is analogous to a Fourier analysis of the motions and its accuracy did not guarantee the physical reality of epicycles. 

Thus, in a study on the properties of dipole systems, most promise is shown by the representation of chain interactions, which, first, reflects the tendency toward ordering of dipole moments along the axes of chains with a small interchain to intrachain interaction ratio. Second, this type of representation makes it possible to use, with great accuracy, analytical equations summing the interactions of all the dipoles on the lattice. Third, there are grounds for the use of the generalized approximation of an interchain self-consistent field presented in Refs. 62 and 63 to describe the orientational phase transitions. 

Denote the self-consistent field exerted on a molecule j by neighboring molecules as rjV where V represents the absolute magnitudes of quantities (2.3.25) and (2.3.27) for various ground states of nonpolar molecules on square and triangular lattices. Then the equation for t] appears as ... 

It is possible to divide electron correlation as dynamic and nondynamic correlations. Dynamic correlation is associated with instant correlation between electrons occupying the same spatial orbitals and the nondynamic correlation is associated with the electrons avoiding each other by occupying different spatial orbitals. Thus, the ground state electronic wave function cannot be described with a single Slater determinant (Figure 3.3) and multiconfiguration self-consistent field (MCSCF) procedures are necessary to include dynamic electron correlation. 

Koopmann s theorem establishes a connection between the molecular orbitals of the 2jV-electron system, just discussed, and the corresponding (2N- 1 Electron system obtained by ionization. The theorem states If one expands the (2N - 1) molecular spin-orbitals of the ground state of the ionized system in terms of the 2N molecular spin-orbitals of the ground state of the neutral system, then one finds that the orbital space of the ionized system is spanned by the (2N - 1) canonical orbitals with the lowest orbital energies ek i.e. to this approximation the canonical self-consistent-field orbital with highest orbital energy is vacated upon ionization. This theorem holds only for the canonical SCF orbitals. 13>... 

Most of these developments may be applied most directly within the framework of the isolated molecule method, in which the reactivity indices are the charges and self-polarizabilities of the unperturbed ground state of a given molecule calculations based on the localization model (e.g. Nesbet, 1962) have made less progress, and will not be considered. It is therefore natural to enquire whether indices similar to and tt,, in Hiickel theory can still be defined, and calculated more precisely, in self-consistent field theory. The obvious questions are... 

TABLE 1. Self-Consistent Field energies (in hartree) of the He atom for some excited states as a function of the size, M, of the even-tempered basis set used to parametrize the orbitals. In the column headed (a) the same even-tempered basis set optimized for the ground state, is used for aU states ... 

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