Interaction parameter, configuration

Apart from the interest in the properties of the excited configurations themselves, their influence on the f-electrons has been studied extensively. As mentioned in the beginning of this section, mixing with excited configurations is responsible for the observed intensities of f-f transitions. This feature will be discussed in sect. 5.3.1. The influence on the center of gravity of the multiplets is also taken into account in most studies via the two-body and three-body configuration interaction parameters. 

For f configurations with n = 3 or greater three body electrostatic configuration interaction parameters have been introduced by Judd [7,8]. These are written in the form... 

Another advance permitted by configuration interaction is a precise calculation of other properties such as the magnetic behaviour under weak fields. The Zeeman effect in PrCb is totally reproduced by the configuration interaction parameters (Garcia and Faucher 1989). Unfortunately, the same parameters permit only partial reproduction of the electronic transition oscillator strength (Garcia and Faucher 1992). 

Of particular interest has been the study of the polymer configurations at the solid-liquid interface. Beginning with lattice theories, early models of polymer adsorption captured most of the features of adsorption such as the loop, train, and tail structures and the influence of the surface interaction parameter (see Refs. 57, 58, 62 for reviews of older theories). These lattice models have been expanded on in recent years using modem computational methods [63,64] and have allowed the calculation of equilibrium partitioning between a poly-... 

A is a parameter that can be varied to give the correct amount of ionic character. Another way to view the valence bond picture is that the incorporation of ionic character corrects the overemphasis that the valence bond treatment places on electron correlation. The molecular orbital wavefimction underestimates electron correlation and requires methods such as configuration interaction to correct for it. Although the presence of ionic structures in species such as H2 appears coimterintuitive to many chemists, such species are widely used to explain certain other phenomena such as the ortho/para or meta directing properties of substituted benzene compounds imder electrophilic attack. Moverover, it has been shown that the ionic structures correspond to the deformation of the atomic orbitals when daey are involved in chemical bonds. 

Note Configuration Interaction significantly increases computing time. For calculations of ground-state energies, MINDO/3, MNDO, AMI, and PM3 methods may already include in their parameters some effects of Configuration Interaction. 

Green, L. C., Mulder, M. M., Milner, P. C., Lewis, M. N., Woll, J. W., Jr., Kolchin, E. K., and Mace, D., Phys. Rev. 96, 319, (iii) Analysis of the three parameter wave function of Hylleraas for the He I ground state in terms of central field wave-functions/ Configurational interaction. 

A more accurate analysis of this problem incorporating renormalization results, is possible [86], but the essential result is the same, namely that stretched, tethered chains interact less strongly with one another than the same chains in bulk. The appropriate comparison is with a bulk-like system of chains in a brush confined by an impenetrable wall a distance RF (the Flory radius of gyration) from the tethering surface. These confined chains, which are incapable of stretching, assume configurations similar to those of free chains. However, the volume fraction here is q> = N(a/d)2 RF N2/5(a/d)5/3, as opposed to cp = N(a/d)2 L (a/d)4/3 in the unconfined, tethered layer. Consequently, the chain-chain interaction parameter becomes x ab N3/2(a/d)5/2 %ab- Thus, tethered chains tend to mix, or at least resist phase separation, more readily than their bulk counterparts because chain stretching lowers the effective concentration within the layer. The effective interaction parameters can be used in further analysis of phase separation processes... 

The description of configuration interaction given for rr-electron methods is also valid for all-valence-electron methods. Recently, two papers were published in which the half-electron method was combined with a modified CNDO method (69) and the MINDO/2 method was combined with the Roothaan method (70). Appropriate semiempirical parameters and applications of all-valence-electron methods are most probably the same as those reviewed for closed-shell systems (71). 

The thermodynamic behavior of the dilute polymer solution depends on three factors (1) the molecular weight, (2) the thermodynamic interaction parameters and ki, or ipi and 0, which characterize the segment-solvent interaction, and (3) the configuration, or size, of the... 

When parameters of the Pariser-Parr-Pople configuration interaction molecular orbital (PPP-CI MO) method were modified so as to reproduce the Aol)s values for l,3-di(5-aryl-l,3,4-oxadiazol-2-yl)benzenes 16 and 17, the calculated HOMO and LUMO energy levels corresponded with the experimental ionization potential and electron affinity values. The relationships between the electrical properties and molecular structures for the dyes were investigated. The absorption maximum wavelengths for amorphous films were found to be nearly equal to those for solution samples <1997PCA2350>. 

Larsson and co-workers have used relation (18) to calculate Tjb for organic molecules in which two centers are bridged by saturated groups [65,66], and for mixed valence systems [67]. The stationary states /i and /2 are determined by a CNDO/S method, with extensive configuration interaction and use of semi-empirical parameters. The nuclear configuration Q where relation (18) is valid is adjusted so as to satisfy the delocalization property expressed by (17). These... 

Again these interaction parameters are assumed to be independent of temperature and coverage. The total (configurational) energy of the system is... 

I. Selection of parameters and the basis of configuration interaction in closed shell and restricted open shell semiempirical methods. J. Phys. Chem. 77, 107 (1973). 

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