Configuration state functions compared

Compared to nonrelativistic CSF expansions classified according to their LS symmetry, the situation becomes more complicated for relativistic expansions, since usually many more relativistic configuration state functions (CSFs) have to be used to represent the a given nonrelativistic CSF analog. This has been discussed for LS- and //-coupled atomic CSFs [473,474]. 

The full calculational result [BEN83] for 15 Er is compared with experiment in fig. 3. The calculations are based on the Nilsson-Strutinsky cranking method where we follow individual configurations as functions of spin [BEN85 ] The energy of each state is minimised with respect to deformation, e, y, and 4. The calculated bands denoted by 1, 2 and 3 are the (kn/2 11/2 11/2) configurations of fig. 2. Compared... 

A theoretical justification of the scaling procedure was given by Pupyshev et al [14]. They compared the force field Fhf obtained in the Hartree-Fock (HF) limit with the force-field Fa obtained in the configuration interaction (Cl) technique, where the electron correlation effects are taken into account by mixing the HF ground state function with electronic excitations from the occupied one-electron HF states to the virtual (unoccupied) HF states. It was assumed that the force constants F01 obtained in the Cl approximation simulate the exact harmonic force field while those, extracted from the HF approximation FHF cast the quantum-mechanical force field F1-"1. It was demonstrated that under conditions listed below ... 

Thus the oscillator strengths for the transitions from these three levels were calculated and the theoretical absorption spectra were obtained by convolution with a Gaussian function with 0.16 eV FWHM (fig. 28). As shown in the figure, the shape of the spectrum strongly depends on the initial states. Therefore, the experimental spectrum taken at room temperature is inappropriate for the analysis of energy level structure in 4f25d configuration. Thus we compare the theoretical spectra with the excitation spectrum measured at 6 K (Reid et al., 2000). 

The state function of ifo. The LE function of ethylene contributes mainly to S2(about 21 ). The result accords with the fact that the experimental data on the photochemical reaction of PVCi are explained on the bases of Woodward-Hoffmann s rule. CT configurations from the occupied MO(OMO) of the ground state of benzene to the unoccupied MO(UMO) of ethylene and the OMO of ethylene to the UMO of benzene increase 16.6 % and 4.6 respectively, compared with So.(Pig.6) These contributions decrease the bond order of the central double bond in S2. In S- the contributions of the LE of ethylene and CT are small... 

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. 

Plotting U as a function of L (or equivalently, to the end-to-end distance r of the modeled coil) permits us to predict the coil stretching behavior at different values of the parameter et, where t is the relaxation time of the dumbbell (Fig. 10). When et < 0.15, the only minimum in the potential curve is at r = 0 and all the dumbbell configurations are in the coil state. As et increases (to 0.20 in the Fig. 10), a second minimum appears which corresponds to a stretched state. Since the potential barrier (AU) between the two minima can be large compared to kBT, coiled molecules require a very long time, to the order of t exp (AU/kBT), to diffuse by Brownian motion over the barrier to the stretched state at any stage, there will be a distribution of long-lived metastable states with different chain conformations. With further increases in et, the second minimum deepens. The barrier decreases then disappears at et = 0.5. At this critical strain rate denoted by ecs, the transition from the coiled to the stretched state should occur instantaneously. 

---