Atomic orbitals electron probability curves

In the graphs in Figure 5-20, the electron probability density at a given distance from the nucleus is plotted against distance from the nucleus, for s orbitals. It is found that the electron probability density curve is the same regardless of the direction in the atom. We... 

Figure 2.3 Contour plots of several low-lying H atom orbitals. Curves are surfaces on which the wavefunction exhibits constant values solid and dashed curves correspond to positive and negative values, respectively. The outermost contour in all cases defines a surface containing 90% of the electron probability density. The incremental change in wavefunction value between adjacent contours is 0.04, 0.008, 0.015, 0.003, 0.005, and 0.003 bohr respectively for the Is, 2s, 2p, 3p, and 3d orbitals. Boxes exhibit side lengths of 20 bohrs (Is, 2s, 2p) and 40 bohrs (3s, 3p, 3c0, so that orbital sizes can be compared. Straight dashed lines in 3p and 3d 2 plots show locations of nodes.

Is it possible to improve the results for NiH on the CASSCF level of accuracy by extending the active subspace The answer to this question is most probably no . The next important feature to include would be the radial correlation effects in the 3d shell of the nickel atom. The active subspace then has to include two sets of 3d orbitals together with the NiH electrons distributed among 12 orbitals. Such a calculation is well within the limits of the present capabilities, but it is not at all certain that it would give a balanced description of the correlation effects of the entire potential curve ... 

The slope of the repulsive potential at R" (or at the R" values of the two maxima in the v" = 1 probability distribution) may be determined from the width of ct(E). The vertical excitation energy of the repulsive state at JR" is determined by the E at which a E) reaches its maximum value. In this semi-classical approximation, the repulsive potential curve can be determined from a E) provided that /i(i .) varies no more rapidly than linearly in R (Child, et al., 1983). When a sufficient quantity of cr E) data is obtained from free-bound absorption or emission transitions originating from several bound vibrational levels, it is then also possible to determine the shape of the bound potential (Le Roy, et al., 1988). The /(-dependence of /i(JR) 2 can arise from two sources (i) the /(-dependence of the fractional contributions of several different A-S basis states to a single relativistic adiabatic fi-state (ii) /(-variation of the transition moment between A S basis states arising from the molecule to separated atom evolution of the LCAO characters of the occupied orbitals (iii) /(-variation of the configurational character (Configuration Interaction) of either electronic... 

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