Slater distributions

By approaching the charge density fluctuations with spherical charge densities, the Slater distributions are... 

Figure 1. Evolution of the radial electron density for argon from each of the three limits described in Table 1. The limits (top row) are those given by the Thomas-Fermi approximation, the non-interacting electron model, and the large-dimension limit. The abscissae are Hn-ear in y/r, where r is given in units of (IS/JV) for the first column, (18/Z) Co for the second, and (D/Zy a<, for the third. All curves except the Thomas-Fermi limit were obtained by adding Slater distributions whose exponents were determined from the subhamiltonian minima described in Sec. 4.

For some systems qiiasiperiodic (or nearly qiiasiperiodic) motion exists above the unimoleciilar tlireshold, and intrinsic non-RRKM lifetime distributions result. This type of behaviour has been found for Hamiltonians with low uninioleciilar tliresholds, widely separated frequencies and/or disparate masses [12,, ]. Thus, classical trajectory simulations perfomied for realistic Hamiltonians predict that, for some molecules, the uninioleciilar rate constant may be strongly sensitive to the modes excited in the molecule, in agreement with the Slater theory. This property is called mode specificity and is discussed in the next section. 

As computational facilities improve, electronic wavefunctions tend to become more and more complicated. A configuration interaction (Cl) calculation on a medium-sized molecule might be a linear combination of a million Slater determinants, and it is very easy to lose sight of the chemistry and the chemical intuition , to say nothing of the visualization of the results. Such wavefunctions seem to give no simple physical picture of the electron distribution, and so we must seek to find ways of extracting information that is chemically useful. 

The nuclear charges and the fixed charge distribution, the so-called core, which is not affected by any change in the sr-electron distribution. The singlet ground state wave function therefore describes only the n system and is given by a single closed-shell Slater determinant Aq which is constructed from a set of 5r-molecular spin orbitals (SMO) ( la), ( 2 ). etc. 

N2 = 2. For carbon, the subshells are expansions of 6, respectively, 4, Slater-type functions, that is, V = 6, v2 = 4. Because of the spherical averaging of pc and pv, the occupancies of orbitals with the same n and l values are the same, regardless of their m values. In other words, the electrons in a subshell are evenly distributed among the orbitals with different values of the magnetic quantum number m. 

To determine the image, the first step is to determine the distribution of tunneling current as a function of the position of the apex atom. We set the center of the coordinate system at the nucleus of the sample atom. The tunneling matrix element as a function of the position r of the nucleus of the apex atom can be evaluated by applying the derivative rule to the Slater wavefunctions. The tunneling conductance as a function of r, g(r), is proportional to the square of the tunneling matrix element ... 

A similar SCF calculation of ferrocene has been made by Shustorovich and Dyatkina (73) in which Slater functions were used for the iron orbitals. These calculations gave an exactly opposite charge distribution to that of Dahl and Ballhausen, owing to the more contracted metal orbitals used by the latter authors. Because values of overlap integrals of the type S (2pa3da) and S(2p7T3d7T) calculated by the latter authors are almost identical with those calculated directly from the Watson functions (74), it seems that the charge distribution calculated by Dahl and Ballhausen is the correct one. 

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