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The HF energies of the valence orbitals of the rst- and second-row transition elements and of neighboring atoms are plotted as a function of atomic number in Figure 132 The 2p orbital energies of B, C, N, O, and F are also plotted, and these form the basis for the orbital energies in terms of the j j scale shown at the right In the case of the rst-row transition elements, Sc Zn, the 3d orbital energies shown in Figure 132 correspond to atomic con gurations s 2 d n The s 1 d n 1 con gurations (not shown) are higher by from 01 hartree (Sc) to 025 hartree (Zn) due to the excess coulombic repulsion which ensues upon increasing the electron population of the d orbital by one electron.

The Coulombic repulsion within the 4s orbital is o set by increased penetration to the nucleus and the energy of the 4s orbital between the s 2 d n and s 1 d n 1 con gurations changes by only about one-tenth of the 3d orbital change The average value is shown in Figure 132 The d orbital energies shown should be representative of the energies of the lowest nonbonding orbitals in the metal complexes shown later in Figures 134 136 It is clear that while the early transition elements, Sc and Ti, have 3d orbital energies which are higher than the 2p orbital energy of C, the 3d orbital energies fall sharply across the row, with the later energies comparable to the 2p orbital energies of O and F.

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The variational method is used to nd the optimum expansion in terms of the con gurations; that is, the energy is expressed as an expectation value as was done in equation (A.9), E CI g Hg dt jgCI j 2 dt

The 4d orbital energies of the s 2 d n con guration of the second-row transition metals, Y Cd, are also plotted in Figure 132 The valence con gurations s 0 d n 2 and s 1 d n 1 (not shown) are higher by 007 hartree (Y) to 016 hartree (Cd) The smaller values compared to the 3d orbital case may be due to the intrinsically larger 4d orbitals The 4d orbital energies are a little higher and parallel to the corresponding 3d energies The 5d orbital energies of the third-row transition metals were not calculated Their position shown in Figure 132 is based on extrapolation In each of the valence orbital sets shown in the preceding gures, the highest was essentially the unoccupied n 1 p orbital, the energies of which were also not determined by the calculations Their position, shown in Figure 13.

2 near 1X5j j, is anticipated on the basis that the occupied p orbitals of Ga and In are similar and start at 1j j..

It is well known that the cell loss rate of a multiplexer depends on the maximum burst length generated by the source with respect to the amount of buffering. To consider this, the algorithm modifies the above on off model as follows. It defines a basic time interval TN s Bvbr

Vds,f o(t ) Vds(t ) Ids(t )

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The derivative of the vector of the phasors of the nonlinear currents is best computed analytically if the derivative of the currents as functions of the voltages is explicitly available: iNL (t) = G(v(t))

(mm) 33.5 33.9 33.5

I=J,

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