By Stache H.W. (ed.)
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45) Vn = C I2 VI I + 2VI C C I CC + CC2 VCC . 46) Multiplying Eq. 44) by TCC and VCC in turn and subtracting the result from the corresponding Eq. 45) or Eq. 48) and we see that the differences depend on how the off-diagonal matrix elements compare to the overlap times the diagonal elements. A similar expression for G e is more complicated: G e − G CC = 2(G I C − G CC S I C )C I CC + (G I I − G CC )C I2 . 6 They have the same first order density matrices. 5 Why is the H2 molecule stable? 1. Numerical values for overlap, kinetic energy, nuclear attraction, and electron repulsion matrix elements in the two-state calculation.
5. Comparison of MCVB coefficients for orthogonalized AOs and raw AOs at the internuclear distance of 20 bohr. No. Type Symmetry function Orth. 6. Comparison of EGSO weights for orthogonalized and raw AOs at an internuclear distance of 20 bohr. No. Type Symmetry function Orth. 6. Now the orthogonalized AOs give the asymptotic function with one configuration, while it requires three for the raw AOs. The energies are the same, of course. The EGSO weights imply the same situation. A little reflection will show that the three terms in the raw VB function are just those required to reconstruct the proper H1s orbital.
The rate of convergence at various levels will certainly depend upon the order in which the basis functions are added, but not the ultimate value. 3 A 2 × 2 generalized eigenvalue problem The generalized eigenvalue problem is unfortunately considerably more complicated than its regular counterpart when S = I . There are possibilities for accidental cases when basis functions apparently should mix, but they do not. We can give a simple example of this for a 2 × 2 system. 2. A qualitative graph showing schematically the interleaving of the eigenvalues for a series of linear variation problems for n = 1, .
Anionic surfactants by Stache H.W. (ed.)