Canonical orthogonalization application

Figure 4.9 Application of the canonical orthonormalization procedure of Section 3.6 to the calculation of the 1 s and 2s eigenfunctions and eigenvalues approximations for the Is and 2s orbitals in hydrogen over Slater functions. Note the exact fit of the Is Slater, which is an eigenfunction of the Fock matrix for the hydrogen atom and the relatively close agreement of the ls/2s linear combinations based on simple canonical orthogonalization and also direct orthonormalization using the matrix procedure of Section 3.7.

Exercise 3.7. Application of the canonical and symmetric orthogonalization routines to the construction of sto-3g) approximations to the hydrogen Is and 2s radial orbitals. 

Figure 3.15 Application of the canonical procedure to render the Is and 2s sto-ng> basis sets of Table 1.6 mutually orthogonal as is seen in the value of the overlap integral in cell G 16 compared to the value 0.4846, cell D 16 of the unmixed originals. Note that the new functions are not normalized, cells G 15 and G 17 and that multiplication by the appropriate normalization constants cells I 12 and I 13 is required.

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