SECULAR EQUATION H-eS c

The new equation represents the eigenvalue problem, which we solve by diago-nalization of H (Appendix K, p. 982). Thus, 

If we ask whether the eigenvalues of the matrices H are H identical, the answer would be no. However, in quantum chemistry we do not calculate the eigenvalues of H, but solve the secular equation H — eS )c = 0. If H changes with respeet to H, there is a corresponding change of S when compared to S. This 

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Next, this problem is reduced to the Ritz method (see Appendices L, p. el07 and K, p. el05), and subsequently to the secular equations H — eS) c = 0. It is worth noting here that, e.g., the Cl wave function for the ground state of the helium atom would be linear combinations of the determinants where the largest c coefficient occurs in front of the o determinant constructed (say from the spinorbitals sa and Isf), but the nonzero contribution would also come from the other determinants constructed from the Isa and 2s f spinorbitals (one of the doubly excited determinants). The Cl wave functions for all states (ground and excited) are linear combinations of the same Slater determinants, they differ only in the c coefficients. 

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