Eigenfunctions composition

The metal carbonyls Ni(CO)4, Fe(CO)s, and Cr(CO)6 are observed to be diamagnetic. This follows from the theoretical discussion if it is assumed that an electron-pair bond is formed with each carbonyl for the nine eigenfunctions available (3d64s4p3) are completely filled by the n bonds and 2(9 — n) additional electrons attached to the metal atom (n = 4, 5, 6). The theory also explains the observed composition of these unusual sub-... 

Let x be an eigenfunction of Hx, normalized to unity. Then the wavefunc-tion for the composite system is... 

The functions on the right-hand side of this equation are termed composite functions and consist of products of atomic eigenfunctions properly coupled and antisymmetrized as follows ... 

The London theory uses second-order perturbation theory in its usual (R.S.) form an infinite sum over a complete basis set. The set taken for the composite system of two interacting molecules a and b consists of all products of the complete set of eigenfunctions of a and b separately. Thus, the London theory not only assumes that there is no overlap between the ground-state atoms but also that there is no overlap between any of the virtual atomic excited states. ... 

From 00 we can construct further eigenfunctions of Hq, if one of the (ground-state) occupied orbitals is replaced by an empty one. To express this we introduce the composite index / = (/, k), wWe i indicates the band and k the quasi-momentum, and denote occupied orbitals by. . and unfilled ones hy A,B,C,.... In this way the eigenfunctions and eigenvalues of Hq can be classified as... 

The molecular eigenfunctions are inserted (2.118) and grouped by decomposition in irreducible representations of the group for the atomic orbitals of the allyl molecule X=A +2B, for which, by considering the composition of x SALC from (2.109), are obtained also the adjacent factors, for example ... 

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