Wave functions anti-bonding

FIGURE 1.4 Quantum mechanical explanation of the bonding and anti-bonding spin behavior as based on the overlapping of atomic wave-functions in bonding (upper representations) following by their probabihty density realizations towards spectral observation (bottom representations). 

If the individual wave functions are added (i.e., are in phase), the molecular orbital, /b, is bonding. If they are subtracted (i.e., are out-of-phase), the molecular orbital,( /a, is anti-bonding. 

The equations for the bonding and anti-bonding wave functions used in Figure 3.3 are ... 

The equations for the bonding and anti-bonding molecular orbital wave functions for the linear combinations of the two Is atomic orbitals of the two hydrogen atoms may now be written in the forms ... 

In the MO framework, The Hartree-Fock wave function Thf takes the form of an anti symmetrized orbital product, which in the case of H2 is the Slater determinant involving the spin-up and spin-down counterparts of the bonding orbital cg, as in eq 2 ... 

The complete wave functions in terms of the quantum numbers t anti / arc given by Pauling, L. The Nature of the Chemical Bond Cornell University Ithaca, NY, 1960 (n = 1-6) and Portcrlicld, W. W. Iiiort/aiiic Chemistry A Unified Approach Addison-Wesley Reading, MA, 1984 (n = 1-3). 

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