Perturbation at an Atom in the Simple Hiickel MO Method

Summing over all the MOs times the number of electrons in each MO gives the first-order correction to the total energy  

EXAMPLE 12-5 Consider the methylene cyclopropene molecule, C4H4, in the HMO approximation. (See Appendix 6 for data.) At which carbon will a perturbation involving a affect the total n energy the most Calculate the energy to first order if the value of a at that atom increases to a -I- 0.1000 6. Calculate the energy change, to first order, of each of the four MOs. 

Calculation of first-order corrections to the MOs proceeds in a straightforward manner using Eq. (12-19) (see Problem 12-17). One of the results of interest from such a calculation is the change in 7r-electron density at atom / due to a change in the coulomb integral at atom k. The differential expression is 

The quantity of interest Tti,k is called the atom-atom polarizability. We will now derive an expression for in terms of MO coefficients and energies. 

We assume that our MOs fall into a completely occupied set / i. (j m and a completely empty setcpm+i, We take 5 a to be positive, which means that center 

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