Secular determinant and equations

Write down the secular determinant and equations for the general case (not specifying anything about r 2 and Let r 2 = r22 write the new secular determinant, c. Now, suppose that the r distance is long enough so that S 3 0. Simplify the secular determinant further. 

Using the results from (c) let H, = -13.60 eV, H,2 = -14.18 eV and S,2 = 0.596. Solve for 6 — 63 and determine the orbital coefficients for For H3 in a geometry given by and equilateral triangle write down the secular determinant and equations. Using the parameters in part (d) compute the eigenvalues and eigenvectors associated with each MO. 

What is symmetry In this book we are interested in two uses of this word. First, we are interested in the symmetiy of a molecule. When looking at objects, we invariably have some feel as to whether they are highly symmetric or alternatively not very symmetric. This needs to be quantified in some way. Second, we need to classify, in terms of some symmetry description, the molecular orbitals of molecules and fragments. It is just this aspect that tremendously simplifies the construction of molecular orbitals rather than blindly, mechanically solving the secular determinant and equations of Chapter I. Once this symmetry classification has been done, with the use of a few mathematical tools, we will be in a good position to understand how symmetry controls the orbital structure in molecules. 

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