Homework 1 Part 2

Homework 1 Part 2 - re orthogonal. equations n = a n n and...

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1. As seen in class, the Huckel systems, like that of benzen for butadiene, shown below Before we move on, a little Down to business: A. Write out the Secular D B. Find the determinate o of α and β. (It may help C. Using your calculated e diagram for butadiene 2. In the following problem, y and their eigenfunctions ar Given the two eigenvalue e Multiply the first equation b of the second equation and equations from each other Given that by the definition of a Herm explanation, make sure you eigenfunctions are orthogo Homework 1 Part 2 (Due Jan. 18 th ) l theory may be used to calculate the energy levels o ne. We will calculate the energy levels, as well as the w. e silliness is in order: Determinate for butadiene, with Huckel approximati of this matrix and calculate all the energy levels for b p to use the substitution g G ±²³ ´ and solve for x firs energy levels from the previous question, draw out t with its electrons filled. you will prove that the eigenvalues of Hermitian ope
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Unformatted text preview: re orthogonal. equations n = a n n and m = a m m by m and integrate over all space. Then, take the co d multiply it by n , and integrate over all space. Subt r and label this equation as (4 1). u u g G U itian operator, discuss the two possibilities n=m and u prove that the eigenvalues are real numbers and t onal. of conjugated pi e wavefunctions tions. butadiene in terms st) the energy level erators are real complex conjugate tract the two d nm. In your that the two 3. The following are the three normalized sp 2 hybrid orbitals. Show that 1 is normalized and that 1 is orthogonal to 2 . Which orbital is missing from these equations and why is it missing? g G 1 u3 2 + 2 3 2 g 1 u3 2 1 u6 2 + 1 u2 2 g 1 u3 2 1 u6 2 1 u2 2...
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Homework 1 Part 2 - re orthogonal. equations n = a n n and...

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