Homework 1 Part 2

# Homework 1 Part 2 - re orthogonal equations Âφ n = a n φ...

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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 Âφ n = a n φ n and Âφ m = a m φ m by φ m and integrate over all space. Then, take the co d multiply it by φ n , and integrate over all space. Subt r and label this equation as (4 – 1). µ¶ · ¸ ¶ ¹ u º» ¼ ¹ u ½ ²½ ¼ · ¾g 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 n≠m. In your that the two 3. The following are the three normalized sp 2 hybrid orbitals. Show that Ψ 1 is normalized and that Ψ 1 is orthogonal to Ψ 2 . Which orbital is missing from these equations and why is it missing? g G ± 1 u3 2² + ³ 2 3 2´ µ g ¶ ± 1 u3 2² · 1 u6 2´ µ + 1 u2 2´ ¸ g ¹ ± 1 u3 2² · 1 u6 2´ µ · 1 u2 2´ ¸...
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Homework 1 Part 2 - re orthogonal equations Âφ n = a n φ...

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