3 Improving Huckel Theory for Ethene Huckel theory uses a set of very strong approximations on the matrix elements of the Hamiltonian. Let's examine how we might improve these approximations for a simple conjugated molecule like ethene. For all calculations that follow you can use a = -11.4eV and B = -2.8eV. (A) Explain all fundamental assumptions of Huckel theory relative to the fully accurate solution that would be obtained by Hartree-Fock theory. (B) In reality, the calculation for the orbital overlap between 2pz orbitals on the carbon atoms of ethene comes out to ~ 0.27. Using this value of the overlap matrix and the Hamiltonian assumptions you stated in (A) calculate the total π-electron energy of ethene. How different is this result from the plain Huckel theory result for ethene? (C) Use Extended Huckel theory (Hij = ½½ * 1.75 * Sij * (Hii + Hjj)) to calculate the matrix elements Hij using what you have calculated from (B). Using these matrix elements, as well as the overlap matrix elements in the previous question, calculate the new total π-electron energy of ethene and compare it to your previous answers. (D) Assuming that each Carbon atom has an effective nuclear charge of Z = 3.25, write down the full electronic Hamiltonian for ethene accounting for only the T-electrons. How does the Hamiltonian you wrote down relate to the matrix elements a and ẞ appearing in Huckel theory. (E) Does the Huckel theory wavefunction obey all postulates of quantum mechanics? Explain your answer. If it violates any of the postulates, explain mathematically how you would correct Huckel theory.

Introduction to Chemical Engineering Thermodynamics

8th Edition

ISBN:9781259696527

Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart

Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart

Chapter1: Introduction

Section: Chapter Questions

Problem 1.1P

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Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer.Very very grateful!Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer.

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