Question

\begin{pmatrix} 0 & 1 & 0 & 0 & 0 & 0 \\ 1 & 0 & 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 & 0 & 1 \\ 0 & 0 & 0 & 0 & 1 & 0 \end{pmatrix} \text{Diagonalize} \begin{pmatrix} 1.802 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1.247 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0.445 & 0 & 0 & 0 \\ 0 & 0 & 0 & -0.445 & 0 & 0 \\ 0 & 0 & 0 & 0 & -1.247 & 0 \\ 0 & 0 & 0 & 0 & 0 & -1.802 \end{pmatrix}

          \begin{pmatrix} 0 & 1 & 0 & 0 & 0 & 0 \\ 1 & 0 & 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 & 0 & 1 \\ 0 & 0 & 0 & 0 & 1 & 0 \end{pmatrix} \text{Diagonalize} \begin{pmatrix} 1.802 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1.247 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0.445 & 0 & 0 & 0 \\ 0 & 0 & 0 & -0.445 & 0 & 0 \\ 0 & 0 & 0 & 0 & -1.247 & 0 \\ 0 & 0 & 0 & 0 & 0 & -1.802 \end{pmatrix}

< p m a t r i x >
Diagonalize
< p m a t r i x >

Added by Todd A.

Chemistry: Structure and Properties

Nivaldo Tro 2nd Edition

Instant Answer

Solved by Expert Sri K

06/19/2022

Step 1

Step 1: The Hamiltonian matrix for hexatriene can be written as: \[ \begin{bmatrix} 0 & 1 & 0 & 0 & 0 & 0 \\ 1 & 0 & 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 & 0 & 1 \\ 0 & 0 & 0 & 0 & 1 & 0 \\ \end{bmatrix} \] Show more…

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Using the Huckel Molecular Orbital Theory, (a) please write down the Hamiltonian matrix for hexatriene, (b) diagonalize the matrix to obtain the energy of MOs, and (c) draw the MO diagram, labeling the HOMO and LUMO. (Hint: 010000 01000 010100 001010 000101 000010 1.802 0 0000 0 1.2470000 00 0.445000 000-0.44500 0000-1.2470 00000-1.802 Diagonalize