Chapter 2, Problem 2G.22E

Interpretation Introduction

Interpretation:

The normalization constant $\left(\text{N}\right)$ for antibonding orbital has to be determined. Also, show bonding and antibonding orbitals are mutually orthogonal for below wave functions.

  $\begin{array}{l}\psi ={\psi }_{\text{A1s}}-{\psi }_{\text{B1s}}\left(\text{antibonding}\right)\\ {\psi }^{\prime }={\psi }_{\text{A1s}}+{\psi }_{\text{B1s}}\left(\text{bonding}\right)\end{array}$

Concept Introduction:

For normalization constant:

The addition of probabilities to 1 is defined as normalization. A normalize wavefunction follows the rule as follows:

  ${\displaystyle \int {\psi }_{\cdot }}\psi \text{ dΓ}=1$

The two wavefunctions are orthogonal when there is no interaction between the atomic electrons and another atom and follows the rule as:

  ${\displaystyle \int {\psi }_{\cdot }}{\psi }^{\prime }\text{ dΓ}=0$