The **key difference** between Born Oppenheimer approximation and Condon approximation is that **Born Oppenheimer approximation is useful in explaining the wave functions of atomic nuclei and electrons in a molecule, whereas the Condon approximation is important in explaining the intensity of the vibronic transitions of atoms**.

The terms Born Oppenheimer approximation and Condon approximation or Franck-Condon principle are important terms in quantum chemistry.

### CONTENTS

1. Overview and Key Difference

2. What is Born Oppenheimer Approximation

3. What is Condon Approximation

4. Side by Side Comparison – Born Oppenheimer Approximation vs Condon Approximation in Tabular Form

5. Summary

## What is Born Oppenheimer Approximation?

Born Oppenheimer approximation is a well-known mathematical approximation in molecular dynamics. The term is used mainly in quantum chemistry and molecular physics. It explains that the wave functions of atomic nuclei and electrons in a molecule can be treated separately depending on the fact that the nuclei are heavier than the electrons. The approximation approach was named after Max Born and J. Robert Oppenheimer in 1927. The origin of this approximation was in the early period of quantum mechanics.

The Born Oppenheimer approximation is useful in quantum chemistry to speed up the computation of the molecular wavefunctions and other properties for large molecules. However, we can observe some cases where the assumption of separable motion no longer holds. This makes the approximation invalid (also called a breakdown). However, it was used as a starting point for other refined methods.

In the field of molecular spectroscopy, we can use the Born Oppenheimer approximation as the sum of independent terms of molecular energy such as E_{total} = E_{electronic} + E_{vibrational} + E_{nuclear} _{spin}. Typically, nuclear spin energy is very small, so it is omitted from the calculations. The term electronic energies or E_{electronic} include kinetic energy, interelectronic repulsions, internuclear repulsions, and electron-nuclear attractions, etc.

Generally, Born Oppenheimer approximation tends to recognize large differences between the electron mass and the masses of atomic nuclei where the time scales of their motion are also considered. E.g. at a given amount of kinetic energy, the nuclei tend to move slower than the electrons. According to Born Oppenheimer approximation, the wavefunction of a molecule is the product of an electronic wavefunction and a nuclear wavefunction.

## What is Condon Approximation?

Condon approximation or Franck-Condon principle is a rule in quantum chemistry and spectroscopy that explains the intensity of vibronic transitions. We can define vibronic transitions as the simultaneous changes in electronic and vibrational energy levels of a molecule that takes place due to the absorption or the emission of a photon of the appropriate energy.

Condon approximation states that during an electronic transition that takes place in an atom, a change from one vibrational energy level to another level usually happens if the two vibrational wave functions tend to overlap in significant amounts.

This principle was developed by James Frack and Edward Condon in 1926. This principle has a well-established semi-classical interpretation depending on the original contributions of these scientists.

## What is the Difference Between Born Oppenheimer Approximation and Condon Approximation?

The terms Born Oppenheimer approximation and Condon approximation or the Franck-Condon principle are important terms in quantum chemistry. The key difference between Born Oppenheimer approximation and Condon approximation is that the Born Oppenheimer approximation is useful in explaining the wave functions of atomic nuclei and electrons in a molecule, whereas the Condon approximation is important in explaining the intensity of the vibronic transitions of atoms.

Below is a summary of the difference between Born Oppenheimer approximation and Condon approximation in tabular form.

## Summary – Born Oppenheimer Approximation vs Condon Approximation

The terms Born Oppenheimer approximation and Condon approximation or Franck-Condon principle are important terms in quantum chemistry. The key difference between Born Oppenheimer approximation and Condon approximation is that the Born Oppenheimer approximation is useful in explaining the wave functions of atomic nuclei and electrons in a molecule, whereas the Condon approximation is important in explaining the intensity of the vibronic transitions of atoms.

##### Reference:

1. “10.1: The Born-Oppenheimer Approximation.” *Chemistry LibreTexts*, Libretexts, 10 Aug. 2020, Available here.

##### Image Courtesy:

1. “Franck Condon Diagram” By Samoza (CC BY-SA 3.0) via Commons Wikimedia

## Leave a Reply