Born-Oppenheimer approximation & distance

In summary, the Born-Oppenheimer approximation is a concept in quantum mechanics that separates the motion of electrons and nuclei in molecules. It works by calculating electronic energy levels while keeping the nuclei fixed, and then using those energy levels to calculate nuclear motion. However, it has limitations due to the assumption of complete separation between the motions and neglect of nuclear effects on energy levels. Distance is a crucial factor in this approximation, determining the potential energy surface for nuclear motion and influencing molecular stability. Real-world applications include computational chemistry, spectroscopy, materials science, nanotechnology, and atmospheric chemistry.
  • #1
QuarkDecay
47
2
According to the Born-Oppenheimer approximation, what does the internuclear distance Req depend on?
  • Atomic number Z?
  • Rotational Energy of the nuclei?
  • Electrons' kinetic energy?
  • Coulomb interaction between the two nuclei?
  • Coulomb interaction between the electrons?
  • Vibrational energy of the molecule?
There could be more than one right answer. I'm confused because my books just show the calulations, but don't correlate the rest of the different types of interactions on them
 
Chemistry news on Phys.org
  • #2
You can find arguments for basically all of them.
 

1. What is the Born-Oppenheimer approximation?

The Born-Oppenheimer approximation is a theoretical framework used in quantum chemistry to simplify the calculation of electronic wavefunctions in molecules. It assumes that the motion of the atomic nuclei is much slower than the motion of the electrons, allowing the two to be treated separately.

2. How does the Born-Oppenheimer approximation work?

The Born-Oppenheimer approximation works by separating the total wavefunction of a molecule into two parts: the electronic wavefunction and the nuclear wavefunction. The electronic wavefunction is solved first, assuming that the nuclei are fixed in space, and then the nuclear wavefunction is solved using the electronic wavefunction as a potential energy surface.

3. What is the significance of the Born-Oppenheimer approximation?

The Born-Oppenheimer approximation is significant because it allows for the calculation of molecular properties and behavior without having to consider the complex interactions between the electrons and nuclei. This simplification makes it possible to study and understand the electronic structure of molecules, which is crucial in many fields of chemistry and physics.

4. How does distance play a role in the Born-Oppenheimer approximation?

Distance is an important factor in the Born-Oppenheimer approximation because it determines the strength of the interaction between the electrons and nuclei. The approximation assumes that the nuclei are fixed in space, so the distance between them affects the potential energy surface used to solve for the nuclear wavefunction.

5. What are the limitations of the Born-Oppenheimer approximation?

The Born-Oppenheimer approximation is limited by its assumption that the nuclei are fixed in space, which is not always the case. In some cases, the motion of the nuclei cannot be neglected and more advanced methods, such as molecular dynamics, must be used. Additionally, the approximation is not accurate for highly excited electronic states or for molecules with strong electron-nuclear coupling.

Similar threads

I Kinetic Energy and Potential Energy of Electrons
    • Quantum Physics
Replies
15
Views
2K
Interpreting Energy diagrams for polyatomic molecules
    • Chemistry
Replies
6
Views
2K
I Molecules when Born-Oppenheimer approximation doesn't work
    • Atomic and Condensed Matter
Replies
15
Views
2K
I Born-Oppenheimer approximations in molecules
    • Atomic and Condensed Matter
Replies
4
Views
2K
I Electron angular momentum in diatomic molecules
    • Atomic and Condensed Matter
Replies
4
Views
2K
I Understanding the Born-Oppenheimer Approximation: A Mathematical Proof
    • Atomic and Condensed Matter
Replies
1
Views
2K
I Vibrational energy in molecules
    • Atomic and Condensed Matter
Replies
12
Views
2K
I Why Bremsstrahlung <20keV for Tungsten?
    • High Energy, Nuclear, Particle Physics
Replies
17
Views
2K
Electrons and their little role in nuclear physics
    • Introductory Physics Homework Help
Replies
1
Views
753
I Effective Hamiltonian to Rotational Term Values
    • Atomic and Condensed Matter
Replies
0
Views
381

Hot Threads

Recent Insights

Back
Top