Born oppenheimer approximation vs adiabatic approximation

In summary, the Born Oppenheimer Approximation is a mathematical approximation used in quantum mechanics that allows for the calculation of some important properties of atoms and molecules.
  • #1
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I'm learning to deal with h2+ (hydrogen ion) problems and the like, which sure entails the infamous born oppenheimer approximation .
i know the word "adiabatic" in a thermal sense, that is , an adiabatic process is the one in which no heat transfer occurs between the things of question and surroundings.
but , I don't quite understand that in quantum mechanics ,how the notion of "adiabatic" enters the story, say, in particular born oppenheimer approximation and adiabatic approximation is synonym .
it's said that the notion of adiabatic has a lots of applications in many branches of physics, would anyone please but tell me some of them?

many thanks in advance :D
 
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  • #3
Adiabatic in thermodynamics has a different meaning than in molecular quantum mechanics.
In greek it signifies "no passage" or "no trespassing", however who or what is not passing is different in different contexts:
On a greek airport, it is persons, in thermodynamic it is heat and in molecular physics it is no passing from one potential energy surface (electronic state) to the other.
 
  • #4
many thanks first! I got to apologize for delayed reply .
Actually I'd took a glance at the wiki's explanation contained in the first link before I put up
this question here. I usually distrust wiki. However, The second link is quite helpful. I'm reading it now while typing message to you . Seems like even serious science stuffs in wiki can be trusted sometimes.
regards :D
 
  • #5
THanks very much for your reply. I think your interpretation of adiabatic hit the spot. I guess adiabatic ,roughly speaking , pretty much has to do with an isolation from the environment in a certain form. but it still remains to us the question why in particular born oppenheimer approximation is another name for adiabatic approximation in quantum mechanical sense .
cheers,
 

What is the Born Oppenheimer Approximation?

The Born Oppenheimer Approximation is a theoretical model used in quantum chemistry and molecular physics. It assumes that the motion of atomic nuclei and electrons in a molecule can be treated separately, with the nuclei considered stationary and the electrons moving in response to their fixed positions.

What is the Adiabatic Approximation?

The Adiabatic Approximation is another theoretical model used in quantum chemistry and molecular physics. It assumes that the motion of electrons in a molecule is much faster than the motion of the atomic nuclei, allowing the electrons to adjust to the nuclear motion instantaneously. This approximation is often used in molecular dynamics simulations.

What is the difference between the Born Oppenheimer and Adiabatic Approximations?

The main difference between the two approximations is in how they treat the motion of atomic nuclei. In the Born Oppenheimer Approximation, the nuclei are considered stationary and the electrons move in response to their fixed positions. In the Adiabatic Approximation, the electrons are considered to adjust to the nuclear motion instantaneously, allowing for a more dynamic treatment of the system.

Which approximation is more accurate?

The accuracy of each approximation depends on the specific system being studied. In general, the Born Oppenheimer Approximation is better suited for molecules with large mass differences between the nuclei and electrons, while the Adiabatic Approximation is more accurate for molecules with small mass differences.

How do these approximations impact computational methods in quantum chemistry?

The use of these approximations can greatly simplify the computational methods used in quantum chemistry, making calculations more feasible and efficient. However, the approximations can also introduce errors and limitations in certain systems, so careful consideration must be given when choosing which approximation to use.

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