What are Jacobi coordinates, and why are they useful?

[AxiomOfChoice]

What are "Jacobi coordinates," and why are they useful?

I am working on a quantum chemistry problem involving triatomic molecules. My advisor keeps talking about "Jacobi coordinates" and how they're a calculational convenience when it comes time to write out the Hamiltonian. Can someone describe them to me, and why they make life easier? I can't seem to find a good resource for this on the Web...

 

[Meir Achuz]

Jacobi coordinates are coordinates for three bodies of equal mass, using the cm of two of them. The coordinates I like to use are
R=(r1+r2+r3)/3
r=(r1-r2)/2
rho=(2/3)[r3-(r1+r2)/2].
The more common Jacobi coordinates divide by square roots to make equations more symmetric, but they get more complicated in practice.
If one of the bodies has a different mass, then masses have to enter.

 

[Entropia]

Jacobi coordinates are a set of coordinates used to describe the positions of particles in a triatomic molecule. They consist of three variables: the distance between the two outer atoms, the angle between the two outer atoms and the central atom, and the distance between the central atom and the center of mass of the molecule.

These coordinates are useful because they simplify the mathematical expressions used to describe the motion of the particles in the molecule. By using Jacobi coordinates, the Hamiltonian (the mathematical expression that describes the total energy of the system) can be written in a more compact and efficient way, making it easier to solve and analyze the quantum chemistry problem.

Furthermore, Jacobi coordinates allow for a more intuitive understanding of the system, as they correspond to the physical parameters that are most commonly measured in experiments. This makes it easier for scientists to interpret and compare their results with experimental data.

In summary, Jacobi coordinates are a useful tool in quantum chemistry as they simplify the mathematical description of a triatomic molecule and provide a more intuitive understanding of the system.