In quantum chemistry, the Dunham expansion is an expression for the rotational-vibrational

energy level A quantum mechanical system or particle that is bound—that is, confined spatially—can only take on certain discrete values of energy, called energy levels. This contrasts with classical particles, which can have any amount of energy. The t ...

s of a

diatomic molecule Diatomic molecules () are molecules composed of only two atoms, of the same or different chemical elements. If a diatomic molecule consists of two atoms of the same element, such as hydrogen () or oxygen (), then it is said to be homonuclear. O ...

: :

E(v,J,\Omega) = \sum_ Y_ (v+1/2)^k (J+1) - \Omega^2 l,

where

v

and

J

are the vibrational and rotational quantum numbers, and

\Omega

is the projection of

J

along the internuclear axis in the body-fixed frame. The constant coefficients

Y_

are called Dunham parameters with

Y_

representing the electronic energy. The expression derives from a semiclassical treatment of a perturbational approach to deriving the energy levels. The Dunham parameters are typically calculated by a

least-squares The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems (sets of equations in which there are more equations than unknowns) by minimizing the sum of the squares of the res ...

fitting procedure of energy levels with the quantum numbers.

Relation to conventional band spectrum constants

This table adapts the sign conventions from the book of Huber and Herzberg.

References

Spectroscopy Molecular vibration {{applied-math-stub

Relation to conventional band spectrum constants

See also

References