“Hund's cases”的意思、由来-开放百科全书

In rotational-vibrational and electronic spectroscopy of diatomic molecules, Hund's coupling cases are idealized cases where specific terms appearing in the molecular Hamiltonian and involving couplings between angular momenta are assumed to dominate over all other terms. There are five cases, traditionally notated with the letters (a) through (e). Most diatomic molecules are somewhere between the idealized cases (a) and (b).^[1]

Angular momenta

To describe the Hund's coupling cases, we use the following angular momenta (where boldface letters indicate vector quantities):

Choosing the applicable Hund's case

Hund's coupling cases are idealizations. The appropriate case for a given situation can be found by comparing three strengths: the electrostatic coupling of

to the internuclear axis, the spin-orbit coupling, and the rotational coupling of

and

to the total angular momentum

The last two rows are degenerate because they have the same good quantum numbers.^[2]

Case (a)

In case (a),

is electrostatically coupled to the internuclear axis, and

is coupled to

by spin-orbit coupling. Then both

and

have well-defined axial components

and

, respectively.

defines a vector of magnitude

pointing along the internuclear axis. Combined with the rotational angular momentum of the nuclei

, we have

. In this case, the precession of

and

around the nuclear axis is assumed to be much faster than the nutation of

and

around

The good quantum numbers in case (a) are

and

. We express the rotational energy operator as

, where

is a rotational constant. There are, ideally,

fine-structure states, each with rotational levels having relative energies

starting with

.^[1]

Case (b)

In case (b), the spin-orbit coupling is weak or non-existent (in the case

). In this case, we take

and

and assume

precesses quickly around the internuclear axis.

The good quantum numbers in case (b) are

, and

. We express the rotational energy operator as

, where

is a rotational constant. The rotational levels therefore have relative energies

starting with

.^[1]

Case (c)

In case (c), the spin-orbit coupling is stronger than the coupling to the internuclear axis, and

and

from case (a) cannot be defined. Instead

and

combine to form

, which has a projection along the internuclear axis of magnitude

. Then

, as in case (a).

Case (d)

In case (d), the rotational coupling between

and

is much stronger than the electrostatic coupling of

to the internuclear axis. Thus we form

by coupling

and

and the form

by coupling

and

The good quantum numbers in case (d) are

, and

. Because

is a good quantum number, the rotational energy is simply

.^[1]

Case (e)

In case (e), we first form

and then form

by coupling

and

. This case is rare but has been observed.^[3]

The good quantum numbers in case (e) are

, and

. Because

is once again a good quantum number, the rotational energy is

.^[1]

References

1. ^¹²³⁴⁵{{cite book|first1=John M.|last1=Brown|first2=Alan|last2=Carrington|title=Rotational Spectroscopy of Diatomic Molecules|publisher= Cambridge University Press|year=2003|isbn= 0521530784}}
2. ^{{Cite journal | last1 = Nikitin | first1 = E. E. | last2 = Zare | first2 = R. N. | doi = 10.1080/00268979400100074 | title = Correlation diagrams for Hund's coupling cases in diatomic molecules with high rotational angular momentum | journal = Molecular Physics | volume = 82 | pages = 85 | year = 1994 | pmid = | pmc = | bibcode = 1994MolPh..82...85N }}
3. ^{{Cite journal | last1 = Carrington | first1 = A. | last2 = Pyne | first2 = C. H. | last3 = Shaw | first3 = A. M. | last4 = Taylor | first4 = S. M. | last5 = Hutson | first5 = J. M. | last6 = Law | first6 = M. M. | doi = 10.1063/1.472999 | title = Microwave spectroscopy and interaction potential of the long-range He⋯Kr+ ion: An example of Hund's case (e) | journal = The Journal of Chemical Physics | volume = 105 | issue = 19 | pages = 8602 | year = 1996 | pmid = | pmc = |bibcode = 1996JChPh.105.8602C }}