Molecule Types Asymmetric Tops <Prev Next>

Asymmetric Top Hamiltonian

The asymmetric top Hamiltonian used is either of the A or S standard reduced forms proposed by Watson (Watson, 1977). The SReduction flag at the Molecule level determines which one, with a setting of false implying the A reduction is used. When reporting these constants it is important to specify both the reduction and the axis system used. Note that, for open shell systems with S > 0, J should be replaced with N in the discussion below, part from in the parameter names.

The rigid rotor part can be specified in two ways, independent of the reduction:

or the equivalent form (which can give better determined parameters):

where:

and:

The different forms of the centrifugal distortion terms do not have a simple relationship:

 

A reduction

Quartic

Sextic

Octic


 

S reduction

Quartic

Sextic

Octic

Note that various symbols are in use for many of the centrifugal distortion constants; in particular different symbols are typically used for the A and S reduction constants rather than as here. Some of these are listed below, together with the name PGOPHER uses.

PGOPHER

A reduction

S reduction

A

A

B

B

C

C

BBar

Bdelta

DJ

ΔJ

DJ

DJK  

ΔJK

DJK

DK

ΔK

DK

deltaJ

δJ

d1

deltaK

δK

d2

HJ

ΦJ

HJ

HJK

ΦJK

HJK

HKJ

ΦKJ

HKJ

HK

ΦK

HK

phiJ

φJ

h1

phiJK

φJK

h2

phiK

φK

h3

LJ

LJ

 

LJJK

LJJK

 

LJK

LJK

 

LKKJ

LKKJ

 

LK

LK

 

llJ

lJ

 

llJK

lJK

 

llKJ

lKJ

 

llK

lK

 

References