Molecule Types Symmetric Tops | <Prev Next> |
Colour | Colour - set to "None" to take value from elsewhere as explained in Determining Colours and J ranges. |
RveSelect | Only include given rovibronic symmetry - for normal use set to 'all' |
S | Electron Spin |
Symmetry | Symmetry |
Kmin | Minimum |K| to use; "all" (default) for no lower limit. |
Kmax | Maximum |K| to use; "all" (default) for no upper limit. |
The Hamiltonian used is (for prolate tops read A for C):
with the following off-diagonal matrix elements, which are responsible for l-doubling::
A note on the sign convention for these constants is appropriate. This is discussed in a G. J.Cartwright and I. M. Mills, J. Molec. Spectrosc.34, 415 (1970), though that they define their constants, q(+) and q(-), in a way to factor out the expected vibrational dependence, specifically:
q+ = ½ρ[(vt+1)2 - lt2]½q(+)
q- = ½ρ[(vt+1)2 - lt2]½q(-)
The constant ρ defines the sign convention, and Cartwright and Mills suggest a value of -1 should be used for this. The sign convention can also be defined by looking at the spitting of the l = K = ±1 levels. Note that equation (5) of this paper is slightly unclear; the magnitude of the spitting between these otherwise degenerate levels is q+N(N+1) with the PGOPHER definition of q rather then the Cartwright and Mills definition. The PGOPHER definition means a positive value of q+ puts the even J, K=1 A1 rotational level below the A2 level, whereas a positive value of the Cartwright and Mills constant, q(+), gives the opposite order.
l doubling is also observed in degenerate electronic states of symmetric top molecules; while the physical origin is different, the J and K dependence of the matrix elements is the same so PGOPHER can be used for such cases also. The classic example is the B state of NH3 (see for example M. N. R. Ashfold, R. N. Dixon, N. Little, R. J. Stickland and C. M. Western, J. Chem. Phys., 89, 1754 (1988)) with the published q values being simply -q+ as used by PGOPHER.
Origin | State Origin. |
Width | Linewidth (rotation independent) for state; see Width and Lifetime effects |
B | Rotational constants perpendicular to symmetry axis. |
C | A or C - the rotational constant about symmetry axis. |
DJ | J2(J+1)2 Quartic Centrifugal Distortion |
DJK | J(J+1)K2 Quartic Centrifugal Distortion |
DK | K4 Quartic Centrifugal Distortion |
zeta=ζ | Coriolis coupling constant. |
etaJ=ηJ | J(J+1) dependence of Coriolis coupling constant. |
etaK=ηK | K2 dependence of Coriolis coupling constant. |
qplus=q+ | l doubling constant. |
qminus=q- | l doubling constant. |
r | l doubling constant. |
DqJ | Centrifugal distortion of qplus l doubling constant. |
DqK | Centrifugal distortion of qplus l doubling constant. |
DrJ | Centrifugal distortion of r l doubling constant. |
DrK | Centrifugal distortion of r l doubling constant. |
HJ | J3(J+1)3 Sextic Centrifugal Distortion |
HJK | J2(J+1)2K2 Sextic Centrifugal Distortion |
HKJ | J(J+1)K4 Sextic Centrifugal Distortion |
HK | K6 Sextic Centrifugal Distortion |
LJ | J4(J+1)4 Octic Centrifugal Distortion |
LJJK | J3(J+1)3K2 Octic Centrifugal Distortion |
LJK | J2(J+1)2K4 Octic Centrifugal Distortion |
LKKJ | J(J+1)K6 Octic Centrifugal Distortion |
LK | K8 Octic Centrifugal Distortion |
ebb | xx/yy Spin-Rotation interaction |
ecc | zz Spin-Rotation interaction |
DsN | quartic spin rotation parameter |
DsNK | quartic spin rotation parameter |
DsKN | quartic spin rotation parameter |
DsK | quartic spin rotation parameter |
alpha | Diagonal spin-spin coupling constant (=D/3) |
beta | Off-Diagonal spin-spin coupling constant (=E) |
aeff | Effective spin-orbit parameter |
wK | multiplier of <K2> for linewidth; see Width and Lifetime effects |
wJ | multiplier of <J(J+1)-K2> for linewidth; see Width and Lifetime effects |