Molecule Types Symmetric Tops  <Prev Next> 
There is one of these for each perturbation parameter in each state. There are many possible perturbation types, as described below. To see the actual matrix elements used in any particular case, right click on the perturbation and select "Matrix Elements". The resulting expressions will be displayed in the log window, and should be understood as being multiplied by the Value parameter.
Note that if degenerate states are involved, careful selection
of the lPower and lChange values
will be required. For example, the common A_{1}  E
Coriolis interaction requires pPower = 1, lPower
= 1 and lChange = 1. If the combination of values are
set wrong, the resulting matrix element will typically be zero,
or give an error message about a symmetry mismatch.
Nucleus  Index, starting from 1, of nuclear spin involved in perturbation; 0 (default) for those not involving a nuclear spin. 
SymSelect  Symmetry select 
ScalePrev  Scale factor with respect to preceding perturbation 
JPower  Twice power of N^{2} = N(N+1) (= J(J+1)
for closed shell systems with S = 0). 
zPower  Power of N_{z}; If both zPower and pPower are non zero
then the effective operator is either: N^{JPower/2}[N_{z}^{zPower}, N_{+}^{pPower}+N_{}^{pPower}]_{+}
or N^{JPower/2}[N_{z}^{zPower1},[N_{z}, N_{+}^{pPower}+N_{}^{pPower}]_{+}]_{+} if zPower is odd and < 2 
pPower  Power of N_{±} 
lPower  Select l
dependence; valid values are 0 (l independent), 1 or 1. If lChange is 0, the
matrix element is multiplied by l*lPower,
otherwise the matrix element is multiplied by sign(l'l)*lPower. 
lChange  Power of l_{+} or l_{}; < 0 implies opposite sign to change in K; valid values are 2..2 
KSelect  K the perturbation applies to 
SPower  Twice power of S^{2} = S(S+1) 
SzPower  Power of S_{z}.
If this is combined with a rotational operator, the overall
operator is:[N^{JPower/2}[N_{z}^{zPower}, N_{+}^{pPower}+N_{}^{pPower}]_{+},S_{z}^{SzPower}]+ 
SpPower  Power of S_{±}.
If this is combined with a rotational operator, the overall
operator is (if pPower and SpPower have
the same sign):[N^{JPower/2}[N_{z}^{zPower},N_{+}^{pPower}]_{+}, S_{+}^{SpPower}]_{+} + [N^{JPower/2}[N_{z}^{zPower},N_{}^{pPower}]_{+}, S_{}^{SpPower}]_{+ }If pPower and SpPower have opposite signs: [N^{JPower/2}[N_{z}^{zPower},N_{+}^{pPower}]_{+}, S_{}^{SpPower}]_{+} + [N^{JPower/2}[N_{z}^{zPower},N_{}^{pPower}]_{+}, S_{+}^{SpPower}]_{+} 
NSPower  Power of N.S. 
Value  Size of perturbation; the expressions and operators given here should be understood to be multiplied by this. 
Operator 
JPower 
zPower 
pPower 
lPower 
lChange 
Scale Factor 
Notes 

B  N^{2}  2 
0  0 
0  0  1 
Both terms required to replicate B[J(J+1)  K^{2}] 
N_{z}^{2}  0 
2 
0 
0 
0 
1 

C  N_{z}^{2}  0  2  0  0 
0  1 

DJ  N^{4} ≡ N^{2}(N+1)^{2}  4  0  0  0  0  1  
DJK  N^{2}N_{z}^{2} ≡ N(N+1)K^{2}  2  2 
0  0  0  1  
DK  N_{z}^{4}≡ K^{4}  0  4 
0  0  0  1  
zeta 
N_{z}l_{z}  0 
1 
0 
1 
0 
2C 
In this form, parameter must be 2Cζ, not 2ζ 
etaJ 
^{ }N^{2}N_{z}l_{z}  2 
1 
0 
1 
0 
1 

etaK 
^{}N_{z}^{3}l_{z}  0 
3 
0 
1 
0 
1 

qplus 
N_{+}^{2}l_{+}^{2}+N_{}^{2}l_{}^{2}  0 
0 
2 
0 
2 
½ 

qminus 
N_{+}^{2}l_{}^{2}+N_{}^{2}l_{+}^{2}  0 
0 
2 
0 
2 
½  
r 
[N_{+}l_{}^{2}+N_{}l_{+}^{2},N_{z}]_{+}  0 
1 
1 
0 
2 
1 

DqJ 
N^{2}(N_{+}^{2}l_{+}^{2}+N_{}^{2}l_{}^{2})  2 
0 
2 
0 
2 
½  
DqK 
[N_{+}^{2}l_{+}^{2}+N_{}^{2}l_{}^{2},N_{z}^{2}]_{+}  0 
2 
2 
0 
2 
½  
DrJ 
N^{2}[N_{+}l_{}^{2}+N_{}l_{+}^{2},N_{z}]_{+}  0 
1 
1 
0 
2 
1 

DrK 
[[N_{+}l_{}^{2}+N_{}l_{+}^{2},N_{z}]_{+},N_{z}^{2}]_{+}  0 
3 
1 
0 
2 
1 
zPower <= 3 flags use of two
anticommutators 
HJ  N^{6}  6  0  0  0  0  1 

HJK  N^{4}N_{z}^{2}  4  2 
0  0  0  1 

HKJ  N^{2}N_{z}^{4}  2  4 
0  0  0  1 

HK  N_{z}^{6}  0  6 
0  0  0  1 

LJ  N^{8}  8  0  0  0  0  1 

LJJK  N^{6}N_{z}^{2}  6  0  0  0  0  1 

LJK  N^{4}N_{z}^{4}  4  0  0  0  0  1 

LKKJ  N^{2}N_{z}^{6}  2  0  0  0  0  1 

LK  N_{z}^{8}  0  0  0  0  0  1 
Operator 
JPower 
zPower 
pPower 
lPower 
lChange  SzPower 
SpPower 
SPower 
NSPower 
Scale Factor 

ebb  N_{+}S_{} + S_{+}N_{}+
N_{}S_{+} + S_{}N_{+} = 2(N_{+}S_{} + N_{}S_{+}) = 8(N_{x}S_{x}+N_{y}S_{y}) 
0 
0 
1 
0 
0 
0 
1 
0 
0 
1/4 
ecc 
N_{z}S_{z} + S_{z}N_{z}
=2N_{z}S_{z} 
0 
1 
0 
0 
0 
1 
0 
0 
0 
½ 
DsN  N^{2}N.S  2 
0 
0 
0 
0 
0 
0 
0 
1 
1 
DsNK 
[N^{2}, N_{z}S_{z}]_{+}  2 
1 
0 
0 
0 
1 
0 
0 
0 
½ 
DsKN 
N.S N_{z}^{2}  0 
2 
0 
0 
0 
1 
0 
0 
1 
1 
DsK 
[N_{z}^{3}, S_{z}]_{+}
= 2N_{z}^{3}S_{z} 
0 
3 
0 
0 
0 
1 
0 
0 
0 
½ 
alpha 
S_{z}^{2}  0 
0 
0 
0 
0 
2 
0 
0 
0 
3 
S^{2}  0 
0 
0 
0 
0 
0 
0 
2 
0 
1 

beta 
S_{+}^{2}S_{}^{2}  0 
0 
0 
0 
0 
0 
2 
0 
0 
½ 
aeff 
l_{z}S_{z}  0 
0 
0 
1 
0 
1 
0 
0 
0 
1 